https://wiki.swarma.org/api.php?action=feedcontributions&user=Jxzhou&feedformat=atom集智百科 - 复杂系统|人工智能|复杂科学|复杂网络|自组织 - 用户贡献 [zh-cn]2024-03-28T14:22:11Z用户贡献MediaWiki 1.35.0https://wiki.swarma.org/index.php?title=%E9%9B%86%E4%BD%93%E6%99%BA%E8%83%BD&diff=25554集体智能2021-08-06T15:11:50Z<p>Jxzhou:</p>
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<div>此词条由Jie翻译<br />
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[[文件:CI types1s 2.jpg|400px|thumb|right|集体智能的类型]]<br />
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{{Group intelligence}}<br />
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{{Recommender systems}}<br />
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Collective intelligence (CI) is shared or group intelligence that [[Emergence|emerges]] from the [[collaboration]], collective efforts, and competition of many individuals and appears in [[consensus decision making]]. The term appears in [[sociobiology]], [[political science]] and in context of mass [[peer review]] and [[crowdsourcing]] applications. It may involve [[consensus]], [[social capital]] and formalisms such as [[voting systems]], [[social media]] and other means of quantifying mass activity. Collective IQ is a measure of collective intelligence, although it is often used interchangeably with the term collective intelligence. Collective intelligence has also been attributed to [[bacteria]]and animals.<br />
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Collective intelligence (CI) is shared or group intelligence that emerges from the collaboration, collective efforts, and competition of many individuals and appears in consensus decision making. The term appears in sociobiology, political science and in context of mass peer review and crowdsourcing applications. It may involve consensus, social capital and formalisms such as voting systems, social media and other means of quantifying mass activity. Collective IQ is a measure of collective intelligence, although it is often used interchangeably with the term collective intelligence. Collective intelligence has also been attributed to bacteria and animals.<br />
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<font color="#ff8000"> 集体智能 Collective intelligence</font>(简称CI,或称为<font color="#ff8000"> 集体智力</font>,<font color="#ff8000"> 集体智慧</font>等)指的是共享的或群体的智慧,源于众多个体的协作、共同努力和竞争,最终在决策中达到共识。其术语经常出现在社会生物学,政治科学以及大规模同行评议和众包应用中。它可能牵涉到<font color="#ff8000"> 大众共识</font>,<font color="#ff8000"> 社会资本</font>和形式体系,例如<font color="#ff8000"> 投票系统</font>,社交媒体和其他方式的群众活动。另一个概念是<font color="#ff8000"> 群体智商 Collective IQ</font>,它是用来度量集体智能的,尽管它通常会与集体智能一词互换使用。集体智能也可以在细菌和动物群体中形成。<br />
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It can be understood as an [[emergent property]] from the [[synergies]] among: 1) data-[[information]]-knowledge; 2) software-hardware; and 3) experts (those with new insights as well as recognized authorities) that continually learns from feedback to produce just-in-time knowledge for better decisions than these three elements acting alone; or more narrowly as an emergent property between people and ways of processing information. This notion of collective intelligence is referred to as "symbiotic intelligence" by Norman Lee Johnson. The concept is used in [[sociology]], [[Prediction market|business]], [[computer science]] and mass communications: it also appears in [[science fiction]]. [[Pierre Lévy]] defines collective intelligence as, "It is a form of universally distributed intelligence, constantly enhanced, coordinated in real time, and resulting in the effective mobilization of skills. I'll add the following indispensable characteristic to this definition: The basis and goal of collective intelligence is mutual recognition and enrichment of individuals rather than the cult of fetishized or [[hypostatized]] communities." According to researchers Pierre Lévy and [[Derrick de Kerckhove]], it refers to capacity of networked [[ICTs]] (Information communication technologies) to enhance the collective pool of social knowledge by simultaneously expanding the extent of human interactions.<br />
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It can be understood as an emergent property from the synergies among: 1) data-information-knowledge; 2) software-hardware; and 3) experts (those with new insights as well as recognized authorities) that continually learns from feedback to produce just-in-time knowledge for better decisions than these three elements acting alone; or more narrowly as an emergent property between people and ways of processing information. This notion of collective intelligence is referred to as "symbiotic intelligence" by Norman Lee Johnson. The concept is used in sociology, business, computer science and mass communications: it also appears in science fiction. Pierre Lévy defines collective intelligence as, "It is a form of universally distributed intelligence, constantly enhanced, coordinated in real time, and resulting in the effective mobilization of skills. I'll add the following indispensable characteristic to this definition: The basis and goal of collective intelligence is mutual recognition and enrichment of individuals rather than the cult of fetishized or hypostatized communities." According to researchers Pierre Lévy and Derrick de Kerckhove, it refers to capacity of networked ICTs (Information communication technologies) to enhance the collective pool of social knowledge by simultaneously expanding the extent of human interactions.<br />
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以下三个要素在经过<font color="#ff8000"> 协同</font>作用后,产生的增效现象被理解为一种<font color="#ff8000"> 涌现特性</font>:<br />
1)数据信息知识;<br />
2)软硬件;<br />
3)专家(具有最新见解且公认权威的专家)<br />
通过不断从反馈中学习并产生实时性知识,这三个要素的<font color="#ff8000"> 协同</font>增效作用比它们单独采取行动来说,做出的决策会更好;或更狭义地讲,这是人与信息处理方式之间的一种<font color="#ff8000"> 涌现特性</font>。诺曼·李·约翰逊 Norman Lee Johnson将这种集体智能的概念称为<font color="#ff8000"> 共生智能 symbiotic intelligence</font>。该概念用于社会学,商业,计算机科学和大众传播学:当然,它也出现在科幻小说中。皮埃尔·列维 Pierre Lévy给出了集体智能另一个定义:“它是一种普遍的分布式智慧,通过不断增强和实时合作来有效地调动技能。我将在此定义中添加以下必不可少的特征:集体智能的基本原则和目标是丰富个体并实现相互认可,而不是对物质化或实体化社区的疯狂迷恋。”根据研究人员ierre Lévy和德里克·德·科克霍夫Derrick de Kerckhove的说法,它指的是网络<font color="#ff8000"> ICTs</font>(信息通信技术Information communication technologies)通过扩大人类互动范围来增强社会知识群体的能力。<br />
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Collective intelligence strongly contributes to the shift of knowledge and power from the individual to the collective. According to [[Eric S. Raymond]] (1998) and JC Herz (2005), [[open source]] intelligence will eventually generate superior outcomes to knowledge generated by proprietary software developed within corporations ([[Terry Flew|Flew]] 2008). Media theorist [[Henry Jenkins]] sees collective intelligence as an 'alternative source of media power', related to convergence culture. He draws attention to education and the way people are learning to participate in knowledge cultures outside formal learning settings. Henry Jenkins criticizes schools which promote 'autonomous problem solvers and self-contained learners' while remaining hostile to learning through the means of collective intelligence. Both Pierre Lévy (2007) and Henry Jenkins (2008) support the claim that collective intelligence is important for [[democratization]], as it is interlinked with knowledge-based culture and sustained by collective idea sharing, and thus contributes to a better understanding of diverse society.<br />
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Collective intelligence strongly contributes to the shift of knowledge and power from the individual to the collective. According to Eric S. Raymond (1998) and JC Herz (2005), open source intelligence will eventually generate superior outcomes to knowledge generated by proprietary software developed within corporations (Flew 2008). Media theorist Henry Jenkins sees collective intelligence as an 'alternative source of media power', related to convergence culture. He draws attention to education and the way people are learning to participate in knowledge cultures outside formal learning settings. Henry Jenkins criticizes schools which promote 'autonomous problem solvers and self-contained learners' while remaining hostile to learning through the means of collective intelligence. Both Pierre Lévy (2007) and Henry Jenkins (2008) support the claim that collective intelligence is important for democratization, as it is interlinked with knowledge-based culture and sustained by collective idea sharing, and thus contributes to a better understanding of diverse society.<br />
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集体智能极大地促进了知识和权力从个人到集体的转移。埃里克·雷蒙德Eric S. Raymond(1998)和杰西·赫兹JC Herz(2005)认为,相较于一个公司通过内部开发专有软件来创造知识,开源智慧则终将产生更优异的成果(Flew 2008)。媒体理论家亨利·詹金斯Henry Jenkins将集体智能视为与融合文化相关的“媒体力量的替代来源”。他提请人们关注教育,特别是基于传统教育设置之外的知识文化参与方式。Henry Jenkins批评学校提倡的“自主解决问题者和独立学习者”,同时又反对通过集体智能来学习。Pierre Lévy(2007)和Henry Jenkins(2008)也都支持这样的说法,即集体智能对民主化很重要,因为它与以知识为基础的文化相互联系,并通过群体的思想共享来维持,从而有助于更好地理解多元化社会。<br />
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Similar to the [[G factor (psychometrics)|''g'' factor (''g'')]] for general individual intelligence, a new scientific understanding of collective intelligence aims to extract a general collective intelligence factor c factor for groups indicating a group's ability to perform a wide range of tasks. Definition, operationalization and statistical methods are derived from ''g''. Similarly as ''g'' is highly interrelated with the concept of [[Intelligence quotient|IQ]], this measurement of collective intelligence can be interpreted as intelligence quotient for groups (Group-IQ) even though the score is not a quotient per se. Causes for ''c'' and predictive validity are investigated as well.<br />
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Similar to the g factor (g) for general individual intelligence, a new scientific understanding of collective intelligence aims to extract a general collective intelligence factor c factor for groups indicating a group's ability to perform a wide range of tasks. Definition, operationalization and statistical methods are derived from g. Similarly as g is highly interrelated with the concept of IQ, this measurement of collective intelligence can be interpreted as intelligence quotient for groups (Group-IQ) even though the score is not a quotient per se. Causes for c and predictive validity are investigated as well.<br />
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与测试个人智力的<font color=“#ff8000”> g因子</font>相似,对群体智力的最新科学理解主要是提取群体的综合智力因子”c因子”,以表明一个群体执行各种任务的能力。其定义,操作方式和统计方法均同于<font color=“#ff8000”> g因子</font>测试法。同样地,由于g与IQ的概念高度相关,因此这种群体智力的度量也可以解释为<font color="#ff8000"> 群体的智商(Group-IQ)</font>,即使该分数自身不是商。另外,还研究c值的成因和预测其有效性。<br />
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Collective intelligence is used to help create widely known platforms including [[Google]], Wikipedia and [[political groups]]. Google is a major search engine that is made of millions of websites that have been created by people all around the world. It has the ability to share knowledge and creativity with each other to collaborate and expand thoughts and expressions. Google includes five key dynamics within their teams to create a well-collaborated system. Dynamics include [[psychological safety]], [[dependability]], structure & clarity, meaning of work and impact of work. Their ideas behind their rediscovery of collective intelligence is to ensure that all workers can express themselves without any fear of potential embarrassment. Google's teamwork is said to be one of the main reasons for their success by including the use of emotional and collective intelligence to ensure teamwork is involved in any discussions. The system behind Google exemplifies the combining of knowledge of the web-to-people not just knowledge of people-to-people.<br />
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Collective intelligence is used to help create widely known platforms including Google, Wikipedia and political groups. Google is a major search engine that is made of millions of websites that have been created by people all around the world. It has the ability to share knowledge and creativity with each other to collaborate and expand thoughts and expressions. Google includes five key dynamics within their teams to create a well-collaborated system. Dynamics include psychological safety, dependability, structure & clarity, meaning of work and impact of work. Their ideas behind their rediscovery of collective intelligence is to ensure that all workers can express themselves without any fear of potential embarrassment. Google's teamwork is said to be one of the main reasons for their success by including the use of emotional and collective intelligence to ensure teamwork is involved in any discussions. The system behind Google exemplifies the combining of knowledge of the web-to-people not just knowledge of people-to-people. <br />
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集体智能可用于帮助创建广为人知的平台,包括Google,Wikipedia和政治团体。Google就是主打搜索引擎的例子,它可以看作是由世界各地的人们共同创建数百万个网站的集合。它能够通过彼此共享知识和创造力,来协作并拓展思维与表达。Google团队包含五大关键动力,以创建一个协作良好的系统。它们是:心理安全性,可靠性,架构和清晰度,工作的含义以及工作的影响。他们重新发现集体智能的核心价值其实是确保所有员工都能够表达自己的意见,而不必担心其带来的尴尬。据说Google的团队合作是其成功的主要原因之一,其中包括运用情绪管理和集体智能来确保合作团队能参与任何讨论。Google背后的系统例证了网络与人知识的结合,而不仅仅是人与人知识的结合。<br />
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Writers who have influenced the idea of collective intelligence include [[Francis Galton]], [[Douglas Hofstadter]] (1979), Peter Russell (1983), [[Tom Atlee]] (1993), [[Pierre Lévy (philosopher)|Pierre Lévy]] (1994), [[Howard Bloom]] (1995), [[Francis Heylighen]] (1995), [[Douglas Engelbart]], [[Louis Rosenberg (entrepreneur)|Louis Rosenberg]], [[Cliff Joslyn]], [[Ron Dembo]], [[Gottfried Mayer-Kress]] (2003).<br />
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Writers who have influenced the idea of collective intelligence include Francis Galton, Douglas Hofstadter (1979), Peter Russell (1983), Tom Atlee (1993), Pierre Lévy (1994), Howard Bloom (1995), Francis Heylighen (1995), Douglas Engelbart, Louis Rosenberg, Cliff Joslyn, Ron Dembo, Gottfried Mayer-Kress (2003).<br />
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影响集体智能思想的作家包括弗朗西斯·加尔顿Francis Galton,道格拉斯·霍夫斯塔特Douglas Hofstadter(1979),彼得·罗素Peter Russell(1983),汤姆·阿特利Tom Atlee(1993),Pierre Lévy(1994),霍华德·布鲁姆Howard Bloom(1995),弗朗西斯·海里根Francis Heylighen(1995),道格拉斯·恩格巴特Douglas Engelbart,路易·罗森伯格Louis Rosenberg,克里夫·乔斯林Cliff Joslyn,罗恩·丹博Ron Dembo,戈特弗里德·梅耶·克雷斯Gottfried Mayer-Kress(2003)。<br />
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== History 历史==<br />
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[[文件:World Brain HG Wells 1938.jpg|250px|thumb|left|世界脑 H.G. Wells (1936–1938)]]<br />
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The concept (although not so named) originated in 1785 with the [[Marquis de Condorcet]], whose "jury theorem" states that if each member of a voting group is more likely than not to make a correct decision, the probability that the highest vote of the group is the correct decision increases with the number of members of the group (see [[Condorcet's jury theorem]]). Many theorists have interpreted [[Aristotle]]'s statement in the [[Politics]] that "a feast to which many contribute is better than a dinner provided out of a single purse" to mean that just as many may bring different dishes to the table, so in a deliberation many may contribute different pieces of information to generate a better decision. Recent scholarship, however, suggests that this was probably not what Aristotle meant but is a modern interpretation based on what we now know about team intelligence.<br />
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The concept (although not so named) originated in 1785 with the Marquis de Condorcet, whose "jury theorem" states that if each member of a voting group is more likely than not to make a correct decision, the probability that the highest vote of the group is the correct decision increases with the number of members of the group (see Condorcet's jury theorem). Many theorists have interpreted Aristotle's statement in the Politics that "a feast to which many contribute is better than a dinner provided out of a single purse" to mean that just as many may bring different dishes to the table, so in a deliberation many may contribute different pieces of information to generate a better decision. Recent scholarship, however, suggests that this was probably not what Aristotle meant but is a modern interpretation based on what we now know about team intelligence.<br />
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这个概念(尽管没有如此命名)起源于1785年的侯爵·孔多塞Marquis de Condorcet,其<font color=“#ff8000”> 陪审原理</font>指出,如果一个投票组的每个成员更有可能做出正确的决定,则该组中最高的票数是正确决定的概率会随着该组成员的数量增加而增加。(请参阅Condorcet<font color=“#ff8000”> 陪审原理</font>)。许多理论学家已经解释了亚里士多德 Aristotle在他的著作《政治》中的说法,即“集体盛宴相比较独自晚餐更加美味”,意思是每个人都可以带来各自的菜肴摆在餐桌上。引申为许多人可能会提供不同的信息片段以产生更好的决策。然而,最近的一项研究表明,这可能不是Aristotle的意思,而是根据目前我们对团队智能的了解做出的现代解释。<br />
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A precursor of the concept is found in entomologist [[William Morton Wheeler]]'s observation that seemingly independent individuals can cooperate so closely as to become indistinguishable from a single organism (1910). Wheeler saw this collaborative process at work in [[ants]] that acted like the cells of a single beast he called a [[superorganism]].<br />
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A precursor of the concept is found in entomologist William Morton Wheeler's observation that seemingly independent individuals can cooperate so closely as to become indistinguishable from a single organism (1910). Wheeler saw this collaborative process at work in ants that acted like the cells of a single beast he called a superorganism.<br />
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一开始昆虫学家威廉·莫顿·惠勒William Morton Wheeler意识到了这一概念(1910),他观察到独立的个体之间可以紧密合作,以至于无法与某单个生物区分开。他在蚂蚁身上看到了这种协作过程,它们就像野兽的细胞一样,他称其为<font color=“#ff8000”> 超有机体</font>。<br />
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In 1912 [[Émile Durkheim]] identified society as the sole source of human logical thought. He argued in "[[The Elementary Forms of Religious Life]]" that society constitutes a higher intelligence because it transcends the individual over space and time. Other antecedents are [[Vladimir Vernadsky]] and [[Pierre Teilhard de Chardin]]'s concept of "[[noosphere]]" and [[H.G. Wells]]'s concept of "[[world brain]]" (see also the term "[[global brain]]"). Peter Russell, [[Elisabet Sahtouris]], and [[Barbara Marx Hubbard]] (originator of the term "conscious evolution") are inspired by the visions of a noosphere&nbsp;– a transcendent, rapidly evolving collective intelligence&nbsp;– an informational cortex of the planet. The notion has more recently been examined by the philosopher Pierre Lévy. In a 1962 research report, [[Douglas Engelbart]] linked collective intelligence to organizational effectiveness, and predicted that pro-actively 'augmenting human intellect' would yield a multiplier effect in group problem solving: "Three people working together in this augmented mode [would] seem to be more than three times as effective in solving a complex problem as is one augmented person working alone". In 1994, he coined the term 'collective IQ' as a measure of collective intelligence, to focus attention on the opportunity to significantly raise collective IQ in business and society.<br />
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In 1912 Émile Durkheim identified society as the sole source of human logical thought. He argued in "The Elementary Forms of Religious Life" that society constitutes a higher intelligence because it transcends the individual over space and time. Other antecedents are Vladimir Vernadsky and Pierre Teilhard de Chardin's concept of "noosphere" and H.G. Wells's concept of "world brain" (see also the term "global brain"). Peter Russell, Elisabet Sahtouris, and Barbara Marx Hubbard (originator of the term "conscious evolution") are inspired by the visions of a noosphere&nbsp;– a transcendent, rapidly evolving collective intelligence&nbsp;– an informational cortex of the planet. The notion has more recently been examined by the philosopher Pierre Lévy. In a 1962 research report, Douglas Engelbart linked collective intelligence to organizational effectiveness, and predicted that pro-actively 'augmenting human intellect' would yield a multiplier effect in group problem solving: "Three people working together in this augmented mode [would] seem to be more than three times as effective in solving a complex problem as is one augmented person working alone". In 1994, he coined the term 'collective IQ' as a measure of collective intelligence, to focus attention on the opportunity to significantly raise collective IQ in business and society.<br />
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1912年,埃米尔·涂尔干Émile Durkheim将社会定义为人类逻辑思维的唯一来源。他在《宗教生活的基本形式》一书中指出,社会构成了一种更高的智慧,因为它在时空上超越了个人。其他先例还有弗拉基米尔·韦尔纳斯基Vladimir Vernadsky和皮埃尔·泰尔哈德·德·夏尔丁Pierre Teilhard de Chardin的<font color=“#ff8000”> 智能圈</font>概念以及赫伯特·乔治·威尔斯H.G. Wells的“<font color="#ff8000"> 世界脑World brain</font>”概念(另请参见“<font color="#ff8000"> 全球大脑Global brain</font>"”一词)。Peter Russell,伊丽莎白·萨赫图里斯Elisabet Sahtouris和芭芭拉·马克思·哈伯德Barbara Marx Hubbard(<font color=“#ff8000”> 意识演化</font>一词的发起者)受到了<font color=“#ff8000”> 智能圈</font>的启发,即超自然的,迅速发展的集体智能,相当于地球的大脑信息皮质层。哲学家Pierre Lévy最近对该概念进行了研究。在1962年的一份研究报告中,Douglas Engelbart将集体智能与组织有效性联系起来,并预测说,积极地“增强人类智慧”将在解决群体问题方面产生事半功倍的效果:“以这种增强模式工作的三个人在解决复杂问题上的效率似乎是一个单独工作的人(同等增强幅度)的三倍以上”。1994年,他创造了<font color=“#ff8000”> 群体智商</font>一词来衡量集体智能,以集中精力在商业和社会中寻找显著提高群体智商的机会。<br />
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The idea of collective intelligence also forms the framework for contemporary democratic theories often referred to as [[epistemic democracy]]. Epistemic democratic theories refer to the capacity of the populace, either through deliberation or aggregation of knowledge, to track the truth and relies on mechanisms to synthesize and apply collective intelligence.<br />
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The idea of collective intelligence also forms the framework for contemporary democratic theories often referred to as epistemic democracy. Epistemic democratic theories refer to the capacity of the populace, either through deliberation or aggregation of knowledge, to track the truth and relies on mechanisms to synthesize and apply collective intelligence.<br />
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集体智能的概念也构成了当代民主理论的框架,这些理论通常被称为<font color="#ff8000"> 认知民主Epistemic democracy</font>。指的是民众的能力,即通过审议或汇总知识来追踪真相,并依靠这种机制来综合运用集体智能。<br />
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Collective intelligence was introduced into the machine learning community in the late 20th century, and matured into a broader consideration of how to design "collectives" of self-interested adaptive agents to meet a system-wide goal. This was related to single-agent work on "reward shaping" and has been taken forward by numerous researchers in the game theory and engineering communities.<br />
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Collective intelligence was introduced into the machine learning community in the late 20th century, and matured into a broader consideration of how to design "collectives" of self-interested adaptive agents to meet a system-wide goal. This was related to single-agent work on "reward shaping" and has been taken forward by numerous researchers in the game theory and engineering communities.<br />
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集体智能在20世纪后期被引入机器学习社区,后被广泛认作为一种方法,即如何设计自利的自适应主体“群落”来满足系统范围内的目标要求。这与有关“奖励设计”的单主体工作有关,并已被博弈论和工程界的许多研究人员所推广。<br />
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== Dimensions 维度==<br />
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[[文件:Complex adaptive system.gif|thumb|复杂自适应系统模型l]]<br />
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[[Howard Bloom]] has discussed mass behavior – [[collective behavior]] from the level of quarks to the level of bacterial, plant, animal, and human societies. He stresses the biological adaptations that have turned most of this earth's living beings into components of what he calls "a learning machine". In 1986 Bloom combined the concepts of [[apoptosis]], [[parallel distributed processing]], [[group selection]], and the superorganism to produce a theory of how collective intelligence works. Later he showed how the collective intelligences of competing bacterial colonies and human societies can be explained in terms of computer-generated "[[complex adaptive systems]]" and the "[[genetic algorithms]]", concepts pioneered by [[John Henry Holland|John Holland]].<br />
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Howard Bloom has discussed mass behavior – collective behavior from the level of quarks to the level of bacterial, plant, animal, and human societies. He stresses the biological adaptations that have turned most of this earth's living beings into components of what he calls "a learning machine". In 1986 Bloom combined the concepts of apoptosis, parallel distributed processing, group selection, and the superorganism to produce a theory of how collective intelligence works. Later he showed how the collective intelligences of competing bacterial colonies and human societies can be explained in terms of computer-generated "complex adaptive systems" and the "genetic algorithms", concepts pioneered by John Holland.<br />
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Howard Bloom曾讨论过大众行为(从夸克到细菌,植物,动物和人类社会的群体行为)。他强调说,生物适应性使得地球上大多数生物已经变成了所谓的“学习机器”。1986年,Bloom将<font color="#ff8000"> 细胞凋亡Apoptosis</font>,<font color="#ff8000"> 并行分布处理Parallel distributed processing</font>,<font color="#ff8000"> 群体选择Group selection</font>和<font color="#ff8000"> 超有机体Superorganism</font>的概念结合在一起,产生了关于集体智能如何运作的理论。后来,他展示了如何用计算机生成的<font color="#ff8000"> 复杂自适应系统Complex adaptive systems</font>和<font color="#ff8000"> 遗传算法Genetic algorithms</font>( 由约翰·霍兰德John Holland所开创的概念)来解释竞争性细菌群落和人类社会的集体智能。<br />
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Bloom traced the evolution of collective intelligence to our bacterial ancestors 1 billion years ago and demonstrated how a multi-species intelligence has worked since the beginning of life. Ant societies exhibit more intelligence, in terms of technology, than any other animal except for humans and co-operate in keeping livestock, for example [[aphid]]s for "milking".<br />
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Bloom traced the evolution of collective intelligence to our bacterial ancestors 1 billion years ago and demonstrated how a multi-species intelligence has worked since the beginning of life. Ant societies exhibit more intelligence, in terms of technology, than any other animal except for humans and co-operate in keeping livestock, for example aphids for "milking". Leaf cutters care for fungi and carry leaves to feed the fungi.<br />
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Bloom追溯了10亿年前我们细菌祖先集体智能的演变过程,并展现出自生命开始以来多物种智慧是如何发挥作用的。类似蚂蚁社会在技术层面上,表现出了比人类社群以外的任何动物更多的智慧。它们合作饲养牲畜,例如“挤奶”的蚜虫。切叶蚁负责护理真菌,并用叶子喂食真菌。<br />
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[[David Skrbina]] cites the concept of a 'group mind' as being derived from Plato's concept of [[panpsychism]] (that mind or consciousness is omnipresent and exists in all matter). He develops the concept of a 'group mind' as articulated by [[Thomas Hobbes]] in "Leviathan" and [[Gustav Fechner|Fechner]]'s arguments for a [[collective consciousness]] of mankind. He cites [[Émile Durkheim|Durkheim]] as the most notable advocate of a "collective consciousness" and [[Teilhard de Chardin]] as a thinker who has developed the philosophical implications of the group mind.<br />
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David Skrbina cites the concept of a 'group mind' as being derived from Plato's concept of panpsychism (that mind or consciousness is omnipresent and exists in all matter). He develops the concept of a 'group mind' as articulated by Thomas Hobbes in "Leviathan" and Fechner's arguments for a collective consciousness of mankind. He cites Durkheim as the most notable advocate of a "collective consciousness" and Teilhard de Chardin as a thinker who has developed the philosophical implications of the group mind.<br />
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大卫·斯科宾纳David Skrbina引用了<font color="#ff8000"> 群体意识(Group mind)</font>的概念,该概念源自柏拉图的<font color="#ff8000"> 泛心论Panpsychism</font>(即思想或意识无所不在,并存在于所有事物中)。他进一步发展了托马斯·霍布斯Thomas Hobbes在<font color=“#ff8000”> 利维坦</font>中表达的“群体意识”的概念,以及费希纳关于人类集体意识的论点。他认为Durkheim是“集体意识”最著名的拥护者,并且认为Teilhard de Chardin作为思想家,曾提出了<font color="#ff8000"> 群体意识(Group mind)</font>的哲学含义。<br />
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Tom Atlee focuses primarily on humans and on work to upgrade what Howard Bloom calls "the group IQ". Atlee feels that collective intelligence can be encouraged "to overcome '[[groupthink]]' and individual [[cognitive bias]] in order to allow a collective to cooperate on one process – while achieving enhanced intellectual performance." George Pór defined the collective intelligence phenomenon as "the capacity of human communities to evolve towards higher order complexity and harmony, through such innovation mechanisms as differentiation and integration, competition and collaboration." Atlee and Pór state that "collective intelligence also involves achieving a single focus of attention and standard of metrics which provide an appropriate threshold of action". Their approach is rooted in [[scientific community metaphor]].<br />
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Tom Atlee focuses primarily on humans and on work to upgrade what Howard Bloom calls "the group IQ". Atlee feels that collective intelligence can be encouraged "to overcome 'groupthink' and individual cognitive bias in order to allow a collective to cooperate on one process – while achieving enhanced intellectual performance." George Pór defined the collective intelligence phenomenon as "the capacity of human communities to evolve towards higher order complexity and harmony, through such innovation mechanisms as differentiation and integration, competition and collaboration." Atlee and Pór state that "collective intelligence also involves achieving a single focus of attention and standard of metrics which provide an appropriate threshold of action". Their approach is rooted in scientific community metaphor.<br />
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Tom Atlee则主要关注人类,以及如何提升Howard Bloom所说的<font color=“#ff8000”> 群体智商</font>。Atlee认为,可以鼓励集体智能去“克服‘群体思维'和个人的认知偏见,以使集体在一个过程中进行合作,同时产生更高的智力表现。”乔治·珀尔George Pór将集体智能现象定义为一种能力,即“人类社区通过差异化,融合,竞争和协作等创新机制,向更高层次复杂性协调发展”。 Atlee和Pór指出“集体智能还涉及实现<font color="#32CD32">注意力集中</font>和度量标准的统一,从而提供适当的行动阈值”。 <font color="#32CD32">他们的方法植根于科学共同体的隐喻</font>。<br />
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The term group intelligence is sometimes used interchangeably with the term collective intelligence. Anita Woolley presents Collective intelligence as a measure of group intelligence and group creativity.The features of composition that lead to increased levels of collective intelligence in groups include criteria such as higher numbers of women in the group as well as increased diversity of the group.<br />
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The term group intelligence is sometimes used interchangeably with the term collective intelligence. Anita Woolley presents Collective intelligence as a measure of group intelligence and group creativity. The idea is that a measure of collective intelligence covers a broad range of features of the group, mainly group composition and group interaction. The features of composition that lead to increased levels of collective intelligence in groups include criteria such as higher numbers of women in the group as well as increased diversity of the group.<br />
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术语<font color="#ff8000"> 团体智慧Collective intelligence</font>有时可以与<font color="#ff8000"> 集体智能Collective intelligence</font>一词互换使用。安妮塔·伍利Anita Woolley认为集体智能,可以衡量集体智慧和创造力。即集体智能的度量能涵盖群体的广泛特征,主要包括群体组成和群体互动。导致群体中集体智能水平提高的组成特征包括:群体中女性人数增加以及群体内多样性增加等。<br />
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Atlee and Pór suggest that the field of collective intelligence should primarily be seen as a human enterprise in which mind-sets, a willingness to share and an openness to the value of distributed intelligence for the common good are paramount, though group theory and [[artificial intelligence]] have something to offer. Individuals who respect collective intelligence are confident of their own abilities and recognize that the whole is indeed greater than the sum of any individual parts. Maximizing collective intelligence relies on the ability of an organization to accept and develop "The Golden Suggestion", which is any potentially useful input from any member.[[Groupthink]] often hampers collective intelligence by limiting input to a select few individuals or filtering potential Golden Suggestions without fully developing them to implementation.<br />
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Atlee and Pór suggest that the field of collective intelligence should primarily be seen as a human enterprise in which mind-sets, a willingness to share and an openness to the value of distributed intelligence for the common good are paramount, though group theory and artificial intelligence have something to offer. Maximizing collective intelligence relies on the ability of an organization to accept and develop "The Golden Suggestion", which is any potentially useful input from any member. Groupthink often hampers collective intelligence by limiting input to a select few individuals or filtering potential Golden Suggestions without fully developing them to implementation.<br />
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Atlee和Pór还认为,集体智能领域应首先被视为是全体人类的事业。尽管群体理论和人工智能可以提供一些帮助,但是当我们在这个巨大的公司内协作时,为了共同利益,观念模式、分享意愿,以及对分布式智能的开明尤为重要。尊重集体智能的个体对自己的能力充满信心,并承认整体确实大于任何单个部分的总和。最大化集体智能取决于组织接受和发展“黄金建议”的能力,即任何成员都可能提供有用的信息。通过将输入限制为少数几个人,或过滤掉潜在的“黄金建议”,团体迷思通常阻碍集体智能的发展和实施。<br />
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[[Robert David Steele Vivas]] in ''The New Craft of Intelligence'' portrayed all citizens as "intelligence minutemen," drawing only on legal and ethical sources of information, able to create a "public intelligence" that keeps public officials and corporate managers honest, turning the concept of "national intelligence" (previously concerned about spies and secrecy) on its head.<br />
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Robert David Steele Vivas in The New Craft of Intelligence portrayed all citizens as "intelligence minutemen," drawing only on legal and ethical sources of information, able to create a "public intelligence" that keeps public officials and corporate managers honest, turning the concept of "national intelligence" (previously concerned about spies and secrecy) on its head.<br />
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罗伯特·戴维·斯蒂尔·维瓦斯Robert David Steele Vivas在《智慧前沿The New Craft of Intelligence》中将所有公民描绘为“情报干事”,描绘了仅利用法律和道德信息,就能够创造出使公共官员和公司经理保持诚信的“公共情报”,从而改变高层的“国家情报”(以前涉及间谍和保密系统)。<br />
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[[文件:多智能系统协作Stigmergic Collaboration:大规模协作的理论框架.jpg|thumb|多智能系统协作Stigmergic Collaboration:大规模协作的理论框架]]<br />
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According to [[Don Tapscott]] and [[Anthony D. Williams (author)|Anthony D. Williams]], collective intelligence is [[mass collaboration]]. In order for this concept to happen, four principles need to exist;<br />
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According to Don Tapscott and Anthony D. Williams, collective intelligence is mass collaboration. In order for this concept to happen, four principles need to exist;<br />
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根据唐·塔普斯科特Don Tapscott和安东尼·威廉姆斯Anthony D. Williams的说法,集体智能就是大规模协作。为了使这个概念成立,需要满足以下四个原则。<br />
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; Openness: [[idea sharing|Sharing ideas]] and [[intellectual property]]: though these resources provide the edge over competitors more benefits accrue from allowing others to share ideas and gain significant improvement and scrutiny through collaboration.<br />
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Openness: Sharing ideas and intellectual property: though these resources provide the edge over competitors more benefits accrue from allowing others to share ideas and gain significant improvement and scrutiny through collaboration.<br />
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开放性<br><br />
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共享想法和知识产权:尽管这些资源为竞争者提供了优势,但允许其他人共享想法可以带来更多好处,并通过协作获得重大改进和审查。<br />
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; Peering: Horizontal organization as with the 'opening up' of the Linux program where users are free to modify and develop it provided that they make it available for others. Peering succeeds because it encourages [[self-organization]]&nbsp;– a style of production that works more effectively than hierarchical management for certain tasks.<br />
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Peering: Horizontal organization as with the 'opening up' of the Linux program where users are free to modify and develop it provided that they make it available for others. Peering succeeds because it encourages self-organization&nbsp;– a style of production that works more effectively than hierarchical management for certain tasks.<br />
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<font color=“#32CD32”>对等性</font><br><br />
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<font color=“#ff8000”> 横向组织</font>具有和Linux程序一样的“开放性”,用户在被允许的情况下,可以自由修改和开发该程序。这种<font color=“#32CD32”>对等性</font>的成功是因为它鼓励自组织形式,这种形式的生产方式比某些任务的分层管理更有效。<br />
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; [[Sharing]]: Companies have started to share some ideas while maintaining some degree of control over others, like potential and critical [[patent rights]]. Limiting all intellectual property shuts out opportunities, while sharing some expands markets and brings out products faster.<br />
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Sharing: Companies have started to share some ideas while maintaining some degree of control over others, like potential and critical patent rights. Limiting all intellectual property shuts out opportunities, while sharing some expands markets and brings out products faster.<br />
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共享<br><br />
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一些公司已经开始分享他们的想法,但是同时又对其部分想法保持一定程度的控制,例如潜在的和关键的专利权。限制所有知识产权会失去一些机会,而共享则会扩大市场并更快地推出产品。<br />
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; Acting Globally: The advancement in communication technology has prompted the rise of global companies at low overhead costs. The [[internet]] is widespread, therefore a globally integrated company has no geographical boundaries and may access new markets, ideas and technology.<br />
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Acting Globally: The advancement in communication technology has prompted the rise of global companies at low overhead costs. The internet is widespread, therefore a globally integrated company has no geographical boundaries and may access new markets, ideas and technology.<br />
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全球行动<br><br />
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通信技术的进步以较低的间接成本促使了全球公司的兴起。互联网遍布全球,因此一家全球一体化的公司打破了地域限制,他们可以访问任何新市场,新思想和新技术。<br />
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== Collective intelligence factor ''c'' 集体智力因子c ==<br />
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[[文件:陡坡图显示了伍利等人(2010)的两项初始研究成果,其中包括第一因素的可释方差百分比。.png|缩略图|右|陡坡图显示了伍利等人(2010)的两项初始研究成果,其中包括第一因素的可释方差百分比。]]<br />
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A new scientific understanding of collective intelligence defines it as a group's general ability to perform a wide range of tasks. Definition, operationalization and statistical methods are similar to the [[G factor (psychometrics)|psychometric approach of general individual intelligence]]. Hereby, an individual's performance on a given set of cognitive tasks is used to measure general cognitive ability indicated by the general intelligence [[G factor (psychometrics)|factor ''g'']] extracted via [[factor analysis]]. In the same vein as ''g'' serves to display between-individual performance differences on cognitive tasks, collective intelligence research aims to find a parallel intelligence factor for groups) displaying between-group differences on task performance. The collective intelligence score then is used to predict how this same group will perform on any other similar task in the future. Yet tasks, hereby, refer to mental or intellectual tasks performed by small groups even though the concept is hoped to be transferable to other performances and any groups or crowds reaching from families to companies and even whole cities. Since individuals' ''g'' factor scores are highly correlated with full-scale [[Intelligence quotient|IQ]] scores, which are in turn regarded as good estimates of ''g'', this measurement of collective intelligence can also be seen as an intelligence indicator or quotient respectively for a group (Group-IQ) parallel to an individual's intelligence quotient (IQ) even though the score is not a quotient per se.<br />
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A new scientific understanding of collective intelligence defines it as a group's general ability to perform a wide range of tasks. Definition, operationalization and statistical methods are similar to the [[G factor (psychometrics)|psychometric approach of general individual intelligence]]. Hereby, an individual's performance on a given set of cognitive tasks is used to measure general cognitive ability indicated by the general intelligence [[G factor (psychometrics)|factor ''g'']] extracted via [[factor analysis]]. In the same vein as g serves to display between-individual performance differences on cognitive tasks, collective intelligence research aims to find a parallel intelligence factor for groups c factor') displaying between-group differences on task performance. The collective intelligence score then is used to predict how this same group will perform on any other similar task in the future. Yet tasks, hereby, refer to mental or intellectual tasks performed by small groups Since individuals' g factor scores are highly correlated with full-scale IQ scores, which are in turn regarded as good estimates of g, this measurement of collective intelligence can also be seen as an intelligence indicator or quotient respectively for a group (Group-IQ) parallel to an individual's intelligence quotient (IQ) even though the score is not a quotient per se.<br />
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对集体智能最新的科学理解,是将其定义为一个团队执行各种任务的综合能力。定义,可操作性和统计方法类似于<FONT COLOR=“#32CD32”>G因素(心理测量学,常规个人智力的计量方法)</FONT>。因此,在给定的一组认知任务上的个人表现被用于计量综合认知能力,通过因子分析法算出其<font color=“#32CD32”>智力因子g</font>。同理,g用于表达认知任务与个体之间的表现差异,集体智能研究的目的是为群体“c因子”(也称为“集体智力因子”(CI))找到一个类似的智力因子,以显示任务表现上群体间的差异。然后,将集体智力得分用于预测该组将来执行其他类似任务的表现。然而,目前任务的内容设置还局限在针对小团体的心智任务,尽管一开始的概念是希望能涉及的更广泛,比如说从家庭到公司甚至整个城市的任何团体或人群。由于个体的<font color=“#ff8000”> g因子</font>得分与全方位IQ得分密切相关,并且后者还可以恰当的估计<font color=“#ff8000”> g因子</font>,因此集体智能测量的结果同样可以被视为是一个群体的智力指标或商(Group-IQ),类似于个人智商(IQ),虽然该分数本身不是商。<br />
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Mathematically, ''c'' and ''g'' are both variables summarizing positive correlations among different tasks supposing that performance on one task is comparable with performance on other similar tasks. ''c'' thus is a source of variance among groups and can only be considered as a group's standing on the ''c'' factor compared to other groups in a given relevant population. The concept is in contrast to competing hypotheses including other correlational structures to explain group intelligence, such as a composition out of several equally important but independent factors as found in [[Big Five personality traits|individual personality research]].<br />
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Mathematically, c and g are both variables summarizing positive correlations among different tasks supposing that performance on one task is comparable with performance on other similar tasks. c thus is a source of variance among groups and can only be considered as a group's standing on the c factor compared to other groups in a given relevant population. The concept is in contrast to competing hypotheses including other correlational structures to explain group intelligence, such as a composition out of several equally important but independent factors as found in [[Big Five personality traits|individual personality research]].<br />
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从数学上讲,c和g都是变量,假设不同团队或个人在不同任务(但相似)中的表现具有可比性,这两个变量均描述了该团队或个人在不同任务之间的正相关性。<font color=“#32CD32”>因此,c表示的是团队之间的差异,在给定相关人口设置的其他组相比,它仅被视为该组在c因子上的设置结果。g</font><font color=“#32CD32”>需要注意的是,该概念与竞争假设(包括其他可以解释群体智能的相关结构)形成对比,例如由个体人格研究中发现的一些同样重要但相互独立的因素组合。g</font><br />
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Besides, this scientific idea also aims to explore the causes affecting collective intelligence, such as group size, collaboration tools or group members' interpersonal skills. The [[MIT Center for Collective Intelligence]], for instance, announced the detection of ''The Genome of Collective Intelligence'' as one of its main goals aiming to develop a ''taxonomy of organizational building blocks, or genes, that can be combined and recombined to harness the intelligence of crowds''.<br />
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Besides, this scientific idea also aims to explore the causes affecting collective intelligence, such as group size, collaboration tools or group members' interpersonal skills. The MIT Center for Collective Intelligence, for instance, announced the detection of The Genome of Collective Intelligence as one of its main goals aiming to develop a taxonomy of organizational building blocks, or genes, that can be combined and recombined to harness the intelligence of crowds.<br />
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此外,这一科学思想还旨在探讨影响集体智能的原因,例如小组规模,协作工具或小组成员的人际交往能力。例如,麻省理工学院的集体智能中心宣布检测“集体智能的基因组”是其主要目标之一,旨在建立一种分类法,可以组织构建模块或基因组,并对其进行重组,以利用群体的智力。<br />
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=== Causes 原因 ===<br />
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Individual intelligence is shown to be genetically and environmentally influenced. Analogously, collective intelligence research aims to explore reasons why certain groups perform more intelligent than other groups given that ''c'' is just moderately correlated with the intelligence of individual group members. According to Woolley et al.'s results, neither team cohesion nor motivation or satisfaction is correlated with ''c''. However, they claim that three factors were found as significant correlates: the variance in the number of speaking turns, group members' average social sensitivity and the proportion of females. All three had similar predictive power for ''c'', but only social sensitivity was statistically significant (b=0.33, P=0.05).<br />
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Individual intelligence is shown to be genetically and environmentally influenced. Analogously, collective intelligence research aims to explore reasons why certain groups perform more intelligent than other groups given that c is just moderately correlated with the intelligence of individual group members. According to Woolley et al.'s results, neither team cohesion nor motivation or satisfaction is correlated with c. However, they claim that three factors were found as significant correlates: the variance in the number of speaking turns, group members' average social sensitivity and the proportion of females. All three had similar predictive power for c, but only social sensitivity was statistically significant (b=0.33, P=0.05).<br />
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个体智力受到遗传与环境影响。类似地,集体智力的研究目的是探索为什么某些群体比其他群体表现地更聪明,假设因子c与群体中单个成员的智力适度相关。根据Woolley等人的结果,团队凝聚力,动机或满意度都与因子c无关。但是,他们声称发现了三个非常重要的相关因素:成员发表意见的次数,成员社会敏感度平均值和女性比例。这三者对因子c具有相似的预测能力,但目前只有社会敏感度具有统计学意义(b = 0.33,P = 0.05)。<br />
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The number speaking turns indicates that "groups where a few people dominated the conversation were less collectively intelligent than those with a more equal distribution of conversational turn-taking". Hence, providing multiple team members the chance to speak up made a group more intelligent.<br />
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The number speaking turns indicates that "groups where a few people dominated the conversation were less collectively intelligent than those with a more equal distribution of conversational turn-taking". Hence, providing multiple team members the chance to speak up made a group more intelligent.<br />
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成员发表意见的次数表明“由少数人主导的群体,其集体智力不及那些对话轮流分配更为平均的群体。”因此,为多个团队成员提供发言的机会可以让团队更加聪明。<br />
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Group members' social sensitivity was measured via the Reading the Mind in the Eyes Test (RME) and correlated .26 with c. or 'mind reading', which refers to the ability to attribute mental states, such as beliefs, desires or intents, to other people and in how far people understand that others have beliefs, desires, intentions or perspectives different from their own ones. and constantly differentiates control groups from individuals with functional autism or Asperger Syndrome. ToM can be regarded as an associated subset of skills and abilities within the broader concept of emotional intelligence.<br />
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Group members' social sensitivity was measured via the Reading the Mind in the Eyes Test (RME) and correlated .26 with c. or 'mind reading', which refers to the ability to attribute mental states, such as beliefs, desires or intents, to other people and in how far people understand that others have beliefs, desires, intentions or perspectives different from their own ones. and constantly differentiates control groups from individuals with functional autism or Asperger Syndrome. ToM can be regarded as an associated subset of skills and abilities within the broader concept of emotional intelligence.<br />
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<font color="#32CD32">小组成员的社交敏感度通过“<font color="#ff8000"> 眼神阅读测试Reading the Mind in the Eyes Test</font>”(RME)并与c关联(0.26)或<font color=“#ff8000”> 读心术</font>进行测量。这里要求参与者检测图片中呈现的其他人眼中表达的思维或感觉,并以选择题形式进行评估。该测试旨在衡量人们的<font color="#ff8000"> 心智理论Theory of mind(ToM)</font>,也称为“心理化”或“思想阅读”,指的是感受他人心理状态的能力(例如信念,欲望或意图),当他们的信念,欲望,意图或观点与自己有所不同时,能在多大程度上理解他人。RME是针对成人的ToM测试,显示出足够的重测信度,并不断将对照组与患有功能性自闭症或阿斯伯格综合症的个体区分开来。它是成人ToM最广泛接受和验证良好的测试之一。在更宽泛的情商概念中,ToM可被视为技能的相关子集。</font><br />
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The proportion of females as a predictor of ''c'' was largely mediated by social sensitivity ([[Sobel test|Sobel]] z = 1.93, P= 0.03) which is in vein with previous research showing that women score higher on social sensitivity tests. While a [[Mediation (statistics)|mediation]], statistically speaking, clarifies the mechanism underlying the relationship between a dependent and an independent variable,Wolley agreed in an interview with the Harvard Business Review that these findings are saying that groups of women are smarter than groups of men.[46] However, she relativizes this stating that the actual important thing is the high social sensitivity of group members.[46]<br />
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The proportion of females as a predictor of c was largely mediated by social sensitivity (Sobel z = 1.93, P= 0.03) Wolley agreed in an interview with the Harvard Business Review that these findings are saying that groups of women are smarter than groups of men. However, she relativizes this stating that the actual important thing is the high social sensitivity of group members.<br />
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女性占比作为因子c的预测因素主要是通过社会敏感性<font color=“#32CD32”>介导</font>(Sobel z = 1.93,P = 0.03),这与之前的研究结果相符,即女性在社会敏感性测试中得分更高。从统计学上讲,<font color=“#32CD32”>介导</font>,从统计学上讲,澄清了因变量和自变量之间关系的基本机制。伍利在接受《哈佛商业评论》采访时曾表示这个发现说明了女性群体比男性群体更聪明。但是,她也就这个结论<font color=“#32CD32”>做了相对化的陈述</font>,实际上重要的是团体成员的高度社会敏感性。<br />
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It is theorized that the collective intelligence factor ''c'' is an emergent property resulting from bottom-up as well as top-down processes. Hereby, bottom-up processes cover aggregated group-member characteristics. Top-down processes cover group structures and norms that influence a group's way of collaborating and coordinating.<br />
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It is theorized that the collective intelligence factor c is an emergent property resulting from bottom-up as well as top-down processes. Hereby, bottom-up processes cover aggregated group-member characteristics. Top-down processes cover group structures and norms that influence a group's way of collaborating and coordinating.<br />
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从理论上讲,集体智力因子c是由自下而上和自上而下共同产生的<font color=“#ff8000”> 涌现特性</font>。因此,自下而上的过程涉及聚合组成员的特征,自上而下的过程涉及团队结构,以及协作协调方式对团队风格的影响。<br />
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=== Processes 处理程序===<br />
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[[文件:集体智能因子c的预测。Woolley,Aggarwal和Malone建议(2015).png|缩略图|右|集体智能因子c的预测。Woolley,Aggarwal和Malone建议(2015)]]<br />
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==== Top-down processes 自上而下 ====<br />
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Top-down processes cover group interaction, such as structures, processes, and norms. Research further suggest that collectively intelligent groups communicate more in general as well as more equally; same applies for participation and is shown for face-to-face as well as online groups communicating only via writing.<br />
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Top-down processes cover group interaction, such as structures, processes, and norms. An example of such top-down processes is conversational turn-taking. Research further suggest that collectively intelligent groups communicate more in general as well as more equally; same applies for participation and is shown for face-to-face as well as online groups communicating only via writing.<br />
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自上而下的处理包括团队交互分析,涉及例如结构,程序和规范。这种自上而下的过程的一个例子是话轮转换机制。研究进一步表明,集体智慧的群体大体上能进行平等地交流。此过程同样适用于参与形式的沟通,类似面对面以及通过书面形式进行的在线小组交流。<br />
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==== Bottom-up processes 自下而上 ====<br />
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Bottom-up processes include group composition, namely the characteristics of group members which are aggregated to the team level. An example of such bottom-up processes is the average social sensitivity or the average and maximum intelligence scores of group members. Furthermore, collective intelligence was found to be related to a group's cognitive diversity including thinking styles and perspectives. Groups that are moderately diverse in [[cognitive style]] have higher collective intelligence than those who are very similar in cognitive style or very different. Consequently, groups where members are too similar to each other lack the variety of perspectives and skills needed to perform well. On the other hand, groups whose members are too different seem to have difficulties to communicate and coordinate effectively.<br />
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Bottom-up processes include group composition, including thinking styles and perspectives. Groups that are moderately diverse in cognitive style have higher collective intelligence than those who are very similar in cognitive style or very different. Consequently, groups where members are too similar to each other lack the variety of perspectives and skills needed to perform well. On the other hand, groups whose members are too different seem to have difficulties to communicate and coordinate effectively.<br />
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自下而上的处理包括小组组成分析,即小组成员的特征,这些特征汇总直接影响到团队级别。例子之一包括社会敏感度平均值或小组成员的平均和最大智力得分。此外,人们发现集体智能与一个群体的认知多样性有关,包括思维方式和观点。认知风格适度的群体,相比较认知风格非常相似或非常不同的群体,具有更高的集体智能。因为成员彼此之间过于相似会造成该群体缺乏不同的观点(往往团队任务表现好的具有各种观点)和技能。另一方面,成员差异太大的团体可能会难以有效地沟通和协调。<br />
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==== Serial vs Parallel processes 串行与并行 ====<br />
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For most of human history, collective intelligence was confined to small tribal groups in which opinions were aggregated through real-time parallel interactions among members. In modern times, mass communication, mass media, and networking technologies have enabled collective intelligence to span massive groups, distributed across continents and time-zones. To accommodate this shift in scale, collective intelligence in large-scale groups been dominated by serialized polling processes such as aggregating up-votes, likes, and ratings over time. While modern systems benefit from larger group size, the serialized process has been found to introduce substantial noise that distorts the collective output of the group. In one significant study of serialized collective intelligence, it was found that the first vote contributed to a serialized voting system can distort the final result by 34%.<br />
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For most of human history, collective intelligence was confined to small tribal groups in which opinions were aggregated through real-time parallel interactions among members. In modern times, mass communication, mass media, and networking technologies have enabled collective intelligence to span massive groups, distributed across continents and time-zones. To accommodate this shift in scale, collective intelligence in large-scale groups been dominated by serialized polling processes such as aggregating up-votes, likes, and ratings over time. While modern systems benefit from larger group size, the serialized process has been found to introduce substantial noise that distorts the collective output of the group. In one significant study of serialized collective intelligence, it was found that the first vote contributed to a serialized voting system can distort the final result by 34%.<br />
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在大多数人类历史中,集体智能都局限于少数部落群体,它们通过成员之间的实时并行互动来收集意见。而现代,因为大众传播,媒体和网络技术的发展使集体智能可以跨越各大洲和时区,这是一个极其庞大的群体。为了适应规模上的这种变化,大规模集体智能被序列化投票过程所控制,例如随着时间的推移去汇总投票,赞赏和评级。在工程领域中,汇总各种工程决策可以识别分析优秀的经典设计。尽管现代系统受益于更大的群规模,但事实上发现串行化处理过程会引入大量噪声,从而使群组的集体输出失真。在一项有关序列化集体智能的重要研究中发现,对序列化投票系统做出贡献的第一票可能使最终结果失真34%。<br />
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To address the problems of serialized aggregation of input among large-scale groups, recent advancements collective intelligence have worked to replace serialized votes, polls, and markets, with parallel systems such as "[[Swarm intelligence|human swarms]]" modeled after synchronous swarms in nature. Based on natural process of [[Swarm Intelligence]], these artificial swarms of networked humans enable participants to work together in parallel to answer questions and make predictions as an emergent collective intelligence. In one high-profile example, a human swarm challenge by CBS Interactive to predict the Kentucky Derby. The swarm correctly predicted the first four horses, in order, defying 542–1 odds and turning a $20 bet into $10,800.<br />
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To address the problems of serialized aggregation of input among large-scale groups, recent advancements collective intelligence have worked to replace serialized votes, polls, and markets, with parallel systems such as "human swarms" modeled after synchronous swarms in nature. Based on natural process of Swarm Intelligence, these artificial swarms of networked humans enable participants to work together in parallel to answer questions and make predictions as an emergent collective intelligence. In one high-profile example, a human swarm challenge by CBS Interactive to predict the Kentucky Derby. The swarm correctly predicted the first four horses, in order, defying 542–1 odds and turning a $20 bet into $10,800.<br />
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为了解决大规模群体之间因为输入序列化汇总的问题,目前的进展是,集体智能已经淘汰了序列化的选票,民意测验和市场,进而采用了以自然群体为蓝本的并行系统,例如“人类集群Human swarms”。基于<font color="#ff8000"> 群体智能Swarm Intelligence</font>(注意区分Collective intelligence)的自然执行过程,这些由人类联网组成的人工集群使参与者可以并行工作来解决问题,并为涌现集体智能做出预测。在一个引人注目的示例中,CBS Interactive(美国著名媒体公司)进行了人类集群的挑战以预测肯塔基德比(美国著名跑马赛)。这群人正确地预测了前四匹马,顺次击败了542-1的赔率,将20美元的赌注变成了10,800美元。<br />
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The value of parallel collective intelligence was demonstrated in medical applications by researchers at [[Stanford University School of Medicine]] and [[Unanimous A.I.|Unanimous AI]] in a set of published studies wherein groups of human doctors were connected by real-time swarming algorithms and tasked with diagnosing chest x-rays for the presence of pneumonia. When working together as "human swarms," the groups of experienced radiologists demonstrated a 33% reduction in diagnostic errors as compared to traditional methods.<br />
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The value of parallel collective intelligence was demonstrated in medical applications by researchers at Stanford University School of Medicine and Unanimous AI in a set of published studies wherein groups of human doctors were connected by real-time swarming algorithms and tasked with diagnosing chest x-rays for the presence of pneumonia. When working together as "human swarms," the groups of experienced radiologists demonstrated a 33% reduction in diagnostic errors as compared to traditional methods.<br />
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斯坦福大学医学院和Unanimous A.I.的研究人员证明了在医学应用中并行集体智能的价值,在已发表的研究中,它们采用了实时集群算法将一组人类医生联系在一起,运用胸部X射线来诊断肺炎的存在。当作为“人类集群”一起工作时,经验丰富的放射科医生小组相比较传统方法,诊断错误减少了33%。<br />
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=== Evidence 证据 ===<br />
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[[文件:Standardized Regression Coefficients.png|缩略图|伍利等人(2010年)的两项初始研究中发现了集体智力因子c的标准化回归系数。c和平均(最高)成员智力得分在判据任务上得到回归。]]<br />
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Woolley, Chabris, Pentland, Hashmi, & Malone (2010), the originators of this scientific understanding of collective intelligence, found a single statistical factor for collective intelligence in their research across 192 groups with people randomly recruited from the public. In Woolley et al.'s two initial studies, groups worked together on different tasks from the [[The Circumplex Model of Group Tasks|McGrath Task Circumplex]], a well-established taxonomy of group tasks. Tasks were chosen from all four quadrants of the circumplex and included visual puzzles, brainstorming, making collective moral judgments, and negotiating over limited resources. The results in these tasks were taken to conduct a [[factor analysis]]. Both studies showed support for a general collective intelligence factor ''c'' underlying differences in group performance with an initial eigenvalue accounting for 43% (44% in study 2) of the variance, whereas the next factor accounted for only 18% (20%). That fits the range normally found in research regarding a [[G factor (psychometrics)|general individual intelligence factor ''g'']] typically accounting for 40% to 50% percent of between-individual performance differences on cognitive tests.<br />
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Woolley, Chabris, Pentland, Hashmi, & Malone (2010), a well-established taxonomy of group tasks. Tasks were chosen from all four quadrants of the circumplex and included visual puzzles, brainstorming, making collective moral judgments, and negotiating over limited resources. The results in these tasks were taken to conduct a factor analysis. Both studies showed support for a general collective intelligence factor c underlying differences in group performance with an initial eigenvalue accounting for 43% (44% in study 2) of the variance, whereas the next factor accounted for only 18% (20%). That fits the range normally found in research regarding a general individual intelligence factor g typically accounting for 40% to 50% percent of between-individual performance differences on cognitive tests.<br />
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伍利,察布里斯,彭特兰,哈什米(2010)是集体智能这一科学概念的创始人,他们在192个群体的研究中发现了集体智能的单一统计因子,这192个群体的成员均是从公众中随机招募的。研究中,每个组群都是基于<font color="#ff8000"> 麦格拉思任务环McGrath Task Circumplex</font>(一种完善的小组任务分类法)进行合作。这些任务是从四个象限中选择的,包括视觉难题,头脑风暴,集体道德判断以及就有限的资源进行谈判。将这些任务中的结果用于因子分析。两项研究均显示出了综合集群智力因子c的特征,并且根据群体的不同表现出了一定的差异,其初始特征值约占这些差异的43%(研究2中为44%),而另一个因子仅占18%(20%)。该数据与综合个体智力因子g的范围相符,通常在认知测验中占个体间性能差异的40%至50%。<br />
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Afterwards, a more complex criterion task was absolved by each group measuring whether the extracted ''c'' factor had predictive power for performance outside the original task batteries. Criterion tasks were playing [[Draughts|checkers (draughts)]] against a standardized computer in the first and a complex architectural design task in the second study. In a [[regression analysis]] using both individual intelligence of group members and ''c'' to predict performance on the criterion tasks, ''c'' had a significant effect, but average and maximum individual intelligence had not. While average (r=0.15, P=0.04) and maximum intelligence (r=0.19, P=0.008) of individual group members were moderately correlated with ''c'', ''c'' was still a much better predictor of the criterion tasks. According to Woolley et al., this supports the existence of a collective intelligence factor ''c,'' because it demonstrates an effect over and beyond group members' individual intelligence and thus that ''c'' is more than just the aggregation of the individual IQs or the influence of the group member with the highest IQ.<br />
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Afterwards, a more complex criterion task was absolved by each group measuring whether the extracted c factor had predictive power for performance outside the original task batteries. Criterion tasks were playing checkers (draughts) against a standardized computer in the first and a complex architectural design task in the second study. In a regression analysis using both individual intelligence of group members and c to predict performance on the criterion tasks, c had a significant effect, but average and maximum individual intelligence had not. While average (r=0.15, P=0.04) and maximum intelligence (r=0.19, P=0.008) of individual group members were moderately correlated with c, c was still a much better predictor of the criterion tasks. According to Woolley et al., this supports the existence of a collective intelligence factor c, because it demonstrates an effect over and beyond group members' individual intelligence and thus that c is more than just the aggregation of the individual IQs or the influence of the group member with the highest IQ.<br />
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后来每个小组进行测试,验证提取c因子是否具有预测原始任务以外的能力,进而解决了更为复杂的判据任务。在第一个研究中,判据任务是在标准计算机上玩跳棋(国际跳棋),在第二个研究中则是复杂的建筑设计任务。在使用组员个人智力和c因子来预测判据任务执行情况的回归分析中,c具有显著作用,而平均和最大的个人智力则没有。虽然单个组成员的平均智力(r = 0.15,P = 0.04)和最高智力(r = 0.19,P = 0.008)与c有中等程度的相关性,但是c仍然是判据任务更好的预测指标。根据伍利等人的说法,该结果支持了集群智力因子c的存在,因为它证明了超出小组成员个人智力外的影响,因此c不仅仅是个人智商的累加,或单纯受到智商最高组员的影响。<br />
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Engel et al. (2014) replicated Woolley et al.'s findings applying an accelerated battery of tasks with a first factor in the factor analysis explaining 49% of the between-group variance in performance with the following factors explaining less than half of this amount. Moreover, they found a similar result for groups working together online communicating only via text and confirmed the role of female proportion and social sensitivity in causing collective intelligence in both cases. Similarly to Wolley et al., they also measured social sensitivity with the RME which is actually meant to measure people's ability to detect mental states in other peoples' eyes. The online collaborating participants, however, did neither know nor see each other at all. The authors conclude that scores on the RME must be related to a broader set of abilities of social reasoning than only drawing inferences from other people's eye expressions.<br />
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Engel et al. (2014) replicated Woolley et al.'s findings applying an accelerated battery of tasks with a first factor in the factor analysis explaining 49% of the between-group variance in performance with the following factors explaining less than half of this amount. Moreover, they found a similar result for groups working together online communicating only via text and confirmed the role of female proportion and social sensitivity in causing collective intelligence in both cases. Similarly to Wolley et al., they also measured social sensitivity with the RME which is actually meant to measure people's ability to detect mental states in other peoples' eyes. The online collaborating participants, however, did neither know nor see each other at all. The authors conclude that scores on the RME must be related to a broader set of abilities of social reasoning than only drawing inferences from other people's eye expressions.<br />
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恩格尔等人的研究(2014)在重复了伍利组员之前的研究发现,将加速任务组合与因子分析中的第一因素结合在一起,可以解释组间表现差异的49%,而其他因素解释占该比例一半以下。此外,他们在仅通过文本进行在线交流的小组中发现了相似的结果,并证实了女性比例和社会敏感性在两种情况下引起集体智能的作用。他们还模仿伍利小组使用RME来衡量社会敏感度,为了衡测试者感受他人眼中心理状态的能力。但是,在线合作参与者根本不认识也不见面。作者得出的结论是,RME的分数必须与更广泛的社会推理能力相关,而不仅仅是从其他人的眼神表情中得出推论。<br />
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A collective intelligence factor ''c'' in the sense of Woolley et al. was further found in groups of MBA students working together over the course of a semester, as well as in groups from different cultures and groups in different contexts in terms of short-term versus long-term groups. None of these investigations considered team members' individual intelligence scores as control variables.<br />
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A collective intelligence factor c in the sense of Woolley et al. in online gaming groups as well as in groups from different cultures and groups in different contexts in terms of short-term versus long-term groups. None of these investigations considered team members' individual intelligence scores as control variables.<br />
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伍利他们进一步在MBA学生群体中(时间跨度为一学期),在线游戏玩家群体中以及来自不同文化和不同背景的其他群体中(时间跨度分别为短期和长期组)发现了集体智力因子c。这些调查均未将团队成员的个人智力得分视为控制变量。<br />
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Note as well that the field of collective intelligence research is quite young and published empirical evidence is relatively rare yet. However, various proposals and working papers are in progress or already completed but (supposedly) still in a [[scholarly peer review]]ing publication process.<br />
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Note as well that the field of collective intelligence research is quite young and published empirical evidence is relatively rare yet. However, various proposals and working papers are in progress or already completed but (supposedly) still in a scholarly peer reviewing publication process.<br />
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注意的是,集体智能研究领域仍处在初始阶段,而且公开的经验证据还很少。各种提议和文章正在进行或已经完成,但(据说)仍处于学术同行评审出版过程中。<br />
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=== Predictive validity 预测有效性 ===<br />
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Next to predicting a group's performance on more complex criterion tasks as shown in the original experiments, the collective intelligence factor ''c'' was also found to predict group performance in diverse tasks in MBA classes lasting over several months. Thereby, highly collectively intelligent groups earned significantly higher scores on their group assignments although their members did not do any better on other individually performed assignments. Moreover, highly collective intelligent teams improved performance over time suggesting that more collectively intelligent teams learn better. This is another potential parallel to individual intelligence where more intelligent people are found to acquire new material quicker.<br />
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Next to predicting a group's performance on more complex criterion tasks as shown in the original experiments, the collective intelligence factor ''c'' was also found to predict group performance in diverse tasks in MBA classes lasting over several months. Thereby, highly collectively intelligent groups earned significantly higher scores on their group assignments although their members did not do any better on other individually performed assignments. Moreover, highly collective intelligent teams improved performance over time suggesting that more collectively intelligent teams learn better. This is another potential parallel to individual intelligence where more intelligent people are found to acquire new material quicker.<br />
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集体智力因子c除了能预测团队在判据任务(初始实验中相对较复杂任务)上的表现外,还能够预测持续数月的MBA课程中各种任务的团队绩效。因此,尽管组员在其他单独执行任务上没有做得很好,但具有高度集体智能的小组在团队任务上得分明显更高。此外,具有高度集体智能的团队会随着时间推移逐渐提高能力,这表明团队智力的集合性越高,其本身的学习能力约好。这类似于个人智力的性质,即聪明人越多,团队可以更快地获取新材料。<br />
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Individual intelligence can be used to predict plenty of life outcomes from school attainment to health outcomes Whether collective intelligence is able to predict other outcomes besides group performance on mental tasks has still to be investigated.<br />
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Individual intelligence can be used to predict plenty of life outcomes from school attainment and career success to health outcomes and even mortality. Whether collective intelligence is able to predict other outcomes besides group performance on mental tasks has still to be investigated.<br />
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个体智力可以用来预测从学业事业的成功到健康甚至死亡的大量生活场景。除了在智力任务上的表现外,集体智能是否能够预测其他结果尚待研究。<br />
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=== Potential connections to individual intelligence 与个人智力的潜在联系 ===<br />
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Gladwell (2008) showed that the relationship between individual IQ and success works only to a certain point and that additional IQ points over an estimate of IQ 120 do not translate into real life advantages. If a similar border exists for Group-IQ or if advantages are linear and infinite, has still to be explored. Similarly, demand for further research on possible connections of individual and collective intelligence exists within plenty of other potentially transferable logics of individual intelligence, such as, for instance, the development over time a group's collective intelligence potentially offers simpler opportunities for improvement by exchanging team members or implementing structures and technologies. as well as watching drama movies.In how far such training ultimately improves collective intelligence through social sensitivity remains an open question.<br />
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Gladwell (2008) showed that the relationship between individual IQ and success works only to a certain point and that additional IQ points over an estimate of IQ 120 do not translate into real life advantages. If a similar border exists for Group-IQ or if advantages are linear and infinite, has still to be explored. Similarly, demand for further research on possible connections of individual and collective intelligence exists within plenty of other potentially transferable logics of individual intelligence, such as, for instance, the development over time or the question of improving intelligence. Whereas it is controversial whether human intelligence can be enhanced via training, as well as watching drama movies. In how far such training ultimately improves collective intelligence through social sensitivity remains an open question.<br />
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格拉德威尔Gladwell(2008)指出,个人智商与成功之间的关系仅在一定程度上起作用,而且智商超过120以上的其他智力点并不能转化为现实生活中的优势。是否Group-IQ存在相似的边界?或者优势是线性的和无限的?这仍然有待探索。同样,对个人智力和集体智力之间的联系也需要进一步探究,是否存在个人智力其他潜在因素可以转移到集体智力中?例如随着时间的推移自我进化或智力提高。尽管目前对于是否能通过培训来增强人类智力这一论点存在争议,但一个团队的集体智力是可以潜在性地通过交换组员或实施结构和技术上的提升来改进的。此外,人们发现阅读文学小说以及看戏曲电影至少可以暂时改善社会敏感性。但是社会敏感性培训最终是否能提高集体智力以及在多大程度上提高集体智力,这仍然是一个悬而未决的问题。<br />
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There are further more advanced concepts and factor models attempting to explain individual cognitive ability including the categorization of intelligence in fluid and crystallized intelligence or the hierarchical model of intelligence differences. Further supplementing explanations and conceptualizations for the factor structure of the Genomes of collective intelligence besides a general c factor', though, are missing yet.<br />
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There are further more advanced concepts and factor models attempting to explain individual cognitive ability including the categorization of intelligence in fluid and crystallized intelligence or the hierarchical model of intelligence differences. Further supplementing explanations and conceptualizations for the factor structure of the Genomes of collective intelligence besides a general c factor', though, are missing yet.<br />
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还有更多更高级的概念和因子模型试图解释个体的认知能力,包括流体智力和晶体智力或智力差异的分层模型。但是,除了通用的“c因子”外,目前并没有对集体智力基因组的因子结构采取进一步补充说明和概念化。<br />
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=== Controversies 争议 ===<br />
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Other scholars explain team performance by aggregating team members' general intelligence to the team level instead of building an own overall collective intelligence measure. Devine and Philips (2001) showed in a meta-analysis that mean cognitive ability predicts team performance in laboratory settings (.37) as well as field settings (.14) – note that this is only a small effect. Suggesting a strong dependence on the relevant tasks, other scholars showed that tasks requiring a high degree of communication and cooperation are found to be most influenced by the team member with the lowest cognitive ability. Tasks in which selecting the best team member is the most successful strategy, are shown to be most influenced by the member with the highest cognitive ability.<br />
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Other scholars explain team performance by aggregating team members' general intelligence to the team level instead of building an own overall collective intelligence measure. Devine and Philips (2001) showed in a meta-analysis that mean cognitive ability predicts team performance in laboratory settings (.37) as well as field settings (.14) – note that this is only a small effect. Suggesting a strong dependence on the relevant tasks, other scholars showed that tasks requiring a high degree of communication and cooperation are found to be most influenced by the team member with the lowest cognitive ability. Tasks in which selecting the best team member is the most successful strategy, are shown to be most influenced by the member with the highest cognitive ability.<br />
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有的学者通过将团队成员的综合智力进行汇总到团队级别来解释团队能力,而不是建立团队自身的集群智力指标。迪瓦恩Devine和飞利浦Philips(2001)在一项Meta综合分析中表明,认知能力可以预测团队在实验室环境(.37)和现场环境(.14)中的表现,但是请注意,这只是很小的影响。其他学者认为这相当依赖于不同的相关任务,他们表示那些需要高度沟通与合作的任务其实受认知能力最低组员的影响最大。因此选择最佳组员是成功的关键策略,这些任务受认知能力最高的成员影响最大。<br />
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Since Woolley et al.'s results do not show any influence of group satisfaction, [[group cohesiveness]], or motivation, they, at least implicitly, challenge these concepts regarding the importance for group performance in general and thus contrast meta-analytically proven evidence concerning the positive effects of [[Group cohesiveness|group cohesion]], motivation and satisfaction on group performance.<br />
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Since Woolley et al.'s[9] results do not show any influence of group satisfaction, group cohesiveness, or motivation, they, at least implicitly, challenge these concepts regarding the importance for group performance in general and thus contrast meta-analytically proven evidence concerning the positive effects of group cohesion,[106][107][108] motivation[109][110] and satisfaction[111] on group performance.<br />
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由于伍利等人的结果并未显示出团队满意度,团队凝聚力或动机的任何影响,因此他们仅隐含地挑战了这些观点,并表示了其总体上对团队绩效的重要性。通过Meta综合分析,他们证明了团队凝聚力,动机和满意度对团队绩效的积极影响。<br />
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Noteworthy is also that the involved researchers among the confirming findings widely overlap with each other and with the authors participating in the original first study around Anita Woolley.<br />
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Noteworthy is also that the involved researchers among the confirming findings widely overlap with each other and with the authors participating in the original first study around Anita Woolley.<br />
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值得一提的是,确认结果中涉及的研究人员之间,以及与参与有关Anita Woolley最初第一项研究的作者之间也存在广泛的重叠。<br />
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== Alternative mathematical techniques 其他数学替代技术 ==<br />
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=== Computational collective intelligence 计算集体智能 ===<br />
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[[文件:计算集体智能.jpg|缩略图|右|计算集体智能]]<br />
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In 2001, Tadeusz (Tad) Szuba from the [[Akademia Górniczo-Hutnicza|AGH University]] in Poland proposed a formal model for the phenomenon of collective intelligence. It is assumed to be an unconscious, random, parallel, and distributed computational process, run in mathematical logic by the social structure.<br />
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In 2001, Tadeusz (Tad) Szuba from the AGH University in Poland proposed a formal model for the phenomenon of collective intelligence. It is assumed to be an unconscious, random, parallel, and distributed computational process, run in mathematical logic by the social structure.<br />
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2001年,来自波兰AGH科技大学的Tadeusz(Tad)Szuba提出了一种具有集体智能现象的正式模型。模型假定是一个无意识,随机,并行和分布式的计算程序,其社会结构以数学逻辑方式运行。<br />
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In this model, beings and information are modeled as abstract information molecules carrying expressions of mathematical logic. They are quasi-randomly displacing due to their interaction with their environments with their intended displacements. Their interaction in abstract computational space creates multi-thread inference process which we perceive as collective intelligence. Thus, a non-[[Alan Turing|Turing]] model of computation is used. This theory allows simple formal definition of collective intelligence as the property of [[social structure]] and seems to be working well for a wide spectrum of beings, from bacterial colonies up to human social structures. Collective intelligence considered as a specific computational process is providing a straightforward explanation of several social phenomena. For this model of collective intelligence, the formal definition of IQS (IQ Social) was proposed and was defined as "the probability function over the time and domain of N-element inferences which are reflecting inference activity of the social structure". While IQS seems to be computationally hard, modeling of social structure in terms of a computational process as described above gives a chance for approximation. Prospective applications are optimization of companies through the maximization of their IQS, and the analysis of drug resistance against collective intelligence of bacterial colonies.<br />
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In this model, beings and information are modeled as abstract information molecules carrying expressions of mathematical logic. They are quasi-randomly displacing due to their interaction with their environments with their intended displacements. Their interaction in abstract computational space creates multi-thread inference process which we perceive as collective intelligence. Thus, a non-Turing model of computation is used. This theory allows simple formal definition of collective intelligence as the property of social structure and seems to be working well for a wide spectrum of beings, from bacterial colonies up to human social structures. Collective intelligence considered as a specific computational process is providing a straightforward explanation of several social phenomena. For this model of collective intelligence, the formal definition of IQS (IQ Social) was proposed and was defined as "the probability function over the time and domain of N-element inferences which are reflecting inference activity of the social structure". While IQS seems to be computationally hard, modeling of social structure in terms of a computational process as described above gives a chance for approximation. Prospective applications are optimization of companies through the maximization of their IQS, and the analysis of drug resistance against collective intelligence of bacterial colonies.<br />
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在此模型中,将真实环境中的生物和信息两部分进行建模,表示为带有数学逻辑表达式的抽象信息分子。由于它们与环境之间的相互作用,以及它们自身带有的目标位移属性,会准随机地进行挪动。随后,它们会在抽象的计算空间中交互,进而创建多线程推导处理程序,其过程则被视为集体智能。因此,非图灵计算模型被采用。该理论将集体智能简单定义为社会结构的属性,而且似乎对于各类生物(从细菌菌落到人类社会结构)均适用。集体智能被视为是一种特定的计算过程,它为几种社会现象提供了直接的解释。对于这种集体智能模型,科学家们提出了IQS(即IQ社会)的正式定义,并将其定义为“在时间和N元素推理域(反映社会结构推理活动)上的概率函数”。IQS在计算上似乎很难,但是根据如上所述的计算过程对社会结构进行建模的话,可以得到近似的结果。通过最大化IQS,公司可以优化其潜在的应用,另外医学上,也可以对细菌菌落的集体智能进行建模,来分析耐药性。<br />
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=== Collective intelligence quotient 集体智商 ===<br />
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One measure sometimes applied, especially by more artificial intelligence focused theorists, is a "collective intelligence quotient" (or "cooperation quotient") – which can be normalized from the "individual" [[intelligence quotient]] (IQ) – thus making it possible to determine the marginal intelligence added by each new individual participating in the [[collective action]], thus using [[Metric (mathematics)|metrics]] to avoid the hazards of [[group think]] and [[stupidity]].<br />
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One measure sometimes applied, especially by more artificial intelligence focused theorists, is a "collective intelligence quotient" (or "cooperation quotient") – which can be normalized from the "individual" intelligence quotient (IQ) – thus making it possible to determine the marginal intelligence added by each new individual participating in the collective action, thus using metrics to avoid the hazards of group think and stupidity<br />
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有时候我们会采用另一种度量方式表达,称为“<font color="#ff8000"> 集体智商Collective intelligence quotient</font>” (或“<font color="#ff8000"> 合作商Cooperation quotient</font>”),它特别受到以人工智能为研究重点的理论家的青睐。它可以由“个体”智商归一化处理后得到。因此可以进一步确定参加集体行动的新增组员所带来的额外边际智商,还可以使用度量标准来避免由群体愚蠢思维带来的危险。<br />
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== Applications 应用 ==<br />
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==== Elicitation of point estimates 评估点提取 ====<br />
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Here, the goal is to get an estimate (in a single value) of something. For example, estimating the weight of an object, or the release date of a product or probability of success of a project etc. as seen in prediction markets like Intrade, HSX or InklingMarkets and also in several implementations of crowdsourced estimation of a numeric outcome. Essentially, we try to get the average value of the estimates provided by the members in the crowd.<br />
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Here, the goal is to get an estimate (in a single value) of something. For example, estimating the weight of an object, or the release date of a product or probability of success of a project etc. as seen in prediction markets like Intrade, HSX or InklingMarkets and also in several implementations of crowdsourced estimation of a numeric outcome. Essentially, we try to get the average value of the estimates provided by the members in the crowd.<br />
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关于集体智能,其应用目标之一是获得某种事务的估计值(单个值)。例如估算物体的重量,产品的发布日期或项目成功的概率等。其应用场景可以是在Intrade,HSX或InklingMarkets等预测市场中,亦或在对数字结果进行众包估计的几种实操过程中。从本质上讲是尝试获取指定群体中成员提供的估计平均值。<br />
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==== Opinion aggregation 意见汇总 ====<br />
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In this situation, opinions are gathered from the crowd regarding an idea, issue or product. For example, trying to get a rating (on some scale) of a product sold online (such as Amazon's star rating system). Here, the emphasis is to collect and simply aggregate the ratings provided by customers/users.<br />
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In this situation, opinions are gathered from the crowd regarding an idea, issue or product. For example, trying to get a rating (on some scale) of a product sold online (such as Amazon's star rating system). Here, the emphasis is to collect and simply aggregate the ratings provided by customers/users.<br />
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在这种场景下,集体智能可用于收集人群中相关的不同想法,问题或产品的意见。例如,尝试对在线销售的产品(例如亚马逊的星级评分系统)进行某种程度的评级。这里重点是收集并简单地汇总客户/用户提供的评级。<br />
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==== Idea Collection 想法收集 ====<br />
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In these problems, someone solicits ideas for projects, designs or solutions from the crowd. For example, ideas on solving a [[data science]] problem (as in [[Kaggle]]) or getting a good design for a T-shirt (as in [[Threadless]]) or in getting answers to simple problems that only humans can do well (as in Amazon's Mechanical Turk). The objective is to gather the ideas and devise some selection criteria to choose the best ideas.<br />
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In these problems, someone solicits ideas for projects, designs or solutions from the crowd. For example, ideas on solving a data science problem (as in Kaggle) or getting a good design for a T-shirt (as in Threadless) or in getting answers to simple problems that only humans can do well (as in Amazon's Mechanical Turk). The objective is to gather the ideas and devise some selection criteria to choose the best ideas.<br />
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在处理问题的时候,集体智能也可以用于从人群中收集相关项目的想法,设计或解决方案。例如,关于解决数据科学问题的想法(类似在Kaggle中),获得T恤衫良好设计的想法(类似在Threadless中),或者收集仅人类能处理的简单问题的答案(类似在Amazon的Mechanical Turk中)。目的是收集各种想法并从中设计选择标准来筛选最佳方案。<br />
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[[James Surowiecki]] divides the advantages of disorganized decision-making into three main categories, which are cognition, cooperation and coordination.<br />
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James Surowiecki divides the advantages of disorganized decision-making into three main categories, which are cognition, cooperation and coordination.<br />
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纽约客商业专栏作家詹姆斯·苏洛维奇James Surowiecki将无组织决策的优势分为三个主要类别,即认知,合作和协调。<br />
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=== Cognition 认知 ===<br />
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==== Market judgment 市场判断 ====<br />
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Because of the Internet's ability to rapidly convey large amounts of information throughout the world, the use of collective intelligence to predict stock prices and stock price direction has become increasingly viable. Websites aggregate stock market information that is as current as possible so professional or amateur stock analysts can publish their viewpoints, enabling amateur investors to submit their financial opinions and create an aggregate opinion. The opinion of all investor can be weighed equally so that a pivotal premise of the effective application of collective intelligence can be applied: the masses, including a broad spectrum of stock market expertise, can be utilized to more accurately predict the behavior of financial markets.<br />
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Because of the Internet's ability to rapidly convey large amounts of information throughout the world, the use of collective intelligence to predict stock prices and stock price direction has become increasingly viable. Websites aggregate stock market information that is as current as possible so professional or amateur stock analysts can publish their viewpoints, enabling amateur investors to submit their financial opinions and create an aggregate opinion.The opinion of all investor can be weighed equally so that a pivotal premise of the effective application of collective intelligence can be applied: the masses, including a broad spectrum of stock market expertise, can be utilized to more accurately predict the behavior of financial markets.<br />
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由于英特网具有在全球范围内快速传递大量信息的能力,因此使用集体智能来预测股票价格和股票价格方向已变得越来越可行。网站汇总了尽可能最新的股票市场信息,以便专业或业余股票分析师可以发布其观点,从而使业余投资者可以提交其金融见解并创建汇总意见。这些投资者的意见可以加权平均,以便将有效地运用集体智能作为关键前提:利用群众,包括广泛的股市专业知识,来更准确地预测金融市场的行为。<br />
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Collective intelligence underpins the [[efficient-market hypothesis]] of [[Eugene Fama]] in which 89 out of 115 selected funds underperformed relative to the index during the period from 1955 to 1964. But after removing the loading charge (up-front fee) only 72 underperformed while after removing brokerage costs only 58 underperformed. On the basis of such evidence [[index fund]]s became popular investment vehicles using the collective intelligence of the market, rather than the judgement of professional fund managers, as an investment strategy.<br />
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Collective intelligence underpins the efficient-market hypothesis of Eugene Fama&nbsp;– although the term collective intelligence is not used explicitly in his paper. Fama cites research conducted by Michael Jensen in which 89 out of 115 selected funds underperformed relative to the index during the period from 1955 to 1964. But after removing the loading charge (up-front fee) only 72 underperformed while after removing brokerage costs only 58 underperformed. On the basis of such evidence index funds became popular investment vehicles using the collective intelligence of the market, rather than the judgement of professional fund managers, as an investment strategy.<br />
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集体智能巩固了尤金·法玛Eugene Fama的有效市场假说,尽管集体智能这个词在他的论文中并未明确使用。法玛引用了迈克尔·詹森Michael Jensen的研究,在1955年至1964年期间,115个精选基金中有89个相对于该指数表现不佳。但是,在取消了加载费用(前期费用)之后,只有72个基金表现不佳,而在去除经纪费用之后,剩下了58个。在这些证据的基础上,指数基金成为了市场投资工具,使用市场的集体智能而不是专业基金经理的判断作为投资策略。<br />
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==== Predictions in politics and technology 政治和技术预测 ====<br />
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[[文件:美国2016年使用的投票方法.svg|缩略图|右|美国2016年使用的投票方法]]<br />
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Political parties mobilize large numbers of people to form policy, select candidates and finance and run election campaigns. Knowledge focusing through various [[voting]] methods allows perspectives to converge through the assumption that uninformed voting is to some degree random and can be filtered from the decision process leaving only a residue of informed consensus. Critics point out that often bad ideas, misunderstandings, and misconceptions are widely held, and that structuring of the decision process must favor experts who are presumably less prone to random or misinformed voting in a given context.<br />
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Political parties mobilize large numbers of people to form policy, select candidates and finance and run election campaigns. Knowledge focusing through various voting methods allows perspectives to converge through the assumption that uninformed voting is to some degree random and can be filtered from the decision process leaving only a residue of informed consensus.Critics point out that often bad ideas, misunderstandings, and misconceptions are widely held, and that structuring of the decision process must favor experts who are presumably less prone to random or misinformed voting in a given context.<br />
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政党动员了大量人力制定政策,选拔候选人和资助并开展竞选活动。通过各种投票方法集中信息,使观点融合假设,不知情者的投票在某种程度上可视为是随机的,可以从决策过程中过滤掉,仅留下有共识的知情者的投票。批评家指出,坏主意,误解和谬见通常会广泛存在,因此决策过程的结构必须有利于那些在给定背景下,不大可能出现随机或者误导投票的专家。<br />
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Companies such as Affinnova (acquired by Nielsen), [[Google]], [[InnoCentive]], [[Marketocracy]], and [[Threadless]] have successfully employed the concept of collective intelligence in bringing about the next generation of technological changes through their research and development (R&D), customer service, and knowledge management. An example of such application is Google's Project Aristotle in 2012, where the effect of collective intelligence on team makeup was examined in hundreds of the company's R&D teams.<br />
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Companies such as Affinnova (acquired by Nielsen), Google, InnoCentive, Marketocracy, and Threadless have successfully employed the concept of collective intelligence in bringing about the next generation of technological changes through their research and development (R&D), customer service, and knowledge management. An example of such application is Google's Project Aristotle in 2012, where the effect of collective intelligence on team makeup was examined in hundreds of the company's R&D teams.<br />
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诸如Affinnova(被尼尔森收购),Google,InnoCentive,Marketocracy和Threadless等公司已经成功地采用了集体智能的概念,通过其研发(R&D),客户服务和知识管理实现了下一代技术变革。 <br />
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=== Cooperation 合作 ===<br />
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==== Networks of trust 信任网络====<br />
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[[文件:集体智能在千年计划中的应用.png|缩略图|左|集体智能在千年计划中的应用]]<br />
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In 2012, the ''Global Futures Collective Intelligence System'' (GFIS) was created by [[The Millennium Project]], which epitomizes collective intelligence as the synergistic intersection among data/information/knowledge, software/hardware, and expertise/insights that has a recursive learning process for better decision-making than the individual players alone.<br />
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In 2012, the Global Futures Collective Intelligence System (GFIS) was created by The Millennium Project, which epitomizes collective intelligence as the synergistic intersection among data/information/knowledge, software/hardware, and expertise/insights that has a recursive learning process for better decision-making than the individual players alone.<br />
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2012年,千年计划创建了<font color="#ff8000"> 全球集体智能系统Global Futures Collective Intelligence System(GFIS)</font>,因为它将数据/信息/知识,软件/硬件以及技术/见解进行了协同处理,使其成为了集体智能最贴切的代表。与单独的各项参与模块相比,它具有递归学习的处理能力,可以更好地进行决策。<br />
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[[New media]] are often associated with the promotion and enhancement of collective intelligence. The ability of new media to easily store and retrieve information, predominantly through databases and the Internet, allows for it to be shared without difficulty. Thus, through interaction with new media, knowledge easily passes between sources {{Harv|Flew|2008}} resulting in a form of collective intelligence. The use of interactive new media, particularly the internet, promotes online interaction and this distribution of knowledge between users.<br />
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New media are often associated with the promotion and enhancement of collective intelligence. The ability of new media to easily store and retrieve information, predominantly through databases and the Internet, allows for it to be shared without difficulty. Thus, through interaction with new media, knowledge easily passes between sources resulting in a form of collective intelligence. The use of interactive new media, particularly the internet, promotes online interaction and this distribution of knowledge between users.<br />
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另外新媒体也可以促进增强集体智能。其通过数据库和英特网轻松存储和检索信息的能力使得信息共享毫无困难。因此,通过与新媒体的互动,知识很容易在资源之间传递(Flew 2008),从而形成了集体智能。交互式新媒体(尤其是互联网)的使用促进了在线互动以及用户之间的知识分配。<br />
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[[Francis Heylighen]], [[Valentin Turchin]], and Gottfried Mayer-Kress are among those who view collective intelligence through the lens of computer science and [[cybernetics]]. In their view, the Internet enables collective intelligence at the widest, planetary scale, thus facilitating the emergence of a [[global brain]].<br />
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Francis Heylighen, Valentin Turchin, and Gottfried Mayer-Kress are among those who view collective intelligence through the lens of computer science and cybernetics. In their view, the Internet enables collective intelligence at the widest, planetary scale, thus facilitating the emergence of a global brain.<br />
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弗朗西斯·海里格森Francis Heylighen,瓦伦丁·图尔钦Valentin Turchin和Gottfried Mayer-Kress都是通过计算机科学和控制论的视角看待集体智能。他们认为,互联网可以在最广泛的地球尺度上实现集体智能,从而促进全球大脑的出现。<br />
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The developer of the World Wide Web, [[Tim Berners-Lee]], aimed to promote sharing and publishing of information globally. Later his employer opened up the technology for free use. In the early '90s, the Internet's potential was still untapped, until the mid-1990s when 'critical mass', as termed by the head of the Advanced Research Project Agency (ARPA), Dr. [[J.C.R. Licklider]], demanded more accessibility and utility. The driving force of this Internet-based collective intelligence is the digitization of information and communication. [[Henry Jenkins]], a key theorist of new media and media convergence draws on the theory that collective intelligence can be attributed to media convergence and participatory culture {{Harv|Flew|2008}}. He criticizes contemporary education for failing to incorporate online trends of collective problem solving into the classroom, stating "whereas a collective intelligence community encourages ownership of work as a group, schools grade individuals". Jenkins argues that interaction within a knowledge community builds vital skills for young people, and teamwork through collective intelligence communities contribute to the development of such skills.<br />
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The developer of the World Wide Web, Tim Berners-Lee, aimed to promote sharing and publishing of information globally. Later his employer opened up the technology for free use. In the early '90s, the Internet's potential was still untapped, until the mid-1990s when 'critical mass', as termed by the head of the Advanced Research Project Agency (ARPA), Dr. J.C.R. Licklider, demanded more accessibility and utility. The driving force of this Internet-based collective intelligence is the digitization of information and communication. Henry Jenkins, a key theorist of new media and media convergence draws on the theory that collective intelligence can be attributed to media convergence and participatory culture . He criticizes contemporary education for failing to incorporate online trends of collective problem solving into the classroom, stating "whereas a collective intelligence community encourages ownership of work as a group, schools grade individuals". Jenkins argues that interaction within a knowledge community builds vital skills for young people, and teamwork through collective intelligence communities contribute to the development of such skills. Collective intelligence is not merely a quantitative contribution of information from all cultures, it is also qualitative.<br />
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万维网创始人蒂姆·伯纳斯·李Tim Berners-Lee,曾以促进全球信息共享和发作为目标开发了万维网。后来,他的雇主开放了该技术以供大家免费使用。在90年代初期,互联网的潜力一直没有得到开发,直到1990年代中期,高级研究计划局(ARPA)负责人J.C.R. Licklider博士将其称为“临界质量”,并要求其具有更强的可访问性和实用性。这种基于互联网的集体智能驱动力是信息和通信的数字化。研究新媒体出现和媒体融合的关键理论家Henry Jenkins借鉴了其概念,认为集体智能可以归因于媒体融合和参与性文化(Flew 2008)。他批判当代教育未能将集体智能理念的趋势纳入课堂,比如说可以通过在线集群智慧解决问题这一思想。并指出“通过集体智能社区鼓励以集体为单位进行工作学习,而学校则需要对个人评分”。詹金斯认为,知识社区内的互动为年轻人创造了至关重要的技能,而通过集体智能社区的团队合作则有助于此类技能的发展。集体智能不仅是来自所有文化信息的定量贡献,同样也是定性存在。<br />
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[[Pierre Lévy|Lévy]] and [[Derrick de Kerckhove|de Kerckhove]] consider CI from a mass communications perspective, focusing on the ability of networked information and communication technologies to enhance the community knowledge pool. They suggest that these communications tools enable humans to interact and to share and collaborate with both ease and speed (Flew 2008). With the development of the [[Internet]] and its widespread use, the opportunity to contribute to knowledge-building communities, such as [[Wikipedia]], is greater than ever before. These computer networks give participating users the opportunity to store and to retrieve knowledge through the collective access to these databases and allow them to "harness the hive" Press.|year=2008|isbn=|location=Melbourne|pages=|quote=|via=}}</ref> Researchers at the [[MIT Center for Collective Intelligence]] research and explore collective intelligence of groups of people and computers.<br />
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Lévy and de Kerckhove consider CI from a mass communications perspective, focusing on the ability of networked information and communication technologies to enhance the community knowledge pool. They suggest that these communications tools enable humans to interact and to share and collaborate with both ease and speed (Flew 2008). With the development of the Internet and its widespread use, the opportunity to contribute to knowledge-building communities, such as Wikipedia, is greater than ever before. These computer networks give participating users the opportunity to store and to retrieve knowledge through the collective access to these databases and allow them to "harness the hive" Researchers at the MIT Center for Collective Intelligence research and explore collective intelligence of groups of people and computers.<br />
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莱维Lévy和德克霍夫de Kerckhove从大众传播的角度考虑了CI,特别是专注用网络信息和通信技术来增强社区知识库的能力。他们认为,这些通信工具可以使人们能够轻松快捷地进行交互,共享和协作(Flew 2008)。随着互联网的发展及其广泛使用,为诸如Wikipedia之类的知识社区做出贡献的机会比以往任何时候都要大。这些计算机网络使参与活动的用户有机会通过对这些数据库的集体式访问来存储和检索知识,同时还允许他们“驾驭蜂巢”,这是麻省理工学院集体智能中心的研究人员的任务,它们一直在探索人和计算机群体的集体智能。<br />
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In this context collective intelligence is often confused with [[shared knowledge]]. The former is the sum total of information held individually by members of a community while the latter is information that is believed to be true and known by all members of the community. Collective intelligence as represented by [[Web 2.0]] has less user engagement than [[collaborative intelligence]]. An art project using Web 2.0 platforms is "Shared Galaxy", an experiment developed by an anonymous artist to create a collective identity that shows up as one person on several platforms like MySpace, Facebook, YouTube and Second Life. The password is written in the profiles and the accounts named "Shared Galaxy" are open to be used by anyone. In this way many take part in being one. Another art project using collective intelligence to produce artistic work is Curatron, where a large group of artists together decides on a smaller group that they think would make a good collaborative group. The process is used based on an algorithm computing the collective preferences In creating what he calls 'CI-Art', Nova Scotia based artist Mathew Aldred follows Pierry Lévy's definition of collective intelligence. Aldred's CI-Art event in March 2016 involved over four hundred people from the community of Oxford, Nova Scotia, and internationally. Later work developed by Aldred used the UNU [[swarm intelligence]] system to create digital drawings and paintings. The Oxford Riverside Gallery (Nova Scotia) held a public CI-Art event in May 2016, which connected with online participants internationally.<br />
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In this context collective intelligence is often confused with shared knowledge. The former is the sum total of information held individually by members of a community while the latter is information that is believed to be true and known by all members of the community. Collective intelligence as represented by Web 2.0 has less user engagement than collaborative intelligence. An art project using Web 2.0 platforms is "Shared Galaxy", an experiment developed by an anonymous artist to create a collective identity that shows up as one person on several platforms like MySpace, Facebook, YouTube and Second Life. The password is written in the profiles and the accounts named "Shared Galaxy" are open to be used by anyone. In this way many take part in being one. Another art project using collective intelligence to produce artistic work is Curatron, where a large group of artists together decides on a smaller group that they think would make a good collaborative group. The process is used based on an algorithm computing the collective preferences In creating what he calls 'CI-Art', Nova Scotia based artist Mathew Aldred follows Pierry Lévy's definition of collective intelligence. Aldred's CI-Art event in March 2016 involved over four hundred people from the community of Oxford, Nova Scotia, and internationally. Later work developed by Aldred used the UNU swarm intelligence system to create digital drawings and paintings. The Oxford Riverside Gallery (Nova Scotia) held a public CI-Art event in May 2016, which connected with online participants internationally.<br />
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在这种情况下,集体智能常常与共享知识相混淆。前者是社区成员单独持有的信息的总和,而后者是社区所有成员都认为是真实且已知的信息。以Web 2.0为代表的集体智能比协作智能具有更少的用户参与度。使用Web 2.0平台的艺术项目“共享银河”,是一个由匿名艺术家开发的实验,目的是创建一个集体身份,并在MySpace,Facebook,YouTube和Second Life等多个平台上以这个集体身份出现。密码将写在配置文件中,并且名为“ Shared Galaxy”的帐户开放给任何人使用。通过这种方式,许多人成为一体。Curatron是另一个利用集体智能创作艺术作品的艺术项目,其中一大批艺术家共同决定建立一个较小的团队,他们对其团队的协作表现非常自信。该项目基于一种计算集体偏好的算法。在创建他所谓的“ CI艺术”时,新斯科舍省的艺术家马修·阿尔德雷德Mathew Aldred遵循了皮耶·列维对集体智能的定义。2016年3月,奥尔德雷德的CI-Art活动吸引了来自牛津,新斯科舍省和全球的400多人参加。奥尔德雷德后来开发的工作使用联合国大学群体智能系统来创建数字绘图。牛津河畔画廊(新斯科舍省)于2016年5月举办了一次公共CI艺术活动,与国际在线参与者建立联系。<br />
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[[文件:Collaborative tagging.png|缩略图|左|育儿社交网络和协作标签是自动IPTV内容阻止系统的基础]]<br />
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In [[social bookmarking]] (also called collaborative tagging), users assign tags to resources shared with other users, which gives rise to a type of information organisation that emerges from this [[crowdsourcing]] process. The resulting information structure can be seen as reflecting the collective knowledge (or collective intelligence) of a community of users and is commonly called a "[[Folksonomy]]", and the process can be captured by [[models of collaborative tagging]].<br />
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In social bookmarking (also called collaborative tagging), users assign tags to resources shared with other users, which gives rise to a type of information organisation that emerges from this crowdsourcing process. The resulting information structure can be seen as reflecting the collective knowledge (or collective intelligence) of a community of users and is commonly called a "Folksonomy", and the process can be captured by models of collaborative tagging.<br />
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在社交书签(也称为协作标签)中,用户将标签分配给与其他用户共享的资源中,继而从这种众包过程中产生了一种信息组织。最终的信息结构可以看作反映用户社区的集体知识(或集体智能),通常被称为“大众分类”,这个过程可以通过协作标记模型来捕获。<br />
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Recent research using data from the social bookmarking website [[Delicious (website)|Delicious]], has shown that collaborative tagging systems exhibit a form of [[complex system]]s (or [[Self-organization|self-organizing]]) dynamics.Harry Halpin, Valentin Robu, Hana Shepherd Although there is no central controlled vocabulary to constrain the actions of individual users, the distributions of tags that describe different resources has been shown to converge over time to a stable [[power law]] distributions. Once such stable distributions form, examining the [[correlation]]s between different tags can be used to construct simple folksonomy graphs, which can be efficiently partitioned to obtained a form of community or shared vocabularies.Valentin Robu, Harry Halpin, <br />
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Recent research using data from the social bookmarking website Delicious, has shown that collaborative tagging systems exhibit a form of complex systems (or self-organizing) dynamics. Although there is no central controlled vocabulary to constrain the actions of individual users, the distributions of tags that describe different resources has been shown to converge over time to a stable power law distributions. Such vocabularies can be seen as a form of collective intelligence, emerging from the decentralised actions of a community of users. The Wall-it Project is also an example of social bookmarking.<br />
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近期,通过对社会书签网站Delicious的数据的研究表明,协作标签系统表现出一种复杂的系统(或自组织)动态形式。尽管没有中央控制来约束单个用户的操作,但是不同资源标签的分布已显示出会随着时间推移,逐渐收敛到稳定的幂律分布。一旦这种稳定的分布形成,就可以利用不同标签之间的相关性来构建简单的大众分类图,进而可以对其有效的划分,以获得社区或共享词汇表的形式。这些词汇可以看作是集体智能的一种形式,它源于用户社区的分散行动。Wall-it项目也是社交书签的一个示例。<br />
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==== P2P business P2P业务 ====<br />
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Research performed by Tapscott and Williams has provided a few examples of the benefits of collective intelligence to business:<br />
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Research performed by Tapscott and Williams has provided a few examples of the benefits of collective intelligence to business:<br />
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Tapscott和Williams进行的研究提供了一些示例,说明了集体智能对企业的好处:<br />
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;Talent utilization<br />
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Talent utilization<br />
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人才利用<br />
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:At the rate technology is changing, no firm can fully keep up in the innovations needed to compete. Instead, smart firms are drawing on the power of mass collaboration to involve participation of the people they could not employ. This also helps generate continual interest in the firm in the form of those drawn to new idea creation as well as investment opportunities.<ref name="Tapscott, D. 2008" /><br />
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At the rate technology is changing, no firm can fully keep up in the innovations needed to compete. Instead, smart firms are drawing on the power of mass collaboration to involve participation of the people they could not employ. This also helps generate continual interest in the firm in the form of those drawn to new idea creation as well as investment opportunities.<br />
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随着技术发展速率的变化,没有一家公司能够完全跟上竞争所需的创新。相反,聪明的公司正在利用大规模协作的力量来吸引他们无法雇用的人员。这也有助于公司持续地有兴趣去吸引新创意和投资机会的出现。<br />
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;Demand creation<br />
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Demand creation<br />
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需求创造<br />
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:Firms can create a new market for complementary goods by engaging in open source community. Firms also are able to expand into new fields that they previously would not have been able to without the addition of resources and collaboration from the community. This creates, as mentioned before, a new market for complementary goods for the products in said new fields.<ref name="Tapscott, D. 2008" /><br />
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Firms can create a new market for complementary goods by engaging in open source community. Firms also are able to expand into new fields that they previously would not have been able to without the addition of resources and collaboration from the community. This creates, as mentioned before, a new market for complementary goods for the products in said new fields.<br />
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企业可以通过参与开放源代码社区来创建互补商品的新市场。即使没有社区的资源和协作,企业也可以扩展到以前无法实现的新领域。如前所述,这为所述新领域中商品的互补产品创造了新市场。<br />
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;Costs reduction<br />
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Costs reduction<br />
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降低成本<br />
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:Mass collaboration can help to reduce costs dramatically. Firms can release a specific software or product to be evaluated or debugged by online communities. The results will be more personal, robust and error-free products created in a short amount of time and costs. New ideas can also be generated and explored by collaboration of online communities creating opportunities for free R&D outside the confines of the company.<ref name="Tapscott, D. 2008" /><br />
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Mass collaboration can help to reduce costs dramatically. Firms can release a specific software or product to be evaluated or debugged by online communities. The results will be more personal, robust and error-free products created in a short amount of time and costs. New ideas can also be generated and explored by collaboration of online communities creating opportunities for free R&D outside the confines of the company.<br />
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大规模协作可以帮助大幅降低成本。公司可以发布特定软件或产品,以供在线社区进行评估或调试。最终将会在较短的时间和成本下生产出更具个性化,功能强大且无失误的产品。在线社区的协作也可以产生和探索新的想法,从而为公司范围之外的免费研发创造机会。<br />
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==== Open source software 开源软件 ====<br />
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Cultural theorist and online community developer, John Banks considered the contribution of online fan communities in the creation of the [[Trainz]] product. He argued that its commercial success was fundamentally dependent upon "the formation and growth of an active and vibrant online fan community that would both actively promote the product and create content- extensions and additions to the game software".<br />
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Cultural theorist and online community developer, John Banks considered the contribution of online fan communities in the creation of the Trainz product. He argued that its commercial success was fundamentally dependent upon "the formation and growth of an active and vibrant online fan community that would both actively promote the product and create content- extensions and additions to the game software".<br />
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文化理论家和在线社区开发人员约翰·班克斯John Banks考虑在线粉丝社区对Trainz产品创作的贡献。他认为,其商业上的成功从根本上取决于“一个活跃在线粉丝社区的形成和发展,既可以积极地推广该产品,也可以为游戏软件创建内容扩展”。<br />
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The increase in user created content and interactivity gives rise to issues of control over the game itself and ownership of the player-created content. This gives rise to fundamental legal issues, highlighted by Lessig and Bray and Konsynski, such as [[intellectual property]] and property ownership rights.<br />
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The increase in user created content and interactivity gives rise to issues of control over the game itself and ownership of the player-created content. This gives rise to fundamental legal issues, highlighted by Lessig and Bray and Konsynski, such as intellectual property and property ownership rights.<br />
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随着用户创建的内容和用户之间的交互性持续增加,会引发了对游戏自身和玩家的控制权问题,因为大量内容是由玩家创造。lessig,Bray和Konsynski对此列出一系列相关法律问题,例如知识产权和财产所有权。<br />
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Gosney extends this issue of Collective Intelligence in videogames one step further in his discussion of [[alternate reality gaming]]. This genre, he describes as an "across-media game that deliberately blurs the line between the in-game and out-of-game experiences" as events that happen outside the game reality "reach out" into the player's lives in order to bring them together. Solving the game requires "the collective and collaborative efforts of multiple players"; thus the issue of collective and collaborative team play is essential to ARG. Gosney argues that the Alternate Reality genre of gaming dictates an unprecedented level of collaboration and "collective intelligence" in order to solve the mystery of the game.<br />
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Gosney extends this issue of Collective Intelligence in videogames one step further in his discussion of alternate reality gaming. This genre, he describes as an "across-media game that deliberately blurs the line between the in-game and out-of-game experiences" as events that happen outside the game reality "reach out" into the player's lives in order to bring them together. Solving the game requires "the collective and collaborative efforts of multiple players"; thus the issue of collective and collaborative team play is essential to ARG. Gosney argues that the Alternate Reality genre of gaming dictates an unprecedented level of collaboration and "collective intelligence" in order to solve the mystery of the game.<br />
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戈斯尼Gosney在他对替代现实游戏的讨论中,将集体智能扩展到了电子游戏中。他将这种类型描述为“一种跨媒体游戏,故意模糊游戏内体验与游戏外体验之间的界线”,因为发生在游戏现实之外的事件会“渗透”到玩家的生活中。为了使他们在一起。游戏需要“多个玩家的集体和协作”;因此,集体和协作团队合作的问题对于ARG至关重要。戈斯尼认为,游戏的替代现实类型要求了前所未有的协作水平和“集体智慧”,以解决游戏的奥秘。<br />
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==== Benefits of co-operation 合作受益 ====<br />
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Co-operation helps to solve most important and most interesting multi-science problems. In his book, James Surowiecki mentioned that most scientists think that benefits of co-operation have much more value when compared to potential costs. Co-operation works also because at best it guarantees number of different viewpoints. Because of the possibilities of technology global co-operation is nowadays much easier and productive than before. It is clear that, when co-operation goes from university level to global it has significant benefits.<br />
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Co-operation helps to solve most important and most interesting multi-science problems. In his book, James Surowiecki mentioned that most scientists think that benefits of co-operation have much more value when compared to potential costs. Co-operation works also because at best it guarantees number of different viewpoints. Because of the possibilities of technology global co-operation is nowadays much easier and productive than before. It is clear that, when co-operation goes from university level to global it has significant benefits.<br />
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合作有助于解决最重要且最有趣的多学科问题。詹姆斯·苏洛维奇James Surowiecki在他的书中提到,大多数科学家认为与潜在成本相比,合作带来的益处具有更大的价值。合作之所以有效,是因为它保证许多不同观点的存在。如今由于技术带来的可能性越来越大,全球合作比以往更加容易而且富有成效。显然,合作从学术研究延申到了全球合作实践,此时它会带来的收益将越来越重要。<br />
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For example, why do scientists co-operate? Science has become more and more isolated and each science field has spread even more and it is impossible for one person to be aware of all developments. This is true especially in experimental research where highly advanced equipment requires special skills. With co-operation scientists can use information from different fields and use it effectively instead of gathering all the information just by reading by themselves."<br />
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For example, why do scientists co-operate? Science has become more and more isolated and each science field has spread even more and it is impossible for one person to be aware of all developments. This is true especially in experimental research where highly advanced equipment requires special skills. With co-operation scientists can use information from different fields and use it effectively instead of gathering all the information just by reading by themselves."<br />
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例如,科学家为什么要合作?科学变得越来越孤立,因为每个科学领域的传播越来越广泛,一个人不可能意识到所有的发展。尤其是需要特殊技能的实验研究,因为高度先进的设备操作需要一定的知识背景。通过合作,科学家们可以利用不同领域的信息并有效地利用它,而不仅仅是靠自己阅读来收集所有信息。<br />
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=== Coordination 协调 ===<br />
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==== Ad-hoc communities 临时社区 ====<br />
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Military, trade unions, and corporations satisfy some definitions of CI – the most rigorous definition would require a capacity to respond to very arbitrary conditions without orders or guidance from "law" or "customers" to constrain actions. Online advertising companies are using collective intelligence to bypass traditional marketing and creative agencies.<br />
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Military, trade unions, and corporations satisfy some definitions of CI – the most rigorous definition would require a capacity to respond to very arbitrary conditions without orders or guidance from "law" or "customers" to constrain actions. Online advertising companies are using collective intelligence to bypass traditional marketing and creative agencies.<br />
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军事,贸易协会和公司一定程度上都满足CI的某些定义,其最严格的定义是要求能够对任意条件做出响应反馈,而不须要“法律”或“客户”的命令或指导来限制行动。在线广告公司正在利用集体智能绕过传统的营销和创意代理。<br />
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The UNU open platform for "human swarming" (or "social swarming") establishes real-time closed-loop systems around groups of networked users molded after biological swarms, enabling human participants to behave as a unified collective intelligence. When connected to UNU, groups of distributed users collectively answer questions and make predictions in real-time. Early testing shows that human swarms can out-predict individuals. In 2016, an UNU swarm was challenged by a reporter to predict the winners of the Kentucky Derby, and successfully picked the first four horses, in order, beating 540 to 1 odds.<br />
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The UNU open platform for "human swarming" (or "social swarming") establishes real-time closed-loop systems around groups of networked users molded after biological swarms, enabling human participants to behave as a unified collective intelligence. When connected to UNU, groups of distributed users collectively answer questions and make predictions in real-time. Early testing shows that human swarms can out-predict individuals.<br />
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联合国大学的“人类集群”(或“社会集群)开放平台,围绕生物集群网络用户建立了实时闭环系统,使人类参与者能够模拟集体智能一样行动。当连接到联合国大学后,成群的散户共同回答问题并实时做出预测。早期测试表明,人类集群可以预测个体。2016年,一名记者向联合国大学群发起挑战,以预测肯塔基德比的获胜者,并成功选出了前四匹马,以540比1的优势胜出。<br />
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Specialized information sites such as Digital Photography Review or Camera Labs is an example of collective intelligence. Anyone who has an access to the internet can contribute to distributing their knowledge over the world through the specialized information sites.<br />
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Specialized information sites such as Digital Photography Review or Camera Labs is an example of collective intelligence. Anyone who has an access to the internet can contribute to distributing their knowledge over the world through the specialized information sites.<br />
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诸如Digital Photography Review或Camera Labs之类的专业信息网站就是集体智能的一个例子。任何可以访问互联网的人都可以通过专门的信息站点为世界范围内传播知识做出贡献。<br />
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In [[learner-generated context]] a group of users marshal resources to create an ecology that meets their needs often (but not only) in relation to the co-configuration, co-creation and co-design of a particular learning space that allows learners to create their own context. Learner-generated contexts represent an ''ad hoc'' community that facilitates coordination of collective action in a network of trust. An example of learner-generated context is found on the Internet when collaborative users pool knowledge in a "[[shared intelligence]] space". As the Internet has developed so has the concept of CI as a shared public forum. The global accessibility and availability of the Internet has allowed more people than ever to contribute and access ideas. (Flew 2008)<br />
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In learner-generated context a group of users marshal resources to create an ecology that meets their needs often (but not only) in relation to the co-configuration, co-creation and co-design of a particular learning space that allows learners to create their own context. Learner-generated contexts represent an ad hoc community that facilitates coordination of collective action in a network of trust. An example of learner-generated context is found on the Internet when collaborative users pool knowledge in a "shared intelligence space". As the Internet has developed so has the concept of CI as a shared public forum. The global accessibility and availability of the Internet has allowed more people than ever to contribute and access ideas. (Flew 2008)<br />
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在“学以创用环境”下,一组用户调配资源以创建其生态来满足它们的需求(但不仅如此),即特定学习空间的共同配置,创造和设计。它们允许学习者创建自己的环境。“学以创用环境”代表一个特设社区,可促进在信任网络中协调集体行动。当协作用户在“共享智能空间”中的汇总知识时,可以在互联网上找到学习者生成的具有上下文的一个示例。随着互联网的发展,CI作为共享论坛的概念也不断发展。互联网的全球可访问性和可使用性比以往任何时候都更欢迎群众贡献和获取想法。(2008年Flew)<br />
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Games such as The Sims Series, and Second Life are designed to be non-linear and to depend on collective intelligence for expansion. This way of sharing is gradually evolving and influencing the mindset of the current and future generations.[128] For them, collective intelligence has become a norm. In Terry Flew's discussion of 'interactivity' in the online games environment, the ongoing interactive dialogue between users and game developers,[161] he refers to Pierre Lévy's concept of Collective Intelligence (Lévy 1998) and argues this is active in videogames as clans or guilds in MMORPG constantly work to achieve goals. Henry Jenkins proposes that the participatory cultures emerging between games producers, media companies, and the end-users mark a fundamental shift in the nature of media production and consumption. Jenkins argues that this new participatory culture arises at the intersection of three broad new media trends.[162] Firstly, the development of new media tools/technologies enabling the creation of content. Secondly, the rise of subcultures promoting such creations, and lastly, the growth of value adding media conglomerates, which foster image, idea and narrative flow.<br />
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Games such as The Sims Series, and Second Life are designed to be non-linear and to depend on collective intelligence for expansion. This way of sharing is gradually evolving and influencing the mindset of the current and future generations. he refers to Pierre Lévy's concept of Collective Intelligence and argues this is active in videogames as clans or guilds in MMORPG constantly work to achieve goals. Henry Jenkins proposes that the participatory cultures emerging between games producers, media companies, and the end-users mark a fundamental shift in the nature of media production and consumption. Jenkins argues that this new participatory culture arises at the intersection of three broad new media trends. Firstly, the development of new media tools/technologies enabling the creation of content. Secondly, the rise of subcultures promoting such creations, and lastly, the growth of value adding media conglomerates, which foster image, idea and narrative flow.<br />
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《模拟人生》系列和《第二人生》等游戏的设计是非线性的,并依靠集体智能进行扩展。这种共享方式会自我进化,并同步影响当前及未来新生代产品的思维方式。对于他们来说,集体智能已经成为了一种常态。在特里·弗尔Terry Flew关于对网络游戏环境“交互性”的讨论中(即用户与游戏开发人员之间的交互对话),他提到了Pierre Lévy的“集体智能”概念(Lévy 1998),并认为这在电子游戏中非常活跃,就像是MMORPG中的部族或公会一样,会不断努力去实现目标。Henry Jenkins提出,游戏生产商,媒体公司和终端用户之间形成的参与式文化,标志着媒体的生产消费性质在根本性转变。詹金斯认为,这种新的参与式文化源于三大新媒体趋势的交融。首先,开发的新媒体工具/技术促使内容的创建。然后亚文化的兴起促进了这种创造,最后,增值媒体集团壮大了形象,思想和叙事的传播。<br />
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==== Coordinating collective actions 协调集体行动 ====<br />
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[[文件:Improvisational actors.jpg|缩略图|右|After School Improv的演员学习了有关即兴创作和表演的重要课程]]<br />
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Improvisational actors also experience a type of collective intelligence which they term "group mind", as theatrical improvisation relies on mutual cooperation and agreement, leading to the unity of "group mind".<br />
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Improvisational actors also experience a type of collective intelligence which they term "group mind", as theatrical improvisation relies on mutual cooperation and agreement, leading to the unity of "group mind".<br />
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即兴表演也相当于一种集体智能,他们称之为“集体思维”,因为戏剧即兴表演依靠演员相互合作并达成共识,从而导致“集体思维”的统一。<br />
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Growth of the Internet and mobile telecom has also produced "swarming" or "rendezvous" events that enable meetings or even dates on demand. The full impact has yet to be felt but the [[anti-globalization movement]], for example, relies heavily on e-mail, cell phones, pagers, SMS and other means of organizing. Such resources could combine into a form of collective intelligence accountable only to the current participants yet with some strong moral or linguistic guidance from generations of contributors – or even take on a more obviously democratic form to advance shared goal.<br />
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Growth of the Internet and mobile telecom has also produced "swarming" or "rendezvous" events that enable meetings or even dates on demand. The Indymedia organization does this in a more journalistic way. Such resources could combine into a form of collective intelligence accountable only to the current participants yet with some strong moral or linguistic guidance from generations of contributors – or even take on a more obviously democratic form to advance shared goal.<br />
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互联网和移动电信的发展也产生了“聚集”或“约会”的事件,这些事件使即时会议甚至约会成为可能。反全球化运动目前尚未产生全面的影响,但是它在很大程度上依赖于电子邮件,手机,传呼机,SMS和其他组织方式。Indymedia组织以更具新闻性的方式进行此操作。这些资源可以合并为仅对当前参与者负责的集体智能形式,但需要几代贡献者提供强有力的道德或语言指导,甚至可以采取更为明显的民主形式来推进共同目标。<br />
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A further application of collective intelligence is found in the "Community Engineering for Innovations". In such an integrated framework proposed by Ebner et al., idea competitions and virtual communities are combined to better realize the potential of the collective intelligence of the participants, particularly in open-source R&D. In management theory the use of collective intelligence and crowd sourcing leads to innovations and very robust answers to quantitative issues. Therefore, collective intelligence and crowd sourcing is not necessaryly leading to the best solution to economic problems, but to a stable, good solution.<br />
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A further application of collective intelligence is found in the "Community Engineering for Innovations". In such an integrated framework proposed by Ebner et al., idea competitions and virtual communities are combined to better realize the potential of the collective intelligence of the participants, particularly in open-source R&D. In management theory the use of collective intelligence and crowd sourcing leads to innovations and very robust answers to quantitative issues. Therefore, collective intelligence and crowd sourcing is not necessaryly leading to the best solution to economic problems, but to a stable, good solution.<br />
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在“创新的社区工程”中可以找到集体智能的进一步应用。在埃布纳Ebner等人提出的这种集成框架中,将创意竞赛和虚拟社区相结合,可以更好地实现参与者集体智能的潜力,尤其是在开源研发中。在管理理论中,集体智能和众包带来了创新,并为定量问题提供了非常有力的答案。因此,集体智能和众包并不一定会创造出一系列针对经济问题的最佳解决方案,但是会提供一种稳定而良好的解决方案。<br />
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==== Coordination in different types of tasks 协调不同类型的任务 ====<br />
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Collective actions or tasks require different amounts of coordination depending on the complexity of the task. Tasks vary from being highly independent simple tasks that require very little coordination to complex interdependent tasks that are built by many individuals and require a lot of coordination. In the article written by Kittur, Lee and Kraut the writers introduce a problem in cooperation: "When tasks require high coordination because the work is highly interdependent, having more contributors can increase process losses, reducing the effectiveness of the group below what individual members could optimally accomplish". Having a team too large the overall effectiveness may suffer even when the extra contributors increase the resources. In the end the overall costs from coordination might overwhelm other costs.<br />
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Collective actions or tasks require different amounts of coordination depending on the complexity of the task. Tasks vary from being highly independent simple tasks that require very little coordination to complex interdependent tasks that are built by many individuals and require a lot of coordination. In the article written by Kittur, Lee and Kraut the writers introduce a problem in cooperation: "When tasks require high coordination because the work is highly interdependent, having more contributors can increase process losses, reducing the effectiveness of the group below what individual members could optimally accomplish". Having a team too large the overall effectiveness may suffer even when the extra contributors increase the resources. In the end the overall costs from coordination might overwhelm other costs.<br />
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当进行集体行动时,需要根据任务内容的复杂程度进行相应的协调。从独立的简单任务(几乎不需要协调)到复杂的互助任务(由多人构建且需要大量协调)。在Kittur,Lee和Kraut撰写的文章中,作者引出了合作中的一个问题:“当处理复杂任务需要高度协调时,安排更多的贡献者会造成过程损失增加,降低团队的效率,反而不如单个成员完成任务理想”。如果团队规模太大,即使额外的贡献者增加了资源,总体效率也会受到影响。最后,协调产生的总成本可能超过其他成本。<br />
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Group collective intelligence is a property that emerges through coordination from both bottom-up and top-down processes. In a bottom-up process the different characteristics of each member are involved in contributing and enhancing coordination. Top-down processes are more strict and fixed with norms, group structures and routines that in their own way enhance the group's collective work.<br />
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Group collective intelligence is a property that emerges through coordination from both bottom-up and top-down processes. In a bottom-up process the different characteristics of each member are involved in contributing and enhancing coordination. Top-down processes are more strict and fixed with norms, group structures and routines that in their own way enhance the group's collective work.<br />
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团队集体智能是通过自下而上和自上而下的过程的协调而出现的一种特性。在自下而上的过程中,每个不同特性的成员都参与了贡献并加强整体协调能力。而自上而下的过程更加严格,并根据规范,结构和例行程序加以巩固,以自身特有的方式加强小组的集体工作效率。<br />
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== Alternative views 其他观点==<br />
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=== A tool for combating self-preservation 打击自我保护的工具===<br />
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Tom Atlee reflects that, although humans have an innate ability to gather and analyze data, they are affected by culture, education and social institutions.A single person tends to make decisions motivated by self-preservation. Therefore, without collective intelligence, humans may drive themselves into extinction based on their selfish needs.<br />
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Tom Atlee reflects that, although humans have an innate ability to gather and analyze data, they are affected by culture, education and social institutions. A single person tends to make decisions motivated by self-preservation. Therefore, without collective intelligence, humans may drive themselves into extinction based on their selfish needs.<br />
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汤姆·阿特利Tom Atlee反映,尽管人类具有天生的收集和分析数据的能力,但他们同时也受到文化,教育和社会制度的影响。一个人会倾向于自我保护而做出决策。因此,在没有集体智慧的情况下,人类可能会基于自私的需求而使自己灭绝。<br />
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=== Separation from IQism 区别于智商主义===<br />
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Phillip Brown and Hugh Lauder quotes Bowles and [[Herbert Gintis|Gintis]] (1976) that in order to truly define collective intelligence, it is crucial to separate 'intelligence' from IQism. They go on to argue that intelligence is an achievement and can only be developed if allowed to. For example, earlier on, groups from the lower levels of society are severely restricted from aggregating and pooling their intelligence. This is because the elites fear that the collective intelligence would convince the people to rebel. If there is no such capacity and relations, there would be no infrastructure on which collective intelligence is built. This reflects how powerful collective intelligence can be if left to develop.<br />
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Phillip Brown and Hugh Lauder quotes Bowles and Gintis (1976) that in order to truly define collective intelligence, it is crucial to separate 'intelligence' from IQism. They go on to argue that intelligence is an achievement and can only be developed if allowed to. For example, earlier on, groups from the lower levels of society are severely restricted from aggregating and pooling their intelligence. This is because the elites fear that the collective intelligence would convince the people to rebel. If there is no such capacity and relations, there would be no infrastructure on which collective intelligence is built . This reflects how powerful collective intelligence can be if left to develop.<br />
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菲利普·布朗Phillip Brown和休·劳德Hugh Lauder引述鲍尔斯Bowles和金蒂斯Gintis(1976)的观点,为了真正定义集体智能,它们认为将“智能”和智商主义分开是至关重要的。他们争辩说,智力其实是需要经过允许才能够得到发展的成就。例如,早期来自社会底层的群体受到严格限制,它们无法聚集头脑风暴提高它们的智力。这是因为精英们担心集体智能会造成人民叛乱。如果没有这样的资格和关系,就不会有建立集体智能的基础设施(Brown&Lauder 2000,第230页)。很明显如果任其发展,集体智能将会变得异常强大。<br />
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=== Artificial intelligence views 人工智能观点===<br />
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Skeptics, especially those critical of artificial intelligence and more inclined to believe that risk of [[bodily harm]] and bodily action are the basis of all unity between people, are more likely to emphasize the capacity of a group to take action and withstand harm as one fluid [[mass mobilization]], shrugging off harms the way a body shrugs off the loss of a few cells. This strain of thought is most obvious in the [[anti-globalization movement]] and characterized by the works of [[John Zerzan]], [[Carol Moore]], and [[Starhawk]], who typically shun academics. These theorists are more likely to refer to ecological and [[collective wisdom]] and to the role of [[consensus process]] in making ontological distinctions than to any form of "intelligence" as such, which they often argue does not exist, or is mere "cleverness".<br />
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Skeptics, especially those critical of artificial intelligence and more inclined to believe that risk of bodily harm and bodily action are the basis of all unity between people, are more likely to emphasize the capacity of a group to take action and withstand harm as one fluid mass mobilization, shrugging off harms the way a body shrugs off the loss of a few cells. This strain of thought is most obvious in the anti-globalization movement and characterized by the works of John Zerzan, Carol Moore, and Starhawk, who typically shun academics. These theorists are more likely to refer to ecological and collective wisdom and to the role of consensus process in making ontological distinctions than to any form of "intelligence" as such, which they often argue does not exist, or is mere "cleverness".<br />
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怀疑论者,特别是那些对人工智能持批评态度的人,更倾向于相信人身体上的行为和伤害是人与人之间一切团结的基础,他们更倾向于强调一个群体采取行动和承受伤害的能力是一种流动物质,就像耸耸肩甩掉细胞一样甩掉所有伤害他们的东西。这种思想张力在反全球化运动中最为明显,约翰·泽赞John Zerzan,卡罗尔·摩尔Carol Moore和星鹰Starhawk的作品强调了这个属性,他们通常会避开学术方面的思考。这些理论家更倾向于提及生态和集体智慧,以及共识过程中进行本体论区分,他们通常认为不存在仅仅是“聪明”的任何形式的“智能”。<br />
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Harsh critics of artificial intelligence on ethical grounds are likely to promote collective wisdom-building methods, such as the [[new tribalists]] and the [[Gaianism|Gaians]]. Whether these can be said to be collective intelligence systems is an open question. Some, e.g. [[Bill Joy]], simply wish to avoid any form of autonomous artificial intelligence and seem willing to work on rigorous collective intelligence in order to remove any possible niche for AI.<br />
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Harsh critics of artificial intelligence on ethical grounds are likely to promote collective wisdom-building methods, such as the new tribalists and the Gaians. Whether these can be said to be collective intelligence systems is an open question. Some, e.g. Bill Joy, simply wish to avoid any form of autonomous artificial intelligence and seem willing to work on rigorous collective intelligence in order to remove any possible niche for AI.<br />
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出于道德考虑,对人工智能的严厉批评很可能会促使集体智慧的方法建立,例如新部落主义者New tribalists和盖亚主义者Gaians。这些是否可以说是集体智能系统是一个待解决的问题。例如比尔·乔伊Bill Joy等学者希望能避免使用任何形式的自主人工智能,并且似乎愿意研究严格的集体智能,以消除AI的任何潜在利基。<br />
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In contrast to these views, Artificial Intelligence companies such as [[Amazon Mechanical Turk]] and [[CrowdFlower]] are using collective intelligence and [[crowdsourcing]] or [[consensus-based assessment]] to collect the enormous amounts of data for [[machine learning]] algorithms such as [[Keras]] and [[IBM Watson]].<br />
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In contrast to these views, Artificial Intelligence companies such as Amazon Mechanical Turk and CrowdFlower are using collective intelligence and crowdsourcing or consensus-based assessment to collect the enormous amounts of data for machine learning algorithms such as Keras and IBM Watson.<br />
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与这些观点相反,Amazon Mechanical Turk和CrowdFlower等公司正在使用集体智能和众包或基于共识的评估系统来收集用于机器学习算法的大量数据。<br />
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=== Solving climate change 解决气候变化 ===<br />
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Global collective intelligence is seen as the key in solving the challenges humankind faces now and in the future. [[Climate change]] is an example of a global issue which collective intelligence is currently trying to tackle. With the help of collective intelligence applications such as online [[crowdsourcing]], people across the globe are collaborating in developing solutions to climate change.<br />
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Global collective intelligence is seen as the key in solving the challenges humankind faces now and in the future. Climate change is an example of a global issue which collective intelligence is currently trying to tackle. With the help of collective intelligence applications such as online crowdsourcing, people across the globe are collaborating in developing solutions to climate change.<br />
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全球集体智能被认为是解决人类现在和将来面临挑战的关键。气候变化就是这个全球性问题的例子,目前集体智能正在努力解决这一问题。<br />
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== See also 其他参考资料 ==<br />
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{{Div col|colwidth=40em}}<br />
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=== Similar concepts and applications 相似概念及应用 ===<br />
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* [[Citizen science]]<br />
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* [[Civic intelligence]]<br />
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* [[Collaborative filtering]]<br />
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* [[Collaborative innovation network]]<br />
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* [[Collective decision-making]]<br />
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* [[Collective effervescence]]<br />
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* [[Collective memory]]<br />
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* [[Collective problem solving]]<br />
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* [[Crowd psychology]]<br />
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* [[Global Consciousness Project]]<br />
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* [[Group behaviour]]<br />
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* [[Group mind (science fiction)]]<br />
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* [[Knowledge ecosystem]]<br />
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* {{annotated link|Noogenesis}} <br />
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* [[Open source intelligence]]<br />
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* [[Recommendation system]]<br />
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* [[Smart mob]]<br />
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* [[Social commerce]]<br />
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* [[Social information processing]]<br />
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* [[Stigmergy]]<br />
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* [[Raymond Cattell#Innovations and accomplishments|Syntality]]<br />
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* ''[[The Wisdom of Crowds]]''<br />
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* [[Think tank]]<br />
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* [[Wiki]]<br />
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* <font color="#ff8000"> 全民科学</font><br />
* <font color="#ff8000"> 公民智力</font><br />
* <font color="#ff8000"> 协同过滤</font><br />
* <font color="#ff8000"> 合作创新网络</font><br />
* <font color="#ff8000"> 群体决策</font><br />
* <font color="#ff8000"> 集体欢腾</font><br />
* <font color="#ff8000"> 集体泡腾</font><br />
* <font color="#ff8000"> 集体记忆</font><br />
* <font color="#ff8000"> 解决集体问题</font><br />
* <font color="#ff8000"> 群众心理学</font><br />
* <font color="#ff8000"> 全球意识项目</font><br />
* <font color="#ff8000"> 群体行为</font><br />
* <font color="#ff8000"> 集体思维(科幻小说)</font><br />
* <font color="#ff8000"> 知识生态系统</font><br />
* <font color="#ff8000"> 心里演化-智力的涌现与发展</font><br />
* <font color="#ff8000"> 开源智力</font><br />
* <font color="#ff8000"> 推荐系统</font><br />
* <font color="#ff8000"> 聪明行动族</font><br />
* <font color="#ff8000"> 社会商务</font><br />
* <font color="#ff8000"> 社会信息处理</font><br />
* <font color="#ff8000"> 共识主动性</font><br />
* <font color="#ff8000"> 群体个性</font><br />
* <font color="#ff8000"> 群众智慧</font><br />
* <font color="#ff8000"> 智囊团</font><br />
* <font color="#ff8000"> 维基百科</font><br />
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=== Computation and computer science 计算与计算机科学 ===<br />
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* [[Bees algorithm]]<br />
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* [[Cellular automaton]]<br />
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* [[Collaborative human interpreter]]<br />
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* [[Collaborative software]]<br />
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* [[Connectivity (graph theory)]]<br />
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* [[Enterprise bookmarking]]<br />
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* [[Human-based computation]]<br />
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* [[Open-source software]]<br />
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* [[Organismic computing]]<br />
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* [[Preference elicitation]]<br />
<br />
* <font color="#ff8000"> 蜂群算法</font><br />
* <font color="#ff8000"> 元胞自动机</font><br />
* <font color="#ff8000"> 协同人力翻译</font><br />
* <font color="#ff8000"> 协同软件</font><br />
* <font color="#ff8000"> 连通性(图论)</font><br />
* <font color="#ff8000"> 企业书签</font><br />
* <font color="#ff8000"> 基于人员的计算</font><br />
* <font color="#ff8000"> 开源软件</font><br />
* <font color="#ff8000"> 有机计算</font><br />
* <font color="#ff8000"> 偏好诱导</font><br />
<br />
<br />
<br />
=== Others 其他 ===<br />
<br />
* [[Customer engagement]]<br />
<br />
* [[Dispersed knowledge]]<br />
<br />
* [[Distributed cognition]]<br />
<br />
* [[Facilitation (business)]]<br />
<br />
* [[Facilitator]]<br />
<br />
* [[Hundredth monkey effect]]<br />
<br />
* [[Keeping up with the Joneses]]<br />
<br />
* [[Library]]<br />
<br />
* [[Library of Alexandria]]<br />
<br />
* [[Meme]]<br />
<br />
* [[Open-space meeting]]<br />
<br />
* <font color="#ff8000"> 客户参与</font><br />
* <font color="#ff8000"> 分散性知识</font><br />
* <font color="#ff8000"> 分布式认知</font><br />
* <font color="#ff8000"> 便利(商业)</font><br />
* <font color="#ff8000"> 促进者</font><br />
* <font color="#ff8000"> 第一百只猴子效应</font><br />
* <font color="#ff8000"> 跟上琼斯</font><br />
* <font color="#ff8000"> 图书馆</font><br />
* <font color="#ff8000"> 亚历山大图书馆</font><br />
* <font color="#ff8000"> 模因(模仿传递行为)</font><br />
* <font color="#ff8000"> 开放空间会议</font><br />
<br />
<br />
{{Div col end}}<br />
<br />
== Notes and references 参考文献 ==<br />
<br />
{{reflist|30em}}<br />
<br />
<br />
<br />
== Bibliography 参考书籍==<br />
<br />
{{refbegin}}<br />
<br />
* {{cite book | ref=harv<br />
<br />
| last=Brown | first=Philip<br />
<br />
| last=Brown | first=Philip<br />
<br />
第一个菲利普<br />
<br />
| last2=Lauder | first2=Hugh<br />
<br />
| last2=Lauder | first2=Hugh<br />
<br />
2 Lauder | first2 Hugh<br />
<br />
| year=2000<br />
<br />
| year=2000<br />
<br />
2000年<br />
<br />
| chapter=Collective intelligence<br />
<br />
| chapter=Collective intelligence<br />
<br />
集体智慧<br />
<br />
|editor=S. Baron |editor2=J. Field |editor3=T Schuller<br />
<br />
|editor=S. Baron |editor2=J. Field |editor3=T Schuller<br />
<br />
编辑 s。男爵 | 编辑。3 t Schuller<br />
<br />
| title=Social Capital: Critical Perspectives<br />
<br />
| title=Social Capital: Critical Perspectives<br />
<br />
社会资本: 批判的视角<br />
<br />
| publisher=Oxford University Press | location=New York |url=https://books.google.com/?id=nvivgiFfPr0C&printsec=frontcover#v=onepage<br />
<br />
| publisher=Oxford University Press | location=New York |url=https://books.google.com/?id=nvivgiFfPr0C&printsec=frontcover#v=onepage<br />
<br />
2012年10月15日,纽约,牛津 https://books.google.com/?id=nvivgiffpr0c&printsec=frontcover#v=onepage 出版社<br />
<br />
| isbn=9780191583247 }}<br />
<br />
| isbn=9780191583247 }}<br />
<br />
9780191583247}<br />
<br />
* {{cite book | ref=harv<br />
<br />
| last=Brown | first=Philip<br />
<br />
| last=Brown | first=Philip<br />
<br />
第一个菲利普<br />
<br />
| last2=Lauder | first2=Hugh<br />
<br />
| last2=Lauder | first2=Hugh<br />
<br />
2 Lauder | first2 Hugh<br />
<br />
| year=2001<br />
<br />
| year=2001<br />
<br />
2001年<br />
<br />
| chapter=Collective intelligence (chapter 13)<br />
<br />
| chapter=Collective intelligence (chapter 13)<br />
<br />
| 第十三章集体智慧<br />
<br />
|editor=Brown |editor2=Lauder<br />
<br />
|editor=Brown |editor2=Lauder<br />
<br />
2 Lauder<br />
<br />
| title=Capitalism and social progress: the future of society in a global economy<br />
<br />
| title=Capitalism and social progress: the future of society in a global economy<br />
<br />
| 题目: 资本主义和社会进步: 全球经济中社会的未来<br />
<br />
| publisher=Palgrave<br />
<br />
| publisher=Palgrave<br />
<br />
| 出版商 Palgrave<br />
<br />
| url=https://books.google.com/?id=rF8YDAAAQBAJ&printsec=frontcover#v=onepage<br />
<br />
| url=https://books.google.com/?id=rF8YDAAAQBAJ&printsec=frontcover#v=onepage<br />
<br />
Https://books.google.com/?id=rf8ydaaaqbaj&printsec=frontcover#v=onepage<br />
<br />
| isbn=9780333985380 }}<br />
<br />
| isbn=9780333985380 }}<br />
<br />
9780333985380}<br />
<br />
* {{cite journal<br />
<br />
| last=Fadul | first=Jose A.<br />
<br />
| last=Fadul | first=Jose A.<br />
<br />
最后一个法杜尔 | 第一个何塞 a。<br />
<br />
| year=2009<br />
<br />
| year=2009<br />
<br />
2009年<br />
<br />
| title=Collective Learning: Applying Distributed Cognition for Collective Intelligence<br />
<br />
| title=Collective Learning: Applying Distributed Cognition for Collective Intelligence<br />
<br />
集体学习: 应用分布式认知促进集体智慧<br />
<br />
| journal=The International Journal of Learning<br />
<br />
| journal=The International Journal of Learning<br />
<br />
国际学习期刊<br />
<br />
| volume = 16<br />
<br />
| volume = 16<br />
<br />
第16卷<br />
<br />
| issue = 4<br />
<br />
| issue = 4<br />
<br />
第四期<br />
<br />
| pages= 211–220<br />
<br />
| pages= 211–220<br />
<br />
第211-220页<br />
<br />
| doi=10.18848/1447-9494/cgp/v16i04/46223<br />
<br />
| doi=10.18848/1447-9494/cgp/v16i04/46223<br />
<br />
| doi 10.18848 / 1447-9494 / cgp / v16i04 / 46223<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
* CIA. (2008). [https://www.cia.gov/library/publications/the-world-factbook/geos/xx.html ''The World Factbook'']. (accessed 3 September 2008)<br />
<br />
* {{cite book | ref=harv<br />
<br />
| last = Fladerer | first=Johannes-Paul<br />
<br />
| last = Fladerer | first=Johannes-Paul<br />
<br />
| 最后一个花匠 | 第一个约翰内斯-保罗<br />
<br />
| year=2019<br />
<br />
| year=2019<br />
<br />
2019年<br />
<br />
|title=The Wisdom of the Many: How to create Self-Organisation and how to use Collective Intelligence in Companies and in Society From Management to ManagemANT<br />
<br />
|title=The Wisdom of the Many: How to create Self-Organisation and how to use Collective Intelligence in Companies and in Society From Management to ManagemANT<br />
<br />
| 题目: 多人的智慧: 如何建立自我组织,以及如何在公司和社会中运用集体智慧,从管理到管理<br />
<br />
| publisher=BoD<br />
<br />
| publisher=BoD<br />
<br />
| 出版商 BoD<br />
<br />
| location=Norderstedt<br />
<br />
| location=Norderstedt<br />
<br />
| 位置 Norderstedt<br />
<br />
| isbn =978-3750422421<br />
<br />
| isbn =978-3750422421<br />
<br />
978-3750422421<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
* {{cite book | ref=harv<br />
<br />
| last=Flew | first=Terry<br />
<br />
| last=Flew | first=Terry<br />
<br />
最后一次飞行 | 第一次特里<br />
<br />
| year= 2008<br />
<br />
| year= 2008<br />
<br />
2008年<br />
<br />
| title=New Media: an introduction<br />
<br />
| title=New Media: an introduction<br />
<br />
| 标题新媒体: 介绍<br />
<br />
| publisher=Oxford University Press | location=Melbourne<br />
<br />
| publisher=Oxford University Press | location=Melbourne<br />
<br />
牛津大学出版社 | 位置: 墨尔本<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
* {{cite book | ref=harv<br />
<br />
| last=Hamann | first=Heiko<br />
<br />
| last=Hamann | first=Heiko<br />
<br />
最后的哈曼 | 第一个海科<br />
<br />
| year=2018<br />
<br />
| year=2018<br />
<br />
2018年<br />
<br />
| title=Swarm Robotics: A Formal Approach<br />
<br />
| title=Swarm Robotics: A Formal Approach<br />
<br />
标题: 群机器人: 一种正式的方法<br />
<br />
| publisher=Springer | location=New York<br />
<br />
| publisher=Springer | location=New York<br />
<br />
| 出版商 Springer | 位置: 纽约<br />
<br />
| url=https://books.google.com/?id=pnNLDwAAQBAJ&printsec=frontcover#v=snippet&q=%22collective%20intelligence%22&f=false<br />
<br />
| url=https://books.google.com/?id=pnNLDwAAQBAJ&printsec=frontcover#v=snippet&q=%22collective%20intelligence%22&f=false<br />
<br />
Https://books.google.com/?id=pnnldwaaqbaj&printsec=frontcover#v=snippet&q=%22collective%20intelligence%22&f=false<br />
<br />
| isbn=9783319745282 }}<br />
<br />
| isbn=9783319745282 }}<br />
<br />
9783319745282}<br />
<br />
* {{cite book | ref=harv<br />
<br />
| last=Hofstadter | first=Douglas<br />
<br />
| last=Hofstadter | first=Douglas<br />
<br />
最后的侯世达 | 第一个道格拉斯<br />
<br />
| author-link=Douglas Hofstadter<br />
<br />
| author-link=Douglas Hofstadter<br />
<br />
| 作者链接侯世达<br />
<br />
| year=1979<br />
<br />
| year=1979<br />
<br />
1979年<br />
<br />
| title=Gödel, Escher, Bach: an Eternal Golden Braid<br />
<br />
| title=Gödel, Escher, Bach: an Eternal Golden Braid<br />
<br />
巴赫: 永恒的金色辫子<br />
<br />
| publisher=Basic Books | location=New York<br />
<br />
| publisher=Basic Books | location=New York<br />
<br />
| 出版商 Basic Books | 位置: 纽约<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
* Leiner, Barry, Cerf, Vinton, Clark, David, Kahn, Robert, Kleinrock, Leonard, Lynch, Daniel, Postel, Jon, Roberts, Larry and Wolff, Stephen. 2003. [http://www.isoc.org/internet/history/brief.shtml ''A Brief History of the Internet'']. Version 3.32 (accessed 3 September 2008)<br />
<br />
* Noubel, Jean-François; (2004, rev. 2007), "[http://publishing.yudu.com/Library/Arswi/CollectiveIntelligen/resources/index.htm?skipFlashCheck=true Collective Intelligence: the Invisible Revolution]"<br />
<br />
* {{cite book | ref=harv<br />
<br />
| last=Por | first=George<br />
<br />
| last=Por | first=George<br />
<br />
乔治<br />
<br />
| year=1995<br />
<br />
| year=1995<br />
<br />
1995年<br />
<br />
| chapter= The Quest for Collective intelligence<br />
<br />
| chapter= The Quest for Collective intelligence<br />
<br />
寻求集体智慧<br />
<br />
| editor=K. Gozdz<br />
<br />
| editor=K. Gozdz<br />
<br />
编辑 k。Gozdz<br />
<br />
| title=Community Building: Renewing Spirit and Learning in Business<br />
<br />
| title=Community Building: Renewing Spirit and Learning in Business<br />
<br />
社区建设: 在商业中更新精神和学习<br />
<br />
| publisher=New Leaders Press | location=San Francisco<br />
<br />
| publisher=New Leaders Press | location=San Francisco<br />
<br />
出版商 New Leaders 出版社旧金山<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
* {{cite book | ref=harv<br />
<br />
| last=Rheingold | first=Howard<br />
<br />
| last=Rheingold | first=Howard<br />
<br />
最后的莱茵戈尔德 | 第一个霍华德<br />
<br />
| author-link=Howard Rheingold<br />
<br />
| author-link=Howard Rheingold<br />
<br />
| 作者链接霍华德·莱茵戈德<br />
<br />
| year=2002<br />
<br />
| year=2002<br />
<br />
2002年<br />
<br />
| title=Smart Mobs: The Next Social Revolution<br />
<br />
| title=Smart Mobs: The Next Social Revolution<br />
<br />
聪明的暴徒: 下一场社会革命<br />
<br />
| publisher=Basic Books<br />
<br />
| publisher=Basic Books<br />
<br />
| 出版商 Basic Books<br />
<br />
| title-link=Smart Mobs: The Next Social Revolution }}<br />
<br />
| title-link=Smart Mobs: The Next Social Revolution }}<br />
<br />
| 标题链接聪明的暴徒: 下一场社会革命}<br />
<br />
* {{cite book | ref=harv<br />
<br />
| last=Ron | first=Sun<br />
<br />
| last=Ron | first=Sun<br />
<br />
第一个太阳<br />
<br />
| year=1979<br />
<br />
| year=1979<br />
<br />
1979年<br />
<br />
| title=Cognition and Multi-Agent Interaction<br />
<br />
| title=Cognition and Multi-Agent Interaction<br />
<br />
认知与多智能体交互<br />
<br />
| publisher=Cambridge University Press<br />
<br />
| publisher=Cambridge University Press<br />
<br />
出版商剑桥大学出版社<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
* Rosenberg, L. (2015). [https://web.archive.org/web/20151027132802/https://mitpress.mit.edu/sites/default/files/titles/content/ecal2015/ch117.html Human Swarms, a real time method for Collective Intelligence]. Proceedings of the European Conference on Artificial Life (ECAL 2015), pp.&nbsp;658–659.<br />
<br />
* {{cite journal | ref=harv<br />
<br />
| last=Riedl | first=Christoph<br />
<br />
| last=Riedl | first=Christoph<br />
<br />
克里斯多夫<br />
<br />
| last2=Blohm | first2=Ivo<br />
<br />
| last2=Blohm | first2=Ivo<br />
<br />
2 Blohm | first2 Ivo<br />
<br />
| last3=Leimeister | first3=Jan Marco<br />
<br />
| last3=Leimeister | first3=Jan Marco<br />
<br />
3 Leimeister | first3 Jan Marco<br />
<br />
| last4=Krcmar | first4=Helmut<br />
<br />
| last4=Krcmar | first4=Helmut<br />
<br />
4 Krcmar | first4 Helmut<br />
<br />
| year=2010<br />
<br />
| year=2010<br />
<br />
2010年<br />
<br />
| title=Rating Scales for Collective Intelligence in Innovation Communities: Why Quick and Easy Decision Making Does Not Get It Right | url=http://home.in.tum.de/~riedlc/res/RiedlEtAl2010-ICIS.pdf<br />
<br />
| title=Rating Scales for Collective Intelligence in Innovation Communities: Why Quick and Easy Decision Making Does Not Get It Right | url=http://home.in.tum.de/~riedlc/res/RiedlEtAl2010-ICIS.pdf<br />
<br />
为什么快速简单的决策没有得到正确的 http://home.in.tum.de/~riedlc/res/riedletal2010-icis.pdf <br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
* {{cite journal<br />
<br />
| ref=harv<br />
<br />
| ref=harv<br />
<br />
不会有事的<br />
<br />
| last=Leimeister<br />
<br />
| last=Leimeister<br />
<br />
最后的莱梅斯特<br />
<br />
| first=Jan Marco<br />
<br />
| first=Jan Marco<br />
<br />
作者: Jan Marco<br />
<br />
| year=2010<br />
<br />
| year=2010<br />
<br />
2010年<br />
<br />
| title=Intelligence<br />
<br />
| title=Intelligence<br />
<br />
| 题目: 情报<br />
<br />
| url=http://aisel.aisnet.org/bise/vol2/iss4/6/<br />
<br />
| url=http://aisel.aisnet.org/bise/vol2/iss4/6/<br />
<br />
Http://aisel.aisnet.org/bise/vol2/iss4/6/ <br />
<br />
| archive-url=https://web.archive.org/web/20110726084723/http://aisel.aisnet.org/bise/vol2/iss4/6/<br />
<br />
| archive-url=https://web.archive.org/web/20110726084723/http://aisel.aisnet.org/bise/vol2/iss4/6/<br />
<br />
| 档案-网址 https://web.archive.org/web/20110726084723/http://aisel.aisnet.org/bise/vol2/iss4/6/ <br />
<br />
| url-status=live<br />
<br />
| url-status=live<br />
<br />
状态直播<br />
<br />
| archive-date=2011-07-26<br />
<br />
| archive-date=2011-07-26<br />
<br />
| 档案-日期2011-07-26<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
* {{cite book | ref=harv | last=Roy Chowdhury | first=Soudip | last2=Rodriguez | first2=Carlos | last3=Daniel | first3=Florian | last4=Casati | first4=Fabio | year=2010 | title=Wisdom-aware computing: on the interactive recommendation of composition knowledge | pages=[https://archive.org/details/serviceorientedc0000maxi/page/144 144–155] | url=https://archive.org/details/serviceorientedc0000maxi/page/144 | isbn=9783642193934 | series=Icsoc'10 }}<br />
<br />
* Stephen R. Diasio, Nuria Agell, "The evolution of expertise in decision support technologies: A challenge for organizations," cscwd, pp.&nbsp;692–697, 2009 13th International Conference on Computer Supported Cooperative Work in Design, 2009. https://web.archive.org/web/20121009235747/http://www.computer.org/portal/web/csdl/doi/10.1109/CSCWD.2009.4968139<br />
<br />
* {{cite book|title=Uses and Abuses of Intelligence|editor1-first=Jean|editor1-last=Raven |year=2008|publisher=Royal Fireworks Press|location=Unionville (NY)|isbn=978-0-89824-356-7|lay-url=http://www.rfwp.com/3567.htm|laydate=6 July 2010|ref=harv}}<br />
<br />
* Kaiser, C., Kröckel, J., Bodendorf, F. (2010). [https://web.archive.org/web/20120121230742/http://www.computer.org/portal/web/csdl/doi/10.1109/HICSS.2010.356 Swarm Intelligence for Analyzing Opinions in Online Communities]. Proceedings of the 43rd Hawaii International Conference on System Sciences, pp.&nbsp;1–9.<br />
<br />
* {{cite book | ref=harv<br />
<br />
| last=Radakov | first=Dmitriĭ Viktorovich<br />
<br />
| last=Radakov | first=Dmitriĭ Viktorovich<br />
<br />
| last=Radakov | first=Dmitriĭ Viktorovich<br />
<br />
| year=1973<br />
<br />
| year=1973<br />
<br />
1973年<br />
<br />
|editor=J. Wiley<br />
<br />
|editor=J. Wiley<br />
<br />
编辑 j。威利<br />
<br />
| title=Schooling in the ecology of fish<br />
<br />
| title=Schooling in the ecology of fish<br />
<br />
| 题目: 鱼类生态中的群落现象<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
{{refend}}<br />
<br />
<br />
<br />
== External links 相关链接 ==<br />
<br />
{{Library resources box}}<br />
<br />
<br />
<br />
* [http://blogofcollectiveintelligence.com/ Blog of Collective Intelligence]<br />
<br />
* [http://themp.org GFIS&nbsp;– Global Futures Intelligence System]<br />
<br />
* [http://ciresearchinstitute.org CIRI&nbsp;– the Collective Intelligence Research Institute] – a R&D non-profit organization on collective intelligence<br />
<br />
* [http://gccsr.org An application of Collective Intelligence for the Global Climate Change Situation Room] designed and implemented by The Millennium Project in Gimcheon, South Korea in 2009.<br />
<br />
* [http://scripts.mit.edu/~cci/wiki/index.php?title=Main_Page MIT Handbook of Collective Intelligence]<br />
<br />
* [http://www.scn.org/commnet/civic-intelligence.html Cultivating Society's Civic Intelligence] Doug Schuler ''Journal of Society, Information and Communication'', vol 4 No. 2.<br />
<br />
* Jennifer H. Watkins (2007). [http://escholarship.org/uc/item/8mg0p0zc Prediction Markets as an Aggregation Mechanism for Collective Intelligence] Los Alamos National Laboratory article on Collective Intelligence<br />
<br />
* [[Hideyasu Sasaki]] (2010). [https://web.archive.org/web/20101002143636/http://sites.google.com/site/hsasakilab/Home/ijoci/ijoci-vol-1-no-1 International Journal of Organizational and Collective Intelligence (IJOCI)], vol 1 No. 1.<br />
<br />
* Olivier Zara, [https://web.archive.org/web/20060306124022/http://www.axiopole.com/pdf/Managing_collective_intelligence.pdf ''Managing Collective Intelligence, Toward a New Corporate Governance''], Axiopole editions, 2004<br />
<br />
* [https://web.archive.org/web/20170925233103/http://collectiveintel.net/ The collective intelligence framework], open-source framework for leveraging collective intelligence<br />
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* Raimund Minichbauer (2012). [http://eipcp.net/transversal/0112/minichbauer/en Fragmented Collectives. On the Politics of "Collective Intelligence" in Electronic Networks], transversal 01 12, 'unsettling knowledges'<br />
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* Blog of Collective Intelligence 集体智能博客<br />
* GFIS – Global Futures Intelligence System GFIS –全球期货情报系统<br />
* CIRI – the Collective Intelligence Research Institute – a R&D non-profit organization on collective intelligence CIRI –集体情报研究院–集体情报研发非营利组织<br />
* An application of Collective Intelligence for the Global Climate Change Situation Room designed and implemented by The Millennium Project in Gimcheon, South Korea in 2009. 集体智能应用于全球气候变化室,由韩国金泉千禧项目于2009年设计和实施。<br />
* MIT Handbook of Collective Intelligence 麻省理工学院集体智能手册<br />
* Cultivating Society's Civic Intelligence 培养社会公民智力 Doug Schuler Journal of Society, Information and Communication, vol 4 No. 2. <br />
* Jennifer H. Watkins (2007). Prediction Markets as an Aggregation Mechanism for Collective Intelligence 预测市场作为集体智能的聚集机制 Los Alamos National Laboratory article on Collective Intelligence<br />
* Hideyasu Sasaki (2010). International Journal of Organizational and Collective Intelligence (IJOCI) 国际组织和集体智能杂志, vol 1 No. 1.<br />
* Olivier Zara, Managing Collective Intelligence, Toward a New Corporate Governance 《管理集体智能,迈向新的公司治理》, Axiopole editions, 2004<br />
* The collective intelligence framework 集体智能框架, open-source framework for leveraging collective intelligence<br />
* Raimund Minichbauer (2012). Fragmented Collectives. On the Politics of "Collective Intelligence" in Electronic Networks 零散的集体。关于电子网络中的“集体情报”政治,, transversal 01 12, 'unsettling knowledges'<br />
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Category:Artificial intelligence<br />
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类别: 人工智能<br />
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Category:Multi-robot systems<br />
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类别: 多机器人系统<br />
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<small>This page was moved from [[wikipedia:en:Collective intelligence]]. Its edit history can be viewed at [[集体智能/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%AF%B9%E7%A7%B0%E6%80%A7%E7%A0%B4%E7%BC%BA&diff=24827对称性破缺2021-07-28T02:01:33Z<p>Jxzhou:/* See also 参见 */</p>
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[[图一:一个小球位于中央山丘的山峰处(C)。这是一种不稳定平衡:一个很小的扰动会使它落到左边(L)或右边(R)稳定点。尽管山丘是对称的,没有理由让球落在哪一侧,但观察到的最终状态仍然是不对称的,它总会落到某一侧]]。<br />
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在物理学中,一个作用于系统的(无限)小扰动使系统跨过临界点,通过决定去向分叉的哪个分支来决定系统的命运,这种现象叫做'''<font color="#ff8000">对称性破缺</font>'''。对于一个观测不到扰动(或“噪声”)的外部观察者来说,这个选择看起来是任意的。这个过程被称为对称性破缺,因为这种转变通常使系统从一个对称但无序的状态进入一个或多个确定的状态。在'''<font color="#ff8000">斑图生成</font>'''中对称性破缺起着重要作用。<br />
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1972年,诺贝尔奖得主P·W·安德森(P.W.Anderson)在《科学》(Science)杂志上发表了一篇名为《多则异也》("More is different")的论文<ref>{{cite journal | last=Anderson | first=P.W. | title=More is Different | journal=Science | volume=177 | issue=4047| pages=393–396 | year=1972 | url=http://robotics.cs.tamu.edu/dshell/cs689/papers/anderson72more_is_different.pdf | doi=10.1126/science.177.4047.393 | pmid=17796623 | format=|bibcode = 1972Sci...177..393A }}</ref>,文中使用对称性破缺的思想表明,即使'''<font color="#ff8000">还原论</font>'''是正确的,但它的逆命题'''<font color="#ff8000">建构主义</font>'''是错误的。建构主义认为,在给出描述各组成部分的理论的情况下科学家可以轻易地预测复杂现象。<br />
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对称性破缺可以分为'''<font color="#ff8000">显性对称性破缺</font>'''和'''<font color="#ff8000">自发对称性破缺</font>'''两种类型,二者的区别是,在破缺对称性下系统的运动方程是否不变或者基态是否保持不变。<br />
==显性对称性破缺==<br />
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在'''<font color="#ff8000">显性对称性破缺</font>'''中,描述系统的运动方程在破缺对称下是不同的。在哈密顿力学或拉格朗日力学中,假若系统的哈密顿量(或拉格朗日量)中至少一项显性地打破了给定的对称性,就发生了显性对称性破缺。<br />
==自发对称性破缺==<br />
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在'''<font color="#ff8000">自发对称性破缺</font>'''中,系统的运动方程是不变的,但系统发生了变化。这是因为系统的背景(时空)——真空态——是非恒定的。这种对称性破缺可以用一个序参量进行参数化。这类对称破缺的一个特殊情况是'''<font color="#ff8000">动力学对称性破缺</font>'''。<br />
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Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state ends up in an asymmetric state.[1][2][3] In particular, it can describe systems where the equations of motion or the Lagrangian obey symmetries, but the lowest-energy vacuum solutions do not exhibit that same symmetry. When the system goes to one of those vacuum solutions, the symmetry is broken for perturbations around that vacuum even though the entire Lagrangian retains that symmetry.<br />
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自发对称破缺是一个自发的对称破缺过程,它使处于对称状态的物理系统最终处于非对称状态。特别地,它可以描述运动方程或拉格朗日方程服从某种对称性,但最低能量真空解不具有该对称性的系统。当系统进入其中一个真空解时,真空解周围的扰动会破坏系统对称性,尽管整个拉格朗日方程仍然保持了对称性。<br />
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==Examples 例子==<br />
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===Sombrero potential Sombrero势===<br />
Consider a symmetric upward dome with a trough circling the bottom. If a ball is put at the very peak of the dome, the system is symmetric with respect to a rotation around the center axis. But the ball may ''spontaneously break'' this symmetry by rolling down the dome into the trough, a point of lowest energy. Afterward, the ball has come to a rest at some fixed point on the perimeter. The dome and the ball retain their individual symmetry, but the system does not.<ref>{{cite book |first=Gerald M. |last=Edelman |title=Bright Air, Brilliant Fire: On the Matter of the Mind |location=New York |publisher=BasicBooks |year=1992 |url=https://archive.org/details/brightairbrillia00gera |url-access=registration |page=[https://archive.org/details/brightairbrillia00gera/page/203 203] }}</ref><br />
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考虑一个对称向上的圆顶,底部环绕着一个槽。如果把一个球放在圆顶的最顶端,这个系统是围绕中心轴旋转对称的。但球体可能会沿着穹顶滚动到能量最低的槽中,从而自发地打破这种对称性。然后,球在圆周上某个固定的点上停下来。圆顶和球保持了各自的对称,但系统却没有保持对称性。<br />
[[Image:Mexican hat potential polar.svg|270px|thumb|left|Graph of Goldstone's "[[sombrero]]" potential function <math>V(\phi)</math>.|链接=Special:FilePath/Mexican_hat_potential_polar.svg]]<br />
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In the simplest idealized relativistic model, the spontaneously broken symmetry is summarized through an illustrative [[scalar field theory]]. The relevant [[Lagrangian (field theory)|Lagrangian]] of a scalar field <math>\phi</math>, which essentially dictates how a system behaves, can be split up into kinetic and potential terms,<br />
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在最简单的理想相对论模型中,可以用一个解释性的标量场理论总结自发对称性破缺。一个标量场 <math>\phi</math>的拉格朗日量从本质上决定了系统的行为,它可以分解成动能项和势能项:<br />
{{NumBlk|::|<math>\mathcal{L} = \partial^\mu \phi \partial_\mu \phi - V(\phi).</math>|{{EquationRef|1}}}}<br />
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It is in this potential term <math>V(\phi)</math> that the symmetry breaking is triggered. An example of a potential, due to [[Jeffrey Goldstone]]<ref>{{Cite journal | last1 = Goldstone | first1 = J. | doi = 10.1007/BF02812722 | title = Field theories with " Superconductor " solutions | journal = Il Nuovo Cimento | volume = 19 | issue = 1 | pages = 154–164 | year = 1961 | bibcode = 1961NCim...19..154G | s2cid = 120409034 | url = http://cds.cern.ch/record/343400 }}</ref> is illustrated in the graph at the left.<br />
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正是在势能项 <math>V(\phi)</math> 中触发了对称性破缺。例如左图所示的 [[Jeffrey Goldstone]] 给出的势能函数:<br />
{{NumBlk|::|<math>V(\phi) = -5|\phi|^2 + |\phi|^4 \,</math>.|{{EquationRef|2}}}}<br />
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This potential has an infinite number of possible [[minimum|minima]] (vacuum states) given by<br />
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该是函数具有无穷数量的最小值点(真空态)当<br />
{{NumBlk|::|<math>\phi = \sqrt{5} e^{i\theta} </math>.|{{EquationRef|3}}}}<br />
for any real ''θ'' between 0 and 2''π''. The system also has an unstable vacuum state corresponding to {{nowrap|1=''Φ'' = 0}}. This state has a [[Unitary group|U(1)]] symmetry. However, once the system falls into a specific stable vacuum state (amounting to a choice of ''θ''), this symmetry will appear to be lost, or "spontaneously broken".<br />
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其中θ可以取0到2π之间的任何实数。系统也有一个不稳定的真空状态,对应于Φ = 0。这个状态具有U(1)对称。然而,一旦系统落入某个稳定真空状态(相当于选择θ),这种对称性就会消失,或者说“自发破缺”。<br />
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In fact, any other choice of ''θ'' would have exactly the same energy, implying the existence of a massless [[Goldstone boson|Nambu–Goldstone boson]], the mode running around the circle at the minimum of this potential, and indicating there is some memory of the original symmetry in the Lagrangian.<br />
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事实上,任何其他θ的选择都将具有完全相同的能量,这意味着无质量的 [[Goldstone boson|Nambu–Goldstone]] 玻色子的存在,这种模式在势能的最小值绕圆周运动,这也表明存在拉格朗日方程中原始对称性的一些记忆。<br />
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===Other examples 其他例子===<br />
* For [[ferromagnet]]ic materials, the underlying laws are invariant under spatial rotations. Here, the order parameter is the [[magnetization]], which measures the magnetic dipole density. Above the [[Curie temperature]], the order parameter is zero, which is spatially invariant, and there is no symmetry breaking. Below the Curie temperature, however, the magnetization acquires a constant nonvanishing value, which points in a certain direction (in the idealized situation where we have full equilibrium; otherwise, translational symmetry gets broken as well). The residual rotational symmetries which leave the orientation of this vector invariant remain unbroken, unlike the other rotations which do not and are thus spontaneously broken.<br />
* 对于铁磁性材料,其基本物理定律在空间旋转下是不变的。在这里,序参量是衡量磁偶极子密度的磁化强度。在居里温度以上,序参量为零,具有空间不变性,不存在对称性破缺。然而,在居里温度以下,磁化强度变成一个恒定的非零值,指向一个特定的方向(在有充分平衡的理想情况下;否则,平移对称性也会破缺)。使该向量方向不变的旋转对称性仍然保留,而其他旋转对称性自发破缺。<br />
* The laws describing a solid are invariant under the full [[Euclidean group]], but the solid itself spontaneously breaks this group down to a [[space group]]. The displacement and the orientation are the order parameters.<br />
* 描述固体的物理定律在完整的欧几里得群下是不变的,但固体本身会自发地将这个群分解为一个空间群。其中位移和方向是序参量。<br />
* General relativity has a Lorentz symmetry, but in [[Friedmann–Lemaître–Robertson–Walker metric|FRW cosmological models]], the mean 4-velocity field defined by averaging over the velocities of the galaxies (the galaxies act like gas particles at cosmological scales) acts as an order parameter breaking this symmetry. Similar comments can be made about the cosmic microwave background.<br />
* 广义相对论具有洛伦兹对称性,但在FRW宇宙模型中,定义为星系速度平均值(星系在宇宙尺度上的行为就像气体粒子) 的平均 4-速度场,作为序参量会打破这种对称性。对于宇宙微波背景辐射也有类似的评论。<br />
* For the [[electroweak]] model, as explained earlier, a component of the Higgs field provides the order parameter breaking the electroweak gauge symmetry to the electromagnetic gauge symmetry. Like the ferromagnetic example, there is a phase transition at the electroweak temperature. The same comment about us not tending to notice broken symmetries suggests why it took so long for us to discover electroweak unification.<br />
* 对于电弱模型,如前面所解释的,希格斯场的一个分量提供了将电弱规范对称性破缺到电磁规范对称性的序参量。和铁磁的例子一样,在电弱温度下也有相变。同样地由于我们不倾向于注意对称性破缺,导致我们花了这么长时间才发现电弱统一。<br />
* In superconductors, there is a condensed-matter collective field ψ, which acts as the order parameter breaking the electromagnetic gauge symmetry.<br />
* 在超导体中有一个凝聚态集体场ψ,它是打破电磁规范对称性的序参量。<br />
* Take a thin cylindrical plastic rod and push both ends together. Before buckling, the system is symmetric under rotation, and so visibly cylindrically symmetric. But after buckling, it looks different, and asymmetric. Nevertheless, features of the cylindrical symmetry are still there: ignoring friction, it would take no force to freely spin the rod around, displacing the ground state in time, and amounting to an oscillation of vanishing frequency, unlike the radial oscillations in the direction of the buckle. This spinning mode is effectively the requisite [[Goldstone boson|Nambu–Goldstone boson]].<br />
* 拿一个细长的圆柱形塑料杆,把两端推到一起。在屈曲之前,系统在旋转下是对称的,因此具有圆柱对称性。但在弯曲之后,它看起来就不同了,而且是不对称的。然而,圆柱对称性的特征仍然存在:忽略摩擦,杆可以不受外力自由地自旋,在时间上取代基态,相当于一个频率趋于零的振荡,而不是沿屈曲方向的径向振荡。这种自旋模式实际上是必需的[[Goldstone boson|Nambu–Goldstone]] 玻色子。<br />
* Consider a uniform layer of [[fluid]] over an infinite horizontal plane. This system has all the symmetries of the Euclidean plane. But now heat the bottom surface uniformly so that it becomes much hotter than the upper surface. When the temperature gradient becomes large enough, [[convection cell]]s will form, breaking the Euclidean symmetry.<br />
* 考虑无限水平面上的一层均匀的流体,这个系统具有欧几里得平面的所有对称性。但是现在均匀地加热底部表面,使它变得比上表面热得多。当温度梯度足够大时,就会形成对流单元,打破了欧几里得对称。<br />
* Consider a bead on a circular hoop that is rotated about a vertical [[diameter]]. As the [[rotational velocity]] is increased gradually from rest, the bead will initially stay at its initial [[equilibrium point]] at the bottom of the hoop (intuitively stable, lowest [[gravitational potential]]). At a certain critical rotational velocity, this point will become unstable and the bead will jump to one of two other newly created equilibria, [[equidistant]] from the center. Initially, the system is symmetric with respect to the diameter, yet after passing the critical velocity, the bead ends up in one of the two new equilibrium points, thus breaking the symmetry.<br />
* 考虑一个围绕某个竖直的直径旋转的圆形箍上的珠子。当旋转速度从静止逐渐增加时,珠子最初会停留在环底部的初始平衡点(直观上稳定,重力势最低)。在一定的临界旋转速度下,这一点将变得不稳定,珠子将跳到另外两个新创建的离中心等距离的平衡点中的一个。起初,系统相对直径是对称的,但在通过临界速度后,珠子最终停留在两个新的平衡点中的一个,从而打破了对称性。<br />
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==Spontaneous symmetry breaking in physics 物理学中的自发对称性破缺==<br />
[[File:Spontaneous symmetry breaking (explanatory diagram).png|thumb|right|250px|''Spontaneous symmetry breaking illustrated'': At high energy levels (''left''), the ball settles in the center, and the result is symmetric. At lower energy levels (''right''), the overall "rules" remain symmetric, but the symmetric "[[sombrero|Sombrero]]" enforces an asymmetric outcome, since eventually the ball must rest at some random spot on the bottom, "spontaneously", and not all others.|链接=Special:FilePath/Spontaneous_symmetry_breaking_(explanatory_diagram).png]]<br />
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===Particle physics 粒子物理===<br />
In [[particle physics]], the [[force carrier]] particles are normally specified by field equations with [[gauge symmetry]]; their equations predict that certain measurements will be the same at any point in the field. For instance, field equations might predict that the mass of two quarks is constant. Solving the equations to find the mass of each quark might give two solutions. In one solution, quark A is heavier than quark B. In the second solution, quark B is heavier than quark A ''by the same amount''. The symmetry of the equations is not reflected by the individual solutions, but it is reflected by the range of solutions.<br />
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在粒子物理学中,载力子通常由规范对称的场方程表示;这些方程预测到某些测量值在场的任何点上都是相同的。例如,场方程可以预测两个夸克的质量和是常数。通过求解方程来求单个夸克的质量可能会得到两个解。在一个解中,夸克A比夸克B重;在第二个解中,夸克B比夸克A重,并且两个解中质量差相同。方程的对称性不是由单个解来反映的,而是由解的范围来反映的。<br />
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An actual measurement reflects only one solution, representing a breakdown in the symmetry of the underlying theory. "Hidden" is a better term than "broken", because the symmetry is always there in these equations. This phenomenon is called [[Spontaneous magnetization|''spontaneous'']] symmetry breaking (SSB) because ''nothing'' (that we know of) breaks the symmetry in the equations.<ref name="Weinberg2011">{{cite book|author=Steven Weinberg|title=Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature|url=https://books.google.com/books?id=Rsg3PE_9_ccC|date=20 April 2011|publisher=Knopf Doubleday Publishing Group|isbn=978-0-307-78786-6}}</ref>{{rp|194–195}}<br />
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一个实际的测量只反映了一个解,这代表了其潜在理论的对称性的破缺。在这里“隐藏”是比“破缺”更好的术语,因为对称性总是存在于这些方程中。这种现象被称为自发对称破缺(SSB),因为(我们所知道的)没有任何东西会打破方程中的对称性。<br />
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====Chiral symmetry 手性对称性====<br />
{{Main article|Chiral symmetry breaking}}<br />
Chiral symmetry breaking is an example of spontaneous symmetry breaking affecting the [[chiral symmetry]] of the [[strong interactions]] in particle physics. It is a property of [[quantum chromodynamics]], the [[quantum field theory]] describing these interactions, and is responsible for the bulk of the mass (over 99%) of the [[nucleons]], and thus of all common matter, as it converts very light bound [[quarks]] into 100 times heavier constituents of [[baryons]]. The approximate [[Nambu–Goldstone boson]]s in this spontaneous symmetry breaking process are the [[pions]], whose mass is an order of magnitude lighter than the mass of the nucleons. It served as the prototype and significant ingredient of the Higgs mechanism underlying the electroweak symmetry breaking.<br />
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手性对称破缺是粒子物理中影响强相互作用手性对称的自发对称破缺的一个例子。手性对称性破缺是量子色动力学(描述这些相互作用的量子场理论)的一种特性,它是核子的大部分质量(超过99%)的成因,因此也是所有普通物质的主要成因,它将非常轻的束缚夸克转化为100倍重量的重子的成分。在这个自发对称破缺过程中,近似的 [[Nambu–Goldstone boson|Nambu–Goldstone]] 玻色子是介子,其质量比核子的质量轻一个数量级。它是电弱对称破缺的希格斯机制的原型和重要组成部分。<br />
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====Higgs mechanism 希格斯机制====<br />
{{Main article|Higgs mechanism|Yukawa interaction}}<br />
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The strong, weak, and electromagnetic forces can all be understood as arising from [[gauge symmetry|gauge symmetries]]. The [[Higgs mechanism]], the spontaneous symmetry breaking of gauge symmetries, is an important component in understanding the [[superconductivity]] of metals and the origin of particle masses in the standard model of particle physics. One important consequence of the distinction between true symmetries and ''gauge symmetries'', is that the spontaneous breaking of a gauge symmetry does not give rise to characteristic massless Nambu–Goldstone physical modes, but only massive modes, like the plasma mode in a superconductor, or the Higgs mode observed in particle physics.<br />
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强、弱和电磁力都可以理解为来自规范对称。希格斯机制,即规范对称的自发对称破缺机制,是理解金属超导性和粒子物理标准模型中粒子质量起源的重要组成部分。区分真正的对称性和规范对称性的一个重要的结果,是规范对称性的自发破缺不产生典型的无质量 Nambu-Goldstone 物理模式,而只产生有质量的模式,像超导体中的等离子体模式,或者粒子物理学中观察到的希格斯模式。<br />
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In the standard model of particle physics, spontaneous symmetry breaking of the {{nowrap|SU(2) × U(1)}} gauge symmetry associated with the electro-weak force generates masses for several particles, and separates the electromagnetic and weak forces. The [[W and Z bosons]] are the elementary particles that mediate the [[weak interaction]], while the [[photon]] mediates the [[electromagnetic interaction]]. At energies much greater than 100 GeV, all these particles behave in a similar manner. The [[Unified field theory#Modern progress|Weinberg–Salam theory]] predicts that, at lower energies, this symmetry is broken so that the photon and the massive W and Z bosons emerge.<ref>A Brief History of Time, Stephen Hawking, Bantam; 10th anniversary edition (1998). pp. 73–74.{{ISBN?}}</ref> In addition, fermions develop mass consistently.<br />
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在粒子物理的标准模型中,与电弱力相关的SU(2) × U(1)规范对称性自发破缺产生多种粒子的质量,并将电磁力和弱相互作用分离。W玻色子和Z玻色子是介导弱相互作用的基本粒子,而光子介导电磁相互作用。当能量远远大于100 GeV时,所有这些粒子的行为都相似。Weinberg-Salam理论预测,在较低的能量下,这种对称性被打破,光子和大质量的W和Z玻色子就会出现。此外,费米子不断地产生质量。<br />
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Without spontaneous symmetry breaking, the [[Standard Model]] of elementary particle interactions requires the existence of a number of particles. However, some particles (the [[W and Z bosons]]) would then be predicted to be massless, when, in reality, they are observed to have mass. To overcome this, spontaneous symmetry breaking is augmented by the [[Higgs mechanism]] to give these particles mass. It also suggests the presence of a new particle, the [[Higgs boson]], detected in 2012.<br />
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在没有自发对称性破缺的情况下,基本粒子相互作用的标准模型要求大量粒子的存在。而一些粒子(W玻色子和Z玻色子)会被预测为无质量的,但实际上它们被观察到有质量。为了克服这个问题,希格斯机制增强了自发对称破缺,从而赋予这些粒子质量。它还表明一种新粒子——希格斯玻色子——的存在,它在2012年被实验探测到。<br />
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[[Superconductivity]] of metals is a condensed-matter analog of the Higgs phenomena, in which a condensate of Cooper pairs of electrons spontaneously breaks the U(1) gauge symmetry associated with light and electromagnetism.<br />
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金属的超导性是一种类似于希格斯现象的凝聚态物质,其中库珀电子对的凝聚会自发地打破与光和电磁相关的U(1)规范对称性。<br />
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===Condensed matter physics 凝聚态物理===<br />
Most phases of matter can be understood through the lens of spontaneous symmetry breaking. For example, crystals are periodic arrays of atoms that are not invariant under all translations (only under a small subset of translations by a lattice vector). Magnets have north and south poles that are oriented in a specific direction, breaking [[rotational symmetry]]. In addition to these examples, there are a whole host of other symmetry-breaking phases of matter — including nematic phases of liquid crystals, charge- and spin-density waves, superfluids, and many others.<br />
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物质的大多数相态都可以通过自发对称性破缺的透镜来理解。例如,晶体是原子的周期性排列,它并非在所有平移下(仅在晶格向量平移的一个小子集下)都是不变的。磁体有朝向特定方向的南极和北极,打破了旋转对称。除了这些例子,还有一大堆其他的物质对称性破缺相——包括液晶的向列相、电荷和自旋密度波、超流体等等。<br />
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There are several known examples of matter that cannot be described by spontaneous symmetry breaking, including: topologically ordered phases of matter, such as [[Fractional quantum Hall effect|fractional quantum Hall liquids]], and [[Quantum spin liquid|spin-liquids]]. These states do not break any symmetry, but are distinct phases of matter. Unlike the case of spontaneous symmetry breaking, there is not a general framework for describing such states.<ref name=chen>{{cite journal | last1 = Chen | first1 = Xie | author-link3 = Xiao-Gang Wen | last2 = Gu | first2 = Zheng-Cheng | last3 = Wen | first3 = Xiao-Gang | year = 2010 | title = Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order | journal = Phys. Rev. B | volume = 82 | issue = 15| page = 155138 | doi=10.1103/physrevb.82.155138|arxiv = 1004.3835 |bibcode = 2010PhRvB..82o5138C | s2cid = 14593420 }}</ref><br />
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目前已知的不能用自发对称破缺来描述的几个例子包括:物质的拓扑有序相,如分数量子霍尔液体和自旋液体。这些状态并不破坏任何对称性,然而它们是物质的不同相。与自发对称破缺的情况不同,目前还没有一个描述这种状态的一般框架。<br />
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====Continuous symmetry 连续对称性====<br />
The ferromagnet is the canonical system that spontaneously breaks the continuous symmetry of the spins below the [[Curie temperature]] and at {{nowrap|1=''h'' = 0}}, where ''h'' is the external magnetic field. Below the [[Curie temperature]], the energy of the system is invariant under inversion of the magnetization ''m''('''x''') such that {{nowrap|1=''m''('''x''') = −''m''(−'''x''')}}. The symmetry is spontaneously broken as {{nowrap|''h'' → 0}} when the Hamiltonian becomes invariant under the inversion transformation, but the expectation value is not invariant.<br />
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铁磁体是正则系统,它在居里温度以下和h = 0(其中h为外部磁场)的情况下自发打破自旋的连续对称性。在居里温度以下,系统的能量在磁化强度m(x)的反转下(使m(x) =−m(−x))不变。当哈密顿量在反转变换下不变,而期望值不是恒定时,对称性在h→0时自发破坏。<br />
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Spontaneously-symmetry-broken phases of matter are characterized by an order parameter that describes the quantity which breaks the symmetry under consideration. For example, in a magnet, the order parameter is the local magnetization.<br />
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物质的自发对称性破缺相由一个序参量表征,它描述了打破所考虑的对称性的量。例如,在磁铁中,序参量是局部磁化强度。<br />
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Spontaneous breaking of a continuous symmetry is inevitably accompanied by gapless (meaning that these modes do not cost any energy to excite) Nambu–Goldstone modes associated with slow, long-wavelength fluctuations of the order parameter. For example, vibrational modes in a crystal, known as phonons, are associated with slow density fluctuations of the crystal's atoms. The associated Goldstone mode for magnets are oscillating waves of spin known as spin-waves. For symmetry-breaking states, whose order parameter is not a conserved quantity, Nambu–Goldstone modes are typically massless and propagate at a constant velocity.<br />
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连续对称的自发破缺不可避免地伴随着无间隙(意味着这些模式不需要花费任何能量来激发) [[Nambu–Goldstone boson|Nambu–Goldstone]] 模式,它与序参量的缓慢、长波长波动有关。例如,晶体中的振动模式声子,与晶体原子的缓慢密度涨落有关。磁铁相关的 [[Nambu–Goldstone boson|Goldstone]] 模式是自旋振荡波,称为自旋波。对于序参量不是守恒量的对称性破缺态,Nambu-Goldstone模通常是无质量的,并以恒定速度传播。<br />
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An important theorem, due to Mermin and Wagner, states that, at finite temperature, thermally activated fluctuations of Nambu–Goldstone modes destroy the long-range order, and prevent spontaneous symmetry breaking in one- and two-dimensional systems. Similarly, quantum fluctuations of the order parameter prevent most types of continuous symmetry breaking in one-dimensional systems even at zero temperature. (An important exception is ferromagnets, whose order parameter, magnetization, is an exactly conserved quantity and does not have any quantum fluctuations.)<br />
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由Mermin和Wagner提出的一个重要定理指出,在有限温度下, [[Nambu–Goldstone boson|Nambu–Goldstone]] 模式热激活的扰动破坏了长程有序,并阻止了一维和二维系统中对称性的自发破缺。类似地,即使是在零温度下,序参量的量子涨落阻止了一维系统中大多数类型的连续对称破缺。(一个重要的例外是铁磁体,其序参量磁化强度是一个精确的守恒量,不存在任何量子涨落。)<br />
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Other long-range interacting systems, such as cylindrical curved surfaces interacting via the [[Coulomb potential]] or [[Yukawa potential]], have been shown to break translational and rotational symmetries.<ref><br />
{{cite journal<br />
|last1=Kohlstedt |first1=K.L.<br />
|last2=Vernizzi |first2=G.<br />
|last3=Solis |first3=F.J.<br />
|last4=Olvera de la Cruz |first4=M.<br />
|year=2007<br />
|title=Spontaneous Chirality via Long-range Electrostatic Forces<br />
|journal=[[Physical Review Letters]]<br />
|volume=99 |issue=3<br />
|page=030602<br />
|doi=10.1103/PhysRevLett.99.030602<br />
|arxiv = 0704.3435 |bibcode = 2007PhRvL..99c0602K |pmid=17678276|s2cid=37983980<br />
}}</ref> It was shown, in the presence of a symmetric Hamiltonian, and in the limit of infinite volume, the system spontaneously adopts a chiral configuration — i.e., breaks [[mirror plane]] [[symmetry]].<br />
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其他长程相互作用系统,如圆柱曲面通过库仑势或汤川势相互作用,已被证明打破平移和旋转对称。结果表明,在对称哈密顿量存在的情况下,在无限体积的极限下,系统自发地采用手性构型,即打破镜面对称。<br />
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===Dynamical symmetry breaking 动力学对称性破缺===<br />
Dynamical symmetry breaking (DSB) is a special form of spontaneous symmetry breaking in which the ground state of the system has reduced symmetry properties compared to its theoretical description (i.e., [[Lagrangian (field theory)|Lagrangian]]).<br />
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动力学对称性破缺(DSB)是自发对称性破缺的一种特殊形式,在这种情况下,系统的基态相对理论描述(例如拉格朗日量)的对称性降低。<br />
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Dynamical breaking of a global symmetry is a spontaneous symmetry breaking, which happens not at the (classical) tree level (i.e., at the level of the bare action), but due to quantum corrections (i.e., at the level of the [[effective action]]).<br />
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全局对称性的动力学破缺是自发对称性破缺,它不是发生在(经典)树的水平(例如在bare作用的水平),而是由于量子修正(例如在有效作用的水平)。<br />
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Dynamical breaking of a gauge symmetry {{ref|note1}} is subtler. In the conventional spontaneous gauge symmetry breaking, there exists an unstable [[Higgs particle]] in the theory, which drives the vacuum to a symmetry-broken phase. (See, for example, [[electroweak interaction]].) In dynamical gauge symmetry breaking, however, no unstable Higgs particle operates in the theory, but the bound states of the system itself provide the unstable fields that render the phase transition. For example, Bardeen, Hill, and Lindner published a paper that attempts to replace the conventional [[Higgs mechanism]] in the [[standard model]] by a DSB that is driven by a bound state of top-antitop quarks. (Such models, in which a composite particle plays the role of the Higgs boson, are often referred to as "Composite Higgs models".)<ref><br />
{{cite journal<br />
|author1=William A. Bardeen<br />
|author2-link=Christopher T. Hill<br />
|author2=Christopher T. Hill<br />
|author3-link=Manfred Lindner<br />
|author3=Manfred Lindner<br />
|year=1990<br />
|title=Minimal dynamical symmetry breaking of the standard model<br />
|journal=[[Physical Review D]]<br />
|volume=41 |issue=5 |pages=1647–1660<br />
|bibcode=1990PhRvD..41.1647B<br />
|doi=10.1103/PhysRevD.41.1647<br />
|pmid=10012522<br />
|author1-link=William A. Bardeen<br />
}}</ref> Dynamical breaking of gauge symmetries is often due to creation of a [[fermionic condensate]] — e.g., the [[quark condensate]], which is connected to the [[Chiral symmetry breaking|dynamical breaking of chiral symmetry]] in [[quantum chromodynamics]]. Conventional [[superconductivity]] is the paradigmatic example from the condensed matter side, where phonon-mediated attractions lead electrons to become bound in pairs and then condense, thereby breaking the electromagnetic gauge symmetry.<br />
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规范对称性动力学破缺更加微妙。在常规规范对称自发破缺理论中,存在一个不稳定的希格斯粒子,希格斯粒子驱动真空态进入对称破缺相。(例如,参见弱电相互作用。)然而,在规范对称性动力学破缺中,不存在不稳定的希格斯粒子,但系统本身的束缚态提供了导致相变的不稳定场。例如,巴丁、希尔和林德纳发表了一篇论文,试图用一个由顶-反顶夸克束缚状态驱动的DSB来取代标准模型中的传统希格斯机制。(在这种模型中,复合粒子扮演希格斯玻色子的角色,通常被称为“复合希格斯模型”。)规范对称性动力学破缺通常是由于费米凝聚的产生,例如夸克凝聚,它与量子色动力学中手性对称的动力学破缺有关。传统的超导性是凝聚态物质方面的典型例子,声子的吸引导致电子成对结合然后凝聚,从而打破电磁规范对称性。<br />
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==Generalisation and technical usage 广义描述和技术运用==<br />
For spontaneous symmetry breaking to occur, there must be a system in which there are several equally likely outcomes. The system as a whole is therefore [[Symmetry (physics)|symmetric]] with respect to these outcomes. However, if the system is sampled (i.e. if the system is actually used or interacted with in any way), a specific outcome must occur. Though the system as a whole is symmetric, it is never encountered with this symmetry, but only in one specific asymmetric state. Hence, the symmetry is said to be spontaneously broken in that theory. Nevertheless, the fact that each outcome is equally likely is a reflection of the underlying symmetry, which is thus often dubbed "hidden symmetry", and has crucial formal consequences. (See the article on the [[Nambu–Goldstone boson|Goldstone boson]].)<br />
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要发生自发对称性破缺,系统中必须有几个等可能的结果,整个系统相对于这些结果是对称的。然而,如果对系统进行采样(即如果系统被实际使用或以任何方式与之交互),就必须产生特定的结果。虽然系统作为一个整体是对称的,但它从来没有表现出这种对称性,而只是处于一个特定的不对称状态。于是,在该理论中对称性被自发地打破了。然而,每个结果的可能性都相等这一点,反映了潜在的对称性。因此通常被称为“隐藏对称性”,并具有重要的形式结果。(参见有关 [[Nambu–Goldstone boson|Goldstone]]玻色子的文章。)<br />
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When a theory is symmetric with respect to a [[symmetry group]], but requires that one element of the group be distinct, then spontaneous symmetry breaking has occurred. The theory must not dictate ''which'' member is distinct, only that ''one is''. From this point on, the theory can be treated as if this element actually is distinct, with the proviso that any results found in this way must be resymmetrized, by taking the average of each of the elements of the group being the distinct one.<br />
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当一个理论相对于一个对称群是对称的,但要求群中的一个元素是不同的,那么就会发生自发对称性破缺。该理论不能规定''哪个''成员是不同的,而只能规定''那个''成员是不同的。从这一点开始,这个理论就可以被视为这个元素实际上是不同的,附带的条件是,任何以这种方式发现的结果必须是重新对称的,通过取组中每个元素的平均值作为不同的元素。<br />
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The crucial concept in physics theories is the [[order parameter]]. If there is a field (often a background field) which acquires an expectation value (not necessarily a [[vacuum expectation value|''vacuum'' expectation value]]) which is not invariant under the symmetry in question, we say that the system is in the [[ordered phase]], and the symmetry is spontaneously broken. This is because other subsystems interact with the order parameter, which specifies a "frame of reference" to be measured against. In that case, the [[vacuum state]] does not obey the initial symmetry (which would keep it invariant, in the linearly realized '''Wigner mode''' in which it would be a singlet), and, instead changes under the (hidden) symmetry, now implemented in the (nonlinear) '''Nambu–Goldstone mode'''. Normally, in the absence of the Higgs mechanism, massless [[Goldstone boson]]s arise.<br />
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在物理理论中,最重要的概念是序参量。如果有一个场(通常是背景场)得到一个期望值(不一定是真空期望值),这个期望值在理论具有的对称性下不是不变的,我们就说系统处于有序相,对称性自发破缺。这是因为序参量指定了测量其他子系统与之相互作用的“参考框架”。在这种情况下,真空状态不服从初始对称性(这将保持它不变,在线性实现的Wigner模式中,它将是一个单线),而是在(隐藏的)对称下变化,现在在(非线性)'''Nambu–Goldstone'''模式中实现。通常,在没有希格斯机制的情况下,就会出现无质量的戈德斯通玻色子。<br />
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The symmetry group can be discrete, such as the [[space group]] of a crystal, or continuous (e.g., a [[Lie group]]), such as the rotational symmetry of space. However, if the system contains only a single spatial dimension, then only discrete symmetries may be broken in a [[vacuum state]] of the full [[Quantum mechanics|quantum theory]], although a classical solution may break a continuous symmetry.<br />
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对称群可以是离散的,如晶体的空间群,也可以是连续的(如李群),如空间的旋转对称。然而,如果系统只包含一个空间维度,尽管经典解可能打破连续对称性,那么在全量子理论的真空状态下,只有离散的对称性可能被打破。<br />
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==Nobel Prize 诺贝尔奖==<br />
On October 7, 2008, the [[Royal Swedish Academy of Sciences]] awarded the 2008 [[Nobel Prize in Physics]] to three scientists for their work in subatomic physics symmetry breaking. [[Yoichiro Nambu]], of the [[University of Chicago]], won half of the prize for the discovery of the mechanism of spontaneous broken symmetry in the context of the strong interactions, specifically [[chiral symmetry breaking]]. Physicists [[Makoto Kobayashi (physicist)|Makoto Kobayashi]] and [[Toshihide Maskawa]], of [[Kyoto University]], shared the other half of the prize for discovering the origin of the [[Explicit symmetry breaking|explicit breaking]] of CP symmetry in the weak interactions.<ref>{{cite web|author=The Nobel Foundation|title=The Nobel Prize in Physics 2008|url=http://nobelprize.org/nobel_prizes/physics/laureates/2008/index.html|work=nobelprize.org|access-date=January 15, 2008}}</ref> This origin is ultimately reliant on the Higgs mechanism, but, so far understood as a "just so" feature of Higgs couplings, not a spontaneously broken symmetry phenomenon.<br />
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2008年10月7日,瑞典皇家科学院(Royal Swedish Academy of Sciences)将2008年诺贝尔物理学奖授予三位科学家,以表彰他们在亚原子物理对称性破缺方面的工作。芝加哥大学的Yoichiro Nambu获得了一半的奖金,表彰他发现了在强相互作用下对称性自发破缺的机制,特别是手性对称性破缺。京都大学(Kyoto University)物理学家小林诚(Makoto Kobayashi)和正川俊英(Toshihide Maskawa)因发现了弱相互作用中CP对称性显性破缺的起源而分享了另一半奖金。这一起源最终依赖于希格斯机制,但迄今为止被理解为希格斯耦合的“恰好如此”特征,而不是一种自发的对称破缺现象。<br />
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==See also 参见==<br />
{{div col|colwidth=24em}}<br />
* [[Autocatalytic reactions and order creation]]<br />
* [[Catastrophe theory]]<br />
* [[Chiral symmetry breaking]]<br />
* [[CP-violation]]<br />
* [[Fermi ball]]<br />
* [[Gauge gravitation theory]]<br />
* [[Goldstone boson]]<br />
* [[Grand unified theory]]<br />
* [[Higgs mechanism]]<br />
* [[Higgs boson]]<br />
* [[Higgs field (classical)]]<br />
* [[Irreversibility]]<br />
* [[Magnetic catalysis]] of chiral symmetry breaking<br />
* [[Mermin–Wagner theorem]]<br />
* [[Norton's dome]]<br />
* [[Second-order phase transition]]<br />
* [[Spontaneous absolute asymmetric synthesis]] in chemistry<br />
* [[Symmetry breaking]]<br />
* [[Tachyon condensation]]<br />
* [[1964 PRL symmetry breaking papers]]<br />
{{div col end}}参见<br />
<br />
* 自催化反应和秩序产生<br />
<br />
* 灾难理论<br />
* 手性对称性破缺<br />
* CP破坏<br />
* 费米球<br />
* 引力规范理论<br />
* Goldstone 玻色子<br />
* 大统一理论<br />
* 希格斯机制<br />
* 希格斯玻色子<br />
* 希格斯场(经典)<br />
* 不可逆性<br />
* 手性对称破缺的磁性催化<br />
* Mermin–Wagner 理论<br />
* 诺顿的圆顶<br />
* 二阶相变<br />
* 化学中自发绝对非对称合成<br />
* 对称性破缺<br />
* 快子凝聚<br />
* 1964年PRL对称性破缺文章<br />
<br />
==Notes==<br />
* {{note|note1}} Note that (as in fundamental Higgs driven spontaneous gauge symmetry breaking) the term "symmetry breaking" is a misnomer when applied to gauge symmetries.<br />
<br />
==References==<br />
{{Reflist}}<br />
<br />
==External links==<br />
{{wikiquote}}<br />
* For a pedagogic introduction to electroweak symmetry breaking with step by step derivations, not found in texts, of many key relations, see http://www.quantumfieldtheory.info/Electroweak_Sym_breaking.pdf<br />
* [http://hyperphysics.phy-astr.gsu.edu/hbase/forces/unify.html#c2 Spontaneous symmetry breaking]<br />
* [http://prl.aps.org/50years/milestones#1964 Physical Review Letters – 50th Anniversary Milestone Papers]<br />
* [http://cerncourier.com/cws/article/cern/32522 In CERN Courier, Steven Weinberg reflects on spontaneous symmetry breaking]<br />
* [http://www.scholarpedia.org/article/Englert-Brout-Higgs-Guralnik-Hagen-Kibble_mechanism Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism on Scholarpedia]<br />
* [http://www.scholarpedia.org/article/Englert-Brout-Higgs-Guralnik-Hagen-Kibble_mechanism_%28history%29 History of Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism on Scholarpedia]<br />
* [https://arxiv.org/abs/0907.3466 The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles]<br />
* [http://www.worldscinet.com/ijmpa/24/2414/S0217751X09045431.html International Journal of Modern Physics A: The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles]<br />
* [http://www.datafilehost.com/download-7d512618.html Guralnik, G S; Hagen, C R and Kibble, T W B (1967). Broken Symmetries and the Goldstone Theorem. Advances in Physics, vol. 2 Interscience Publishers, New York. pp. 567–708] {{ISBN|0-470-17057-3}}<br />
* [http://lanl.arxiv.org/abs/hep-th/9802142 Spontaneous Symmetry Breaking in Gauge Theories: a Historical Survey]<br />
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{{Standard model of physics}}<br />
{{Quantum mechanics topics}}<br />
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{{DEFAULTSORT:Spontaneous Symmetry Breaking}}<br />
[[Category:Theoretical physics]]<br />
[[Category:Quantum field theory]]<br />
[[Category:Standard Model]]<br />
[[Category:Quantum chromodynamics]]<br />
[[Category:Symmetry]]<br />
[[Category:Quantum phases]]<br />
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*<br />
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==参考文献==<br />
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{{reflist|colwidth=30em}}<br />
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{{DEFAULTSORT:Symmetry Breaking}}<br />
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范畴: 对称<br />
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类别: 模式形成<br />
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[[Category:对称性破缺]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%AF%B9%E7%A7%B0%E6%80%A7%E7%A0%B4%E7%BC%BA&diff=24826对称性破缺2021-07-28T01:51:36Z<p>Jxzhou:</p>
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[[图一:一个小球位于中央山丘的山峰处(C)。这是一种不稳定平衡:一个很小的扰动会使它落到左边(L)或右边(R)稳定点。尽管山丘是对称的,没有理由让球落在哪一侧,但观察到的最终状态仍然是不对称的,它总会落到某一侧]]。<br />
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在物理学中,一个作用于系统的(无限)小扰动使系统跨过临界点,通过决定去向分叉的哪个分支来决定系统的命运,这种现象叫做'''<font color="#ff8000">对称性破缺</font>'''。对于一个观测不到扰动(或“噪声”)的外部观察者来说,这个选择看起来是任意的。这个过程被称为对称性破缺,因为这种转变通常使系统从一个对称但无序的状态进入一个或多个确定的状态。在'''<font color="#ff8000">斑图生成</font>'''中对称性破缺起着重要作用。<br />
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1972年,诺贝尔奖得主P·W·安德森(P.W.Anderson)在《科学》(Science)杂志上发表了一篇名为《多则异也》("More is different")的论文<ref>{{cite journal | last=Anderson | first=P.W. | title=More is Different | journal=Science | volume=177 | issue=4047| pages=393–396 | year=1972 | url=http://robotics.cs.tamu.edu/dshell/cs689/papers/anderson72more_is_different.pdf | doi=10.1126/science.177.4047.393 | pmid=17796623 | format=|bibcode = 1972Sci...177..393A }}</ref>,文中使用对称性破缺的思想表明,即使'''<font color="#ff8000">还原论</font>'''是正确的,但它的逆命题'''<font color="#ff8000">建构主义</font>'''是错误的。建构主义认为,在给出描述各组成部分的理论的情况下科学家可以轻易地预测复杂现象。<br />
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对称性破缺可以分为'''<font color="#ff8000">显性对称性破缺</font>'''和'''<font color="#ff8000">自发对称性破缺</font>'''两种类型,二者的区别是,在破缺对称性下系统的运动方程是否不变或者基态是否保持不变。<br />
==显性对称性破缺==<br />
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在'''<font color="#ff8000">显性对称性破缺</font>'''中,描述系统的运动方程在破缺对称下是不同的。在哈密顿力学或拉格朗日力学中,假若系统的哈密顿量(或拉格朗日量)中至少一项显性地打破了给定的对称性,就发生了显性对称性破缺。<br />
==自发对称性破缺==<br />
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在'''<font color="#ff8000">自发对称性破缺</font>'''中,系统的运动方程是不变的,但系统发生了变化。这是因为系统的背景(时空)——真空态——是非恒定的。这种对称性破缺可以用一个序参量进行参数化。这类对称破缺的一个特殊情况是'''<font color="#ff8000">动力学对称性破缺</font>'''。<br />
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Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state ends up in an asymmetric state.[1][2][3] In particular, it can describe systems where the equations of motion or the Lagrangian obey symmetries, but the lowest-energy vacuum solutions do not exhibit that same symmetry. When the system goes to one of those vacuum solutions, the symmetry is broken for perturbations around that vacuum even though the entire Lagrangian retains that symmetry.<br />
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自发对称破缺是一个自发的对称破缺过程,它使处于对称状态的物理系统最终处于非对称状态。特别地,它可以描述运动方程或拉格朗日方程服从某种对称性,但最低能量真空解不具有该对称性的系统。当系统进入其中一个真空解时,真空解周围的扰动会破坏系统对称性,尽管整个拉格朗日方程仍然保持了对称性。<br />
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==Examples 例子==<br />
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===Sombrero potential Sombrero势===<br />
Consider a symmetric upward dome with a trough circling the bottom. If a ball is put at the very peak of the dome, the system is symmetric with respect to a rotation around the center axis. But the ball may ''spontaneously break'' this symmetry by rolling down the dome into the trough, a point of lowest energy. Afterward, the ball has come to a rest at some fixed point on the perimeter. The dome and the ball retain their individual symmetry, but the system does not.<ref>{{cite book |first=Gerald M. |last=Edelman |title=Bright Air, Brilliant Fire: On the Matter of the Mind |location=New York |publisher=BasicBooks |year=1992 |url=https://archive.org/details/brightairbrillia00gera |url-access=registration |page=[https://archive.org/details/brightairbrillia00gera/page/203 203] }}</ref><br />
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考虑一个对称向上的圆顶,底部环绕着一个槽。如果把一个球放在圆顶的最顶端,这个系统是围绕中心轴旋转对称的。但球体可能会沿着穹顶滚动到能量最低的槽中,从而自发地打破这种对称性。然后,球在圆周上某个固定的点上停下来。圆顶和球保持了各自的对称,但系统却没有保持对称性。<br />
[[Image:Mexican hat potential polar.svg|270px|thumb|left|Graph of Goldstone's "[[sombrero]]" potential function <math>V(\phi)</math>.|链接=Special:FilePath/Mexican_hat_potential_polar.svg]]<br />
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In the simplest idealized relativistic model, the spontaneously broken symmetry is summarized through an illustrative [[scalar field theory]]. The relevant [[Lagrangian (field theory)|Lagrangian]] of a scalar field <math>\phi</math>, which essentially dictates how a system behaves, can be split up into kinetic and potential terms,<br />
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在最简单的理想相对论模型中,可以用一个解释性的标量场理论总结自发对称性破缺。一个标量场 <math>\phi</math>的拉格朗日量从本质上决定了系统的行为,它可以分解成动能项和势能项:<br />
{{NumBlk|::|<math>\mathcal{L} = \partial^\mu \phi \partial_\mu \phi - V(\phi).</math>|{{EquationRef|1}}}}<br />
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It is in this potential term <math>V(\phi)</math> that the symmetry breaking is triggered. An example of a potential, due to [[Jeffrey Goldstone]]<ref>{{Cite journal | last1 = Goldstone | first1 = J. | doi = 10.1007/BF02812722 | title = Field theories with " Superconductor " solutions | journal = Il Nuovo Cimento | volume = 19 | issue = 1 | pages = 154–164 | year = 1961 | bibcode = 1961NCim...19..154G | s2cid = 120409034 | url = http://cds.cern.ch/record/343400 }}</ref> is illustrated in the graph at the left.<br />
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正是在势能项 <math>V(\phi)</math> 中触发了对称性破缺。例如左图所示的 [[Jeffrey Goldstone]] 给出的势能函数:<br />
{{NumBlk|::|<math>V(\phi) = -5|\phi|^2 + |\phi|^4 \,</math>.|{{EquationRef|2}}}}<br />
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This potential has an infinite number of possible [[minimum|minima]] (vacuum states) given by<br />
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该是函数具有无穷数量的最小值点(真空态)当<br />
{{NumBlk|::|<math>\phi = \sqrt{5} e^{i\theta} </math>.|{{EquationRef|3}}}}<br />
for any real ''θ'' between 0 and 2''π''. The system also has an unstable vacuum state corresponding to {{nowrap|1=''Φ'' = 0}}. This state has a [[Unitary group|U(1)]] symmetry. However, once the system falls into a specific stable vacuum state (amounting to a choice of ''θ''), this symmetry will appear to be lost, or "spontaneously broken".<br />
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其中θ可以取0到2π之间的任何实数。系统也有一个不稳定的真空状态,对应于Φ = 0。这个状态具有U(1)对称。然而,一旦系统落入某个稳定真空状态(相当于选择θ),这种对称性就会消失,或者说“自发破缺”。<br />
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In fact, any other choice of ''θ'' would have exactly the same energy, implying the existence of a massless [[Goldstone boson|Nambu–Goldstone boson]], the mode running around the circle at the minimum of this potential, and indicating there is some memory of the original symmetry in the Lagrangian.<br />
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事实上,任何其他θ的选择都将具有完全相同的能量,这意味着无质量的 [[Goldstone boson|Nambu–Goldstone]] 玻色子的存在,这种模式在势能的最小值绕圆周运动,这也表明存在拉格朗日方程中原始对称性的一些记忆。<br />
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===Other examples 其他例子===<br />
* For [[ferromagnet]]ic materials, the underlying laws are invariant under spatial rotations. Here, the order parameter is the [[magnetization]], which measures the magnetic dipole density. Above the [[Curie temperature]], the order parameter is zero, which is spatially invariant, and there is no symmetry breaking. Below the Curie temperature, however, the magnetization acquires a constant nonvanishing value, which points in a certain direction (in the idealized situation where we have full equilibrium; otherwise, translational symmetry gets broken as well). The residual rotational symmetries which leave the orientation of this vector invariant remain unbroken, unlike the other rotations which do not and are thus spontaneously broken.<br />
* 对于铁磁性材料,其基本物理定律在空间旋转下是不变的。在这里,序参量是衡量磁偶极子密度的磁化强度。在居里温度以上,序参量为零,具有空间不变性,不存在对称性破缺。然而,在居里温度以下,磁化强度变成一个恒定的非零值,指向一个特定的方向(在有充分平衡的理想情况下;否则,平移对称性也会破缺)。使该向量方向不变的旋转对称性仍然保留,而其他旋转对称性自发破缺。<br />
* The laws describing a solid are invariant under the full [[Euclidean group]], but the solid itself spontaneously breaks this group down to a [[space group]]. The displacement and the orientation are the order parameters.<br />
* 描述固体的物理定律在完整的欧几里得群下是不变的,但固体本身会自发地将这个群分解为一个空间群。其中位移和方向是序参量。<br />
* General relativity has a Lorentz symmetry, but in [[Friedmann–Lemaître–Robertson–Walker metric|FRW cosmological models]], the mean 4-velocity field defined by averaging over the velocities of the galaxies (the galaxies act like gas particles at cosmological scales) acts as an order parameter breaking this symmetry. Similar comments can be made about the cosmic microwave background.<br />
* 广义相对论具有洛伦兹对称性,但在FRW宇宙模型中,定义为星系速度平均值(星系在宇宙尺度上的行为就像气体粒子) 的平均 4-速度场,作为序参量会打破这种对称性。对于宇宙微波背景辐射也有类似的评论。<br />
* For the [[electroweak]] model, as explained earlier, a component of the Higgs field provides the order parameter breaking the electroweak gauge symmetry to the electromagnetic gauge symmetry. Like the ferromagnetic example, there is a phase transition at the electroweak temperature. The same comment about us not tending to notice broken symmetries suggests why it took so long for us to discover electroweak unification.<br />
* 对于电弱模型,如前面所解释的,希格斯场的一个分量提供了将电弱规范对称性破缺到电磁规范对称性的序参量。和铁磁的例子一样,在电弱温度下也有相变。同样地由于我们不倾向于注意对称性破缺,导致我们花了这么长时间才发现电弱统一。<br />
* In superconductors, there is a condensed-matter collective field ψ, which acts as the order parameter breaking the electromagnetic gauge symmetry.<br />
* 在超导体中有一个凝聚态集体场ψ,它是打破电磁规范对称性的序参量。<br />
* Take a thin cylindrical plastic rod and push both ends together. Before buckling, the system is symmetric under rotation, and so visibly cylindrically symmetric. But after buckling, it looks different, and asymmetric. Nevertheless, features of the cylindrical symmetry are still there: ignoring friction, it would take no force to freely spin the rod around, displacing the ground state in time, and amounting to an oscillation of vanishing frequency, unlike the radial oscillations in the direction of the buckle. This spinning mode is effectively the requisite [[Goldstone boson|Nambu–Goldstone boson]].<br />
* 拿一个细长的圆柱形塑料杆,把两端推到一起。在屈曲之前,系统在旋转下是对称的,因此具有圆柱对称性。但在弯曲之后,它看起来就不同了,而且是不对称的。然而,圆柱对称性的特征仍然存在:忽略摩擦,杆可以不受外力自由地自旋,在时间上取代基态,相当于一个频率趋于零的振荡,而不是沿屈曲方向的径向振荡。这种自旋模式实际上是必需的[[Goldstone boson|Nambu–Goldstone]] 玻色子。<br />
* Consider a uniform layer of [[fluid]] over an infinite horizontal plane. This system has all the symmetries of the Euclidean plane. But now heat the bottom surface uniformly so that it becomes much hotter than the upper surface. When the temperature gradient becomes large enough, [[convection cell]]s will form, breaking the Euclidean symmetry.<br />
* 考虑无限水平面上的一层均匀的流体,这个系统具有欧几里得平面的所有对称性。但是现在均匀地加热底部表面,使它变得比上表面热得多。当温度梯度足够大时,就会形成对流单元,打破了欧几里得对称。<br />
* Consider a bead on a circular hoop that is rotated about a vertical [[diameter]]. As the [[rotational velocity]] is increased gradually from rest, the bead will initially stay at its initial [[equilibrium point]] at the bottom of the hoop (intuitively stable, lowest [[gravitational potential]]). At a certain critical rotational velocity, this point will become unstable and the bead will jump to one of two other newly created equilibria, [[equidistant]] from the center. Initially, the system is symmetric with respect to the diameter, yet after passing the critical velocity, the bead ends up in one of the two new equilibrium points, thus breaking the symmetry.<br />
* 考虑一个围绕某个竖直的直径旋转的圆形箍上的珠子。当旋转速度从静止逐渐增加时,珠子最初会停留在环底部的初始平衡点(直观上稳定,重力势最低)。在一定的临界旋转速度下,这一点将变得不稳定,珠子将跳到另外两个新创建的离中心等距离的平衡点中的一个。起初,系统相对直径是对称的,但在通过临界速度后,珠子最终停留在两个新的平衡点中的一个,从而打破了对称性。<br />
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==Spontaneous symmetry breaking in physics 物理学中的自发对称性破缺==<br />
[[File:Spontaneous symmetry breaking (explanatory diagram).png|thumb|right|250px|''Spontaneous symmetry breaking illustrated'': At high energy levels (''left''), the ball settles in the center, and the result is symmetric. At lower energy levels (''right''), the overall "rules" remain symmetric, but the symmetric "[[sombrero|Sombrero]]" enforces an asymmetric outcome, since eventually the ball must rest at some random spot on the bottom, "spontaneously", and not all others.|链接=Special:FilePath/Spontaneous_symmetry_breaking_(explanatory_diagram).png]]<br />
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===Particle physics 粒子物理===<br />
In [[particle physics]], the [[force carrier]] particles are normally specified by field equations with [[gauge symmetry]]; their equations predict that certain measurements will be the same at any point in the field. For instance, field equations might predict that the mass of two quarks is constant. Solving the equations to find the mass of each quark might give two solutions. In one solution, quark A is heavier than quark B. In the second solution, quark B is heavier than quark A ''by the same amount''. The symmetry of the equations is not reflected by the individual solutions, but it is reflected by the range of solutions.<br />
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在粒子物理学中,载力子通常由规范对称的场方程表示;这些方程预测到某些测量值在场的任何点上都是相同的。例如,场方程可以预测两个夸克的质量和是常数。通过求解方程来求单个夸克的质量可能会得到两个解。在一个解中,夸克A比夸克B重;在第二个解中,夸克B比夸克A重,并且两个解中质量差相同。方程的对称性不是由单个解来反映的,而是由解的范围来反映的。<br />
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An actual measurement reflects only one solution, representing a breakdown in the symmetry of the underlying theory. "Hidden" is a better term than "broken", because the symmetry is always there in these equations. This phenomenon is called [[Spontaneous magnetization|''spontaneous'']] symmetry breaking (SSB) because ''nothing'' (that we know of) breaks the symmetry in the equations.<ref name="Weinberg2011">{{cite book|author=Steven Weinberg|title=Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature|url=https://books.google.com/books?id=Rsg3PE_9_ccC|date=20 April 2011|publisher=Knopf Doubleday Publishing Group|isbn=978-0-307-78786-6}}</ref>{{rp|194–195}}<br />
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一个实际的测量只反映了一个解,这代表了其潜在理论的对称性的破缺。在这里“隐藏”是比“破缺”更好的术语,因为对称性总是存在于这些方程中。这种现象被称为自发对称破缺(SSB),因为(我们所知道的)没有任何东西会打破方程中的对称性。<br />
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====Chiral symmetry 手性对称性====<br />
{{Main article|Chiral symmetry breaking}}<br />
Chiral symmetry breaking is an example of spontaneous symmetry breaking affecting the [[chiral symmetry]] of the [[strong interactions]] in particle physics. It is a property of [[quantum chromodynamics]], the [[quantum field theory]] describing these interactions, and is responsible for the bulk of the mass (over 99%) of the [[nucleons]], and thus of all common matter, as it converts very light bound [[quarks]] into 100 times heavier constituents of [[baryons]]. The approximate [[Nambu–Goldstone boson]]s in this spontaneous symmetry breaking process are the [[pions]], whose mass is an order of magnitude lighter than the mass of the nucleons. It served as the prototype and significant ingredient of the Higgs mechanism underlying the electroweak symmetry breaking.<br />
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手性对称破缺是粒子物理中影响强相互作用手性对称的自发对称破缺的一个例子。手性对称性破缺是量子色动力学(描述这些相互作用的量子场理论)的一种特性,它是核子的大部分质量(超过99%)的成因,因此也是所有普通物质的主要成因,它将非常轻的束缚夸克转化为100倍重量的重子的成分。在这个自发对称破缺过程中,近似的 [[Nambu–Goldstone boson|Nambu–Goldstone]] 玻色子是介子,其质量比核子的质量轻一个数量级。它是电弱对称破缺的希格斯机制的原型和重要组成部分。<br />
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====Higgs mechanism 希格斯机制====<br />
{{Main article|Higgs mechanism|Yukawa interaction}}<br />
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The strong, weak, and electromagnetic forces can all be understood as arising from [[gauge symmetry|gauge symmetries]]. The [[Higgs mechanism]], the spontaneous symmetry breaking of gauge symmetries, is an important component in understanding the [[superconductivity]] of metals and the origin of particle masses in the standard model of particle physics. One important consequence of the distinction between true symmetries and ''gauge symmetries'', is that the spontaneous breaking of a gauge symmetry does not give rise to characteristic massless Nambu–Goldstone physical modes, but only massive modes, like the plasma mode in a superconductor, or the Higgs mode observed in particle physics.<br />
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强、弱和电磁力都可以理解为来自规范对称。希格斯机制,即规范对称的自发对称破缺机制,是理解金属超导性和粒子物理标准模型中粒子质量起源的重要组成部分。区分真正的对称性和规范对称性的一个重要的结果,是规范对称性的自发破缺不产生典型的无质量 Nambu-Goldstone 物理模式,而只产生有质量的模式,像超导体中的等离子体模式,或者粒子物理学中观察到的希格斯模式。<br />
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In the standard model of particle physics, spontaneous symmetry breaking of the {{nowrap|SU(2) × U(1)}} gauge symmetry associated with the electro-weak force generates masses for several particles, and separates the electromagnetic and weak forces. The [[W and Z bosons]] are the elementary particles that mediate the [[weak interaction]], while the [[photon]] mediates the [[electromagnetic interaction]]. At energies much greater than 100 GeV, all these particles behave in a similar manner. The [[Unified field theory#Modern progress|Weinberg–Salam theory]] predicts that, at lower energies, this symmetry is broken so that the photon and the massive W and Z bosons emerge.<ref>A Brief History of Time, Stephen Hawking, Bantam; 10th anniversary edition (1998). pp. 73–74.{{ISBN?}}</ref> In addition, fermions develop mass consistently.<br />
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在粒子物理的标准模型中,与电弱力相关的SU(2) × U(1)规范对称性自发破缺产生多种粒子的质量,并将电磁力和弱相互作用分离。W玻色子和Z玻色子是介导弱相互作用的基本粒子,而光子介导电磁相互作用。当能量远远大于100 GeV时,所有这些粒子的行为都相似。Weinberg-Salam理论预测,在较低的能量下,这种对称性被打破,光子和大质量的W和Z玻色子就会出现。此外,费米子不断地产生质量。<br />
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Without spontaneous symmetry breaking, the [[Standard Model]] of elementary particle interactions requires the existence of a number of particles. However, some particles (the [[W and Z bosons]]) would then be predicted to be massless, when, in reality, they are observed to have mass. To overcome this, spontaneous symmetry breaking is augmented by the [[Higgs mechanism]] to give these particles mass. It also suggests the presence of a new particle, the [[Higgs boson]], detected in 2012.<br />
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在没有自发对称性破缺的情况下,基本粒子相互作用的标准模型要求大量粒子的存在。而一些粒子(W玻色子和Z玻色子)会被预测为无质量的,但实际上它们被观察到有质量。为了克服这个问题,希格斯机制增强了自发对称破缺,从而赋予这些粒子质量。它还表明一种新粒子——希格斯玻色子——的存在,它在2012年被实验探测到。<br />
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[[Superconductivity]] of metals is a condensed-matter analog of the Higgs phenomena, in which a condensate of Cooper pairs of electrons spontaneously breaks the U(1) gauge symmetry associated with light and electromagnetism.<br />
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金属的超导性是一种类似于希格斯现象的凝聚态物质,其中库珀电子对的凝聚会自发地打破与光和电磁相关的U(1)规范对称性。<br />
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===Condensed matter physics 凝聚态物理===<br />
Most phases of matter can be understood through the lens of spontaneous symmetry breaking. For example, crystals are periodic arrays of atoms that are not invariant under all translations (only under a small subset of translations by a lattice vector). Magnets have north and south poles that are oriented in a specific direction, breaking [[rotational symmetry]]. In addition to these examples, there are a whole host of other symmetry-breaking phases of matter — including nematic phases of liquid crystals, charge- and spin-density waves, superfluids, and many others.<br />
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物质的大多数相态都可以通过自发对称性破缺的透镜来理解。例如,晶体是原子的周期性排列,它并非在所有平移下(仅在晶格向量平移的一个小子集下)都是不变的。磁体有朝向特定方向的南极和北极,打破了旋转对称。除了这些例子,还有一大堆其他的物质对称性破缺相——包括液晶的向列相、电荷和自旋密度波、超流体等等。<br />
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There are several known examples of matter that cannot be described by spontaneous symmetry breaking, including: topologically ordered phases of matter, such as [[Fractional quantum Hall effect|fractional quantum Hall liquids]], and [[Quantum spin liquid|spin-liquids]]. These states do not break any symmetry, but are distinct phases of matter. Unlike the case of spontaneous symmetry breaking, there is not a general framework for describing such states.<ref name=chen>{{cite journal | last1 = Chen | first1 = Xie | author-link3 = Xiao-Gang Wen | last2 = Gu | first2 = Zheng-Cheng | last3 = Wen | first3 = Xiao-Gang | year = 2010 | title = Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order | journal = Phys. Rev. B | volume = 82 | issue = 15| page = 155138 | doi=10.1103/physrevb.82.155138|arxiv = 1004.3835 |bibcode = 2010PhRvB..82o5138C | s2cid = 14593420 }}</ref><br />
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目前已知的不能用自发对称破缺来描述的几个例子包括:物质的拓扑有序相,如分数量子霍尔液体和自旋液体。这些状态并不破坏任何对称性,然而它们是物质的不同相。与自发对称破缺的情况不同,目前还没有一个描述这种状态的一般框架。<br />
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====Continuous symmetry 连续对称性====<br />
The ferromagnet is the canonical system that spontaneously breaks the continuous symmetry of the spins below the [[Curie temperature]] and at {{nowrap|1=''h'' = 0}}, where ''h'' is the external magnetic field. Below the [[Curie temperature]], the energy of the system is invariant under inversion of the magnetization ''m''('''x''') such that {{nowrap|1=''m''('''x''') = −''m''(−'''x''')}}. The symmetry is spontaneously broken as {{nowrap|''h'' → 0}} when the Hamiltonian becomes invariant under the inversion transformation, but the expectation value is not invariant.<br />
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铁磁体是正则系统,它在居里温度以下和h = 0(其中h为外部磁场)的情况下自发打破自旋的连续对称性。在居里温度以下,系统的能量在磁化强度m(x)的反转下(使m(x) =−m(−x))不变。当哈密顿量在反转变换下不变,而期望值不是恒定时,对称性在h→0时自发破坏。<br />
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Spontaneously-symmetry-broken phases of matter are characterized by an order parameter that describes the quantity which breaks the symmetry under consideration. For example, in a magnet, the order parameter is the local magnetization.<br />
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物质的自发对称性破缺相由一个序参量表征,它描述了打破所考虑的对称性的量。例如,在磁铁中,序参量是局部磁化强度。<br />
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Spontaneous breaking of a continuous symmetry is inevitably accompanied by gapless (meaning that these modes do not cost any energy to excite) Nambu–Goldstone modes associated with slow, long-wavelength fluctuations of the order parameter. For example, vibrational modes in a crystal, known as phonons, are associated with slow density fluctuations of the crystal's atoms. The associated Goldstone mode for magnets are oscillating waves of spin known as spin-waves. For symmetry-breaking states, whose order parameter is not a conserved quantity, Nambu–Goldstone modes are typically massless and propagate at a constant velocity.<br />
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连续对称的自发破缺不可避免地伴随着无间隙(意味着这些模式不需要花费任何能量来激发) [[Nambu–Goldstone boson|Nambu–Goldstone]] 模式,它与序参量的缓慢、长波长波动有关。例如,晶体中的振动模式声子,与晶体原子的缓慢密度涨落有关。磁铁相关的 [[Nambu–Goldstone boson|Goldstone]] 模式是自旋振荡波,称为自旋波。对于序参量不是守恒量的对称性破缺态,Nambu-Goldstone模通常是无质量的,并以恒定速度传播。<br />
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An important theorem, due to Mermin and Wagner, states that, at finite temperature, thermally activated fluctuations of Nambu–Goldstone modes destroy the long-range order, and prevent spontaneous symmetry breaking in one- and two-dimensional systems. Similarly, quantum fluctuations of the order parameter prevent most types of continuous symmetry breaking in one-dimensional systems even at zero temperature. (An important exception is ferromagnets, whose order parameter, magnetization, is an exactly conserved quantity and does not have any quantum fluctuations.)<br />
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由Mermin和Wagner提出的一个重要定理指出,在有限温度下, [[Nambu–Goldstone boson|Nambu–Goldstone]] 模式热激活的扰动破坏了长程有序,并阻止了一维和二维系统中对称性的自发破缺。类似地,即使是在零温度下,序参量的量子涨落阻止了一维系统中大多数类型的连续对称破缺。(一个重要的例外是铁磁体,其序参量磁化强度是一个精确的守恒量,不存在任何量子涨落。)<br />
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Other long-range interacting systems, such as cylindrical curved surfaces interacting via the [[Coulomb potential]] or [[Yukawa potential]], have been shown to break translational and rotational symmetries.<ref><br />
{{cite journal<br />
|last1=Kohlstedt |first1=K.L.<br />
|last2=Vernizzi |first2=G.<br />
|last3=Solis |first3=F.J.<br />
|last4=Olvera de la Cruz |first4=M.<br />
|year=2007<br />
|title=Spontaneous Chirality via Long-range Electrostatic Forces<br />
|journal=[[Physical Review Letters]]<br />
|volume=99 |issue=3<br />
|page=030602<br />
|doi=10.1103/PhysRevLett.99.030602<br />
|arxiv = 0704.3435 |bibcode = 2007PhRvL..99c0602K |pmid=17678276|s2cid=37983980<br />
}}</ref> It was shown, in the presence of a symmetric Hamiltonian, and in the limit of infinite volume, the system spontaneously adopts a chiral configuration — i.e., breaks [[mirror plane]] [[symmetry]].<br />
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其他长程相互作用系统,如圆柱曲面通过库仑势或汤川势相互作用,已被证明打破平移和旋转对称。结果表明,在对称哈密顿量存在的情况下,在无限体积的极限下,系统自发地采用手性构型,即打破镜面对称。<br />
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===Dynamical symmetry breaking 动力学对称性破缺===<br />
Dynamical symmetry breaking (DSB) is a special form of spontaneous symmetry breaking in which the ground state of the system has reduced symmetry properties compared to its theoretical description (i.e., [[Lagrangian (field theory)|Lagrangian]]).<br />
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动力学对称性破缺(DSB)是自发对称性破缺的一种特殊形式,在这种情况下,系统的基态相对理论描述(例如拉格朗日量)的对称性降低。<br />
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Dynamical breaking of a global symmetry is a spontaneous symmetry breaking, which happens not at the (classical) tree level (i.e., at the level of the bare action), but due to quantum corrections (i.e., at the level of the [[effective action]]).<br />
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全局对称性的动力学破缺是自发对称性破缺,它不是发生在(经典)树的水平(例如在bare作用的水平),而是由于量子修正(例如在有效作用的水平)。<br />
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Dynamical breaking of a gauge symmetry {{ref|note1}} is subtler. In the conventional spontaneous gauge symmetry breaking, there exists an unstable [[Higgs particle]] in the theory, which drives the vacuum to a symmetry-broken phase. (See, for example, [[electroweak interaction]].) In dynamical gauge symmetry breaking, however, no unstable Higgs particle operates in the theory, but the bound states of the system itself provide the unstable fields that render the phase transition. For example, Bardeen, Hill, and Lindner published a paper that attempts to replace the conventional [[Higgs mechanism]] in the [[standard model]] by a DSB that is driven by a bound state of top-antitop quarks. (Such models, in which a composite particle plays the role of the Higgs boson, are often referred to as "Composite Higgs models".)<ref><br />
{{cite journal<br />
|author1=William A. Bardeen<br />
|author2-link=Christopher T. Hill<br />
|author2=Christopher T. Hill<br />
|author3-link=Manfred Lindner<br />
|author3=Manfred Lindner<br />
|year=1990<br />
|title=Minimal dynamical symmetry breaking of the standard model<br />
|journal=[[Physical Review D]]<br />
|volume=41 |issue=5 |pages=1647–1660<br />
|bibcode=1990PhRvD..41.1647B<br />
|doi=10.1103/PhysRevD.41.1647<br />
|pmid=10012522<br />
|author1-link=William A. Bardeen<br />
}}</ref> Dynamical breaking of gauge symmetries is often due to creation of a [[fermionic condensate]] — e.g., the [[quark condensate]], which is connected to the [[Chiral symmetry breaking|dynamical breaking of chiral symmetry]] in [[quantum chromodynamics]]. Conventional [[superconductivity]] is the paradigmatic example from the condensed matter side, where phonon-mediated attractions lead electrons to become bound in pairs and then condense, thereby breaking the electromagnetic gauge symmetry.<br />
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规范对称性动力学破缺更加微妙。在常规规范对称自发破缺理论中,存在一个不稳定的希格斯粒子,希格斯粒子驱动真空态进入对称破缺相。(例如,参见弱电相互作用。)然而,在规范对称性动力学破缺中,不存在不稳定的希格斯粒子,但系统本身的束缚态提供了导致相变的不稳定场。例如,巴丁、希尔和林德纳发表了一篇论文,试图用一个由顶-反顶夸克束缚状态驱动的DSB来取代标准模型中的传统希格斯机制。(在这种模型中,复合粒子扮演希格斯玻色子的角色,通常被称为“复合希格斯模型”。)规范对称性动力学破缺通常是由于费米凝聚的产生,例如夸克凝聚,它与量子色动力学中手性对称的动力学破缺有关。传统的超导性是凝聚态物质方面的典型例子,声子的吸引导致电子成对结合然后凝聚,从而打破电磁规范对称性。<br />
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==Generalisation and technical usage 广义描述和技术运用==<br />
For spontaneous symmetry breaking to occur, there must be a system in which there are several equally likely outcomes. The system as a whole is therefore [[Symmetry (physics)|symmetric]] with respect to these outcomes. However, if the system is sampled (i.e. if the system is actually used or interacted with in any way), a specific outcome must occur. Though the system as a whole is symmetric, it is never encountered with this symmetry, but only in one specific asymmetric state. Hence, the symmetry is said to be spontaneously broken in that theory. Nevertheless, the fact that each outcome is equally likely is a reflection of the underlying symmetry, which is thus often dubbed "hidden symmetry", and has crucial formal consequences. (See the article on the [[Nambu–Goldstone boson|Goldstone boson]].)<br />
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要发生自发对称性破缺,系统中必须有几个等可能的结果,整个系统相对于这些结果是对称的。然而,如果对系统进行采样(即如果系统被实际使用或以任何方式与之交互),就必须产生特定的结果。虽然系统作为一个整体是对称的,但它从来没有表现出这种对称性,而只是处于一个特定的不对称状态。于是,在该理论中对称性被自发地打破了。然而,每个结果的可能性都相等这一点,反映了潜在的对称性。因此通常被称为“隐藏对称性”,并具有重要的形式结果。(参见有关 [[Nambu–Goldstone boson|Goldstone]]玻色子的文章。)<br />
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When a theory is symmetric with respect to a [[symmetry group]], but requires that one element of the group be distinct, then spontaneous symmetry breaking has occurred. The theory must not dictate ''which'' member is distinct, only that ''one is''. From this point on, the theory can be treated as if this element actually is distinct, with the proviso that any results found in this way must be resymmetrized, by taking the average of each of the elements of the group being the distinct one.<br />
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当一个理论相对于一个对称群是对称的,但要求群中的一个元素是不同的,那么就会发生自发对称性破缺。该理论不能规定''哪个''成员是不同的,而只能规定''那个''成员是不同的。从这一点开始,这个理论就可以被视为这个元素实际上是不同的,附带的条件是,任何以这种方式发现的结果必须是重新对称的,通过取组中每个元素的平均值作为不同的元素。<br />
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The crucial concept in physics theories is the [[order parameter]]. If there is a field (often a background field) which acquires an expectation value (not necessarily a [[vacuum expectation value|''vacuum'' expectation value]]) which is not invariant under the symmetry in question, we say that the system is in the [[ordered phase]], and the symmetry is spontaneously broken. This is because other subsystems interact with the order parameter, which specifies a "frame of reference" to be measured against. In that case, the [[vacuum state]] does not obey the initial symmetry (which would keep it invariant, in the linearly realized '''Wigner mode''' in which it would be a singlet), and, instead changes under the (hidden) symmetry, now implemented in the (nonlinear) '''Nambu–Goldstone mode'''. Normally, in the absence of the Higgs mechanism, massless [[Goldstone boson]]s arise.<br />
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在物理理论中,最重要的概念是序参量。如果有一个场(通常是背景场)得到一个期望值(不一定是真空期望值),这个期望值在理论具有的对称性下不是不变的,我们就说系统处于有序相,对称性自发破缺。这是因为序参量指定了测量其他子系统与之相互作用的“参考框架”。在这种情况下,真空状态不服从初始对称性(这将保持它不变,在线性实现的Wigner模式中,它将是一个单线),而是在(隐藏的)对称下变化,现在在(非线性)'''Nambu–Goldstone'''模式中实现。通常,在没有希格斯机制的情况下,就会出现无质量的戈德斯通玻色子。<br />
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The symmetry group can be discrete, such as the [[space group]] of a crystal, or continuous (e.g., a [[Lie group]]), such as the rotational symmetry of space. However, if the system contains only a single spatial dimension, then only discrete symmetries may be broken in a [[vacuum state]] of the full [[Quantum mechanics|quantum theory]], although a classical solution may break a continuous symmetry.<br />
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对称群可以是离散的,如晶体的空间群,也可以是连续的(如李群),如空间的旋转对称。然而,如果系统只包含一个空间维度,尽管经典解可能打破连续对称性,那么在全量子理论的真空状态下,只有离散的对称性可能被打破。<br />
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==Nobel Prize 诺贝尔奖==<br />
On October 7, 2008, the [[Royal Swedish Academy of Sciences]] awarded the 2008 [[Nobel Prize in Physics]] to three scientists for their work in subatomic physics symmetry breaking. [[Yoichiro Nambu]], of the [[University of Chicago]], won half of the prize for the discovery of the mechanism of spontaneous broken symmetry in the context of the strong interactions, specifically [[chiral symmetry breaking]]. Physicists [[Makoto Kobayashi (physicist)|Makoto Kobayashi]] and [[Toshihide Maskawa]], of [[Kyoto University]], shared the other half of the prize for discovering the origin of the [[Explicit symmetry breaking|explicit breaking]] of CP symmetry in the weak interactions.<ref>{{cite web|author=The Nobel Foundation|title=The Nobel Prize in Physics 2008|url=http://nobelprize.org/nobel_prizes/physics/laureates/2008/index.html|work=nobelprize.org|access-date=January 15, 2008}}</ref> This origin is ultimately reliant on the Higgs mechanism, but, so far understood as a "just so" feature of Higgs couplings, not a spontaneously broken symmetry phenomenon.<br />
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2008年10月7日,瑞典皇家科学院(Royal Swedish Academy of Sciences)将2008年诺贝尔物理学奖授予三位科学家,以表彰他们在亚原子物理对称性破缺方面的工作。芝加哥大学的Yoichiro Nambu获得了一半的奖金,表彰他发现了在强相互作用下对称性自发破缺的机制,特别是手性对称性破缺。京都大学(Kyoto University)物理学家小林诚(Makoto Kobayashi)和正川俊英(Toshihide Maskawa)因发现了弱相互作用中CP对称性显性破缺的起源而分享了另一半奖金。这一起源最终依赖于希格斯机制,但迄今为止被理解为希格斯耦合的“恰好如此”特征,而不是一种自发的对称破缺现象。<br />
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==See also 参见==<br />
{{div col|colwidth=24em}}<br />
* [[Autocatalytic reactions and order creation]]<br />
* [[Catastrophe theory]]<br />
* [[Chiral symmetry breaking]]<br />
* [[CP-violation]]<br />
* [[Fermi ball]]<br />
* [[Gauge gravitation theory]]<br />
* [[Goldstone boson]]<br />
* [[Grand unified theory]]<br />
* [[Higgs mechanism]]<br />
* [[Higgs boson]]<br />
* [[Higgs field (classical)]]<br />
* [[Irreversibility]]<br />
* [[Magnetic catalysis]] of chiral symmetry breaking<br />
* [[Mermin–Wagner theorem]]<br />
* [[Norton's dome]]<br />
* [[Second-order phase transition]]<br />
* [[Spontaneous absolute asymmetric synthesis]] in chemistry<br />
* [[Symmetry breaking]]<br />
* [[Tachyon condensation]]<br />
* [[1964 PRL symmetry breaking papers]]<br />
{{div col end}}<br />
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==Notes==<br />
* {{note|note1}} Note that (as in fundamental Higgs driven spontaneous gauge symmetry breaking) the term "symmetry breaking" is a misnomer when applied to gauge symmetries.<br />
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==References==<br />
{{Reflist}}<br />
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==External links==<br />
{{wikiquote}}<br />
* For a pedagogic introduction to electroweak symmetry breaking with step by step derivations, not found in texts, of many key relations, see http://www.quantumfieldtheory.info/Electroweak_Sym_breaking.pdf<br />
* [http://hyperphysics.phy-astr.gsu.edu/hbase/forces/unify.html#c2 Spontaneous symmetry breaking]<br />
* [http://prl.aps.org/50years/milestones#1964 Physical Review Letters – 50th Anniversary Milestone Papers]<br />
* [http://cerncourier.com/cws/article/cern/32522 In CERN Courier, Steven Weinberg reflects on spontaneous symmetry breaking]<br />
* [http://www.scholarpedia.org/article/Englert-Brout-Higgs-Guralnik-Hagen-Kibble_mechanism Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism on Scholarpedia]<br />
* [http://www.scholarpedia.org/article/Englert-Brout-Higgs-Guralnik-Hagen-Kibble_mechanism_%28history%29 History of Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism on Scholarpedia]<br />
* [https://arxiv.org/abs/0907.3466 The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles]<br />
* [http://www.worldscinet.com/ijmpa/24/2414/S0217751X09045431.html International Journal of Modern Physics A: The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles]<br />
* [http://www.datafilehost.com/download-7d512618.html Guralnik, G S; Hagen, C R and Kibble, T W B (1967). Broken Symmetries and the Goldstone Theorem. Advances in Physics, vol. 2 Interscience Publishers, New York. pp. 567–708] {{ISBN|0-470-17057-3}}<br />
* [http://lanl.arxiv.org/abs/hep-th/9802142 Spontaneous Symmetry Breaking in Gauge Theories: a Historical Survey]<br />
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{{Standard model of physics}}<br />
{{Quantum mechanics topics}}<br />
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{{DEFAULTSORT:Spontaneous Symmetry Breaking}}<br />
[[Category:Theoretical physics]]<br />
[[Category:Quantum field theory]]<br />
[[Category:Standard Model]]<br />
[[Category:Quantum chromodynamics]]<br />
[[Category:Symmetry]]<br />
[[Category:Quantum phases]]<br />
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==参考文献==<br />
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{{DEFAULTSORT:Symmetry Breaking}}<br />
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范畴: 对称<br />
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类别: 模式形成<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''<br />
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[[Category:对称性破缺]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%AF%B9%E7%A7%B0%E6%80%A7%E7%A0%B4%E7%BC%BA&diff=24825对称性破缺2021-07-28T01:10:08Z<p>Jxzhou:/* Overview */</p>
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[[图一:一个小球位于中央山丘的山峰处(C)。这是一种不稳定平衡:一个很小的扰动会使它落到左边(L)或右边(R)稳定点。尽管山丘是对称的,没有理由让球落在哪一侧,但观察到的最终状态仍然是不对称的,它总会落到某一侧]]。<br />
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在物理学中,一个作用于系统的(无限)小扰动使系统跨过临界点,通过决定去向分叉的哪个分支来决定系统的命运,这种现象叫做'''<font color="#ff8000">对称性破缺</font>'''。对于一个观测不到扰动(或“噪声”)的外部观察者来说,这个选择看起来是任意的。这个过程被称为对称性破缺,因为这种转变通常使系统从一个对称但无序的状态进入一个或多个确定的状态。在'''<font color="#ff8000">斑图生成</font>'''中对称性破缺起着重要作用。<br />
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1972年,诺贝尔奖得主P·W·安德森(P.W.Anderson)在《科学》(Science)杂志上发表了一篇名为《多即不同》的论文<ref>{{cite journal | last=Anderson | first=P.W. | title=More is Different | journal=Science | volume=177 | issue=4047| pages=393–396 | year=1972 | url=http://robotics.cs.tamu.edu/dshell/cs689/papers/anderson72more_is_different.pdf | doi=10.1126/science.177.4047.393 | pmid=17796623 | format=|bibcode = 1972Sci...177..393A }}</ref>,文中使用对称性破缺的思想表明,即使'''<font color="#ff8000">还原论</font>'''是正确的,但它的逆命题'''<font color="#ff8000">建构主义</font>'''是错误的。建构主义认为,在给出描述各组成部分的理论的情况下科学家可以轻易地预测复杂现象。<br />
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对称性破缺可以分为'''<font color="#ff8000">显性对称性破缺</font>'''和'''<font color="#ff8000">自发对称性破缺</font>'''两种类型,二者的区别是,在破缺对称性下系统的运动方程是否不变或者基态是否保持不变。<br />
==显性对称性破缺==<br />
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在'''<font color="#ff8000">显性对称性破缺</font>'''中,描述系统的运动方程在破缺对称下是不同的。在哈密顿力学或拉格朗日力学中,假若系统的哈密顿量(或拉格朗日量)中至少一项显性地打破了给定的对称性,就发生了显性对称性破缺。<br />
==自发对称性破缺==<br />
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在'''<font color="#ff8000">自发对称性破缺</font>'''中,系统的运动方程是不变的,但系统发生了变化。这是因为系统的背景(时空)——真空态——是非恒定的。这种对称性破缺可以用一个序参量进行参数化。这类对称破缺的一个特殊情况是'''<font color="#ff8000">动力学对称性破缺</font>'''。<br />
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Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state ends up in an asymmetric state.[1][2][3] In particular, it can describe systems where the equations of motion or the Lagrangian obey symmetries, but the lowest-energy vacuum solutions do not exhibit that same symmetry. When the system goes to one of those vacuum solutions, the symmetry is broken for perturbations around that vacuum even though the entire Lagrangian retains that symmetry.<br />
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自发对称破缺是一个自发的对称破缺过程,它使处于对称状态的物理系统最终处于非对称状态。特别地,它可以描述运动方程或拉格朗日方程服从某种对称性,但最低能量真空解不具有该对称性的系统。当系统进入其中一个真空解时,真空解周围的扰动会破坏系统对称性,尽管整个拉格朗日方程仍然保持了对称性。<br />
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==Examples 例子==<br />
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===Sombrero potential===<br />
Consider a symmetric upward dome with a trough circling the bottom. If a ball is put at the very peak of the dome, the system is symmetric with respect to a rotation around the center axis. But the ball may ''spontaneously break'' this symmetry by rolling down the dome into the trough, a point of lowest energy. Afterward, the ball has come to a rest at some fixed point on the perimeter. The dome and the ball retain their individual symmetry, but the system does not.<ref>{{cite book |first=Gerald M. |last=Edelman |title=Bright Air, Brilliant Fire: On the Matter of the Mind |location=New York |publisher=BasicBooks |year=1992 |url=https://archive.org/details/brightairbrillia00gera |url-access=registration |page=[https://archive.org/details/brightairbrillia00gera/page/203 203] }}</ref><br />
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考虑一个对称向上的圆顶,底部环绕着一个槽。如果把一个球放在圆顶的最顶端,这个系统是围绕中心轴旋转对称的。但球体可能会自发地打破这种对称性,因为它会沿着穹顶滚动到能量最低的槽中。然后,球在圆周上某个固定的点上停下来。圆顶和球保持了各自的对称,但系统却没有保持对称性。<br />
[[Image:Mexican hat potential polar.svg|270px|thumb|left|Graph of Goldstone's "[[sombrero]]" potential function <math>V(\phi)</math>.|链接=Special:FilePath/Mexican_hat_potential_polar.svg]]<br />
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In the simplest idealized relativistic model, the spontaneously broken symmetry is summarized through an illustrative [[scalar field theory]]. The relevant [[Lagrangian (field theory)|Lagrangian]] of a scalar field <math>\phi</math>, which essentially dictates how a system behaves, can be split up into kinetic and potential terms,<br />
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在最简单的理想相对论模型中,可以用一个解释性的标量场理论总结自发破对称性。一个标量场 <math>\phi</math>的拉格朗日量从本质上决定了系统的行为,它可以分解成动能项和势能项:<br />
{{NumBlk|::|<math>\mathcal{L} = \partial^\mu \phi \partial_\mu \phi - V(\phi).</math>|{{EquationRef|1}}}}<br />
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It is in this potential term <math>V(\phi)</math> that the symmetry breaking is triggered. An example of a potential, due to [[Jeffrey Goldstone]]<ref>{{Cite journal | last1 = Goldstone | first1 = J. | doi = 10.1007/BF02812722 | title = Field theories with " Superconductor " solutions | journal = Il Nuovo Cimento | volume = 19 | issue = 1 | pages = 154–164 | year = 1961 | bibcode = 1961NCim...19..154G | s2cid = 120409034 | url = http://cds.cern.ch/record/343400 }}</ref> is illustrated in the graph at the left.<br />
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正是在势能项 <math>V(\phi)</math> 中触发了对称性破缺。例如左图所示的 [[Jeffrey Goldstone]] 给出的势能函数:<br />
{{NumBlk|::|<math>V(\phi) = -5|\phi|^2 + |\phi|^4 \,</math>.|{{EquationRef|2}}}}<br />
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This potential has an infinite number of possible [[minimum|minima]] (vacuum states) given by<br />
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该是函数具有无穷数量的最小值点(真空态)当<br />
{{NumBlk|::|<math>\phi = \sqrt{5} e^{i\theta} </math>.|{{EquationRef|3}}}}<br />
for any real ''θ'' between 0 and 2''π''. The system also has an unstable vacuum state corresponding to {{nowrap|1=''Φ'' = 0}}. This state has a [[Unitary group|U(1)]] symmetry. However, once the system falls into a specific stable vacuum state (amounting to a choice of ''θ''), this symmetry will appear to be lost, or "spontaneously broken".<br />
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对于0到2π之间的任何实数θ。系统也有一个不稳定的真空状态,对应于Φ = 0。这个状态具有U(1)对称。然而,一旦系统落入某个稳定真空状态(相当于选择θ),这种对称性就会消失,或者说“自发破缺”。<br />
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In fact, any other choice of ''θ'' would have exactly the same energy, implying the existence of a massless [[Goldstone boson|Nambu–Goldstone boson]], the mode running around the circle at the minimum of this potential, and indicating there is some memory of the original symmetry in the Lagrangian.<br />
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事实上,任何其他θ的选择都将具有完全相同的能量,这意味着无质量的南部-戈德斯通玻色子的存在,这种模式在势能的最小值绕圆运动,并表明存在拉格朗日方程中原始对称性的一些记忆。<br />
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===Other examples===<br />
* For [[ferromagnet]]ic materials, the underlying laws are invariant under spatial rotations. Here, the order parameter is the [[magnetization]], which measures the magnetic dipole density. Above the [[Curie temperature]], the order parameter is zero, which is spatially invariant, and there is no symmetry breaking. Below the Curie temperature, however, the magnetization acquires a constant nonvanishing value, which points in a certain direction (in the idealized situation where we have full equilibrium; otherwise, translational symmetry gets broken as well). The residual rotational symmetries which leave the orientation of this vector invariant remain unbroken, unlike the other rotations which do not and are thus spontaneously broken.<br />
* 对于铁磁性材料,其基本定律在空间旋转下是不变的。在这里,序参量是衡量磁偶极子密度的磁化强度。在居里温度以上,序参量为零,具有空间不变性,不存在对称性破缺。然而,在居里温度以下,磁化强度变成一个恒定的非零值,指向一个特定的方向(在有充分平衡的理想情况下;否则,平移对称性也会破缺)。使该向量方向不变的旋转对称性仍然保留,而其他旋转对称性自发破缺。<br />
* The laws describing a solid are invariant under the full [[Euclidean group]], but the solid itself spontaneously breaks this group down to a [[space group]]. The displacement and the orientation are the order parameters.<br />
* 描述固体的定律在完整的欧几里得群下是不变的,但固体本身会自发地将这个群分解为一个空间群。其中位移和方向是序参量。<br />
* General relativity has a Lorentz symmetry, but in [[Friedmann–Lemaître–Robertson–Walker metric|FRW cosmological models]], the mean 4-velocity field defined by averaging over the velocities of the galaxies (the galaxies act like gas particles at cosmological scales) acts as an order parameter breaking this symmetry. Similar comments can be made about the cosmic microwave background.<br />
* 广义相对论具有洛伦兹对称性,但在FRW宇宙模型中,定义为星系速度的平均值(星系在宇宙尺度上的行为就像气体粒子) 的平均 4-速度场,作为序参量会打破这种对称性。对于宇宙微波背景辐射也有类似的评论。<br />
* For the [[electroweak]] model, as explained earlier, a component of the Higgs field provides the order parameter breaking the electroweak gauge symmetry to the electromagnetic gauge symmetry. Like the ferromagnetic example, there is a phase transition at the electroweak temperature. The same comment about us not tending to notice broken symmetries suggests why it took so long for us to discover electroweak unification.<br />
* 对于电弱模型,如前面所解释的,希格斯场的一个分量提供了将电弱规范对称性破缺到电磁规范对称性的序参量。和铁磁的例子一样,在电弱温度下也有相变。同样的关于我们不倾向于注意破缺对称性的评论,也说明了为什么我们花了这么长时间才发现电弱统一。<br />
* In superconductors, there is a condensed-matter collective field ψ, which acts as the order parameter breaking the electromagnetic gauge symmetry.<br />
* 在超导体中有一个凝聚态集体场ψ,它是打破电磁规范对称性的序参量。<br />
* Take a thin cylindrical plastic rod and push both ends together. Before buckling, the system is symmetric under rotation, and so visibly cylindrically symmetric. But after buckling, it looks different, and asymmetric. Nevertheless, features of the cylindrical symmetry are still there: ignoring friction, it would take no force to freely spin the rod around, displacing the ground state in time, and amounting to an oscillation of vanishing frequency, unlike the radial oscillations in the direction of the buckle. This spinning mode is effectively the requisite [[Goldstone boson|Nambu–Goldstone boson]].<br />
* 拿一个细长的圆柱形塑料杆,把两端推到一起。在屈曲之前,系统在旋转下是对称的,因此可见圆柱对称性。但在弯曲之后,它看起来就不同了,而且是不对称的。然而,圆柱对称性的特征仍然存在:忽略摩擦,杆可以不受外力自由地自旋,在时间上取代基态,等于一个频率趋于零的振荡,而不是沿屈曲方向的径向振荡。这种自旋模式实际上是必需的南部-戈德斯通玻色子。<br />
* Consider a uniform layer of [[fluid]] over an infinite horizontal plane. This system has all the symmetries of the Euclidean plane. But now heat the bottom surface uniformly so that it becomes much hotter than the upper surface. When the temperature gradient becomes large enough, [[convection cell]]s will form, breaking the Euclidean symmetry.<br />
* 考虑无限水平面上的一层均匀的流体。这个系统具有欧几里得平面的所有对称性。但是现在均匀地加热底部表面,使它变得比上表面热得多。当温度梯度足够大时,就会形成对流单元,打破了欧几里得对称。<br />
* Consider a bead on a circular hoop that is rotated about a vertical [[diameter]]. As the [[rotational velocity]] is increased gradually from rest, the bead will initially stay at its initial [[equilibrium point]] at the bottom of the hoop (intuitively stable, lowest [[gravitational potential]]). At a certain critical rotational velocity, this point will become unstable and the bead will jump to one of two other newly created equilibria, [[equidistant]] from the center. Initially, the system is symmetric with respect to the diameter, yet after passing the critical velocity, the bead ends up in one of the two new equilibrium points, thus breaking the symmetry.<br />
* 考虑一个围绕某个竖直的直径旋转的圆形箍上的珠子。当旋转速度从静止逐渐增加时,珠子最初会停留在环底部的初始平衡点(直观上稳定,重力势最低)。在一定的临界旋转速度下,这一点将变得不稳定,珠子将跳到另外两个新创建的离中心等距离的平衡点中的一个。起初,系统相对直径是对称的,但在通过临界速度后,珠子最终停留在两个新的平衡点中的一个,从而打破了对称性。<br />
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==Spontaneous symmetry breaking in physics 物理学中的自发对称性破缺==<br />
[[File:Spontaneous symmetry breaking (explanatory diagram).png|thumb|right|250px|''Spontaneous symmetry breaking illustrated'': At high energy levels (''left''), the ball settles in the center, and the result is symmetric. At lower energy levels (''right''), the overall "rules" remain symmetric, but the symmetric "[[sombrero|Sombrero]]" enforces an asymmetric outcome, since eventually the ball must rest at some random spot on the bottom, "spontaneously", and not all others.|链接=Special:FilePath/Spontaneous_symmetry_breaking_(explanatory_diagram).png]]<br />
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===Particle physics 粒子物理===<br />
In [[particle physics]], the [[force carrier]] particles are normally specified by field equations with [[gauge symmetry]]; their equations predict that certain measurements will be the same at any point in the field. For instance, field equations might predict that the mass of two quarks is constant. Solving the equations to find the mass of each quark might give two solutions. In one solution, quark A is heavier than quark B. In the second solution, quark B is heavier than quark A ''by the same amount''. The symmetry of the equations is not reflected by the individual solutions, but it is reflected by the range of solutions.<br />
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在粒子物理学中,载力子通常由规范对称的场方程表示;它们的方程预测到某些测量值在场的任何点上都是相同的。例如,场方程可以预测两个夸克的质量是常数。通过求解方程来求每个夸克的质量可能会得到两个解。在一个解中,夸克A比夸克B重;在第二个解中,夸克B比夸克A重相同的量。方程的对称性不是由单个解来反映的,而是由解的范围来反映的。<br />
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An actual measurement reflects only one solution, representing a breakdown in the symmetry of the underlying theory. "Hidden" is a better term than "broken", because the symmetry is always there in these equations. This phenomenon is called [[Spontaneous magnetization|''spontaneous'']] symmetry breaking (SSB) because ''nothing'' (that we know of) breaks the symmetry in the equations.<ref name="Weinberg2011">{{cite book|author=Steven Weinberg|title=Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature|url=https://books.google.com/books?id=Rsg3PE_9_ccC|date=20 April 2011|publisher=Knopf Doubleday Publishing Group|isbn=978-0-307-78786-6}}</ref>{{rp|194–195}}<br />
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一个实际的测量只反映了一个解,代表了其潜在理论的对称性的破缺。在这里“隐藏”是比“破坏”更好的术语,因为对称性总是存在于这些方程中。这种现象被称为自发对称破缺(SSB),因为(我们所知道的)没有任何东西会打破方程中的对称性。<br />
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====Chiral symmetry 手性对称性====<br />
{{Main article|Chiral symmetry breaking}}<br />
Chiral symmetry breaking is an example of spontaneous symmetry breaking affecting the [[chiral symmetry]] of the [[strong interactions]] in particle physics. It is a property of [[quantum chromodynamics]], the [[quantum field theory]] describing these interactions, and is responsible for the bulk of the mass (over 99%) of the [[nucleons]], and thus of all common matter, as it converts very light bound [[quarks]] into 100 times heavier constituents of [[baryons]]. The approximate [[Nambu–Goldstone boson]]s in this spontaneous symmetry breaking process are the [[pions]], whose mass is an order of magnitude lighter than the mass of the nucleons. It served as the prototype and significant ingredient of the Higgs mechanism underlying the electroweak symmetry breaking.<br />
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手性对称破缺是粒子物理中影响强相互作用手性对称的自发对称破缺的一个例子。手性对称性破缺是量子色动力学(描述这些相互作用的量子场理论)的一种特性,它是核子的大部分质量(超过99%)的成因,因此也是所有普通物质的主要成因,因为它将非常轻的束缚夸克转化为100倍重量的重子的成分。在这个自发对称破缺过程中,近似的南部-戈德斯通玻色子是介子,其质量比核子的质量轻一个数量级。它是电弱对称破缺的希格斯机制的原型和重要组成部分。<br />
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====Higgs mechanism 希格斯机制====<br />
{{Main article|Higgs mechanism|Yukawa interaction}}<br />
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The strong, weak, and electromagnetic forces can all be understood as arising from [[gauge symmetry|gauge symmetries]]. The [[Higgs mechanism]], the spontaneous symmetry breaking of gauge symmetries, is an important component in understanding the [[superconductivity]] of metals and the origin of particle masses in the standard model of particle physics. One important consequence of the distinction between true symmetries and ''gauge symmetries'', is that the spontaneous breaking of a gauge symmetry does not give rise to characteristic massless Nambu–Goldstone physical modes, but only massive modes, like the plasma mode in a superconductor, or the Higgs mode observed in particle physics.<br />
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强、弱和电磁力都可以理解为来自规范对称。希格斯机制,即规范对称的自发对称破缺机制,是理解金属超导性和粒子物理标准模型中粒子质量起源的重要组成部分。区分真正的对称性和规范对称性的一个重要的结果,是规范对称性的自发破缺不产生典型的无质量Nambu-Goldstone物理模式,而是只产生有质量的模式,像超导体中的等离子体模式,或者粒子物理学中观察到的希格斯模式。<br />
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In the standard model of particle physics, spontaneous symmetry breaking of the {{nowrap|SU(2) × U(1)}} gauge symmetry associated with the electro-weak force generates masses for several particles, and separates the electromagnetic and weak forces. The [[W and Z bosons]] are the elementary particles that mediate the [[weak interaction]], while the [[photon]] mediates the [[electromagnetic interaction]]. At energies much greater than 100 GeV, all these particles behave in a similar manner. The [[Unified field theory#Modern progress|Weinberg–Salam theory]] predicts that, at lower energies, this symmetry is broken so that the photon and the massive W and Z bosons emerge.<ref>A Brief History of Time, Stephen Hawking, Bantam; 10th anniversary edition (1998). pp. 73–74.{{ISBN?}}</ref> In addition, fermions develop mass consistently.<br />
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在粒子物理的标准模型中,与电弱力相关的SU(2) × U(1)规范对称性自发破缺产生多种粒子的质量,并将电磁力和弱相互作用分离。W玻色子和Z玻色子是介导弱相互作用的基本粒子,而光子介导电磁相互作用。当能量远远大于100 GeV时,所有这些粒子的行为都相似。Weinberg-Salam理论预测,在较低的能量下,这种对称性被打破,光子和大质量的W和Z玻色子就会出现。此外,费米子不断地发展质量。<br />
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Without spontaneous symmetry breaking, the [[Standard Model]] of elementary particle interactions requires the existence of a number of particles. However, some particles (the [[W and Z bosons]]) would then be predicted to be massless, when, in reality, they are observed to have mass. To overcome this, spontaneous symmetry breaking is augmented by the [[Higgs mechanism]] to give these particles mass. It also suggests the presence of a new particle, the [[Higgs boson]], detected in 2012.<br />
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在没有自发对称性破缺的情况下,基本粒子相互作用的标准模型要求存在多种粒子。然而,一些粒子(W玻色子和Z玻色子)将被预测为无质量的,而实际上它们被观察到有质量。为了克服这个问题,希格斯机制增强了自发对称破缺,从而赋予这些粒子质量。它还表明一种新粒子——希格斯玻色子——的存在,它在2012年被实验探测到。<br />
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[[Superconductivity]] of metals is a condensed-matter analog of the Higgs phenomena, in which a condensate of Cooper pairs of electrons spontaneously breaks the U(1) gauge symmetry associated with light and electromagnetism.<br />
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金属的超导性是一种类似于希格斯现象的凝聚态物质,其中库珀电子对的凝聚会自发地打破与光和电磁相关的U(1)规范对称。<br />
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===Condensed matter physics 凝聚态物理===<br />
Most phases of matter can be understood through the lens of spontaneous symmetry breaking. For example, crystals are periodic arrays of atoms that are not invariant under all translations (only under a small subset of translations by a lattice vector). Magnets have north and south poles that are oriented in a specific direction, breaking [[rotational symmetry]]. In addition to these examples, there are a whole host of other symmetry-breaking phases of matter — including nematic phases of liquid crystals, charge- and spin-density waves, superfluids, and many others.<br />
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物质的大多数相态都可以通过自发对称性破缺的透镜来理解。例如,晶体是原子的周期性排列,并非在所有平移下(仅在晶格向量平移的一个小子集下)都是不变的。磁体有朝向特定方向的南极和北极,打破了旋转对称。除了这些例子,还有一大堆其他的物质对称性破缺相——包括液晶的向列相、电荷和自旋密度波、超流体等等。<br />
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There are several known examples of matter that cannot be described by spontaneous symmetry breaking, including: topologically ordered phases of matter, such as [[Fractional quantum Hall effect|fractional quantum Hall liquids]], and [[Quantum spin liquid|spin-liquids]]. These states do not break any symmetry, but are distinct phases of matter. Unlike the case of spontaneous symmetry breaking, there is not a general framework for describing such states.<ref name=chen>{{cite journal | last1 = Chen | first1 = Xie | author-link3 = Xiao-Gang Wen | last2 = Gu | first2 = Zheng-Cheng | last3 = Wen | first3 = Xiao-Gang | year = 2010 | title = Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order | journal = Phys. Rev. B | volume = 82 | issue = 15| page = 155138 | doi=10.1103/physrevb.82.155138|arxiv = 1004.3835 |bibcode = 2010PhRvB..82o5138C | s2cid = 14593420 }}</ref><br />
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有几个已知的例子是不能用自发对称破缺来描述的,包括:物质的拓扑有序相,如分数量子霍尔液体和自旋液体。这些状态并不破坏任何对称性,然而是物质的不同相。与自发对称破缺的情况不同,没有一个描述这种状态的一般框架。<br />
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====Continuous symmetry 连续对称性====<br />
The ferromagnet is the canonical system that spontaneously breaks the continuous symmetry of the spins below the [[Curie temperature]] and at {{nowrap|1=''h'' = 0}}, where ''h'' is the external magnetic field. Below the [[Curie temperature]], the energy of the system is invariant under inversion of the magnetization ''m''('''x''') such that {{nowrap|1=''m''('''x''') = −''m''(−'''x''')}}. The symmetry is spontaneously broken as {{nowrap|''h'' → 0}} when the Hamiltonian becomes invariant under the inversion transformation, but the expectation value is not invariant.<br />
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铁磁体是正则系统,它在居里温度以下和h = 0(其中h为外部磁场)的情况下自发打破自旋的连续对称性。在居里温度以下,系统的能量在磁化强度m(x)的反转下(使m(x) =−m(−x))不变。当哈密顿量在反转变换下不变,而期望值不是恒定时,对称性在h→0时自发破坏。<br />
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Spontaneously-symmetry-broken phases of matter are characterized by an order parameter that describes the quantity which breaks the symmetry under consideration. For example, in a magnet, the order parameter is the local magnetization.<br />
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物质的自发对称性破缺相由一个序参量表征,它描述了打破所考虑的对称性的量。例如,在磁铁中,序参量是局部磁化强度。<br />
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Spontaneous breaking of a continuous symmetry is inevitably accompanied by gapless (meaning that these modes do not cost any energy to excite) Nambu–Goldstone modes associated with slow, long-wavelength fluctuations of the order parameter. For example, vibrational modes in a crystal, known as phonons, are associated with slow density fluctuations of the crystal's atoms. The associated Goldstone mode for magnets are oscillating waves of spin known as spin-waves. For symmetry-breaking states, whose order parameter is not a conserved quantity, Nambu–Goldstone modes are typically massless and propagate at a constant velocity.<br />
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连续对称的自发破缺不可避免地伴随着无间隙(意味着这些模式不需要花费任何能量来激发)南部-戈德斯通模式,它与序参量的缓慢、长波长波动有关。例如,晶体中的振动模式,即声子,与晶体原子的缓慢密度涨落有关。磁铁相关的戈德斯通模式是自旋振荡波,称为自旋波。对于序参量不是守恒量的对称性破缺态,Nambu-Goldstone模通常是无质量的,并以恒定速度传播。<br />
<br />
An important theorem, due to Mermin and Wagner, states that, at finite temperature, thermally activated fluctuations of Nambu–Goldstone modes destroy the long-range order, and prevent spontaneous symmetry breaking in one- and two-dimensional systems. Similarly, quantum fluctuations of the order parameter prevent most types of continuous symmetry breaking in one-dimensional systems even at zero temperature. (An important exception is ferromagnets, whose order parameter, magnetization, is an exactly conserved quantity and does not have any quantum fluctuations.)<br />
<br />
由Mermin和Wagner提出的一个重要定理指出,在有限温度下,热激活的南布-戈德斯通模式的扰动破坏了长程有序,并阻止了一维和二维系统中对称性的自发破缺。类似地,即使是在零温度下,序参量的量子涨落阻止了一维系统中大多数类型的连续对称破缺。(一个重要的例外是铁磁体,其序参量磁化强度是一个精确的守恒量,不存在任何量子涨落。)<br />
<br />
Other long-range interacting systems, such as cylindrical curved surfaces interacting via the [[Coulomb potential]] or [[Yukawa potential]], have been shown to break translational and rotational symmetries.<ref><br />
{{cite journal<br />
|last1=Kohlstedt |first1=K.L.<br />
|last2=Vernizzi |first2=G.<br />
|last3=Solis |first3=F.J.<br />
|last4=Olvera de la Cruz |first4=M.<br />
|year=2007<br />
|title=Spontaneous Chirality via Long-range Electrostatic Forces<br />
|journal=[[Physical Review Letters]]<br />
|volume=99 |issue=3<br />
|page=030602<br />
|doi=10.1103/PhysRevLett.99.030602<br />
|arxiv = 0704.3435 |bibcode = 2007PhRvL..99c0602K |pmid=17678276|s2cid=37983980<br />
}}</ref> It was shown, in the presence of a symmetric Hamiltonian, and in the limit of infinite volume, the system spontaneously adopts a chiral configuration — i.e., breaks [[mirror plane]] [[symmetry]].<br />
<br />
其他长程相互作用系统,如圆柱曲面通过库仑势或汤川势相互作用,已被证明打破平移和旋转对称。结果表明,在对称哈密顿量存在的情况下,在无限体积的极限下,系统自发地采用手性构型,即打破镜面对称。<br />
<br />
===Dynamical symmetry breaking 动力学对称性破缺===<br />
Dynamical symmetry breaking (DSB) is a special form of spontaneous symmetry breaking in which the ground state of the system has reduced symmetry properties compared to its theoretical description (i.e., [[Lagrangian (field theory)|Lagrangian]]).<br />
<br />
动力学对称性破缺(DSB)是自发对称性破缺的一种特殊形式,在这种情况下,系统的基态比理论描述(例如拉格朗日量)的对称性降低。<br />
<br />
Dynamical breaking of a global symmetry is a spontaneous symmetry breaking, which happens not at the (classical) tree level (i.e., at the level of the bare action), but due to quantum corrections (i.e., at the level of the [[effective action]]).<br />
<br />
全局对称性的动力学破缺是自发对称性破缺,它不是发生在(经典)树的水平(例如在bare作用的水平),而是由于量子修正(例如在有效作用的水平)。<br />
<br />
Dynamical breaking of a gauge symmetry {{ref|note1}} is subtler. In the conventional spontaneous gauge symmetry breaking, there exists an unstable [[Higgs particle]] in the theory, which drives the vacuum to a symmetry-broken phase. (See, for example, [[electroweak interaction]].) In dynamical gauge symmetry breaking, however, no unstable Higgs particle operates in the theory, but the bound states of the system itself provide the unstable fields that render the phase transition. For example, Bardeen, Hill, and Lindner published a paper that attempts to replace the conventional [[Higgs mechanism]] in the [[standard model]] by a DSB that is driven by a bound state of top-antitop quarks. (Such models, in which a composite particle plays the role of the Higgs boson, are often referred to as "Composite Higgs models".)<ref><br />
{{cite journal<br />
|author1=William A. Bardeen<br />
|author2-link=Christopher T. Hill<br />
|author2=Christopher T. Hill<br />
|author3-link=Manfred Lindner<br />
|author3=Manfred Lindner<br />
|year=1990<br />
|title=Minimal dynamical symmetry breaking of the standard model<br />
|journal=[[Physical Review D]]<br />
|volume=41 |issue=5 |pages=1647–1660<br />
|bibcode=1990PhRvD..41.1647B<br />
|doi=10.1103/PhysRevD.41.1647<br />
|pmid=10012522<br />
|author1-link=William A. Bardeen<br />
}}</ref> Dynamical breaking of gauge symmetries is often due to creation of a [[fermionic condensate]] — e.g., the [[quark condensate]], which is connected to the [[Chiral symmetry breaking|dynamical breaking of chiral symmetry]] in [[quantum chromodynamics]]. Conventional [[superconductivity]] is the paradigmatic example from the condensed matter side, where phonon-mediated attractions lead electrons to become bound in pairs and then condense, thereby breaking the electromagnetic gauge symmetry.<br />
<br />
规范对称性动力学破缺更加微妙。在常规规范对称自发破缺理论中,存在一个不稳定的希格斯粒子,希格斯粒子驱动真空进入对称破缺相。(例如,参见弱电相互作用。)然而,在规范对称性动力学破缺中,不存在不稳定的希格斯粒子,但系统本身的束缚态提供了导致相变的不稳定场。例如,巴丁、希尔和林德纳发表了一篇论文,试图用一个由顶-反顶夸克束缚状态驱动的DSB来取代标准模型中的传统希格斯机制。(在这种模型中,复合粒子扮演希格斯玻色子的角色,通常被称为“复合希格斯模型”。)规范对称性动力学破缺通常是由于费米凝聚的产生,例如夸克凝聚,它与量子色动力学中手性对称的动力学破缺有关。传统的超导性是凝聚态物质方面的典型例子,声子的吸引导致电子成对结合然后凝聚,从而打破电磁规范对称性。<br />
<br />
==Generalisation and technical usage==<br />
For spontaneous symmetry breaking to occur, there must be a system in which there are several equally likely outcomes. The system as a whole is therefore [[Symmetry (physics)|symmetric]] with respect to these outcomes. However, if the system is sampled (i.e. if the system is actually used or interacted with in any way), a specific outcome must occur. Though the system as a whole is symmetric, it is never encountered with this symmetry, but only in one specific asymmetric state. Hence, the symmetry is said to be spontaneously broken in that theory. Nevertheless, the fact that each outcome is equally likely is a reflection of the underlying symmetry, which is thus often dubbed "hidden symmetry", and has crucial formal consequences. (See the article on the [[Nambu–Goldstone boson|Goldstone boson]].)<br />
<br />
要发生自发对称性破缺,系统中必须有几个等可能的结果,整个系统相对于这些结果是对称的。然而,如果对系统进行采样(即如果系统被实际使用或以任何方式与之交互),就必须产生特定的结果。虽然系统作为一个整体是对称的,但它从来没有表现出这种对称性,而只是处于一个特定的不对称状态。于是,在该理论中对称性被自发地打破了。然而,每个结果的可能性都相等这一点,反映了潜在的对称性。因此通常被称为“隐藏对称性”,并具有重要的形式结果。(参见有关戈德斯通玻色子的文章。)<br />
<br />
When a theory is symmetric with respect to a [[symmetry group]], but requires that one element of the group be distinct, then spontaneous symmetry breaking has occurred. The theory must not dictate ''which'' member is distinct, only that ''one is''. From this point on, the theory can be treated as if this element actually is distinct, with the proviso that any results found in this way must be resymmetrized, by taking the average of each of the elements of the group being the distinct one.<br />
<br />
当一个理论相对于一个对称群是对称的,但要求群中的一个元素是不同的,那么就会发生自发对称性破缺。理论不能规定哪个成员是不同的,而只能规定那个成员是不同的。从这一点开始,这个理论就可以被视为这个元素实际上是不同的,附带的条件是,任何以这种方式发现的结果必须是重新对称的,通过取组中每个元素的平均值作为不同的元素。<br />
<br />
The crucial concept in physics theories is the [[order parameter]]. If there is a field (often a background field) which acquires an expectation value (not necessarily a [[vacuum expectation value|''vacuum'' expectation value]]) which is not invariant under the symmetry in question, we say that the system is in the [[ordered phase]], and the symmetry is spontaneously broken. This is because other subsystems interact with the order parameter, which specifies a "frame of reference" to be measured against. In that case, the [[vacuum state]] does not obey the initial symmetry (which would keep it invariant, in the linearly realized '''Wigner mode''' in which it would be a singlet), and, instead changes under the (hidden) symmetry, now implemented in the (nonlinear) '''Nambu–Goldstone mode'''. Normally, in the absence of the Higgs mechanism, massless [[Goldstone boson]]s arise.<br />
<br />
在物理理论中,最重要的概念是序参量。如果有一个场(通常是背景场)得到一个期望值(不一定是真空期望值),这个期望值在理论具有的对称性下不是不变的,我们就说系统处于有序相,对称性自发破缺。这是因为序参量指定了测量其他子系统与之相互作用的“参考框架”。在这种情况下,真空状态不服从初始对称性(这将保持它不变,在线性实现的Wigner模式中,它将是一个单线),而是在(隐藏的)对称下变化,现在在(非线性)南布-戈德斯通模式中实现。通常,在没有希格斯机制的情况下,就会出现无质量的戈德斯通玻色子。<br />
<br />
The symmetry group can be discrete, such as the [[space group]] of a crystal, or continuous (e.g., a [[Lie group]]), such as the rotational symmetry of space. However, if the system contains only a single spatial dimension, then only discrete symmetries may be broken in a [[vacuum state]] of the full [[Quantum mechanics|quantum theory]], although a classical solution may break a continuous symmetry.<br />
<br />
对称群可以是离散的,如晶体的空间群,也可以是连续的(如李群),如空间的旋转对称。然而,如果系统只包含一个空间维度,尽管经典解可能打破连续对称性,那么在全量子理论的真空状态下,只有离散的对称性可能被打破。<br />
<br />
==Nobel Prize==<br />
On October 7, 2008, the [[Royal Swedish Academy of Sciences]] awarded the 2008 [[Nobel Prize in Physics]] to three scientists for their work in subatomic physics symmetry breaking. [[Yoichiro Nambu]], of the [[University of Chicago]], won half of the prize for the discovery of the mechanism of spontaneous broken symmetry in the context of the strong interactions, specifically [[chiral symmetry breaking]]. Physicists [[Makoto Kobayashi (physicist)|Makoto Kobayashi]] and [[Toshihide Maskawa]], of [[Kyoto University]], shared the other half of the prize for discovering the origin of the [[Explicit symmetry breaking|explicit breaking]] of CP symmetry in the weak interactions.<ref>{{cite web|author=The Nobel Foundation|title=The Nobel Prize in Physics 2008|url=http://nobelprize.org/nobel_prizes/physics/laureates/2008/index.html|work=nobelprize.org|access-date=January 15, 2008}}</ref> This origin is ultimately reliant on the Higgs mechanism, but, so far understood as a "just so" feature of Higgs couplings, not a spontaneously broken symmetry phenomenon.<br />
<br />
2008年10月7日,瑞典皇家科学院(Royal Swedish Academy of Sciences)将2008年诺贝尔物理学奖授予三位科学家,以表彰他们在亚原子物理对称性破缺方面的工作。芝加哥大学的Yoichiro Nambu获得了一半的奖金,表彰他发现了在强相互作用下对称性自发破缺的机制,特别是手性对称性破缺。京都大学(Kyoto University)物理学家小林诚(Makoto Kobayashi)和正川俊英(Toshihide Maskawa)因发现了弱相互作用中CP对称性显性破缺的起源而分享了另一半奖金。这一起源最终依赖于希格斯机制,但迄今为止被理解为希格斯耦合的“恰好如此”特征,而不是一种自发的对称破缺现象。<br />
<br />
==See also==<br />
{{div col|colwidth=24em}}<br />
* [[Autocatalytic reactions and order creation]]<br />
* [[Catastrophe theory]]<br />
* [[Chiral symmetry breaking]]<br />
* [[CP-violation]]<br />
* [[Fermi ball]]<br />
* [[Gauge gravitation theory]]<br />
* [[Goldstone boson]]<br />
* [[Grand unified theory]]<br />
* [[Higgs mechanism]]<br />
* [[Higgs boson]]<br />
* [[Higgs field (classical)]]<br />
* [[Irreversibility]]<br />
* [[Magnetic catalysis]] of chiral symmetry breaking<br />
* [[Mermin–Wagner theorem]]<br />
* [[Norton's dome]]<br />
* [[Second-order phase transition]]<br />
* [[Spontaneous absolute asymmetric synthesis]] in chemistry<br />
* [[Symmetry breaking]]<br />
* [[Tachyon condensation]]<br />
* [[1964 PRL symmetry breaking papers]]<br />
{{div col end}}<br />
<br />
==Notes==<br />
* {{note|note1}} Note that (as in fundamental Higgs driven spontaneous gauge symmetry breaking) the term "symmetry breaking" is a misnomer when applied to gauge symmetries.<br />
<br />
==References==<br />
{{Reflist}}<br />
<br />
==External links==<br />
{{wikiquote}}<br />
* For a pedagogic introduction to electroweak symmetry breaking with step by step derivations, not found in texts, of many key relations, see http://www.quantumfieldtheory.info/Electroweak_Sym_breaking.pdf<br />
* [http://hyperphysics.phy-astr.gsu.edu/hbase/forces/unify.html#c2 Spontaneous symmetry breaking]<br />
* [http://prl.aps.org/50years/milestones#1964 Physical Review Letters – 50th Anniversary Milestone Papers]<br />
* [http://cerncourier.com/cws/article/cern/32522 In CERN Courier, Steven Weinberg reflects on spontaneous symmetry breaking]<br />
* [http://www.scholarpedia.org/article/Englert-Brout-Higgs-Guralnik-Hagen-Kibble_mechanism Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism on Scholarpedia]<br />
* [http://www.scholarpedia.org/article/Englert-Brout-Higgs-Guralnik-Hagen-Kibble_mechanism_%28history%29 History of Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism on Scholarpedia]<br />
* [https://arxiv.org/abs/0907.3466 The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles]<br />
* [http://www.worldscinet.com/ijmpa/24/2414/S0217751X09045431.html International Journal of Modern Physics A: The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles]<br />
* [http://www.datafilehost.com/download-7d512618.html Guralnik, G S; Hagen, C R and Kibble, T W B (1967). Broken Symmetries and the Goldstone Theorem. Advances in Physics, vol. 2 Interscience Publishers, New York. pp. 567–708] {{ISBN|0-470-17057-3}}<br />
* [http://lanl.arxiv.org/abs/hep-th/9802142 Spontaneous Symmetry Breaking in Gauge Theories: a Historical Survey]<br />
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{{Standard model of physics}}<br />
{{Quantum mechanics topics}}<br />
<br />
{{DEFAULTSORT:Spontaneous Symmetry Breaking}}<br />
[[Category:Theoretical physics]]<br />
[[Category:Quantum field theory]]<br />
[[Category:Standard Model]]<br />
[[Category:Quantum chromodynamics]]<br />
[[Category:Symmetry]]<br />
[[Category:Quantum phases]]<br />
<br />
==实例==<br />
<br />
对称性破缺可以涵盖以下任何一种情况:<ref>{{cite web|url=http://www.angelfire.com/stars5/astroinfo/gloss/s.html|title=Astronomical Glossary|author=|date=|website=www.angelfire.com}}</ref><br />
* 某些结构的随机形成破坏了物理学基本定律的精确对称性;<br />
* 物理学中最小能量状态的对称性比系统本身少的情形;<br />
* 系统的实际状态由于明显对称的状态不稳定而不能反映动力学的基本对称性的情况(稳定性是以局部不对称为代价的);<br />
* 理论方程具有某种对称性,但其解可能没有(对称性是“隐藏的”)的情况。<br />
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在物理学文献中讨论的首批对称性破缺案例之一,与不可压缩流体在重力和流体静力平衡中均匀旋转的形式有关。在1834年,Jacobi <ref>{{cite journal| last=Jacobi | first=C.G.J. | title=Über die figur des gleichgewichts | journal=[[Annalen der Physik und Chemie]] | volume=109 | issue=33| pages=229–238 | year=1834| doi=10.1002/andp.18341090808 | bibcode=1834AnP...109..229J | url=https://zenodo.org/record/2027349 }}</ref>和后来的 Liouville <ref>{{cite journal| last=Liouville | first=J. | title=Sur la figure d'une masse fluide homogène, en équilibre et douée d'un mouvement de rotation| journal=Journal de l'École Polytechnique | issue=14| pages=289–296 | year=1834}}</ref>讨论了这样一个事实: 当旋转物体的动能相对于引力势能超过一定的临界值时,这个问题的平衡解是三轴椭球。在这个分叉点上,麦克劳林椭球体的轴对称性被破坏。此外,在这个分叉点之上,对于常数角动量,使动能最小化的解是非轴对称的 Jacobi 椭球,而不是 Maclaurin 椭球。<br />
==另请参阅==<br />
<br />
*[[Higgs mechanism]]<br />
<br />
*[[QCD vacuum]]<br />
<br />
*[[Goldstone boson]]<br />
<br />
*[[1964 PRL symmetry breaking papers]]<br />
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*[[希格斯机制]]<br />
<br />
*[[QCD真空]]<br />
<br />
*[[戈德斯通玻色子]]<br />
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*[[1964年PRL对称性破缺论文]]<br />
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==参考文献==<br />
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{{reflist|colwidth=30em}}<br />
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{{DEFAULTSORT:Symmetry Breaking}}<br />
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范畴: 对称<br />
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类别: 模式形成<br />
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本中文词条由XXX编译,XXX审校,XXX总审校,西瓜编辑,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''<br />
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<noinclude><br />
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[[Category:对称性破缺]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%AF%B9%E7%A7%B0%E6%80%A7%E7%A0%B4%E7%BC%BA&diff=24824对称性破缺2021-07-27T14:38:13Z<p>Jxzhou:/* Condensed matter physics */</p>
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[[图一:一个小球位于中央山丘的山峰处(C)。这是一种不稳定平衡:一个很小的扰动会使它落到左边(L)或右边(R)稳定点。尽管山丘是对称的,没有理由让球落在哪一侧,但观察到的最终状态仍然是不对称的,它总会落到某一侧]]。<br />
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在物理学中,一个作用于系统的(无限)小扰动使系统跨过临界点,通过决定去向分叉的哪个分支来决定系统的命运,这种现象叫做'''<font color="#ff8000">对称性破缺</font>'''。对于一个观测不到扰动(或“噪声”)的外部观察者来说,这个选择看起来是任意的。这个过程被称为对称性破缺,因为这种转变通常使系统从一个对称但无序的状态进入一个或多个确定的状态。在'''<font color="#ff8000">斑图生成</font>'''中对称性破缺起着重要作用。<br />
<br />
1972年,诺贝尔奖得主P·W·安德森(P.W.Anderson)在《科学》(Science)杂志上发表了一篇名为《多即不同》的论文<ref>{{cite journal | last=Anderson | first=P.W. | title=More is Different | journal=Science | volume=177 | issue=4047| pages=393–396 | year=1972 | url=http://robotics.cs.tamu.edu/dshell/cs689/papers/anderson72more_is_different.pdf | doi=10.1126/science.177.4047.393 | pmid=17796623 | format=|bibcode = 1972Sci...177..393A }}</ref>,文中使用对称性破缺的思想表明,即使'''<font color="#ff8000">还原论</font>'''是正确的,但它的逆命题'''<font color="#ff8000">建构主义</font>'''是错误的。建构主义认为,在给出描述各组成部分的理论的情况下科学家可以轻易地预测复杂现象。<br />
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对称性破缺可以分为'''<font color="#ff8000">显性对称性破缺</font>'''和'''<font color="#ff8000">自发对称性破缺</font>'''两种类型,二者的区别是,在破缺对称性下系统的运动方程是否不变或者基态是否保持不变。<br />
==显性对称性破缺==<br />
<br />
在'''<font color="#ff8000">显性对称性破缺</font>'''中,描述系统的运动方程在破缺对称下是不同的。在哈密顿力学或拉格朗日力学中,假若系统的哈密顿量(或拉格朗日量)中至少一项显性地打破了给定的对称性,就发生了显性对称性破缺。<br />
==自发对称性破缺==<br />
<br />
在'''<font color="#ff8000">自发对称性破缺</font>'''中,系统的运动方程是不变的,但系统发生了变化。这是因为系统的背景(时空)——真空态——是非恒定的。这种对称性破缺可以用一个序参量进行参数化。这类对称破缺的一个特殊情况是'''<font color="#ff8000">动力学对称性破缺</font>'''。<br />
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Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state ends up in an asymmetric state.[1][2][3] In particular, it can describe systems where the equations of motion or the Lagrangian obey symmetries, but the lowest-energy vacuum solutions do not exhibit that same symmetry. When the system goes to one of those vacuum solutions, the symmetry is broken for perturbations around that vacuum even though the entire Lagrangian retains that symmetry.<br />
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自发对称破缺是一个自发的对称破缺过程,它使处于对称状态的物理系统最终处于非对称状态。特别地,它可以描述运动方程或拉格朗日方程服从某种对称性,但最低能量真空解不具有该对称性的系统。当系统进入其中一个真空解时,真空解周围的扰动会破坏系统对称性,尽管整个拉格朗日方程仍然保持了对称性。<br />
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==Overview==<br />
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In [[explicit symmetry breaking]], if two outcomes are considered, the probability of a pair of outcomes can be different. By definition, spontaneous symmetry breaking requires the existence of a symmetric probability distribution—any pair of outcomes has the same probability. In other words, the underlying laws{{clarify|date=December 2016}} are [[Invariant (physics)|invariant]] under a [[Symmetry (physics)|symmetry]] transformation.<br />
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The system, as a whole{{clarify|date=December 2016}}, changes under such transformations.<br />
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Phases of matter, such as crystals, magnets, and conventional superconductors, as well as simple phase transitions can be described by spontaneous symmetry breaking. Notable exceptions include topological phases of matter like the [[fractional quantum Hall effect]].<br />
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==Examples 例子==<br />
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===Sombrero potential===<br />
Consider a symmetric upward dome with a trough circling the bottom. If a ball is put at the very peak of the dome, the system is symmetric with respect to a rotation around the center axis. But the ball may ''spontaneously break'' this symmetry by rolling down the dome into the trough, a point of lowest energy. Afterward, the ball has come to a rest at some fixed point on the perimeter. The dome and the ball retain their individual symmetry, but the system does not.<ref>{{cite book |first=Gerald M. |last=Edelman |title=Bright Air, Brilliant Fire: On the Matter of the Mind |location=New York |publisher=BasicBooks |year=1992 |url=https://archive.org/details/brightairbrillia00gera |url-access=registration |page=[https://archive.org/details/brightairbrillia00gera/page/203 203] }}</ref><br />
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考虑一个对称向上的圆顶,底部环绕着一个槽。如果把一个球放在圆顶的最顶端,这个系统是围绕中心轴旋转对称的。但球体可能会自发地打破这种对称性,因为它会沿着穹顶滚动到能量最低的槽中。然后,球在圆周上某个固定的点上停下来。圆顶和球保持了各自的对称,但系统却没有保持对称性。<br />
[[Image:Mexican hat potential polar.svg|270px|thumb|left|Graph of Goldstone's "[[sombrero]]" potential function <math>V(\phi)</math>.|链接=Special:FilePath/Mexican_hat_potential_polar.svg]]<br />
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In the simplest idealized relativistic model, the spontaneously broken symmetry is summarized through an illustrative [[scalar field theory]]. The relevant [[Lagrangian (field theory)|Lagrangian]] of a scalar field <math>\phi</math>, which essentially dictates how a system behaves, can be split up into kinetic and potential terms,<br />
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在最简单的理想相对论模型中,可以用一个解释性的标量场理论总结自发破对称性。一个标量场 <math>\phi</math>的拉格朗日量从本质上决定了系统的行为,它可以分解成动能项和势能项:<br />
{{NumBlk|::|<math>\mathcal{L} = \partial^\mu \phi \partial_\mu \phi - V(\phi).</math>|{{EquationRef|1}}}}<br />
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It is in this potential term <math>V(\phi)</math> that the symmetry breaking is triggered. An example of a potential, due to [[Jeffrey Goldstone]]<ref>{{Cite journal | last1 = Goldstone | first1 = J. | doi = 10.1007/BF02812722 | title = Field theories with " Superconductor " solutions | journal = Il Nuovo Cimento | volume = 19 | issue = 1 | pages = 154–164 | year = 1961 | bibcode = 1961NCim...19..154G | s2cid = 120409034 | url = http://cds.cern.ch/record/343400 }}</ref> is illustrated in the graph at the left.<br />
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正是在势能项 <math>V(\phi)</math> 中触发了对称性破缺。例如左图所示的 [[Jeffrey Goldstone]] 给出的势能函数:<br />
{{NumBlk|::|<math>V(\phi) = -5|\phi|^2 + |\phi|^4 \,</math>.|{{EquationRef|2}}}}<br />
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This potential has an infinite number of possible [[minimum|minima]] (vacuum states) given by<br />
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该是函数具有无穷数量的最小值点(真空态)当<br />
{{NumBlk|::|<math>\phi = \sqrt{5} e^{i\theta} </math>.|{{EquationRef|3}}}}<br />
for any real ''θ'' between 0 and 2''π''. The system also has an unstable vacuum state corresponding to {{nowrap|1=''Φ'' = 0}}. This state has a [[Unitary group|U(1)]] symmetry. However, once the system falls into a specific stable vacuum state (amounting to a choice of ''θ''), this symmetry will appear to be lost, or "spontaneously broken".<br />
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对于0到2π之间的任何实数θ。系统也有一个不稳定的真空状态,对应于Φ = 0。这个状态具有U(1)对称。然而,一旦系统落入某个稳定真空状态(相当于选择θ),这种对称性就会消失,或者说“自发破缺”。<br />
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In fact, any other choice of ''θ'' would have exactly the same energy, implying the existence of a massless [[Goldstone boson|Nambu–Goldstone boson]], the mode running around the circle at the minimum of this potential, and indicating there is some memory of the original symmetry in the Lagrangian.<br />
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事实上,任何其他θ的选择都将具有完全相同的能量,这意味着无质量的南部-戈德斯通玻色子的存在,这种模式在势能的最小值绕圆运动,并表明存在拉格朗日方程中原始对称性的一些记忆。<br />
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===Other examples===<br />
* For [[ferromagnet]]ic materials, the underlying laws are invariant under spatial rotations. Here, the order parameter is the [[magnetization]], which measures the magnetic dipole density. Above the [[Curie temperature]], the order parameter is zero, which is spatially invariant, and there is no symmetry breaking. Below the Curie temperature, however, the magnetization acquires a constant nonvanishing value, which points in a certain direction (in the idealized situation where we have full equilibrium; otherwise, translational symmetry gets broken as well). The residual rotational symmetries which leave the orientation of this vector invariant remain unbroken, unlike the other rotations which do not and are thus spontaneously broken.<br />
* 对于铁磁性材料,其基本定律在空间旋转下是不变的。在这里,序参量是衡量磁偶极子密度的磁化强度。在居里温度以上,序参量为零,具有空间不变性,不存在对称性破缺。然而,在居里温度以下,磁化强度变成一个恒定的非零值,指向一个特定的方向(在有充分平衡的理想情况下;否则,平移对称性也会破缺)。使该向量方向不变的旋转对称性仍然保留,而其他旋转对称性自发破缺。<br />
* The laws describing a solid are invariant under the full [[Euclidean group]], but the solid itself spontaneously breaks this group down to a [[space group]]. The displacement and the orientation are the order parameters.<br />
* 描述固体的定律在完整的欧几里得群下是不变的,但固体本身会自发地将这个群分解为一个空间群。其中位移和方向是序参量。<br />
* General relativity has a Lorentz symmetry, but in [[Friedmann–Lemaître–Robertson–Walker metric|FRW cosmological models]], the mean 4-velocity field defined by averaging over the velocities of the galaxies (the galaxies act like gas particles at cosmological scales) acts as an order parameter breaking this symmetry. Similar comments can be made about the cosmic microwave background.<br />
* 广义相对论具有洛伦兹对称性,但在FRW宇宙模型中,定义为星系速度的平均值(星系在宇宙尺度上的行为就像气体粒子) 的平均 4-速度场,作为序参量会打破这种对称性。对于宇宙微波背景辐射也有类似的评论。<br />
* For the [[electroweak]] model, as explained earlier, a component of the Higgs field provides the order parameter breaking the electroweak gauge symmetry to the electromagnetic gauge symmetry. Like the ferromagnetic example, there is a phase transition at the electroweak temperature. The same comment about us not tending to notice broken symmetries suggests why it took so long for us to discover electroweak unification.<br />
* 对于电弱模型,如前面所解释的,希格斯场的一个分量提供了将电弱规范对称性破缺到电磁规范对称性的序参量。和铁磁的例子一样,在电弱温度下也有相变。同样的关于我们不倾向于注意破缺对称性的评论,也说明了为什么我们花了这么长时间才发现电弱统一。<br />
* In superconductors, there is a condensed-matter collective field ψ, which acts as the order parameter breaking the electromagnetic gauge symmetry.<br />
* 在超导体中有一个凝聚态集体场ψ,它是打破电磁规范对称性的序参量。<br />
* Take a thin cylindrical plastic rod and push both ends together. Before buckling, the system is symmetric under rotation, and so visibly cylindrically symmetric. But after buckling, it looks different, and asymmetric. Nevertheless, features of the cylindrical symmetry are still there: ignoring friction, it would take no force to freely spin the rod around, displacing the ground state in time, and amounting to an oscillation of vanishing frequency, unlike the radial oscillations in the direction of the buckle. This spinning mode is effectively the requisite [[Goldstone boson|Nambu–Goldstone boson]].<br />
* 拿一个细长的圆柱形塑料杆,把两端推到一起。在屈曲之前,系统在旋转下是对称的,因此可见圆柱对称性。但在弯曲之后,它看起来就不同了,而且是不对称的。然而,圆柱对称性的特征仍然存在:忽略摩擦,杆可以不受外力自由地自旋,在时间上取代基态,等于一个频率趋于零的振荡,而不是沿屈曲方向的径向振荡。这种自旋模式实际上是必需的南部-戈德斯通玻色子。<br />
* Consider a uniform layer of [[fluid]] over an infinite horizontal plane. This system has all the symmetries of the Euclidean plane. But now heat the bottom surface uniformly so that it becomes much hotter than the upper surface. When the temperature gradient becomes large enough, [[convection cell]]s will form, breaking the Euclidean symmetry.<br />
* 考虑无限水平面上的一层均匀的流体。这个系统具有欧几里得平面的所有对称性。但是现在均匀地加热底部表面,使它变得比上表面热得多。当温度梯度足够大时,就会形成对流单元,打破了欧几里得对称。<br />
* Consider a bead on a circular hoop that is rotated about a vertical [[diameter]]. As the [[rotational velocity]] is increased gradually from rest, the bead will initially stay at its initial [[equilibrium point]] at the bottom of the hoop (intuitively stable, lowest [[gravitational potential]]). At a certain critical rotational velocity, this point will become unstable and the bead will jump to one of two other newly created equilibria, [[equidistant]] from the center. Initially, the system is symmetric with respect to the diameter, yet after passing the critical velocity, the bead ends up in one of the two new equilibrium points, thus breaking the symmetry.<br />
* 考虑一个围绕某个竖直的直径旋转的圆形箍上的珠子。当旋转速度从静止逐渐增加时,珠子最初会停留在环底部的初始平衡点(直观上稳定,重力势最低)。在一定的临界旋转速度下,这一点将变得不稳定,珠子将跳到另外两个新创建的离中心等距离的平衡点中的一个。起初,系统相对直径是对称的,但在通过临界速度后,珠子最终停留在两个新的平衡点中的一个,从而打破了对称性。<br />
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==Spontaneous symmetry breaking in physics 物理学中的自发对称性破缺==<br />
[[File:Spontaneous symmetry breaking (explanatory diagram).png|thumb|right|250px|''Spontaneous symmetry breaking illustrated'': At high energy levels (''left''), the ball settles in the center, and the result is symmetric. At lower energy levels (''right''), the overall "rules" remain symmetric, but the symmetric "[[sombrero|Sombrero]]" enforces an asymmetric outcome, since eventually the ball must rest at some random spot on the bottom, "spontaneously", and not all others.|链接=Special:FilePath/Spontaneous_symmetry_breaking_(explanatory_diagram).png]]<br />
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===Particle physics 粒子物理===<br />
In [[particle physics]], the [[force carrier]] particles are normally specified by field equations with [[gauge symmetry]]; their equations predict that certain measurements will be the same at any point in the field. For instance, field equations might predict that the mass of two quarks is constant. Solving the equations to find the mass of each quark might give two solutions. In one solution, quark A is heavier than quark B. In the second solution, quark B is heavier than quark A ''by the same amount''. The symmetry of the equations is not reflected by the individual solutions, but it is reflected by the range of solutions.<br />
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在粒子物理学中,载力子通常由规范对称的场方程表示;它们的方程预测到某些测量值在场的任何点上都是相同的。例如,场方程可以预测两个夸克的质量是常数。通过求解方程来求每个夸克的质量可能会得到两个解。在一个解中,夸克A比夸克B重;在第二个解中,夸克B比夸克A重相同的量。方程的对称性不是由单个解来反映的,而是由解的范围来反映的。<br />
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An actual measurement reflects only one solution, representing a breakdown in the symmetry of the underlying theory. "Hidden" is a better term than "broken", because the symmetry is always there in these equations. This phenomenon is called [[Spontaneous magnetization|''spontaneous'']] symmetry breaking (SSB) because ''nothing'' (that we know of) breaks the symmetry in the equations.<ref name="Weinberg2011">{{cite book|author=Steven Weinberg|title=Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature|url=https://books.google.com/books?id=Rsg3PE_9_ccC|date=20 April 2011|publisher=Knopf Doubleday Publishing Group|isbn=978-0-307-78786-6}}</ref>{{rp|194–195}}<br />
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一个实际的测量只反映了一个解,代表了其潜在理论的对称性的破缺。在这里“隐藏”是比“破坏”更好的术语,因为对称性总是存在于这些方程中。这种现象被称为自发对称破缺(SSB),因为(我们所知道的)没有任何东西会打破方程中的对称性。<br />
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====Chiral symmetry 手性对称性====<br />
{{Main article|Chiral symmetry breaking}}<br />
Chiral symmetry breaking is an example of spontaneous symmetry breaking affecting the [[chiral symmetry]] of the [[strong interactions]] in particle physics. It is a property of [[quantum chromodynamics]], the [[quantum field theory]] describing these interactions, and is responsible for the bulk of the mass (over 99%) of the [[nucleons]], and thus of all common matter, as it converts very light bound [[quarks]] into 100 times heavier constituents of [[baryons]]. The approximate [[Nambu–Goldstone boson]]s in this spontaneous symmetry breaking process are the [[pions]], whose mass is an order of magnitude lighter than the mass of the nucleons. It served as the prototype and significant ingredient of the Higgs mechanism underlying the electroweak symmetry breaking.<br />
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手性对称破缺是粒子物理中影响强相互作用手性对称的自发对称破缺的一个例子。手性对称性破缺是量子色动力学(描述这些相互作用的量子场理论)的一种特性,它是核子的大部分质量(超过99%)的成因,因此也是所有普通物质的主要成因,因为它将非常轻的束缚夸克转化为100倍重量的重子的成分。在这个自发对称破缺过程中,近似的南部-戈德斯通玻色子是介子,其质量比核子的质量轻一个数量级。它是电弱对称破缺的希格斯机制的原型和重要组成部分。<br />
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====Higgs mechanism 希格斯机制====<br />
{{Main article|Higgs mechanism|Yukawa interaction}}<br />
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The strong, weak, and electromagnetic forces can all be understood as arising from [[gauge symmetry|gauge symmetries]]. The [[Higgs mechanism]], the spontaneous symmetry breaking of gauge symmetries, is an important component in understanding the [[superconductivity]] of metals and the origin of particle masses in the standard model of particle physics. One important consequence of the distinction between true symmetries and ''gauge symmetries'', is that the spontaneous breaking of a gauge symmetry does not give rise to characteristic massless Nambu–Goldstone physical modes, but only massive modes, like the plasma mode in a superconductor, or the Higgs mode observed in particle physics.<br />
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强、弱和电磁力都可以理解为来自规范对称。希格斯机制,即规范对称的自发对称破缺机制,是理解金属超导性和粒子物理标准模型中粒子质量起源的重要组成部分。区分真正的对称性和规范对称性的一个重要的结果,是规范对称性的自发破缺不产生典型的无质量Nambu-Goldstone物理模式,而是只产生有质量的模式,像超导体中的等离子体模式,或者粒子物理学中观察到的希格斯模式。<br />
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In the standard model of particle physics, spontaneous symmetry breaking of the {{nowrap|SU(2) × U(1)}} gauge symmetry associated with the electro-weak force generates masses for several particles, and separates the electromagnetic and weak forces. The [[W and Z bosons]] are the elementary particles that mediate the [[weak interaction]], while the [[photon]] mediates the [[electromagnetic interaction]]. At energies much greater than 100 GeV, all these particles behave in a similar manner. The [[Unified field theory#Modern progress|Weinberg–Salam theory]] predicts that, at lower energies, this symmetry is broken so that the photon and the massive W and Z bosons emerge.<ref>A Brief History of Time, Stephen Hawking, Bantam; 10th anniversary edition (1998). pp. 73–74.{{ISBN?}}</ref> In addition, fermions develop mass consistently.<br />
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在粒子物理的标准模型中,与电弱力相关的SU(2) × U(1)规范对称性自发破缺产生多种粒子的质量,并将电磁力和弱相互作用分离。W玻色子和Z玻色子是介导弱相互作用的基本粒子,而光子介导电磁相互作用。当能量远远大于100 GeV时,所有这些粒子的行为都相似。Weinberg-Salam理论预测,在较低的能量下,这种对称性被打破,光子和大质量的W和Z玻色子就会出现。此外,费米子不断地发展质量。<br />
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Without spontaneous symmetry breaking, the [[Standard Model]] of elementary particle interactions requires the existence of a number of particles. However, some particles (the [[W and Z bosons]]) would then be predicted to be massless, when, in reality, they are observed to have mass. To overcome this, spontaneous symmetry breaking is augmented by the [[Higgs mechanism]] to give these particles mass. It also suggests the presence of a new particle, the [[Higgs boson]], detected in 2012.<br />
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在没有自发对称性破缺的情况下,基本粒子相互作用的标准模型要求存在多种粒子。然而,一些粒子(W玻色子和Z玻色子)将被预测为无质量的,而实际上它们被观察到有质量。为了克服这个问题,希格斯机制增强了自发对称破缺,从而赋予这些粒子质量。它还表明一种新粒子——希格斯玻色子——的存在,它在2012年被实验探测到。<br />
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[[Superconductivity]] of metals is a condensed-matter analog of the Higgs phenomena, in which a condensate of Cooper pairs of electrons spontaneously breaks the U(1) gauge symmetry associated with light and electromagnetism.<br />
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金属的超导性是一种类似于希格斯现象的凝聚态物质,其中库珀电子对的凝聚会自发地打破与光和电磁相关的U(1)规范对称。<br />
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===Condensed matter physics 凝聚态物理===<br />
Most phases of matter can be understood through the lens of spontaneous symmetry breaking. For example, crystals are periodic arrays of atoms that are not invariant under all translations (only under a small subset of translations by a lattice vector). Magnets have north and south poles that are oriented in a specific direction, breaking [[rotational symmetry]]. In addition to these examples, there are a whole host of other symmetry-breaking phases of matter — including nematic phases of liquid crystals, charge- and spin-density waves, superfluids, and many others.<br />
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物质的大多数相态都可以通过自发对称性破缺的透镜来理解。例如,晶体是原子的周期性排列,并非在所有平移下(仅在晶格向量平移的一个小子集下)都是不变的。磁体有朝向特定方向的南极和北极,打破了旋转对称。除了这些例子,还有一大堆其他的物质对称性破缺相——包括液晶的向列相、电荷和自旋密度波、超流体等等。<br />
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There are several known examples of matter that cannot be described by spontaneous symmetry breaking, including: topologically ordered phases of matter, such as [[Fractional quantum Hall effect|fractional quantum Hall liquids]], and [[Quantum spin liquid|spin-liquids]]. These states do not break any symmetry, but are distinct phases of matter. Unlike the case of spontaneous symmetry breaking, there is not a general framework for describing such states.<ref name=chen>{{cite journal | last1 = Chen | first1 = Xie | author-link3 = Xiao-Gang Wen | last2 = Gu | first2 = Zheng-Cheng | last3 = Wen | first3 = Xiao-Gang | year = 2010 | title = Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order | journal = Phys. Rev. B | volume = 82 | issue = 15| page = 155138 | doi=10.1103/physrevb.82.155138|arxiv = 1004.3835 |bibcode = 2010PhRvB..82o5138C | s2cid = 14593420 }}</ref><br />
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有几个已知的例子是不能用自发对称破缺来描述的,包括:物质的拓扑有序相,如分数量子霍尔液体和自旋液体。这些状态并不破坏任何对称性,然而是物质的不同相。与自发对称破缺的情况不同,没有一个描述这种状态的一般框架。<br />
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====Continuous symmetry 连续对称性====<br />
The ferromagnet is the canonical system that spontaneously breaks the continuous symmetry of the spins below the [[Curie temperature]] and at {{nowrap|1=''h'' = 0}}, where ''h'' is the external magnetic field. Below the [[Curie temperature]], the energy of the system is invariant under inversion of the magnetization ''m''('''x''') such that {{nowrap|1=''m''('''x''') = −''m''(−'''x''')}}. The symmetry is spontaneously broken as {{nowrap|''h'' → 0}} when the Hamiltonian becomes invariant under the inversion transformation, but the expectation value is not invariant.<br />
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铁磁体是正则系统,它在居里温度以下和h = 0(其中h为外部磁场)的情况下自发打破自旋的连续对称性。在居里温度以下,系统的能量在磁化强度m(x)的反转下(使m(x) =−m(−x))不变。当哈密顿量在反转变换下不变,而期望值不是恒定时,对称性在h→0时自发破坏。<br />
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Spontaneously-symmetry-broken phases of matter are characterized by an order parameter that describes the quantity which breaks the symmetry under consideration. For example, in a magnet, the order parameter is the local magnetization.<br />
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物质的自发对称性破缺相由一个序参量表征,它描述了打破所考虑的对称性的量。例如,在磁铁中,序参量是局部磁化强度。<br />
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Spontaneous breaking of a continuous symmetry is inevitably accompanied by gapless (meaning that these modes do not cost any energy to excite) Nambu–Goldstone modes associated with slow, long-wavelength fluctuations of the order parameter. For example, vibrational modes in a crystal, known as phonons, are associated with slow density fluctuations of the crystal's atoms. The associated Goldstone mode for magnets are oscillating waves of spin known as spin-waves. For symmetry-breaking states, whose order parameter is not a conserved quantity, Nambu–Goldstone modes are typically massless and propagate at a constant velocity.<br />
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连续对称的自发破缺不可避免地伴随着无间隙(意味着这些模式不需要花费任何能量来激发)南部-戈德斯通模式,它与序参量的缓慢、长波长波动有关。例如,晶体中的振动模式,即声子,与晶体原子的缓慢密度涨落有关。磁铁相关的戈德斯通模式是自旋振荡波,称为自旋波。对于序参量不是守恒量的对称性破缺态,Nambu-Goldstone模通常是无质量的,并以恒定速度传播。<br />
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An important theorem, due to Mermin and Wagner, states that, at finite temperature, thermally activated fluctuations of Nambu–Goldstone modes destroy the long-range order, and prevent spontaneous symmetry breaking in one- and two-dimensional systems. Similarly, quantum fluctuations of the order parameter prevent most types of continuous symmetry breaking in one-dimensional systems even at zero temperature. (An important exception is ferromagnets, whose order parameter, magnetization, is an exactly conserved quantity and does not have any quantum fluctuations.)<br />
<br />
由Mermin和Wagner提出的一个重要定理指出,在有限温度下,热激活的南布-戈德斯通模式的扰动破坏了长程有序,并阻止了一维和二维系统中对称性的自发破缺。类似地,即使是在零温度下,序参量的量子涨落阻止了一维系统中大多数类型的连续对称破缺。(一个重要的例外是铁磁体,其序参量磁化强度是一个精确的守恒量,不存在任何量子涨落。)<br />
<br />
Other long-range interacting systems, such as cylindrical curved surfaces interacting via the [[Coulomb potential]] or [[Yukawa potential]], have been shown to break translational and rotational symmetries.<ref><br />
{{cite journal<br />
|last1=Kohlstedt |first1=K.L.<br />
|last2=Vernizzi |first2=G.<br />
|last3=Solis |first3=F.J.<br />
|last4=Olvera de la Cruz |first4=M.<br />
|year=2007<br />
|title=Spontaneous Chirality via Long-range Electrostatic Forces<br />
|journal=[[Physical Review Letters]]<br />
|volume=99 |issue=3<br />
|page=030602<br />
|doi=10.1103/PhysRevLett.99.030602<br />
|arxiv = 0704.3435 |bibcode = 2007PhRvL..99c0602K |pmid=17678276|s2cid=37983980<br />
}}</ref> It was shown, in the presence of a symmetric Hamiltonian, and in the limit of infinite volume, the system spontaneously adopts a chiral configuration — i.e., breaks [[mirror plane]] [[symmetry]].<br />
<br />
其他长程相互作用系统,如圆柱曲面通过库仑势或汤川势相互作用,已被证明打破平移和旋转对称。结果表明,在对称哈密顿量存在的情况下,在无限体积的极限下,系统自发地采用手性构型,即打破镜面对称。<br />
<br />
===Dynamical symmetry breaking 动力学对称性破缺===<br />
Dynamical symmetry breaking (DSB) is a special form of spontaneous symmetry breaking in which the ground state of the system has reduced symmetry properties compared to its theoretical description (i.e., [[Lagrangian (field theory)|Lagrangian]]).<br />
<br />
动力学对称性破缺(DSB)是自发对称性破缺的一种特殊形式,在这种情况下,系统的基态比理论描述(例如拉格朗日量)的对称性降低。<br />
<br />
Dynamical breaking of a global symmetry is a spontaneous symmetry breaking, which happens not at the (classical) tree level (i.e., at the level of the bare action), but due to quantum corrections (i.e., at the level of the [[effective action]]).<br />
<br />
全局对称性的动力学破缺是自发对称性破缺,它不是发生在(经典)树的水平(例如在bare作用的水平),而是由于量子修正(例如在有效作用的水平)。<br />
<br />
Dynamical breaking of a gauge symmetry {{ref|note1}} is subtler. In the conventional spontaneous gauge symmetry breaking, there exists an unstable [[Higgs particle]] in the theory, which drives the vacuum to a symmetry-broken phase. (See, for example, [[electroweak interaction]].) In dynamical gauge symmetry breaking, however, no unstable Higgs particle operates in the theory, but the bound states of the system itself provide the unstable fields that render the phase transition. For example, Bardeen, Hill, and Lindner published a paper that attempts to replace the conventional [[Higgs mechanism]] in the [[standard model]] by a DSB that is driven by a bound state of top-antitop quarks. (Such models, in which a composite particle plays the role of the Higgs boson, are often referred to as "Composite Higgs models".)<ref><br />
{{cite journal<br />
|author1=William A. Bardeen<br />
|author2-link=Christopher T. Hill<br />
|author2=Christopher T. Hill<br />
|author3-link=Manfred Lindner<br />
|author3=Manfred Lindner<br />
|year=1990<br />
|title=Minimal dynamical symmetry breaking of the standard model<br />
|journal=[[Physical Review D]]<br />
|volume=41 |issue=5 |pages=1647–1660<br />
|bibcode=1990PhRvD..41.1647B<br />
|doi=10.1103/PhysRevD.41.1647<br />
|pmid=10012522<br />
|author1-link=William A. Bardeen<br />
}}</ref> Dynamical breaking of gauge symmetries is often due to creation of a [[fermionic condensate]] — e.g., the [[quark condensate]], which is connected to the [[Chiral symmetry breaking|dynamical breaking of chiral symmetry]] in [[quantum chromodynamics]]. Conventional [[superconductivity]] is the paradigmatic example from the condensed matter side, where phonon-mediated attractions lead electrons to become bound in pairs and then condense, thereby breaking the electromagnetic gauge symmetry.<br />
<br />
规范对称性动力学破缺更加微妙。在常规规范对称自发破缺理论中,存在一个不稳定的希格斯粒子,希格斯粒子驱动真空进入对称破缺相。(例如,参见弱电相互作用。)然而,在规范对称性动力学破缺中,不存在不稳定的希格斯粒子,但系统本身的束缚态提供了导致相变的不稳定场。例如,巴丁、希尔和林德纳发表了一篇论文,试图用一个由顶-反顶夸克束缚状态驱动的DSB来取代标准模型中的传统希格斯机制。(在这种模型中,复合粒子扮演希格斯玻色子的角色,通常被称为“复合希格斯模型”。)规范对称性动力学破缺通常是由于费米凝聚的产生,例如夸克凝聚,它与量子色动力学中手性对称的动力学破缺有关。传统的超导性是凝聚态物质方面的典型例子,声子的吸引导致电子成对结合然后凝聚,从而打破电磁规范对称性。<br />
<br />
==Generalisation and technical usage==<br />
For spontaneous symmetry breaking to occur, there must be a system in which there are several equally likely outcomes. The system as a whole is therefore [[Symmetry (physics)|symmetric]] with respect to these outcomes. However, if the system is sampled (i.e. if the system is actually used or interacted with in any way), a specific outcome must occur. Though the system as a whole is symmetric, it is never encountered with this symmetry, but only in one specific asymmetric state. Hence, the symmetry is said to be spontaneously broken in that theory. Nevertheless, the fact that each outcome is equally likely is a reflection of the underlying symmetry, which is thus often dubbed "hidden symmetry", and has crucial formal consequences. (See the article on the [[Nambu–Goldstone boson|Goldstone boson]].)<br />
<br />
要发生自发对称性破缺,系统中必须有几个等可能的结果,整个系统相对于这些结果是对称的。然而,如果对系统进行采样(即如果系统被实际使用或以任何方式与之交互),就必须产生特定的结果。虽然系统作为一个整体是对称的,但它从来没有表现出这种对称性,而只是处于一个特定的不对称状态。于是,在该理论中对称性被自发地打破了。然而,每个结果的可能性都相等这一点,反映了潜在的对称性。因此通常被称为“隐藏对称性”,并具有重要的形式结果。(参见有关戈德斯通玻色子的文章。)<br />
<br />
When a theory is symmetric with respect to a [[symmetry group]], but requires that one element of the group be distinct, then spontaneous symmetry breaking has occurred. The theory must not dictate ''which'' member is distinct, only that ''one is''. From this point on, the theory can be treated as if this element actually is distinct, with the proviso that any results found in this way must be resymmetrized, by taking the average of each of the elements of the group being the distinct one.<br />
<br />
当一个理论相对于一个对称群是对称的,但要求群中的一个元素是不同的,那么就会发生自发对称性破缺。理论不能规定哪个成员是不同的,而只能规定那个成员是不同的。从这一点开始,这个理论就可以被视为这个元素实际上是不同的,附带的条件是,任何以这种方式发现的结果必须是重新对称的,通过取组中每个元素的平均值作为不同的元素。<br />
<br />
The crucial concept in physics theories is the [[order parameter]]. If there is a field (often a background field) which acquires an expectation value (not necessarily a [[vacuum expectation value|''vacuum'' expectation value]]) which is not invariant under the symmetry in question, we say that the system is in the [[ordered phase]], and the symmetry is spontaneously broken. This is because other subsystems interact with the order parameter, which specifies a "frame of reference" to be measured against. In that case, the [[vacuum state]] does not obey the initial symmetry (which would keep it invariant, in the linearly realized '''Wigner mode''' in which it would be a singlet), and, instead changes under the (hidden) symmetry, now implemented in the (nonlinear) '''Nambu–Goldstone mode'''. Normally, in the absence of the Higgs mechanism, massless [[Goldstone boson]]s arise.<br />
<br />
在物理理论中,最重要的概念是序参量。如果有一个场(通常是背景场)得到一个期望值(不一定是真空期望值),这个期望值在理论具有的对称性下不是不变的,我们就说系统处于有序相,对称性自发破缺。这是因为序参量指定了测量其他子系统与之相互作用的“参考框架”。在这种情况下,真空状态不服从初始对称性(这将保持它不变,在线性实现的Wigner模式中,它将是一个单线),而是在(隐藏的)对称下变化,现在在(非线性)南布-戈德斯通模式中实现。通常,在没有希格斯机制的情况下,就会出现无质量的戈德斯通玻色子。<br />
<br />
The symmetry group can be discrete, such as the [[space group]] of a crystal, or continuous (e.g., a [[Lie group]]), such as the rotational symmetry of space. However, if the system contains only a single spatial dimension, then only discrete symmetries may be broken in a [[vacuum state]] of the full [[Quantum mechanics|quantum theory]], although a classical solution may break a continuous symmetry.<br />
<br />
对称群可以是离散的,如晶体的空间群,也可以是连续的(如李群),如空间的旋转对称。然而,如果系统只包含一个空间维度,尽管经典解可能打破连续对称性,那么在全量子理论的真空状态下,只有离散的对称性可能被打破。<br />
<br />
==Nobel Prize==<br />
On October 7, 2008, the [[Royal Swedish Academy of Sciences]] awarded the 2008 [[Nobel Prize in Physics]] to three scientists for their work in subatomic physics symmetry breaking. [[Yoichiro Nambu]], of the [[University of Chicago]], won half of the prize for the discovery of the mechanism of spontaneous broken symmetry in the context of the strong interactions, specifically [[chiral symmetry breaking]]. Physicists [[Makoto Kobayashi (physicist)|Makoto Kobayashi]] and [[Toshihide Maskawa]], of [[Kyoto University]], shared the other half of the prize for discovering the origin of the [[Explicit symmetry breaking|explicit breaking]] of CP symmetry in the weak interactions.<ref>{{cite web|author=The Nobel Foundation|title=The Nobel Prize in Physics 2008|url=http://nobelprize.org/nobel_prizes/physics/laureates/2008/index.html|work=nobelprize.org|access-date=January 15, 2008}}</ref> This origin is ultimately reliant on the Higgs mechanism, but, so far understood as a "just so" feature of Higgs couplings, not a spontaneously broken symmetry phenomenon.<br />
<br />
2008年10月7日,瑞典皇家科学院(Royal Swedish Academy of Sciences)将2008年诺贝尔物理学奖授予三位科学家,以表彰他们在亚原子物理对称性破缺方面的工作。芝加哥大学的Yoichiro Nambu获得了一半的奖金,表彰他发现了在强相互作用下对称性自发破缺的机制,特别是手性对称性破缺。京都大学(Kyoto University)物理学家小林诚(Makoto Kobayashi)和正川俊英(Toshihide Maskawa)因发现了弱相互作用中CP对称性显性破缺的起源而分享了另一半奖金。这一起源最终依赖于希格斯机制,但迄今为止被理解为希格斯耦合的“恰好如此”特征,而不是一种自发的对称破缺现象。<br />
<br />
==See also==<br />
{{div col|colwidth=24em}}<br />
* [[Autocatalytic reactions and order creation]]<br />
* [[Catastrophe theory]]<br />
* [[Chiral symmetry breaking]]<br />
* [[CP-violation]]<br />
* [[Fermi ball]]<br />
* [[Gauge gravitation theory]]<br />
* [[Goldstone boson]]<br />
* [[Grand unified theory]]<br />
* [[Higgs mechanism]]<br />
* [[Higgs boson]]<br />
* [[Higgs field (classical)]]<br />
* [[Irreversibility]]<br />
* [[Magnetic catalysis]] of chiral symmetry breaking<br />
* [[Mermin–Wagner theorem]]<br />
* [[Norton's dome]]<br />
* [[Second-order phase transition]]<br />
* [[Spontaneous absolute asymmetric synthesis]] in chemistry<br />
* [[Symmetry breaking]]<br />
* [[Tachyon condensation]]<br />
* [[1964 PRL symmetry breaking papers]]<br />
{{div col end}}<br />
<br />
==Notes==<br />
* {{note|note1}} Note that (as in fundamental Higgs driven spontaneous gauge symmetry breaking) the term "symmetry breaking" is a misnomer when applied to gauge symmetries.<br />
<br />
==References==<br />
{{Reflist}}<br />
<br />
==External links==<br />
{{wikiquote}}<br />
* For a pedagogic introduction to electroweak symmetry breaking with step by step derivations, not found in texts, of many key relations, see http://www.quantumfieldtheory.info/Electroweak_Sym_breaking.pdf<br />
* [http://hyperphysics.phy-astr.gsu.edu/hbase/forces/unify.html#c2 Spontaneous symmetry breaking]<br />
* [http://prl.aps.org/50years/milestones#1964 Physical Review Letters – 50th Anniversary Milestone Papers]<br />
* [http://cerncourier.com/cws/article/cern/32522 In CERN Courier, Steven Weinberg reflects on spontaneous symmetry breaking]<br />
* [http://www.scholarpedia.org/article/Englert-Brout-Higgs-Guralnik-Hagen-Kibble_mechanism Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism on Scholarpedia]<br />
* [http://www.scholarpedia.org/article/Englert-Brout-Higgs-Guralnik-Hagen-Kibble_mechanism_%28history%29 History of Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism on Scholarpedia]<br />
* [https://arxiv.org/abs/0907.3466 The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles]<br />
* [http://www.worldscinet.com/ijmpa/24/2414/S0217751X09045431.html International Journal of Modern Physics A: The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles]<br />
* [http://www.datafilehost.com/download-7d512618.html Guralnik, G S; Hagen, C R and Kibble, T W B (1967). Broken Symmetries and the Goldstone Theorem. Advances in Physics, vol. 2 Interscience Publishers, New York. pp. 567–708] {{ISBN|0-470-17057-3}}<br />
* [http://lanl.arxiv.org/abs/hep-th/9802142 Spontaneous Symmetry Breaking in Gauge Theories: a Historical Survey]<br />
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{{Standard model of physics}}<br />
{{Quantum mechanics topics}}<br />
<br />
{{DEFAULTSORT:Spontaneous Symmetry Breaking}}<br />
[[Category:Theoretical physics]]<br />
[[Category:Quantum field theory]]<br />
[[Category:Standard Model]]<br />
[[Category:Quantum chromodynamics]]<br />
[[Category:Symmetry]]<br />
[[Category:Quantum phases]]<br />
<br />
==实例==<br />
<br />
对称性破缺可以涵盖以下任何一种情况:<ref>{{cite web|url=http://www.angelfire.com/stars5/astroinfo/gloss/s.html|title=Astronomical Glossary|author=|date=|website=www.angelfire.com}}</ref><br />
* 某些结构的随机形成破坏了物理学基本定律的精确对称性;<br />
* 物理学中最小能量状态的对称性比系统本身少的情形;<br />
* 系统的实际状态由于明显对称的状态不稳定而不能反映动力学的基本对称性的情况(稳定性是以局部不对称为代价的);<br />
* 理论方程具有某种对称性,但其解可能没有(对称性是“隐藏的”)的情况。<br />
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<br />
在物理学文献中讨论的首批对称性破缺案例之一,与不可压缩流体在重力和流体静力平衡中均匀旋转的形式有关。在1834年,Jacobi <ref>{{cite journal| last=Jacobi | first=C.G.J. | title=Über die figur des gleichgewichts | journal=[[Annalen der Physik und Chemie]] | volume=109 | issue=33| pages=229–238 | year=1834| doi=10.1002/andp.18341090808 | bibcode=1834AnP...109..229J | url=https://zenodo.org/record/2027349 }}</ref>和后来的 Liouville <ref>{{cite journal| last=Liouville | first=J. | title=Sur la figure d'une masse fluide homogène, en équilibre et douée d'un mouvement de rotation| journal=Journal de l'École Polytechnique | issue=14| pages=289–296 | year=1834}}</ref>讨论了这样一个事实: 当旋转物体的动能相对于引力势能超过一定的临界值时,这个问题的平衡解是三轴椭球。在这个分叉点上,麦克劳林椭球体的轴对称性被破坏。此外,在这个分叉点之上,对于常数角动量,使动能最小化的解是非轴对称的 Jacobi 椭球,而不是 Maclaurin 椭球。<br />
==另请参阅==<br />
<br />
*[[Higgs mechanism]]<br />
<br />
*[[QCD vacuum]]<br />
<br />
*[[Goldstone boson]]<br />
<br />
*[[1964 PRL symmetry breaking papers]]<br />
<br />
*[[希格斯机制]]<br />
<br />
*[[QCD真空]]<br />
<br />
*[[戈德斯通玻色子]]<br />
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*[[1964年PRL对称性破缺论文]]<br />
<br />
==参考文献==<br />
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{{reflist|colwidth=30em}}<br />
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{{DEFAULTSORT:Symmetry Breaking}}<br />
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范畴: 对称<br />
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类别: 模式形成<br />
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本中文词条由XXX编译,XXX审校,XXX总审校,西瓜编辑,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''<br />
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<noinclude><br />
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[[Category:对称性破缺]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%AF%B9%E7%A7%B0%E6%80%A7%E7%A0%B4%E7%BC%BA&diff=24823对称性破缺2021-07-27T14:16:15Z<p>Jxzhou:/* Nobel Prize */</p>
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[[图一:一个小球位于中央山丘的山峰处(C)。这是一种不稳定平衡:一个很小的扰动会使它落到左边(L)或右边(R)稳定点。尽管山丘是对称的,没有理由让球落在哪一侧,但观察到的最终状态仍然是不对称的,它总会落到某一侧]]。<br />
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在物理学中,一个作用于系统的(无限)小扰动使系统跨过临界点,通过决定去向分叉的哪个分支来决定系统的命运,这种现象叫做'''<font color="#ff8000">对称性破缺</font>'''。对于一个观测不到扰动(或“噪声”)的外部观察者来说,这个选择看起来是任意的。这个过程被称为对称性破缺,因为这种转变通常使系统从一个对称但无序的状态进入一个或多个确定的状态。在'''<font color="#ff8000">斑图生成</font>'''中对称性破缺起着重要作用。<br />
<br />
1972年,诺贝尔奖得主P·W·安德森(P.W.Anderson)在《科学》(Science)杂志上发表了一篇名为《多即不同》的论文<ref>{{cite journal | last=Anderson | first=P.W. | title=More is Different | journal=Science | volume=177 | issue=4047| pages=393–396 | year=1972 | url=http://robotics.cs.tamu.edu/dshell/cs689/papers/anderson72more_is_different.pdf | doi=10.1126/science.177.4047.393 | pmid=17796623 | format=|bibcode = 1972Sci...177..393A }}</ref>,文中使用对称性破缺的思想表明,即使'''<font color="#ff8000">还原论</font>'''是正确的,但它的逆命题'''<font color="#ff8000">建构主义</font>'''是错误的。建构主义认为,在给出描述各组成部分的理论的情况下科学家可以轻易地预测复杂现象。<br />
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对称性破缺可以分为'''<font color="#ff8000">显性对称性破缺</font>'''和'''<font color="#ff8000">自发对称性破缺</font>'''两种类型,二者的区别是,在破缺对称性下系统的运动方程是否不变或者基态是否保持不变。<br />
==显性对称性破缺==<br />
<br />
在'''<font color="#ff8000">显性对称性破缺</font>'''中,描述系统的运动方程在破缺对称下是不同的。在哈密顿力学或拉格朗日力学中,假若系统的哈密顿量(或拉格朗日量)中至少一项显性地打破了给定的对称性,就发生了显性对称性破缺。<br />
==自发对称性破缺==<br />
<br />
在'''<font color="#ff8000">自发对称性破缺</font>'''中,系统的运动方程是不变的,但系统发生了变化。这是因为系统的背景(时空)——真空态——是非恒定的。这种对称性破缺可以用一个序参量进行参数化。这类对称破缺的一个特殊情况是'''<font color="#ff8000">动力学对称性破缺</font>'''。<br />
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Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state ends up in an asymmetric state.[1][2][3] In particular, it can describe systems where the equations of motion or the Lagrangian obey symmetries, but the lowest-energy vacuum solutions do not exhibit that same symmetry. When the system goes to one of those vacuum solutions, the symmetry is broken for perturbations around that vacuum even though the entire Lagrangian retains that symmetry.<br />
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自发对称破缺是一个自发的对称破缺过程,它使处于对称状态的物理系统最终处于非对称状态。特别地,它可以描述运动方程或拉格朗日方程服从某种对称性,但最低能量真空解不具有该对称性的系统。当系统进入其中一个真空解时,真空解周围的扰动会破坏系统对称性,尽管整个拉格朗日方程仍然保持了对称性。<br />
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==Overview==<br />
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In [[explicit symmetry breaking]], if two outcomes are considered, the probability of a pair of outcomes can be different. By definition, spontaneous symmetry breaking requires the existence of a symmetric probability distribution—any pair of outcomes has the same probability. In other words, the underlying laws{{clarify|date=December 2016}} are [[Invariant (physics)|invariant]] under a [[Symmetry (physics)|symmetry]] transformation.<br />
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The system, as a whole{{clarify|date=December 2016}}, changes under such transformations.<br />
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Phases of matter, such as crystals, magnets, and conventional superconductors, as well as simple phase transitions can be described by spontaneous symmetry breaking. Notable exceptions include topological phases of matter like the [[fractional quantum Hall effect]].<br />
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==Examples 例子==<br />
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===Sombrero potential===<br />
Consider a symmetric upward dome with a trough circling the bottom. If a ball is put at the very peak of the dome, the system is symmetric with respect to a rotation around the center axis. But the ball may ''spontaneously break'' this symmetry by rolling down the dome into the trough, a point of lowest energy. Afterward, the ball has come to a rest at some fixed point on the perimeter. The dome and the ball retain their individual symmetry, but the system does not.<ref>{{cite book |first=Gerald M. |last=Edelman |title=Bright Air, Brilliant Fire: On the Matter of the Mind |location=New York |publisher=BasicBooks |year=1992 |url=https://archive.org/details/brightairbrillia00gera |url-access=registration |page=[https://archive.org/details/brightairbrillia00gera/page/203 203] }}</ref><br />
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考虑一个对称向上的圆顶,底部环绕着一个槽。如果把一个球放在圆顶的最顶端,这个系统是围绕中心轴旋转对称的。但球体可能会自发地打破这种对称性,因为它会沿着穹顶滚动到能量最低的槽中。然后,球在圆周上某个固定的点上停下来。圆顶和球保持了各自的对称,但系统却没有保持对称性。<br />
[[Image:Mexican hat potential polar.svg|270px|thumb|left|Graph of Goldstone's "[[sombrero]]" potential function <math>V(\phi)</math>.|链接=Special:FilePath/Mexican_hat_potential_polar.svg]]<br />
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In the simplest idealized relativistic model, the spontaneously broken symmetry is summarized through an illustrative [[scalar field theory]]. The relevant [[Lagrangian (field theory)|Lagrangian]] of a scalar field <math>\phi</math>, which essentially dictates how a system behaves, can be split up into kinetic and potential terms,<br />
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在最简单的理想相对论模型中,可以用一个解释性的标量场理论总结自发破对称性。一个标量场 <math>\phi</math>的拉格朗日量从本质上决定了系统的行为,它可以分解成动能项和势能项:<br />
{{NumBlk|::|<math>\mathcal{L} = \partial^\mu \phi \partial_\mu \phi - V(\phi).</math>|{{EquationRef|1}}}}<br />
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It is in this potential term <math>V(\phi)</math> that the symmetry breaking is triggered. An example of a potential, due to [[Jeffrey Goldstone]]<ref>{{Cite journal | last1 = Goldstone | first1 = J. | doi = 10.1007/BF02812722 | title = Field theories with " Superconductor " solutions | journal = Il Nuovo Cimento | volume = 19 | issue = 1 | pages = 154–164 | year = 1961 | bibcode = 1961NCim...19..154G | s2cid = 120409034 | url = http://cds.cern.ch/record/343400 }}</ref> is illustrated in the graph at the left.<br />
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正是在势能项 <math>V(\phi)</math> 中触发了对称性破缺。例如左图所示的 [[Jeffrey Goldstone]] 给出的势能函数:<br />
{{NumBlk|::|<math>V(\phi) = -5|\phi|^2 + |\phi|^4 \,</math>.|{{EquationRef|2}}}}<br />
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This potential has an infinite number of possible [[minimum|minima]] (vacuum states) given by<br />
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该是函数具有无穷数量的最小值点(真空态)当<br />
{{NumBlk|::|<math>\phi = \sqrt{5} e^{i\theta} </math>.|{{EquationRef|3}}}}<br />
for any real ''θ'' between 0 and 2''π''. The system also has an unstable vacuum state corresponding to {{nowrap|1=''Φ'' = 0}}. This state has a [[Unitary group|U(1)]] symmetry. However, once the system falls into a specific stable vacuum state (amounting to a choice of ''θ''), this symmetry will appear to be lost, or "spontaneously broken".<br />
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对于0到2π之间的任何实数θ。系统也有一个不稳定的真空状态,对应于Φ = 0。这个状态具有U(1)对称。然而,一旦系统落入某个稳定真空状态(相当于选择θ),这种对称性就会消失,或者说“自发破缺”。<br />
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In fact, any other choice of ''θ'' would have exactly the same energy, implying the existence of a massless [[Goldstone boson|Nambu–Goldstone boson]], the mode running around the circle at the minimum of this potential, and indicating there is some memory of the original symmetry in the Lagrangian.<br />
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事实上,任何其他θ的选择都将具有完全相同的能量,这意味着无质量的南部-戈德斯通玻色子的存在,这种模式在势能的最小值绕圆运动,并表明存在拉格朗日方程中原始对称性的一些记忆。<br />
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===Other examples===<br />
* For [[ferromagnet]]ic materials, the underlying laws are invariant under spatial rotations. Here, the order parameter is the [[magnetization]], which measures the magnetic dipole density. Above the [[Curie temperature]], the order parameter is zero, which is spatially invariant, and there is no symmetry breaking. Below the Curie temperature, however, the magnetization acquires a constant nonvanishing value, which points in a certain direction (in the idealized situation where we have full equilibrium; otherwise, translational symmetry gets broken as well). The residual rotational symmetries which leave the orientation of this vector invariant remain unbroken, unlike the other rotations which do not and are thus spontaneously broken.<br />
* 对于铁磁性材料,其基本定律在空间旋转下是不变的。在这里,序参量是衡量磁偶极子密度的磁化强度。在居里温度以上,序参量为零,具有空间不变性,不存在对称性破缺。然而,在居里温度以下,磁化强度变成一个恒定的非零值,指向一个特定的方向(在有充分平衡的理想情况下;否则,平移对称性也会破缺)。使该向量方向不变的旋转对称性仍然保留,而其他旋转对称性自发破缺。<br />
* The laws describing a solid are invariant under the full [[Euclidean group]], but the solid itself spontaneously breaks this group down to a [[space group]]. The displacement and the orientation are the order parameters.<br />
* 描述固体的定律在完整的欧几里得群下是不变的,但固体本身会自发地将这个群分解为一个空间群。其中位移和方向是序参量。<br />
* General relativity has a Lorentz symmetry, but in [[Friedmann–Lemaître–Robertson–Walker metric|FRW cosmological models]], the mean 4-velocity field defined by averaging over the velocities of the galaxies (the galaxies act like gas particles at cosmological scales) acts as an order parameter breaking this symmetry. Similar comments can be made about the cosmic microwave background.<br />
* 广义相对论具有洛伦兹对称性,但在FRW宇宙模型中,定义为星系速度的平均值(星系在宇宙尺度上的行为就像气体粒子) 的平均 4-速度场,作为序参量会打破这种对称性。对于宇宙微波背景辐射也有类似的评论。<br />
* For the [[electroweak]] model, as explained earlier, a component of the Higgs field provides the order parameter breaking the electroweak gauge symmetry to the electromagnetic gauge symmetry. Like the ferromagnetic example, there is a phase transition at the electroweak temperature. The same comment about us not tending to notice broken symmetries suggests why it took so long for us to discover electroweak unification.<br />
* 对于电弱模型,如前面所解释的,希格斯场的一个分量提供了将电弱规范对称性破缺到电磁规范对称性的序参量。和铁磁的例子一样,在电弱温度下也有相变。同样的关于我们不倾向于注意破缺对称性的评论,也说明了为什么我们花了这么长时间才发现电弱统一。<br />
* In superconductors, there is a condensed-matter collective field ψ, which acts as the order parameter breaking the electromagnetic gauge symmetry.<br />
* 在超导体中有一个凝聚态集体场ψ,它是打破电磁规范对称性的序参量。<br />
* Take a thin cylindrical plastic rod and push both ends together. Before buckling, the system is symmetric under rotation, and so visibly cylindrically symmetric. But after buckling, it looks different, and asymmetric. Nevertheless, features of the cylindrical symmetry are still there: ignoring friction, it would take no force to freely spin the rod around, displacing the ground state in time, and amounting to an oscillation of vanishing frequency, unlike the radial oscillations in the direction of the buckle. This spinning mode is effectively the requisite [[Goldstone boson|Nambu–Goldstone boson]].<br />
* 拿一个细长的圆柱形塑料杆,把两端推到一起。在屈曲之前,系统在旋转下是对称的,因此可见圆柱对称性。但在弯曲之后,它看起来就不同了,而且是不对称的。然而,圆柱对称性的特征仍然存在:忽略摩擦,杆可以不受外力自由地自旋,在时间上取代基态,等于一个频率趋于零的振荡,而不是沿屈曲方向的径向振荡。这种自旋模式实际上是必需的南部-戈德斯通玻色子。<br />
* Consider a uniform layer of [[fluid]] over an infinite horizontal plane. This system has all the symmetries of the Euclidean plane. But now heat the bottom surface uniformly so that it becomes much hotter than the upper surface. When the temperature gradient becomes large enough, [[convection cell]]s will form, breaking the Euclidean symmetry.<br />
* 考虑无限水平面上的一层均匀的流体。这个系统具有欧几里得平面的所有对称性。但是现在均匀地加热底部表面,使它变得比上表面热得多。当温度梯度足够大时,就会形成对流单元,打破了欧几里得对称。<br />
* Consider a bead on a circular hoop that is rotated about a vertical [[diameter]]. As the [[rotational velocity]] is increased gradually from rest, the bead will initially stay at its initial [[equilibrium point]] at the bottom of the hoop (intuitively stable, lowest [[gravitational potential]]). At a certain critical rotational velocity, this point will become unstable and the bead will jump to one of two other newly created equilibria, [[equidistant]] from the center. Initially, the system is symmetric with respect to the diameter, yet after passing the critical velocity, the bead ends up in one of the two new equilibrium points, thus breaking the symmetry.<br />
* 考虑一个围绕某个竖直的直径旋转的圆形箍上的珠子。当旋转速度从静止逐渐增加时,珠子最初会停留在环底部的初始平衡点(直观上稳定,重力势最低)。在一定的临界旋转速度下,这一点将变得不稳定,珠子将跳到另外两个新创建的离中心等距离的平衡点中的一个。起初,系统相对直径是对称的,但在通过临界速度后,珠子最终停留在两个新的平衡点中的一个,从而打破了对称性。<br />
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==Spontaneous symmetry breaking in physics 物理学中的自发对称性破缺==<br />
[[File:Spontaneous symmetry breaking (explanatory diagram).png|thumb|right|250px|''Spontaneous symmetry breaking illustrated'': At high energy levels (''left''), the ball settles in the center, and the result is symmetric. At lower energy levels (''right''), the overall "rules" remain symmetric, but the symmetric "[[sombrero|Sombrero]]" enforces an asymmetric outcome, since eventually the ball must rest at some random spot on the bottom, "spontaneously", and not all others.|链接=Special:FilePath/Spontaneous_symmetry_breaking_(explanatory_diagram).png]]<br />
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===Particle physics 粒子物理===<br />
In [[particle physics]], the [[force carrier]] particles are normally specified by field equations with [[gauge symmetry]]; their equations predict that certain measurements will be the same at any point in the field. For instance, field equations might predict that the mass of two quarks is constant. Solving the equations to find the mass of each quark might give two solutions. In one solution, quark A is heavier than quark B. In the second solution, quark B is heavier than quark A ''by the same amount''. The symmetry of the equations is not reflected by the individual solutions, but it is reflected by the range of solutions.<br />
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在粒子物理学中,载力子通常由规范对称的场方程表示;它们的方程预测到某些测量值在场的任何点上都是相同的。例如,场方程可以预测两个夸克的质量是常数。通过求解方程来求每个夸克的质量可能会得到两个解。在一个解中,夸克A比夸克B重;在第二个解中,夸克B比夸克A重相同的量。方程的对称性不是由单个解来反映的,而是由解的范围来反映的。<br />
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An actual measurement reflects only one solution, representing a breakdown in the symmetry of the underlying theory. "Hidden" is a better term than "broken", because the symmetry is always there in these equations. This phenomenon is called [[Spontaneous magnetization|''spontaneous'']] symmetry breaking (SSB) because ''nothing'' (that we know of) breaks the symmetry in the equations.<ref name="Weinberg2011">{{cite book|author=Steven Weinberg|title=Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature|url=https://books.google.com/books?id=Rsg3PE_9_ccC|date=20 April 2011|publisher=Knopf Doubleday Publishing Group|isbn=978-0-307-78786-6}}</ref>{{rp|194–195}}<br />
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一个实际的测量只反映了一个解,代表了其潜在理论的对称性的破缺。在这里“隐藏”是比“破坏”更好的术语,因为对称性总是存在于这些方程中。这种现象被称为自发对称破缺(SSB),因为(我们所知道的)没有任何东西会打破方程中的对称性。<br />
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====Chiral symmetry 手性对称性====<br />
{{Main article|Chiral symmetry breaking}}<br />
Chiral symmetry breaking is an example of spontaneous symmetry breaking affecting the [[chiral symmetry]] of the [[strong interactions]] in particle physics. It is a property of [[quantum chromodynamics]], the [[quantum field theory]] describing these interactions, and is responsible for the bulk of the mass (over 99%) of the [[nucleons]], and thus of all common matter, as it converts very light bound [[quarks]] into 100 times heavier constituents of [[baryons]]. The approximate [[Nambu–Goldstone boson]]s in this spontaneous symmetry breaking process are the [[pions]], whose mass is an order of magnitude lighter than the mass of the nucleons. It served as the prototype and significant ingredient of the Higgs mechanism underlying the electroweak symmetry breaking.<br />
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手性对称破缺是粒子物理中影响强相互作用手性对称的自发对称破缺的一个例子。手性对称性破缺是量子色动力学(描述这些相互作用的量子场理论)的一种特性,它是核子的大部分质量(超过99%)的成因,因此也是所有普通物质的主要成因,因为它将非常轻的束缚夸克转化为100倍重量的重子的成分。在这个自发对称破缺过程中,近似的南部-戈德斯通玻色子是介子,其质量比核子的质量轻一个数量级。它是电弱对称破缺的希格斯机制的原型和重要组成部分。<br />
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====Higgs mechanism 希格斯机制====<br />
{{Main article|Higgs mechanism|Yukawa interaction}}<br />
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The strong, weak, and electromagnetic forces can all be understood as arising from [[gauge symmetry|gauge symmetries]]. The [[Higgs mechanism]], the spontaneous symmetry breaking of gauge symmetries, is an important component in understanding the [[superconductivity]] of metals and the origin of particle masses in the standard model of particle physics. One important consequence of the distinction between true symmetries and ''gauge symmetries'', is that the spontaneous breaking of a gauge symmetry does not give rise to characteristic massless Nambu–Goldstone physical modes, but only massive modes, like the plasma mode in a superconductor, or the Higgs mode observed in particle physics.<br />
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强、弱和电磁力都可以理解为来自规范对称。希格斯机制,即规范对称的自发对称破缺机制,是理解金属超导性和粒子物理标准模型中粒子质量起源的重要组成部分。区分真正的对称性和规范对称性的一个重要的结果,是规范对称性的自发破缺不产生典型的无质量Nambu-Goldstone物理模式,而是只产生有质量的模式,像超导体中的等离子体模式,或者粒子物理学中观察到的希格斯模式。<br />
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In the standard model of particle physics, spontaneous symmetry breaking of the {{nowrap|SU(2) × U(1)}} gauge symmetry associated with the electro-weak force generates masses for several particles, and separates the electromagnetic and weak forces. The [[W and Z bosons]] are the elementary particles that mediate the [[weak interaction]], while the [[photon]] mediates the [[electromagnetic interaction]]. At energies much greater than 100 GeV, all these particles behave in a similar manner. The [[Unified field theory#Modern progress|Weinberg–Salam theory]] predicts that, at lower energies, this symmetry is broken so that the photon and the massive W and Z bosons emerge.<ref>A Brief History of Time, Stephen Hawking, Bantam; 10th anniversary edition (1998). pp. 73–74.{{ISBN?}}</ref> In addition, fermions develop mass consistently.<br />
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在粒子物理的标准模型中,与电弱力相关的SU(2) × U(1)规范对称性自发破缺产生多种粒子的质量,并将电磁力和弱相互作用分离。W玻色子和Z玻色子是介导弱相互作用的基本粒子,而光子介导电磁相互作用。当能量远远大于100 GeV时,所有这些粒子的行为都相似。Weinberg-Salam理论预测,在较低的能量下,这种对称性被打破,光子和大质量的W和Z玻色子就会出现。此外,费米子不断地发展质量。<br />
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Without spontaneous symmetry breaking, the [[Standard Model]] of elementary particle interactions requires the existence of a number of particles. However, some particles (the [[W and Z bosons]]) would then be predicted to be massless, when, in reality, they are observed to have mass. To overcome this, spontaneous symmetry breaking is augmented by the [[Higgs mechanism]] to give these particles mass. It also suggests the presence of a new particle, the [[Higgs boson]], detected in 2012.<br />
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在没有自发对称性破缺的情况下,基本粒子相互作用的标准模型要求存在多种粒子。然而,一些粒子(W玻色子和Z玻色子)将被预测为无质量的,而实际上它们被观察到有质量。为了克服这个问题,希格斯机制增强了自发对称破缺,从而赋予这些粒子质量。它还表明一种新粒子——希格斯玻色子——的存在,它在2012年被实验探测到。<br />
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[[Superconductivity]] of metals is a condensed-matter analog of the Higgs phenomena, in which a condensate of Cooper pairs of electrons spontaneously breaks the U(1) gauge symmetry associated with light and electromagnetism.<br />
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金属的超导性是一种类似于希格斯现象的凝聚态物质,其中库珀电子对的凝聚会自发地打破与光和电磁相关的U(1)规范对称。<br />
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===Condensed matter physics===<br />
Most phases of matter can be understood through the lens of spontaneous symmetry breaking. For example, crystals are periodic arrays of atoms that are not invariant under all translations (only under a small subset of translations by a lattice vector). Magnets have north and south poles that are oriented in a specific direction, breaking [[rotational symmetry]]. In addition to these examples, there are a whole host of other symmetry-breaking phases of matter — including nematic phases of liquid crystals, charge- and spin-density waves, superfluids, and many others.<br />
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There are several known examples of matter that cannot be described by spontaneous symmetry breaking, including: topologically ordered phases of matter, such as [[Fractional quantum Hall effect|fractional quantum Hall liquids]], and [[Quantum spin liquid|spin-liquids]]. These states do not break any symmetry, but are distinct phases of matter. Unlike the case of spontaneous symmetry breaking, there is not a general framework for describing such states.<ref name=chen>{{cite journal | last1 = Chen | first1 = Xie | author-link3 = Xiao-Gang Wen | last2 = Gu | first2 = Zheng-Cheng | last3 = Wen | first3 = Xiao-Gang | year = 2010 | title = Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order | journal = Phys. Rev. B | volume = 82 | issue = 15| page = 155138 | doi=10.1103/physrevb.82.155138|arxiv = 1004.3835 |bibcode = 2010PhRvB..82o5138C | s2cid = 14593420 }}</ref><br />
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====Continuous symmetry====<br />
The ferromagnet is the canonical system that spontaneously breaks the continuous symmetry of the spins below the [[Curie temperature]] and at {{nowrap|1=''h'' = 0}}, where ''h'' is the external magnetic field. Below the [[Curie temperature]], the energy of the system is invariant under inversion of the magnetization ''m''('''x''') such that {{nowrap|1=''m''('''x''') = −''m''(−'''x''')}}. The symmetry is spontaneously broken as {{nowrap|''h'' → 0}} when the Hamiltonian becomes invariant under the inversion transformation, but the expectation value is not invariant.<br />
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Spontaneously-symmetry-broken phases of matter are characterized by an order parameter that describes the quantity which breaks the symmetry under consideration. For example, in a magnet, the order parameter is the local magnetization.<br />
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Spontaneous breaking of a continuous symmetry is inevitably accompanied by gapless (meaning that these modes do not cost any energy to excite) Nambu–Goldstone modes associated with slow, long-wavelength fluctuations of the order parameter. For example, vibrational modes in a crystal, known as phonons, are associated with slow density fluctuations of the crystal's atoms. The associated Goldstone mode for magnets are oscillating waves of spin known as spin-waves. For symmetry-breaking states, whose order parameter is not a conserved quantity, Nambu–Goldstone modes are typically massless and propagate at a constant velocity.<br />
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An important theorem, due to Mermin and Wagner, states that, at finite temperature, thermally activated fluctuations of Nambu–Goldstone modes destroy the long-range order, and prevent spontaneous symmetry breaking in one- and two-dimensional systems. Similarly, quantum fluctuations of the order parameter prevent most types of continuous symmetry breaking in one-dimensional systems even at zero temperature. (An important exception is ferromagnets, whose order parameter, magnetization, is an exactly conserved quantity and does not have any quantum fluctuations.)<br />
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Other long-range interacting systems, such as cylindrical curved surfaces interacting via the [[Coulomb potential]] or [[Yukawa potential]], have been shown to break translational and rotational symmetries.<ref><br />
{{cite journal<br />
|last1=Kohlstedt |first1=K.L.<br />
|last2=Vernizzi |first2=G.<br />
|last3=Solis |first3=F.J.<br />
|last4=Olvera de la Cruz |first4=M.<br />
|year=2007<br />
|title=Spontaneous Chirality via Long-range Electrostatic Forces<br />
|journal=[[Physical Review Letters]]<br />
|volume=99 |issue=3<br />
|page=030602<br />
|doi=10.1103/PhysRevLett.99.030602<br />
|arxiv = 0704.3435 |bibcode = 2007PhRvL..99c0602K |pmid=17678276|s2cid=37983980<br />
}}</ref> It was shown, in the presence of a symmetric Hamiltonian, and in the limit of infinite volume, the system spontaneously adopts a chiral configuration — i.e., breaks [[mirror plane]] [[symmetry]].<br />
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===Dynamical symmetry breaking 动力学对称性破缺===<br />
Dynamical symmetry breaking (DSB) is a special form of spontaneous symmetry breaking in which the ground state of the system has reduced symmetry properties compared to its theoretical description (i.e., [[Lagrangian (field theory)|Lagrangian]]).<br />
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动力学对称性破缺(DSB)是自发对称性破缺的一种特殊形式,在这种情况下,系统的基态比理论描述(例如拉格朗日量)的对称性降低。<br />
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Dynamical breaking of a global symmetry is a spontaneous symmetry breaking, which happens not at the (classical) tree level (i.e., at the level of the bare action), but due to quantum corrections (i.e., at the level of the [[effective action]]).<br />
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全局对称性的动力学破缺是自发对称性破缺,它不是发生在(经典)树的水平(例如在bare作用的水平),而是由于量子修正(例如在有效作用的水平)。<br />
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Dynamical breaking of a gauge symmetry {{ref|note1}} is subtler. In the conventional spontaneous gauge symmetry breaking, there exists an unstable [[Higgs particle]] in the theory, which drives the vacuum to a symmetry-broken phase. (See, for example, [[electroweak interaction]].) In dynamical gauge symmetry breaking, however, no unstable Higgs particle operates in the theory, but the bound states of the system itself provide the unstable fields that render the phase transition. For example, Bardeen, Hill, and Lindner published a paper that attempts to replace the conventional [[Higgs mechanism]] in the [[standard model]] by a DSB that is driven by a bound state of top-antitop quarks. (Such models, in which a composite particle plays the role of the Higgs boson, are often referred to as "Composite Higgs models".)<ref><br />
{{cite journal<br />
|author1=William A. Bardeen<br />
|author2-link=Christopher T. Hill<br />
|author2=Christopher T. Hill<br />
|author3-link=Manfred Lindner<br />
|author3=Manfred Lindner<br />
|year=1990<br />
|title=Minimal dynamical symmetry breaking of the standard model<br />
|journal=[[Physical Review D]]<br />
|volume=41 |issue=5 |pages=1647–1660<br />
|bibcode=1990PhRvD..41.1647B<br />
|doi=10.1103/PhysRevD.41.1647<br />
|pmid=10012522<br />
|author1-link=William A. Bardeen<br />
}}</ref> Dynamical breaking of gauge symmetries is often due to creation of a [[fermionic condensate]] — e.g., the [[quark condensate]], which is connected to the [[Chiral symmetry breaking|dynamical breaking of chiral symmetry]] in [[quantum chromodynamics]]. Conventional [[superconductivity]] is the paradigmatic example from the condensed matter side, where phonon-mediated attractions lead electrons to become bound in pairs and then condense, thereby breaking the electromagnetic gauge symmetry.<br />
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规范对称性动力学破缺更加微妙。在常规规范对称自发破缺理论中,存在一个不稳定的希格斯粒子,希格斯粒子驱动真空进入对称破缺相。(例如,参见弱电相互作用。)然而,在规范对称性动力学破缺中,不存在不稳定的希格斯粒子,但系统本身的束缚态提供了导致相变的不稳定场。例如,巴丁、希尔和林德纳发表了一篇论文,试图用一个由顶-反顶夸克束缚状态驱动的DSB来取代标准模型中的传统希格斯机制。(在这种模型中,复合粒子扮演希格斯玻色子的角色,通常被称为“复合希格斯模型”。)规范对称性动力学破缺通常是由于费米凝聚的产生,例如夸克凝聚,它与量子色动力学中手性对称的动力学破缺有关。传统的超导性是凝聚态物质方面的典型例子,声子的吸引导致电子成对结合然后凝聚,从而打破电磁规范对称性。<br />
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==Generalisation and technical usage==<br />
For spontaneous symmetry breaking to occur, there must be a system in which there are several equally likely outcomes. The system as a whole is therefore [[Symmetry (physics)|symmetric]] with respect to these outcomes. However, if the system is sampled (i.e. if the system is actually used or interacted with in any way), a specific outcome must occur. Though the system as a whole is symmetric, it is never encountered with this symmetry, but only in one specific asymmetric state. Hence, the symmetry is said to be spontaneously broken in that theory. Nevertheless, the fact that each outcome is equally likely is a reflection of the underlying symmetry, which is thus often dubbed "hidden symmetry", and has crucial formal consequences. (See the article on the [[Nambu–Goldstone boson|Goldstone boson]].)<br />
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要发生自发对称性破缺,系统中必须有几个等可能的结果,整个系统相对于这些结果是对称的。然而,如果对系统进行采样(即如果系统被实际使用或以任何方式与之交互),就必须产生特定的结果。虽然系统作为一个整体是对称的,但它从来没有表现出这种对称性,而只是处于一个特定的不对称状态。于是,在该理论中对称性被自发地打破了。然而,每个结果的可能性都相等这一点,反映了潜在的对称性。因此通常被称为“隐藏对称性”,并具有重要的形式结果。(参见有关戈德斯通玻色子的文章。)<br />
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When a theory is symmetric with respect to a [[symmetry group]], but requires that one element of the group be distinct, then spontaneous symmetry breaking has occurred. The theory must not dictate ''which'' member is distinct, only that ''one is''. From this point on, the theory can be treated as if this element actually is distinct, with the proviso that any results found in this way must be resymmetrized, by taking the average of each of the elements of the group being the distinct one.<br />
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当一个理论相对于一个对称群是对称的,但要求群中的一个元素是不同的,那么就会发生自发对称性破缺。理论不能规定哪个成员是不同的,而只能规定那个成员是不同的。从这一点开始,这个理论就可以被视为这个元素实际上是不同的,附带的条件是,任何以这种方式发现的结果必须是重新对称的,通过取组中每个元素的平均值作为不同的元素。<br />
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The crucial concept in physics theories is the [[order parameter]]. If there is a field (often a background field) which acquires an expectation value (not necessarily a [[vacuum expectation value|''vacuum'' expectation value]]) which is not invariant under the symmetry in question, we say that the system is in the [[ordered phase]], and the symmetry is spontaneously broken. This is because other subsystems interact with the order parameter, which specifies a "frame of reference" to be measured against. In that case, the [[vacuum state]] does not obey the initial symmetry (which would keep it invariant, in the linearly realized '''Wigner mode''' in which it would be a singlet), and, instead changes under the (hidden) symmetry, now implemented in the (nonlinear) '''Nambu–Goldstone mode'''. Normally, in the absence of the Higgs mechanism, massless [[Goldstone boson]]s arise.<br />
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在物理理论中,最重要的概念是序参量。如果有一个场(通常是背景场)得到一个期望值(不一定是真空期望值),这个期望值在理论具有的对称性下不是不变的,我们就说系统处于有序相,对称性自发破缺。这是因为序参量指定了测量其他子系统与之相互作用的“参考框架”。在这种情况下,真空状态不服从初始对称性(这将保持它不变,在线性实现的Wigner模式中,它将是一个单线),而是在(隐藏的)对称下变化,现在在(非线性)南布-戈德斯通模式中实现。通常,在没有希格斯机制的情况下,就会出现无质量的戈德斯通玻色子。<br />
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The symmetry group can be discrete, such as the [[space group]] of a crystal, or continuous (e.g., a [[Lie group]]), such as the rotational symmetry of space. However, if the system contains only a single spatial dimension, then only discrete symmetries may be broken in a [[vacuum state]] of the full [[Quantum mechanics|quantum theory]], although a classical solution may break a continuous symmetry.<br />
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对称群可以是离散的,如晶体的空间群,也可以是连续的(如李群),如空间的旋转对称。然而,如果系统只包含一个空间维度,尽管经典解可能打破连续对称性,那么在全量子理论的真空状态下,只有离散的对称性可能被打破。<br />
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==Nobel Prize==<br />
On October 7, 2008, the [[Royal Swedish Academy of Sciences]] awarded the 2008 [[Nobel Prize in Physics]] to three scientists for their work in subatomic physics symmetry breaking. [[Yoichiro Nambu]], of the [[University of Chicago]], won half of the prize for the discovery of the mechanism of spontaneous broken symmetry in the context of the strong interactions, specifically [[chiral symmetry breaking]]. Physicists [[Makoto Kobayashi (physicist)|Makoto Kobayashi]] and [[Toshihide Maskawa]], of [[Kyoto University]], shared the other half of the prize for discovering the origin of the [[Explicit symmetry breaking|explicit breaking]] of CP symmetry in the weak interactions.<ref>{{cite web|author=The Nobel Foundation|title=The Nobel Prize in Physics 2008|url=http://nobelprize.org/nobel_prizes/physics/laureates/2008/index.html|work=nobelprize.org|access-date=January 15, 2008}}</ref> This origin is ultimately reliant on the Higgs mechanism, but, so far understood as a "just so" feature of Higgs couplings, not a spontaneously broken symmetry phenomenon.<br />
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2008年10月7日,瑞典皇家科学院(Royal Swedish Academy of Sciences)将2008年诺贝尔物理学奖授予三位科学家,以表彰他们在亚原子物理对称性破缺方面的工作。芝加哥大学的Yoichiro Nambu获得了一半的奖金,表彰他发现了在强相互作用下对称性自发破缺的机制,特别是手性对称性破缺。京都大学(Kyoto University)物理学家小林诚(Makoto Kobayashi)和正川俊英(Toshihide Maskawa)因发现了弱相互作用中CP对称性显性破缺的起源而分享了另一半奖金。这一起源最终依赖于希格斯机制,但迄今为止被理解为希格斯耦合的“恰好如此”特征,而不是一种自发的对称破缺现象。<br />
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==See also==<br />
{{div col|colwidth=24em}}<br />
* [[Autocatalytic reactions and order creation]]<br />
* [[Catastrophe theory]]<br />
* [[Chiral symmetry breaking]]<br />
* [[CP-violation]]<br />
* [[Fermi ball]]<br />
* [[Gauge gravitation theory]]<br />
* [[Goldstone boson]]<br />
* [[Grand unified theory]]<br />
* [[Higgs mechanism]]<br />
* [[Higgs boson]]<br />
* [[Higgs field (classical)]]<br />
* [[Irreversibility]]<br />
* [[Magnetic catalysis]] of chiral symmetry breaking<br />
* [[Mermin–Wagner theorem]]<br />
* [[Norton's dome]]<br />
* [[Second-order phase transition]]<br />
* [[Spontaneous absolute asymmetric synthesis]] in chemistry<br />
* [[Symmetry breaking]]<br />
* [[Tachyon condensation]]<br />
* [[1964 PRL symmetry breaking papers]]<br />
{{div col end}}<br />
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==Notes==<br />
* {{note|note1}} Note that (as in fundamental Higgs driven spontaneous gauge symmetry breaking) the term "symmetry breaking" is a misnomer when applied to gauge symmetries.<br />
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==References==<br />
{{Reflist}}<br />
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==External links==<br />
{{wikiquote}}<br />
* For a pedagogic introduction to electroweak symmetry breaking with step by step derivations, not found in texts, of many key relations, see http://www.quantumfieldtheory.info/Electroweak_Sym_breaking.pdf<br />
* [http://hyperphysics.phy-astr.gsu.edu/hbase/forces/unify.html#c2 Spontaneous symmetry breaking]<br />
* [http://prl.aps.org/50years/milestones#1964 Physical Review Letters – 50th Anniversary Milestone Papers]<br />
* [http://cerncourier.com/cws/article/cern/32522 In CERN Courier, Steven Weinberg reflects on spontaneous symmetry breaking]<br />
* [http://www.scholarpedia.org/article/Englert-Brout-Higgs-Guralnik-Hagen-Kibble_mechanism Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism on Scholarpedia]<br />
* [http://www.scholarpedia.org/article/Englert-Brout-Higgs-Guralnik-Hagen-Kibble_mechanism_%28history%29 History of Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism on Scholarpedia]<br />
* [https://arxiv.org/abs/0907.3466 The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles]<br />
* [http://www.worldscinet.com/ijmpa/24/2414/S0217751X09045431.html International Journal of Modern Physics A: The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles]<br />
* [http://www.datafilehost.com/download-7d512618.html Guralnik, G S; Hagen, C R and Kibble, T W B (1967). Broken Symmetries and the Goldstone Theorem. Advances in Physics, vol. 2 Interscience Publishers, New York. pp. 567–708] {{ISBN|0-470-17057-3}}<br />
* [http://lanl.arxiv.org/abs/hep-th/9802142 Spontaneous Symmetry Breaking in Gauge Theories: a Historical Survey]<br />
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{{Standard model of physics}}<br />
{{Quantum mechanics topics}}<br />
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{{DEFAULTSORT:Spontaneous Symmetry Breaking}}<br />
[[Category:Theoretical physics]]<br />
[[Category:Quantum field theory]]<br />
[[Category:Standard Model]]<br />
[[Category:Quantum chromodynamics]]<br />
[[Category:Symmetry]]<br />
[[Category:Quantum phases]]<br />
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==实例==<br />
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对称性破缺可以涵盖以下任何一种情况:<ref>{{cite web|url=http://www.angelfire.com/stars5/astroinfo/gloss/s.html|title=Astronomical Glossary|author=|date=|website=www.angelfire.com}}</ref><br />
* 某些结构的随机形成破坏了物理学基本定律的精确对称性;<br />
* 物理学中最小能量状态的对称性比系统本身少的情形;<br />
* 系统的实际状态由于明显对称的状态不稳定而不能反映动力学的基本对称性的情况(稳定性是以局部不对称为代价的);<br />
* 理论方程具有某种对称性,但其解可能没有(对称性是“隐藏的”)的情况。<br />
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在物理学文献中讨论的首批对称性破缺案例之一,与不可压缩流体在重力和流体静力平衡中均匀旋转的形式有关。在1834年,Jacobi <ref>{{cite journal| last=Jacobi | first=C.G.J. | title=Über die figur des gleichgewichts | journal=[[Annalen der Physik und Chemie]] | volume=109 | issue=33| pages=229–238 | year=1834| doi=10.1002/andp.18341090808 | bibcode=1834AnP...109..229J | url=https://zenodo.org/record/2027349 }}</ref>和后来的 Liouville <ref>{{cite journal| last=Liouville | first=J. | title=Sur la figure d'une masse fluide homogène, en équilibre et douée d'un mouvement de rotation| journal=Journal de l'École Polytechnique | issue=14| pages=289–296 | year=1834}}</ref>讨论了这样一个事实: 当旋转物体的动能相对于引力势能超过一定的临界值时,这个问题的平衡解是三轴椭球。在这个分叉点上,麦克劳林椭球体的轴对称性被破坏。此外,在这个分叉点之上,对于常数角动量,使动能最小化的解是非轴对称的 Jacobi 椭球,而不是 Maclaurin 椭球。<br />
==另请参阅==<br />
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*[[Higgs mechanism]]<br />
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*[[QCD vacuum]]<br />
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*[[Goldstone boson]]<br />
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*[[1964 PRL symmetry breaking papers]]<br />
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*[[希格斯机制]]<br />
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*[[QCD真空]]<br />
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*[[戈德斯通玻色子]]<br />
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*[[1964年PRL对称性破缺论文]]<br />
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==参考文献==<br />
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{{reflist|colwidth=30em}}<br />
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{{DEFAULTSORT:Symmetry Breaking}}<br />
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范畴: 对称<br />
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类别: 模式形成<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''<br />
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<noinclude><br />
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[[Category:对称性破缺]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%AF%B9%E7%A7%B0%E6%80%A7%E7%A0%B4%E7%BC%BA&diff=24822对称性破缺2021-07-27T14:12:54Z<p>Jxzhou:/* Generalisation and technical usage */</p>
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[[图一:一个小球位于中央山丘的山峰处(C)。这是一种不稳定平衡:一个很小的扰动会使它落到左边(L)或右边(R)稳定点。尽管山丘是对称的,没有理由让球落在哪一侧,但观察到的最终状态仍然是不对称的,它总会落到某一侧]]。<br />
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在物理学中,一个作用于系统的(无限)小扰动使系统跨过临界点,通过决定去向分叉的哪个分支来决定系统的命运,这种现象叫做'''<font color="#ff8000">对称性破缺</font>'''。对于一个观测不到扰动(或“噪声”)的外部观察者来说,这个选择看起来是任意的。这个过程被称为对称性破缺,因为这种转变通常使系统从一个对称但无序的状态进入一个或多个确定的状态。在'''<font color="#ff8000">斑图生成</font>'''中对称性破缺起着重要作用。<br />
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1972年,诺贝尔奖得主P·W·安德森(P.W.Anderson)在《科学》(Science)杂志上发表了一篇名为《多即不同》的论文<ref>{{cite journal | last=Anderson | first=P.W. | title=More is Different | journal=Science | volume=177 | issue=4047| pages=393–396 | year=1972 | url=http://robotics.cs.tamu.edu/dshell/cs689/papers/anderson72more_is_different.pdf | doi=10.1126/science.177.4047.393 | pmid=17796623 | format=|bibcode = 1972Sci...177..393A }}</ref>,文中使用对称性破缺的思想表明,即使'''<font color="#ff8000">还原论</font>'''是正确的,但它的逆命题'''<font color="#ff8000">建构主义</font>'''是错误的。建构主义认为,在给出描述各组成部分的理论的情况下科学家可以轻易地预测复杂现象。<br />
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对称性破缺可以分为'''<font color="#ff8000">显性对称性破缺</font>'''和'''<font color="#ff8000">自发对称性破缺</font>'''两种类型,二者的区别是,在破缺对称性下系统的运动方程是否不变或者基态是否保持不变。<br />
==显性对称性破缺==<br />
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在'''<font color="#ff8000">显性对称性破缺</font>'''中,描述系统的运动方程在破缺对称下是不同的。在哈密顿力学或拉格朗日力学中,假若系统的哈密顿量(或拉格朗日量)中至少一项显性地打破了给定的对称性,就发生了显性对称性破缺。<br />
==自发对称性破缺==<br />
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在'''<font color="#ff8000">自发对称性破缺</font>'''中,系统的运动方程是不变的,但系统发生了变化。这是因为系统的背景(时空)——真空态——是非恒定的。这种对称性破缺可以用一个序参量进行参数化。这类对称破缺的一个特殊情况是'''<font color="#ff8000">动力学对称性破缺</font>'''。<br />
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Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state ends up in an asymmetric state.[1][2][3] In particular, it can describe systems where the equations of motion or the Lagrangian obey symmetries, but the lowest-energy vacuum solutions do not exhibit that same symmetry. When the system goes to one of those vacuum solutions, the symmetry is broken for perturbations around that vacuum even though the entire Lagrangian retains that symmetry.<br />
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自发对称破缺是一个自发的对称破缺过程,它使处于对称状态的物理系统最终处于非对称状态。特别地,它可以描述运动方程或拉格朗日方程服从某种对称性,但最低能量真空解不具有该对称性的系统。当系统进入其中一个真空解时,真空解周围的扰动会破坏系统对称性,尽管整个拉格朗日方程仍然保持了对称性。<br />
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==Overview==<br />
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In [[explicit symmetry breaking]], if two outcomes are considered, the probability of a pair of outcomes can be different. By definition, spontaneous symmetry breaking requires the existence of a symmetric probability distribution—any pair of outcomes has the same probability. In other words, the underlying laws{{clarify|date=December 2016}} are [[Invariant (physics)|invariant]] under a [[Symmetry (physics)|symmetry]] transformation.<br />
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The system, as a whole{{clarify|date=December 2016}}, changes under such transformations.<br />
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Phases of matter, such as crystals, magnets, and conventional superconductors, as well as simple phase transitions can be described by spontaneous symmetry breaking. Notable exceptions include topological phases of matter like the [[fractional quantum Hall effect]].<br />
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==Examples 例子==<br />
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===Sombrero potential===<br />
Consider a symmetric upward dome with a trough circling the bottom. If a ball is put at the very peak of the dome, the system is symmetric with respect to a rotation around the center axis. But the ball may ''spontaneously break'' this symmetry by rolling down the dome into the trough, a point of lowest energy. Afterward, the ball has come to a rest at some fixed point on the perimeter. The dome and the ball retain their individual symmetry, but the system does not.<ref>{{cite book |first=Gerald M. |last=Edelman |title=Bright Air, Brilliant Fire: On the Matter of the Mind |location=New York |publisher=BasicBooks |year=1992 |url=https://archive.org/details/brightairbrillia00gera |url-access=registration |page=[https://archive.org/details/brightairbrillia00gera/page/203 203] }}</ref><br />
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考虑一个对称向上的圆顶,底部环绕着一个槽。如果把一个球放在圆顶的最顶端,这个系统是围绕中心轴旋转对称的。但球体可能会自发地打破这种对称性,因为它会沿着穹顶滚动到能量最低的槽中。然后,球在圆周上某个固定的点上停下来。圆顶和球保持了各自的对称,但系统却没有保持对称性。<br />
[[Image:Mexican hat potential polar.svg|270px|thumb|left|Graph of Goldstone's "[[sombrero]]" potential function <math>V(\phi)</math>.|链接=Special:FilePath/Mexican_hat_potential_polar.svg]]<br />
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In the simplest idealized relativistic model, the spontaneously broken symmetry is summarized through an illustrative [[scalar field theory]]. The relevant [[Lagrangian (field theory)|Lagrangian]] of a scalar field <math>\phi</math>, which essentially dictates how a system behaves, can be split up into kinetic and potential terms,<br />
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在最简单的理想相对论模型中,可以用一个解释性的标量场理论总结自发破对称性。一个标量场 <math>\phi</math>的拉格朗日量从本质上决定了系统的行为,它可以分解成动能项和势能项:<br />
{{NumBlk|::|<math>\mathcal{L} = \partial^\mu \phi \partial_\mu \phi - V(\phi).</math>|{{EquationRef|1}}}}<br />
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It is in this potential term <math>V(\phi)</math> that the symmetry breaking is triggered. An example of a potential, due to [[Jeffrey Goldstone]]<ref>{{Cite journal | last1 = Goldstone | first1 = J. | doi = 10.1007/BF02812722 | title = Field theories with " Superconductor " solutions | journal = Il Nuovo Cimento | volume = 19 | issue = 1 | pages = 154–164 | year = 1961 | bibcode = 1961NCim...19..154G | s2cid = 120409034 | url = http://cds.cern.ch/record/343400 }}</ref> is illustrated in the graph at the left.<br />
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正是在势能项 <math>V(\phi)</math> 中触发了对称性破缺。例如左图所示的 [[Jeffrey Goldstone]] 给出的势能函数:<br />
{{NumBlk|::|<math>V(\phi) = -5|\phi|^2 + |\phi|^4 \,</math>.|{{EquationRef|2}}}}<br />
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This potential has an infinite number of possible [[minimum|minima]] (vacuum states) given by<br />
<br />
该是函数具有无穷数量的最小值点(真空态)当<br />
{{NumBlk|::|<math>\phi = \sqrt{5} e^{i\theta} </math>.|{{EquationRef|3}}}}<br />
for any real ''θ'' between 0 and 2''π''. The system also has an unstable vacuum state corresponding to {{nowrap|1=''Φ'' = 0}}. This state has a [[Unitary group|U(1)]] symmetry. However, once the system falls into a specific stable vacuum state (amounting to a choice of ''θ''), this symmetry will appear to be lost, or "spontaneously broken".<br />
<br />
对于0到2π之间的任何实数θ。系统也有一个不稳定的真空状态,对应于Φ = 0。这个状态具有U(1)对称。然而,一旦系统落入某个稳定真空状态(相当于选择θ),这种对称性就会消失,或者说“自发破缺”。<br />
<br />
In fact, any other choice of ''θ'' would have exactly the same energy, implying the existence of a massless [[Goldstone boson|Nambu–Goldstone boson]], the mode running around the circle at the minimum of this potential, and indicating there is some memory of the original symmetry in the Lagrangian.<br />
<br />
事实上,任何其他θ的选择都将具有完全相同的能量,这意味着无质量的南部-戈德斯通玻色子的存在,这种模式在势能的最小值绕圆运动,并表明存在拉格朗日方程中原始对称性的一些记忆。<br />
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===Other examples===<br />
* For [[ferromagnet]]ic materials, the underlying laws are invariant under spatial rotations. Here, the order parameter is the [[magnetization]], which measures the magnetic dipole density. Above the [[Curie temperature]], the order parameter is zero, which is spatially invariant, and there is no symmetry breaking. Below the Curie temperature, however, the magnetization acquires a constant nonvanishing value, which points in a certain direction (in the idealized situation where we have full equilibrium; otherwise, translational symmetry gets broken as well). The residual rotational symmetries which leave the orientation of this vector invariant remain unbroken, unlike the other rotations which do not and are thus spontaneously broken.<br />
* 对于铁磁性材料,其基本定律在空间旋转下是不变的。在这里,序参量是衡量磁偶极子密度的磁化强度。在居里温度以上,序参量为零,具有空间不变性,不存在对称性破缺。然而,在居里温度以下,磁化强度变成一个恒定的非零值,指向一个特定的方向(在有充分平衡的理想情况下;否则,平移对称性也会破缺)。使该向量方向不变的旋转对称性仍然保留,而其他旋转对称性自发破缺。<br />
* The laws describing a solid are invariant under the full [[Euclidean group]], but the solid itself spontaneously breaks this group down to a [[space group]]. The displacement and the orientation are the order parameters.<br />
* 描述固体的定律在完整的欧几里得群下是不变的,但固体本身会自发地将这个群分解为一个空间群。其中位移和方向是序参量。<br />
* General relativity has a Lorentz symmetry, but in [[Friedmann–Lemaître–Robertson–Walker metric|FRW cosmological models]], the mean 4-velocity field defined by averaging over the velocities of the galaxies (the galaxies act like gas particles at cosmological scales) acts as an order parameter breaking this symmetry. Similar comments can be made about the cosmic microwave background.<br />
* 广义相对论具有洛伦兹对称性,但在FRW宇宙模型中,定义为星系速度的平均值(星系在宇宙尺度上的行为就像气体粒子) 的平均 4-速度场,作为序参量会打破这种对称性。对于宇宙微波背景辐射也有类似的评论。<br />
* For the [[electroweak]] model, as explained earlier, a component of the Higgs field provides the order parameter breaking the electroweak gauge symmetry to the electromagnetic gauge symmetry. Like the ferromagnetic example, there is a phase transition at the electroweak temperature. The same comment about us not tending to notice broken symmetries suggests why it took so long for us to discover electroweak unification.<br />
* 对于电弱模型,如前面所解释的,希格斯场的一个分量提供了将电弱规范对称性破缺到电磁规范对称性的序参量。和铁磁的例子一样,在电弱温度下也有相变。同样的关于我们不倾向于注意破缺对称性的评论,也说明了为什么我们花了这么长时间才发现电弱统一。<br />
* In superconductors, there is a condensed-matter collective field ψ, which acts as the order parameter breaking the electromagnetic gauge symmetry.<br />
* 在超导体中有一个凝聚态集体场ψ,它是打破电磁规范对称性的序参量。<br />
* Take a thin cylindrical plastic rod and push both ends together. Before buckling, the system is symmetric under rotation, and so visibly cylindrically symmetric. But after buckling, it looks different, and asymmetric. Nevertheless, features of the cylindrical symmetry are still there: ignoring friction, it would take no force to freely spin the rod around, displacing the ground state in time, and amounting to an oscillation of vanishing frequency, unlike the radial oscillations in the direction of the buckle. This spinning mode is effectively the requisite [[Goldstone boson|Nambu–Goldstone boson]].<br />
* 拿一个细长的圆柱形塑料杆,把两端推到一起。在屈曲之前,系统在旋转下是对称的,因此可见圆柱对称性。但在弯曲之后,它看起来就不同了,而且是不对称的。然而,圆柱对称性的特征仍然存在:忽略摩擦,杆可以不受外力自由地自旋,在时间上取代基态,等于一个频率趋于零的振荡,而不是沿屈曲方向的径向振荡。这种自旋模式实际上是必需的南部-戈德斯通玻色子。<br />
* Consider a uniform layer of [[fluid]] over an infinite horizontal plane. This system has all the symmetries of the Euclidean plane. But now heat the bottom surface uniformly so that it becomes much hotter than the upper surface. When the temperature gradient becomes large enough, [[convection cell]]s will form, breaking the Euclidean symmetry.<br />
* 考虑无限水平面上的一层均匀的流体。这个系统具有欧几里得平面的所有对称性。但是现在均匀地加热底部表面,使它变得比上表面热得多。当温度梯度足够大时,就会形成对流单元,打破了欧几里得对称。<br />
* Consider a bead on a circular hoop that is rotated about a vertical [[diameter]]. As the [[rotational velocity]] is increased gradually from rest, the bead will initially stay at its initial [[equilibrium point]] at the bottom of the hoop (intuitively stable, lowest [[gravitational potential]]). At a certain critical rotational velocity, this point will become unstable and the bead will jump to one of two other newly created equilibria, [[equidistant]] from the center. Initially, the system is symmetric with respect to the diameter, yet after passing the critical velocity, the bead ends up in one of the two new equilibrium points, thus breaking the symmetry.<br />
* 考虑一个围绕某个竖直的直径旋转的圆形箍上的珠子。当旋转速度从静止逐渐增加时,珠子最初会停留在环底部的初始平衡点(直观上稳定,重力势最低)。在一定的临界旋转速度下,这一点将变得不稳定,珠子将跳到另外两个新创建的离中心等距离的平衡点中的一个。起初,系统相对直径是对称的,但在通过临界速度后,珠子最终停留在两个新的平衡点中的一个,从而打破了对称性。<br />
<br />
==Spontaneous symmetry breaking in physics 物理学中的自发对称性破缺==<br />
[[File:Spontaneous symmetry breaking (explanatory diagram).png|thumb|right|250px|''Spontaneous symmetry breaking illustrated'': At high energy levels (''left''), the ball settles in the center, and the result is symmetric. At lower energy levels (''right''), the overall "rules" remain symmetric, but the symmetric "[[sombrero|Sombrero]]" enforces an asymmetric outcome, since eventually the ball must rest at some random spot on the bottom, "spontaneously", and not all others.|链接=Special:FilePath/Spontaneous_symmetry_breaking_(explanatory_diagram).png]]<br />
<br />
===Particle physics 粒子物理===<br />
In [[particle physics]], the [[force carrier]] particles are normally specified by field equations with [[gauge symmetry]]; their equations predict that certain measurements will be the same at any point in the field. For instance, field equations might predict that the mass of two quarks is constant. Solving the equations to find the mass of each quark might give two solutions. In one solution, quark A is heavier than quark B. In the second solution, quark B is heavier than quark A ''by the same amount''. The symmetry of the equations is not reflected by the individual solutions, but it is reflected by the range of solutions.<br />
<br />
在粒子物理学中,载力子通常由规范对称的场方程表示;它们的方程预测到某些测量值在场的任何点上都是相同的。例如,场方程可以预测两个夸克的质量是常数。通过求解方程来求每个夸克的质量可能会得到两个解。在一个解中,夸克A比夸克B重;在第二个解中,夸克B比夸克A重相同的量。方程的对称性不是由单个解来反映的,而是由解的范围来反映的。<br />
<br />
An actual measurement reflects only one solution, representing a breakdown in the symmetry of the underlying theory. "Hidden" is a better term than "broken", because the symmetry is always there in these equations. This phenomenon is called [[Spontaneous magnetization|''spontaneous'']] symmetry breaking (SSB) because ''nothing'' (that we know of) breaks the symmetry in the equations.<ref name="Weinberg2011">{{cite book|author=Steven Weinberg|title=Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature|url=https://books.google.com/books?id=Rsg3PE_9_ccC|date=20 April 2011|publisher=Knopf Doubleday Publishing Group|isbn=978-0-307-78786-6}}</ref>{{rp|194–195}}<br />
<br />
一个实际的测量只反映了一个解,代表了其潜在理论的对称性的破缺。在这里“隐藏”是比“破坏”更好的术语,因为对称性总是存在于这些方程中。这种现象被称为自发对称破缺(SSB),因为(我们所知道的)没有任何东西会打破方程中的对称性。<br />
<br />
====Chiral symmetry 手性对称性====<br />
{{Main article|Chiral symmetry breaking}}<br />
Chiral symmetry breaking is an example of spontaneous symmetry breaking affecting the [[chiral symmetry]] of the [[strong interactions]] in particle physics. It is a property of [[quantum chromodynamics]], the [[quantum field theory]] describing these interactions, and is responsible for the bulk of the mass (over 99%) of the [[nucleons]], and thus of all common matter, as it converts very light bound [[quarks]] into 100 times heavier constituents of [[baryons]]. The approximate [[Nambu–Goldstone boson]]s in this spontaneous symmetry breaking process are the [[pions]], whose mass is an order of magnitude lighter than the mass of the nucleons. It served as the prototype and significant ingredient of the Higgs mechanism underlying the electroweak symmetry breaking.<br />
<br />
手性对称破缺是粒子物理中影响强相互作用手性对称的自发对称破缺的一个例子。手性对称性破缺是量子色动力学(描述这些相互作用的量子场理论)的一种特性,它是核子的大部分质量(超过99%)的成因,因此也是所有普通物质的主要成因,因为它将非常轻的束缚夸克转化为100倍重量的重子的成分。在这个自发对称破缺过程中,近似的南部-戈德斯通玻色子是介子,其质量比核子的质量轻一个数量级。它是电弱对称破缺的希格斯机制的原型和重要组成部分。<br />
<br />
====Higgs mechanism 希格斯机制====<br />
{{Main article|Higgs mechanism|Yukawa interaction}}<br />
<br />
The strong, weak, and electromagnetic forces can all be understood as arising from [[gauge symmetry|gauge symmetries]]. The [[Higgs mechanism]], the spontaneous symmetry breaking of gauge symmetries, is an important component in understanding the [[superconductivity]] of metals and the origin of particle masses in the standard model of particle physics. One important consequence of the distinction between true symmetries and ''gauge symmetries'', is that the spontaneous breaking of a gauge symmetry does not give rise to characteristic massless Nambu–Goldstone physical modes, but only massive modes, like the plasma mode in a superconductor, or the Higgs mode observed in particle physics.<br />
<br />
强、弱和电磁力都可以理解为来自规范对称。希格斯机制,即规范对称的自发对称破缺机制,是理解金属超导性和粒子物理标准模型中粒子质量起源的重要组成部分。区分真正的对称性和规范对称性的一个重要的结果,是规范对称性的自发破缺不产生典型的无质量Nambu-Goldstone物理模式,而是只产生有质量的模式,像超导体中的等离子体模式,或者粒子物理学中观察到的希格斯模式。<br />
<br />
In the standard model of particle physics, spontaneous symmetry breaking of the {{nowrap|SU(2) × U(1)}} gauge symmetry associated with the electro-weak force generates masses for several particles, and separates the electromagnetic and weak forces. The [[W and Z bosons]] are the elementary particles that mediate the [[weak interaction]], while the [[photon]] mediates the [[electromagnetic interaction]]. At energies much greater than 100 GeV, all these particles behave in a similar manner. The [[Unified field theory#Modern progress|Weinberg–Salam theory]] predicts that, at lower energies, this symmetry is broken so that the photon and the massive W and Z bosons emerge.<ref>A Brief History of Time, Stephen Hawking, Bantam; 10th anniversary edition (1998). pp. 73–74.{{ISBN?}}</ref> In addition, fermions develop mass consistently.<br />
<br />
在粒子物理的标准模型中,与电弱力相关的SU(2) × U(1)规范对称性自发破缺产生多种粒子的质量,并将电磁力和弱相互作用分离。W玻色子和Z玻色子是介导弱相互作用的基本粒子,而光子介导电磁相互作用。当能量远远大于100 GeV时,所有这些粒子的行为都相似。Weinberg-Salam理论预测,在较低的能量下,这种对称性被打破,光子和大质量的W和Z玻色子就会出现。此外,费米子不断地发展质量。<br />
<br />
Without spontaneous symmetry breaking, the [[Standard Model]] of elementary particle interactions requires the existence of a number of particles. However, some particles (the [[W and Z bosons]]) would then be predicted to be massless, when, in reality, they are observed to have mass. To overcome this, spontaneous symmetry breaking is augmented by the [[Higgs mechanism]] to give these particles mass. It also suggests the presence of a new particle, the [[Higgs boson]], detected in 2012.<br />
<br />
在没有自发对称性破缺的情况下,基本粒子相互作用的标准模型要求存在多种粒子。然而,一些粒子(W玻色子和Z玻色子)将被预测为无质量的,而实际上它们被观察到有质量。为了克服这个问题,希格斯机制增强了自发对称破缺,从而赋予这些粒子质量。它还表明一种新粒子——希格斯玻色子——的存在,它在2012年被实验探测到。<br />
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[[Superconductivity]] of metals is a condensed-matter analog of the Higgs phenomena, in which a condensate of Cooper pairs of electrons spontaneously breaks the U(1) gauge symmetry associated with light and electromagnetism.<br />
<br />
金属的超导性是一种类似于希格斯现象的凝聚态物质,其中库珀电子对的凝聚会自发地打破与光和电磁相关的U(1)规范对称。<br />
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===Condensed matter physics===<br />
Most phases of matter can be understood through the lens of spontaneous symmetry breaking. For example, crystals are periodic arrays of atoms that are not invariant under all translations (only under a small subset of translations by a lattice vector). Magnets have north and south poles that are oriented in a specific direction, breaking [[rotational symmetry]]. In addition to these examples, there are a whole host of other symmetry-breaking phases of matter — including nematic phases of liquid crystals, charge- and spin-density waves, superfluids, and many others.<br />
<br />
There are several known examples of matter that cannot be described by spontaneous symmetry breaking, including: topologically ordered phases of matter, such as [[Fractional quantum Hall effect|fractional quantum Hall liquids]], and [[Quantum spin liquid|spin-liquids]]. These states do not break any symmetry, but are distinct phases of matter. Unlike the case of spontaneous symmetry breaking, there is not a general framework for describing such states.<ref name=chen>{{cite journal | last1 = Chen | first1 = Xie | author-link3 = Xiao-Gang Wen | last2 = Gu | first2 = Zheng-Cheng | last3 = Wen | first3 = Xiao-Gang | year = 2010 | title = Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order | journal = Phys. Rev. B | volume = 82 | issue = 15| page = 155138 | doi=10.1103/physrevb.82.155138|arxiv = 1004.3835 |bibcode = 2010PhRvB..82o5138C | s2cid = 14593420 }}</ref><br />
<br />
====Continuous symmetry====<br />
The ferromagnet is the canonical system that spontaneously breaks the continuous symmetry of the spins below the [[Curie temperature]] and at {{nowrap|1=''h'' = 0}}, where ''h'' is the external magnetic field. Below the [[Curie temperature]], the energy of the system is invariant under inversion of the magnetization ''m''('''x''') such that {{nowrap|1=''m''('''x''') = −''m''(−'''x''')}}. The symmetry is spontaneously broken as {{nowrap|''h'' → 0}} when the Hamiltonian becomes invariant under the inversion transformation, but the expectation value is not invariant.<br />
<br />
Spontaneously-symmetry-broken phases of matter are characterized by an order parameter that describes the quantity which breaks the symmetry under consideration. For example, in a magnet, the order parameter is the local magnetization.<br />
<br />
Spontaneous breaking of a continuous symmetry is inevitably accompanied by gapless (meaning that these modes do not cost any energy to excite) Nambu–Goldstone modes associated with slow, long-wavelength fluctuations of the order parameter. For example, vibrational modes in a crystal, known as phonons, are associated with slow density fluctuations of the crystal's atoms. The associated Goldstone mode for magnets are oscillating waves of spin known as spin-waves. For symmetry-breaking states, whose order parameter is not a conserved quantity, Nambu–Goldstone modes are typically massless and propagate at a constant velocity.<br />
<br />
An important theorem, due to Mermin and Wagner, states that, at finite temperature, thermally activated fluctuations of Nambu–Goldstone modes destroy the long-range order, and prevent spontaneous symmetry breaking in one- and two-dimensional systems. Similarly, quantum fluctuations of the order parameter prevent most types of continuous symmetry breaking in one-dimensional systems even at zero temperature. (An important exception is ferromagnets, whose order parameter, magnetization, is an exactly conserved quantity and does not have any quantum fluctuations.)<br />
<br />
Other long-range interacting systems, such as cylindrical curved surfaces interacting via the [[Coulomb potential]] or [[Yukawa potential]], have been shown to break translational and rotational symmetries.<ref><br />
{{cite journal<br />
|last1=Kohlstedt |first1=K.L.<br />
|last2=Vernizzi |first2=G.<br />
|last3=Solis |first3=F.J.<br />
|last4=Olvera de la Cruz |first4=M.<br />
|year=2007<br />
|title=Spontaneous Chirality via Long-range Electrostatic Forces<br />
|journal=[[Physical Review Letters]]<br />
|volume=99 |issue=3<br />
|page=030602<br />
|doi=10.1103/PhysRevLett.99.030602<br />
|arxiv = 0704.3435 |bibcode = 2007PhRvL..99c0602K |pmid=17678276|s2cid=37983980<br />
}}</ref> It was shown, in the presence of a symmetric Hamiltonian, and in the limit of infinite volume, the system spontaneously adopts a chiral configuration — i.e., breaks [[mirror plane]] [[symmetry]].<br />
<br />
===Dynamical symmetry breaking 动力学对称性破缺===<br />
Dynamical symmetry breaking (DSB) is a special form of spontaneous symmetry breaking in which the ground state of the system has reduced symmetry properties compared to its theoretical description (i.e., [[Lagrangian (field theory)|Lagrangian]]).<br />
<br />
动力学对称性破缺(DSB)是自发对称性破缺的一种特殊形式,在这种情况下,系统的基态比理论描述(例如拉格朗日量)的对称性降低。<br />
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Dynamical breaking of a global symmetry is a spontaneous symmetry breaking, which happens not at the (classical) tree level (i.e., at the level of the bare action), but due to quantum corrections (i.e., at the level of the [[effective action]]).<br />
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全局对称性的动力学破缺是自发对称性破缺,它不是发生在(经典)树的水平(例如在bare作用的水平),而是由于量子修正(例如在有效作用的水平)。<br />
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Dynamical breaking of a gauge symmetry {{ref|note1}} is subtler. In the conventional spontaneous gauge symmetry breaking, there exists an unstable [[Higgs particle]] in the theory, which drives the vacuum to a symmetry-broken phase. (See, for example, [[electroweak interaction]].) In dynamical gauge symmetry breaking, however, no unstable Higgs particle operates in the theory, but the bound states of the system itself provide the unstable fields that render the phase transition. For example, Bardeen, Hill, and Lindner published a paper that attempts to replace the conventional [[Higgs mechanism]] in the [[standard model]] by a DSB that is driven by a bound state of top-antitop quarks. (Such models, in which a composite particle plays the role of the Higgs boson, are often referred to as "Composite Higgs models".)<ref><br />
{{cite journal<br />
|author1=William A. Bardeen<br />
|author2-link=Christopher T. Hill<br />
|author2=Christopher T. Hill<br />
|author3-link=Manfred Lindner<br />
|author3=Manfred Lindner<br />
|year=1990<br />
|title=Minimal dynamical symmetry breaking of the standard model<br />
|journal=[[Physical Review D]]<br />
|volume=41 |issue=5 |pages=1647–1660<br />
|bibcode=1990PhRvD..41.1647B<br />
|doi=10.1103/PhysRevD.41.1647<br />
|pmid=10012522<br />
|author1-link=William A. Bardeen<br />
}}</ref> Dynamical breaking of gauge symmetries is often due to creation of a [[fermionic condensate]] — e.g., the [[quark condensate]], which is connected to the [[Chiral symmetry breaking|dynamical breaking of chiral symmetry]] in [[quantum chromodynamics]]. Conventional [[superconductivity]] is the paradigmatic example from the condensed matter side, where phonon-mediated attractions lead electrons to become bound in pairs and then condense, thereby breaking the electromagnetic gauge symmetry.<br />
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规范对称性动力学破缺更加微妙。在常规规范对称自发破缺理论中,存在一个不稳定的希格斯粒子,希格斯粒子驱动真空进入对称破缺相。(例如,参见弱电相互作用。)然而,在规范对称性动力学破缺中,不存在不稳定的希格斯粒子,但系统本身的束缚态提供了导致相变的不稳定场。例如,巴丁、希尔和林德纳发表了一篇论文,试图用一个由顶-反顶夸克束缚状态驱动的DSB来取代标准模型中的传统希格斯机制。(在这种模型中,复合粒子扮演希格斯玻色子的角色,通常被称为“复合希格斯模型”。)规范对称性动力学破缺通常是由于费米凝聚的产生,例如夸克凝聚,它与量子色动力学中手性对称的动力学破缺有关。传统的超导性是凝聚态物质方面的典型例子,声子的吸引导致电子成对结合然后凝聚,从而打破电磁规范对称性。<br />
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==Generalisation and technical usage==<br />
For spontaneous symmetry breaking to occur, there must be a system in which there are several equally likely outcomes. The system as a whole is therefore [[Symmetry (physics)|symmetric]] with respect to these outcomes. However, if the system is sampled (i.e. if the system is actually used or interacted with in any way), a specific outcome must occur. Though the system as a whole is symmetric, it is never encountered with this symmetry, but only in one specific asymmetric state. Hence, the symmetry is said to be spontaneously broken in that theory. Nevertheless, the fact that each outcome is equally likely is a reflection of the underlying symmetry, which is thus often dubbed "hidden symmetry", and has crucial formal consequences. (See the article on the [[Nambu–Goldstone boson|Goldstone boson]].)<br />
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要发生自发对称性破缺,系统中必须有几个等可能的结果,整个系统相对于这些结果是对称的。然而,如果对系统进行采样(即如果系统被实际使用或以任何方式与之交互),就必须产生特定的结果。虽然系统作为一个整体是对称的,但它从来没有表现出这种对称性,而只是处于一个特定的不对称状态。于是,在该理论中对称性被自发地打破了。然而,每个结果的可能性都相等这一点,反映了潜在的对称性。因此通常被称为“隐藏对称性”,并具有重要的形式结果。(参见有关戈德斯通玻色子的文章。)<br />
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When a theory is symmetric with respect to a [[symmetry group]], but requires that one element of the group be distinct, then spontaneous symmetry breaking has occurred. The theory must not dictate ''which'' member is distinct, only that ''one is''. From this point on, the theory can be treated as if this element actually is distinct, with the proviso that any results found in this way must be resymmetrized, by taking the average of each of the elements of the group being the distinct one.<br />
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当一个理论相对于一个对称群是对称的,但要求群中的一个元素是不同的,那么就会发生自发对称性破缺。理论不能规定哪个成员是不同的,而只能规定那个成员是不同的。从这一点开始,这个理论就可以被视为这个元素实际上是不同的,附带的条件是,任何以这种方式发现的结果必须是重新对称的,通过取组中每个元素的平均值作为不同的元素。<br />
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The crucial concept in physics theories is the [[order parameter]]. If there is a field (often a background field) which acquires an expectation value (not necessarily a [[vacuum expectation value|''vacuum'' expectation value]]) which is not invariant under the symmetry in question, we say that the system is in the [[ordered phase]], and the symmetry is spontaneously broken. This is because other subsystems interact with the order parameter, which specifies a "frame of reference" to be measured against. In that case, the [[vacuum state]] does not obey the initial symmetry (which would keep it invariant, in the linearly realized '''Wigner mode''' in which it would be a singlet), and, instead changes under the (hidden) symmetry, now implemented in the (nonlinear) '''Nambu–Goldstone mode'''. Normally, in the absence of the Higgs mechanism, massless [[Goldstone boson]]s arise.<br />
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在物理理论中,最重要的概念是序参量。如果有一个场(通常是背景场)得到一个期望值(不一定是真空期望值),这个期望值在理论具有的对称性下不是不变的,我们就说系统处于有序相,对称性自发破缺。这是因为序参量指定了测量其他子系统与之相互作用的“参考框架”。在这种情况下,真空状态不服从初始对称性(这将保持它不变,在线性实现的Wigner模式中,它将是一个单线),而是在(隐藏的)对称下变化,现在在(非线性)南布-戈德斯通模式中实现。通常,在没有希格斯机制的情况下,就会出现无质量的戈德斯通玻色子。<br />
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The symmetry group can be discrete, such as the [[space group]] of a crystal, or continuous (e.g., a [[Lie group]]), such as the rotational symmetry of space. However, if the system contains only a single spatial dimension, then only discrete symmetries may be broken in a [[vacuum state]] of the full [[Quantum mechanics|quantum theory]], although a classical solution may break a continuous symmetry.<br />
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对称群可以是离散的,如晶体的空间群,也可以是连续的(如李群),如空间的旋转对称。然而,如果系统只包含一个空间维度,尽管经典解可能打破连续对称性,那么在全量子理论的真空状态下,只有离散的对称性可能被打破。<br />
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==Nobel Prize==<br />
On October 7, 2008, the [[Royal Swedish Academy of Sciences]] awarded the 2008 [[Nobel Prize in Physics]] to three scientists for their work in subatomic physics symmetry breaking. [[Yoichiro Nambu]], of the [[University of Chicago]], won half of the prize for the discovery of the mechanism of spontaneous broken symmetry in the context of the strong interactions, specifically [[chiral symmetry breaking]]. Physicists [[Makoto Kobayashi (physicist)|Makoto Kobayashi]] and [[Toshihide Maskawa]], of [[Kyoto University]], shared the other half of the prize for discovering the origin of the [[Explicit symmetry breaking|explicit breaking]] of CP symmetry in the weak interactions.<ref>{{cite web|author=The Nobel Foundation|title=The Nobel Prize in Physics 2008|url=http://nobelprize.org/nobel_prizes/physics/laureates/2008/index.html|work=nobelprize.org|access-date=January 15, 2008}}</ref> This origin is ultimately reliant on the Higgs mechanism, but, so far understood as a "just so" feature of Higgs couplings, not a spontaneously broken symmetry phenomenon.<br />
<br />
==See also==<br />
{{div col|colwidth=24em}}<br />
* [[Autocatalytic reactions and order creation]]<br />
* [[Catastrophe theory]]<br />
* [[Chiral symmetry breaking]]<br />
* [[CP-violation]]<br />
* [[Fermi ball]]<br />
* [[Gauge gravitation theory]]<br />
* [[Goldstone boson]]<br />
* [[Grand unified theory]]<br />
* [[Higgs mechanism]]<br />
* [[Higgs boson]]<br />
* [[Higgs field (classical)]]<br />
* [[Irreversibility]]<br />
* [[Magnetic catalysis]] of chiral symmetry breaking<br />
* [[Mermin–Wagner theorem]]<br />
* [[Norton's dome]]<br />
* [[Second-order phase transition]]<br />
* [[Spontaneous absolute asymmetric synthesis]] in chemistry<br />
* [[Symmetry breaking]]<br />
* [[Tachyon condensation]]<br />
* [[1964 PRL symmetry breaking papers]]<br />
{{div col end}}<br />
<br />
==Notes==<br />
* {{note|note1}} Note that (as in fundamental Higgs driven spontaneous gauge symmetry breaking) the term "symmetry breaking" is a misnomer when applied to gauge symmetries.<br />
<br />
==References==<br />
{{Reflist}}<br />
<br />
==External links==<br />
{{wikiquote}}<br />
* For a pedagogic introduction to electroweak symmetry breaking with step by step derivations, not found in texts, of many key relations, see http://www.quantumfieldtheory.info/Electroweak_Sym_breaking.pdf<br />
* [http://hyperphysics.phy-astr.gsu.edu/hbase/forces/unify.html#c2 Spontaneous symmetry breaking]<br />
* [http://prl.aps.org/50years/milestones#1964 Physical Review Letters – 50th Anniversary Milestone Papers]<br />
* [http://cerncourier.com/cws/article/cern/32522 In CERN Courier, Steven Weinberg reflects on spontaneous symmetry breaking]<br />
* [http://www.scholarpedia.org/article/Englert-Brout-Higgs-Guralnik-Hagen-Kibble_mechanism Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism on Scholarpedia]<br />
* [http://www.scholarpedia.org/article/Englert-Brout-Higgs-Guralnik-Hagen-Kibble_mechanism_%28history%29 History of Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism on Scholarpedia]<br />
* [https://arxiv.org/abs/0907.3466 The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles]<br />
* [http://www.worldscinet.com/ijmpa/24/2414/S0217751X09045431.html International Journal of Modern Physics A: The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles]<br />
* [http://www.datafilehost.com/download-7d512618.html Guralnik, G S; Hagen, C R and Kibble, T W B (1967). Broken Symmetries and the Goldstone Theorem. Advances in Physics, vol. 2 Interscience Publishers, New York. pp. 567–708] {{ISBN|0-470-17057-3}}<br />
* [http://lanl.arxiv.org/abs/hep-th/9802142 Spontaneous Symmetry Breaking in Gauge Theories: a Historical Survey]<br />
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{{Standard model of physics}}<br />
{{Quantum mechanics topics}}<br />
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{{DEFAULTSORT:Spontaneous Symmetry Breaking}}<br />
[[Category:Theoretical physics]]<br />
[[Category:Quantum field theory]]<br />
[[Category:Standard Model]]<br />
[[Category:Quantum chromodynamics]]<br />
[[Category:Symmetry]]<br />
[[Category:Quantum phases]]<br />
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==实例==<br />
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对称性破缺可以涵盖以下任何一种情况:<ref>{{cite web|url=http://www.angelfire.com/stars5/astroinfo/gloss/s.html|title=Astronomical Glossary|author=|date=|website=www.angelfire.com}}</ref><br />
* 某些结构的随机形成破坏了物理学基本定律的精确对称性;<br />
* 物理学中最小能量状态的对称性比系统本身少的情形;<br />
* 系统的实际状态由于明显对称的状态不稳定而不能反映动力学的基本对称性的情况(稳定性是以局部不对称为代价的);<br />
* 理论方程具有某种对称性,但其解可能没有(对称性是“隐藏的”)的情况。<br />
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在物理学文献中讨论的首批对称性破缺案例之一,与不可压缩流体在重力和流体静力平衡中均匀旋转的形式有关。在1834年,Jacobi <ref>{{cite journal| last=Jacobi | first=C.G.J. | title=Über die figur des gleichgewichts | journal=[[Annalen der Physik und Chemie]] | volume=109 | issue=33| pages=229–238 | year=1834| doi=10.1002/andp.18341090808 | bibcode=1834AnP...109..229J | url=https://zenodo.org/record/2027349 }}</ref>和后来的 Liouville <ref>{{cite journal| last=Liouville | first=J. | title=Sur la figure d'une masse fluide homogène, en équilibre et douée d'un mouvement de rotation| journal=Journal de l'École Polytechnique | issue=14| pages=289–296 | year=1834}}</ref>讨论了这样一个事实: 当旋转物体的动能相对于引力势能超过一定的临界值时,这个问题的平衡解是三轴椭球。在这个分叉点上,麦克劳林椭球体的轴对称性被破坏。此外,在这个分叉点之上,对于常数角动量,使动能最小化的解是非轴对称的 Jacobi 椭球,而不是 Maclaurin 椭球。<br />
==另请参阅==<br />
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*[[Higgs mechanism]]<br />
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*[[QCD vacuum]]<br />
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*[[Goldstone boson]]<br />
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*[[1964 PRL symmetry breaking papers]]<br />
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*[[希格斯机制]]<br />
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*[[QCD真空]]<br />
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*[[戈德斯通玻色子]]<br />
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*[[1964年PRL对称性破缺论文]]<br />
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==参考文献==<br />
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{{reflist|colwidth=30em}}<br />
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{{DEFAULTSORT:Symmetry Breaking}}<br />
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范畴: 对称<br />
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类别: 模式形成<br />
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本中文词条由XXX编译,XXX审校,XXX总审校,西瓜编辑,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''<br />
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<noinclude><br />
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[[Category:对称性破缺]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%AF%B9%E7%A7%B0%E6%80%A7%E7%A0%B4%E7%BC%BA&diff=24771对称性破缺2021-07-27T03:24:12Z<p>Jxzhou:/* Dynamical symmetry breaking */</p>
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[[图一:一个小球位于中央山丘的山峰处(C)。这是一种不稳定平衡:一个很小的扰动会使它落到左边(L)或右边(R)稳定点。尽管山丘是对称的,没有理由让球落在哪一侧,但观察到的最终状态仍然是不对称的,它总会落到某一侧]]。<br />
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在物理学中,一个作用于系统的(无限)小扰动使系统跨过临界点,通过决定去向分叉的哪个分支来决定系统的命运,这种现象叫做'''<font color="#ff8000">对称性破缺</font>'''。对于一个观测不到扰动(或“噪声”)的外部观察者来说,这个选择看起来是任意的。这个过程被称为对称性破缺,因为这种转变通常使系统从一个对称但无序的状态进入一个或多个确定的状态。在'''<font color="#ff8000">斑图生成</font>'''中对称性破缺起着重要作用。<br />
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1972年,诺贝尔奖得主P·W·安德森(P.W.Anderson)在《科学》(Science)杂志上发表了一篇名为《多即不同》的论文<ref>{{cite journal | last=Anderson | first=P.W. | title=More is Different | journal=Science | volume=177 | issue=4047| pages=393–396 | year=1972 | url=http://robotics.cs.tamu.edu/dshell/cs689/papers/anderson72more_is_different.pdf | doi=10.1126/science.177.4047.393 | pmid=17796623 | format=|bibcode = 1972Sci...177..393A }}</ref>,文中使用对称性破缺的思想表明,即使'''<font color="#ff8000">还原论</font>'''是正确的,但它的逆命题'''<font color="#ff8000">建构主义</font>'''是错误的。建构主义认为,在给出描述各组成部分的理论的情况下科学家可以轻易地预测复杂现象。<br />
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对称性破缺可以分为'''<font color="#ff8000">显性对称性破缺</font>'''和'''<font color="#ff8000">自发对称性破缺</font>'''两种类型,二者的区别是,在破缺对称性下系统的运动方程是否不变或者基态是否保持不变。<br />
==显性对称性破缺==<br />
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在'''<font color="#ff8000">显性对称性破缺</font>'''中,描述系统的运动方程在破缺对称下是不同的。在哈密顿力学或拉格朗日力学中,假若系统的哈密顿量(或拉格朗日量)中至少一项显性地打破了给定的对称性,就发生了显性对称性破缺。<br />
==自发对称性破缺==<br />
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在'''<font color="#ff8000">自发对称性破缺</font>'''中,系统的运动方程是不变的,但系统发生了变化。这是因为系统的背景(时空)——真空态——是非恒定的。这种对称性破缺可以用一个序参量进行参数化。这类对称破缺的一个特殊情况是'''<font color="#ff8000">动力学对称性破缺</font>'''。<br />
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Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state ends up in an asymmetric state.[1][2][3] In particular, it can describe systems where the equations of motion or the Lagrangian obey symmetries, but the lowest-energy vacuum solutions do not exhibit that same symmetry. When the system goes to one of those vacuum solutions, the symmetry is broken for perturbations around that vacuum even though the entire Lagrangian retains that symmetry.<br />
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自发对称破缺是一个自发的对称破缺过程,它使处于对称状态的物理系统最终处于非对称状态。特别地,它可以描述运动方程或拉格朗日方程服从某种对称性,但最低能量真空解不具有该对称性的系统。当系统进入其中一个真空解时,真空解周围的扰动会破坏系统对称性,尽管整个拉格朗日方程仍然保持了对称性。<br />
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==Overview==<br />
<br />
In [[explicit symmetry breaking]], if two outcomes are considered, the probability of a pair of outcomes can be different. By definition, spontaneous symmetry breaking requires the existence of a symmetric probability distribution—any pair of outcomes has the same probability. In other words, the underlying laws{{clarify|date=December 2016}} are [[Invariant (physics)|invariant]] under a [[Symmetry (physics)|symmetry]] transformation.<br />
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The system, as a whole{{clarify|date=December 2016}}, changes under such transformations.<br />
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Phases of matter, such as crystals, magnets, and conventional superconductors, as well as simple phase transitions can be described by spontaneous symmetry breaking. Notable exceptions include topological phases of matter like the [[fractional quantum Hall effect]].<br />
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==Examples 例子==<br />
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===Sombrero potential===<br />
Consider a symmetric upward dome with a trough circling the bottom. If a ball is put at the very peak of the dome, the system is symmetric with respect to a rotation around the center axis. But the ball may ''spontaneously break'' this symmetry by rolling down the dome into the trough, a point of lowest energy. Afterward, the ball has come to a rest at some fixed point on the perimeter. The dome and the ball retain their individual symmetry, but the system does not.<ref>{{cite book |first=Gerald M. |last=Edelman |title=Bright Air, Brilliant Fire: On the Matter of the Mind |location=New York |publisher=BasicBooks |year=1992 |url=https://archive.org/details/brightairbrillia00gera |url-access=registration |page=[https://archive.org/details/brightairbrillia00gera/page/203 203] }}</ref><br />
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考虑一个对称向上的圆顶,底部环绕着一个槽。如果把一个球放在圆顶的最顶端,这个系统是围绕中心轴旋转对称的。但球体可能会自发地打破这种对称性,因为它会沿着穹顶滚动到能量最低的槽中。然后,球在圆周上某个固定的点上停下来。圆顶和球保持了各自的对称,但系统却没有保持对称性。<br />
[[Image:Mexican hat potential polar.svg|270px|thumb|left|Graph of Goldstone's "[[sombrero]]" potential function <math>V(\phi)</math>.|链接=Special:FilePath/Mexican_hat_potential_polar.svg]]<br />
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In the simplest idealized relativistic model, the spontaneously broken symmetry is summarized through an illustrative [[scalar field theory]]. The relevant [[Lagrangian (field theory)|Lagrangian]] of a scalar field <math>\phi</math>, which essentially dictates how a system behaves, can be split up into kinetic and potential terms,<br />
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在最简单的理想相对论模型中,可以用一个解释性的标量场理论总结自发破对称性。一个标量场 <math>\phi</math>的拉格朗日量从本质上决定了系统的行为,它可以分解成动能项和势能项:<br />
{{NumBlk|::|<math>\mathcal{L} = \partial^\mu \phi \partial_\mu \phi - V(\phi).</math>|{{EquationRef|1}}}}<br />
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It is in this potential term <math>V(\phi)</math> that the symmetry breaking is triggered. An example of a potential, due to [[Jeffrey Goldstone]]<ref>{{Cite journal | last1 = Goldstone | first1 = J. | doi = 10.1007/BF02812722 | title = Field theories with " Superconductor " solutions | journal = Il Nuovo Cimento | volume = 19 | issue = 1 | pages = 154–164 | year = 1961 | bibcode = 1961NCim...19..154G | s2cid = 120409034 | url = http://cds.cern.ch/record/343400 }}</ref> is illustrated in the graph at the left.<br />
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正是在势能项 <math>V(\phi)</math> 中触发了对称性破缺。例如左图所示的 [[Jeffrey Goldstone]] 给出的势能函数:<br />
{{NumBlk|::|<math>V(\phi) = -5|\phi|^2 + |\phi|^4 \,</math>.|{{EquationRef|2}}}}<br />
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This potential has an infinite number of possible [[minimum|minima]] (vacuum states) given by<br />
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该是函数具有无穷数量的最小值点(真空态)当<br />
{{NumBlk|::|<math>\phi = \sqrt{5} e^{i\theta} </math>.|{{EquationRef|3}}}}<br />
for any real ''θ'' between 0 and 2''π''. The system also has an unstable vacuum state corresponding to {{nowrap|1=''Φ'' = 0}}. This state has a [[Unitary group|U(1)]] symmetry. However, once the system falls into a specific stable vacuum state (amounting to a choice of ''θ''), this symmetry will appear to be lost, or "spontaneously broken".<br />
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对于0到2π之间的任何实数θ。系统也有一个不稳定的真空状态,对应于Φ = 0。这个状态具有U(1)对称。然而,一旦系统落入某个稳定真空状态(相当于选择θ),这种对称性就会消失,或者说“自发破缺”。<br />
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In fact, any other choice of ''θ'' would have exactly the same energy, implying the existence of a massless [[Goldstone boson|Nambu–Goldstone boson]], the mode running around the circle at the minimum of this potential, and indicating there is some memory of the original symmetry in the Lagrangian.<br />
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事实上,任何其他θ的选择都将具有完全相同的能量,这意味着无质量的南部-戈德斯通玻色子的存在,这种模式在势能的最小值绕圆运动,并表明存在拉格朗日方程中原始对称性的一些记忆。<br />
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===Other examples===<br />
* For [[ferromagnet]]ic materials, the underlying laws are invariant under spatial rotations. Here, the order parameter is the [[magnetization]], which measures the magnetic dipole density. Above the [[Curie temperature]], the order parameter is zero, which is spatially invariant, and there is no symmetry breaking. Below the Curie temperature, however, the magnetization acquires a constant nonvanishing value, which points in a certain direction (in the idealized situation where we have full equilibrium; otherwise, translational symmetry gets broken as well). The residual rotational symmetries which leave the orientation of this vector invariant remain unbroken, unlike the other rotations which do not and are thus spontaneously broken.<br />
* 对于铁磁性材料,其基本定律在空间旋转下是不变的。在这里,序参量是衡量磁偶极子密度的磁化强度。在居里温度以上,序参量为零,具有空间不变性,不存在对称性破缺。然而,在居里温度以下,磁化强度变成一个恒定的非零值,指向一个特定的方向(在有充分平衡的理想情况下;否则,平移对称性也会破缺)。使该向量方向不变的旋转对称性仍然保留,而其他旋转对称性自发破缺。<br />
* The laws describing a solid are invariant under the full [[Euclidean group]], but the solid itself spontaneously breaks this group down to a [[space group]]. The displacement and the orientation are the order parameters.<br />
* 描述固体的定律在完整的欧几里得群下是不变的,但固体本身会自发地将这个群分解为一个空间群。其中位移和方向是序参量。<br />
* General relativity has a Lorentz symmetry, but in [[Friedmann–Lemaître–Robertson–Walker metric|FRW cosmological models]], the mean 4-velocity field defined by averaging over the velocities of the galaxies (the galaxies act like gas particles at cosmological scales) acts as an order parameter breaking this symmetry. Similar comments can be made about the cosmic microwave background.<br />
* 广义相对论具有洛伦兹对称性,但在FRW宇宙模型中,定义为星系速度的平均值(星系在宇宙尺度上的行为就像气体粒子) 的平均 4-速度场,作为序参量会打破这种对称性。对于宇宙微波背景辐射也有类似的评论。<br />
* For the [[electroweak]] model, as explained earlier, a component of the Higgs field provides the order parameter breaking the electroweak gauge symmetry to the electromagnetic gauge symmetry. Like the ferromagnetic example, there is a phase transition at the electroweak temperature. The same comment about us not tending to notice broken symmetries suggests why it took so long for us to discover electroweak unification.<br />
* 对于电弱模型,如前面所解释的,希格斯场的一个分量提供了将电弱规范对称性破缺到电磁规范对称性的序参量。和铁磁的例子一样,在电弱温度下也有相变。同样的关于我们不倾向于注意破缺对称性的评论,也说明了为什么我们花了这么长时间才发现电弱统一。<br />
* In superconductors, there is a condensed-matter collective field ψ, which acts as the order parameter breaking the electromagnetic gauge symmetry.<br />
* 在超导体中有一个凝聚态集体场ψ,它是打破电磁规范对称性的序参量。<br />
* Take a thin cylindrical plastic rod and push both ends together. Before buckling, the system is symmetric under rotation, and so visibly cylindrically symmetric. But after buckling, it looks different, and asymmetric. Nevertheless, features of the cylindrical symmetry are still there: ignoring friction, it would take no force to freely spin the rod around, displacing the ground state in time, and amounting to an oscillation of vanishing frequency, unlike the radial oscillations in the direction of the buckle. This spinning mode is effectively the requisite [[Goldstone boson|Nambu–Goldstone boson]].<br />
* 拿一个细长的圆柱形塑料杆,把两端推到一起。在屈曲之前,系统在旋转下是对称的,因此可见圆柱对称性。但在弯曲之后,它看起来就不同了,而且是不对称的。然而,圆柱对称性的特征仍然存在:忽略摩擦,杆可以不受外力自由地自旋,在时间上取代基态,等于一个频率趋于零的振荡,而不是沿屈曲方向的径向振荡。这种自旋模式实际上是必需的南部-戈德斯通玻色子。<br />
* Consider a uniform layer of [[fluid]] over an infinite horizontal plane. This system has all the symmetries of the Euclidean plane. But now heat the bottom surface uniformly so that it becomes much hotter than the upper surface. When the temperature gradient becomes large enough, [[convection cell]]s will form, breaking the Euclidean symmetry.<br />
* 考虑无限水平面上的一层均匀的流体。这个系统具有欧几里得平面的所有对称性。但是现在均匀地加热底部表面,使它变得比上表面热得多。当温度梯度足够大时,就会形成对流单元,打破了欧几里得对称。<br />
* Consider a bead on a circular hoop that is rotated about a vertical [[diameter]]. As the [[rotational velocity]] is increased gradually from rest, the bead will initially stay at its initial [[equilibrium point]] at the bottom of the hoop (intuitively stable, lowest [[gravitational potential]]). At a certain critical rotational velocity, this point will become unstable and the bead will jump to one of two other newly created equilibria, [[equidistant]] from the center. Initially, the system is symmetric with respect to the diameter, yet after passing the critical velocity, the bead ends up in one of the two new equilibrium points, thus breaking the symmetry.<br />
* 考虑一个围绕某个竖直的直径旋转的圆形箍上的珠子。当旋转速度从静止逐渐增加时,珠子最初会停留在环底部的初始平衡点(直观上稳定,重力势最低)。在一定的临界旋转速度下,这一点将变得不稳定,珠子将跳到另外两个新创建的离中心等距离的平衡点中的一个。起初,系统相对直径是对称的,但在通过临界速度后,珠子最终停留在两个新的平衡点中的一个,从而打破了对称性。<br />
<br />
==Spontaneous symmetry breaking in physics 物理学中的自发对称性破缺==<br />
[[File:Spontaneous symmetry breaking (explanatory diagram).png|thumb|right|250px|''Spontaneous symmetry breaking illustrated'': At high energy levels (''left''), the ball settles in the center, and the result is symmetric. At lower energy levels (''right''), the overall "rules" remain symmetric, but the symmetric "[[sombrero|Sombrero]]" enforces an asymmetric outcome, since eventually the ball must rest at some random spot on the bottom, "spontaneously", and not all others.|链接=Special:FilePath/Spontaneous_symmetry_breaking_(explanatory_diagram).png]]<br />
<br />
===Particle physics 粒子物理===<br />
In [[particle physics]], the [[force carrier]] particles are normally specified by field equations with [[gauge symmetry]]; their equations predict that certain measurements will be the same at any point in the field. For instance, field equations might predict that the mass of two quarks is constant. Solving the equations to find the mass of each quark might give two solutions. In one solution, quark A is heavier than quark B. In the second solution, quark B is heavier than quark A ''by the same amount''. The symmetry of the equations is not reflected by the individual solutions, but it is reflected by the range of solutions.<br />
<br />
在粒子物理学中,载力子通常由规范对称的场方程表示;它们的方程预测到某些测量值在场的任何点上都是相同的。例如,场方程可以预测两个夸克的质量是常数。通过求解方程来求每个夸克的质量可能会得到两个解。在一个解中,夸克A比夸克B重;在第二个解中,夸克B比夸克A重相同的量。方程的对称性不是由单个解来反映的,而是由解的范围来反映的。<br />
<br />
An actual measurement reflects only one solution, representing a breakdown in the symmetry of the underlying theory. "Hidden" is a better term than "broken", because the symmetry is always there in these equations. This phenomenon is called [[Spontaneous magnetization|''spontaneous'']] symmetry breaking (SSB) because ''nothing'' (that we know of) breaks the symmetry in the equations.<ref name="Weinberg2011">{{cite book|author=Steven Weinberg|title=Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature|url=https://books.google.com/books?id=Rsg3PE_9_ccC|date=20 April 2011|publisher=Knopf Doubleday Publishing Group|isbn=978-0-307-78786-6}}</ref>{{rp|194–195}}<br />
<br />
一个实际的测量只反映了一个解,代表了其潜在理论的对称性的破缺。在这里“隐藏”是比“破坏”更好的术语,因为对称性总是存在于这些方程中。这种现象被称为自发对称破缺(SSB),因为(我们所知道的)没有任何东西会打破方程中的对称性。<br />
<br />
====Chiral symmetry 手性对称性====<br />
{{Main article|Chiral symmetry breaking}}<br />
Chiral symmetry breaking is an example of spontaneous symmetry breaking affecting the [[chiral symmetry]] of the [[strong interactions]] in particle physics. It is a property of [[quantum chromodynamics]], the [[quantum field theory]] describing these interactions, and is responsible for the bulk of the mass (over 99%) of the [[nucleons]], and thus of all common matter, as it converts very light bound [[quarks]] into 100 times heavier constituents of [[baryons]]. The approximate [[Nambu–Goldstone boson]]s in this spontaneous symmetry breaking process are the [[pions]], whose mass is an order of magnitude lighter than the mass of the nucleons. It served as the prototype and significant ingredient of the Higgs mechanism underlying the electroweak symmetry breaking.<br />
<br />
手性对称破缺是粒子物理中影响强相互作用手性对称的自发对称破缺的一个例子。手性对称性破缺是量子色动力学(描述这些相互作用的量子场理论)的一种特性,它是核子的大部分质量(超过99%)的成因,因此也是所有普通物质的主要成因,因为它将非常轻的束缚夸克转化为100倍重量的重子的成分。在这个自发对称破缺过程中,近似的南部-戈德斯通玻色子是介子,其质量比核子的质量轻一个数量级。它是电弱对称破缺的希格斯机制的原型和重要组成部分。<br />
<br />
====Higgs mechanism 希格斯机制====<br />
{{Main article|Higgs mechanism|Yukawa interaction}}<br />
<br />
The strong, weak, and electromagnetic forces can all be understood as arising from [[gauge symmetry|gauge symmetries]]. The [[Higgs mechanism]], the spontaneous symmetry breaking of gauge symmetries, is an important component in understanding the [[superconductivity]] of metals and the origin of particle masses in the standard model of particle physics. One important consequence of the distinction between true symmetries and ''gauge symmetries'', is that the spontaneous breaking of a gauge symmetry does not give rise to characteristic massless Nambu–Goldstone physical modes, but only massive modes, like the plasma mode in a superconductor, or the Higgs mode observed in particle physics.<br />
<br />
强、弱和电磁力都可以理解为来自规范对称。希格斯机制,即规范对称的自发对称破缺机制,是理解金属超导性和粒子物理标准模型中粒子质量起源的重要组成部分。区分真正的对称性和规范对称性的一个重要的结果,是规范对称性的自发破缺不产生典型的无质量Nambu-Goldstone物理模式,而是只产生有质量的模式,像超导体中的等离子体模式,或者粒子物理学中观察到的希格斯模式。<br />
<br />
In the standard model of particle physics, spontaneous symmetry breaking of the {{nowrap|SU(2) × U(1)}} gauge symmetry associated with the electro-weak force generates masses for several particles, and separates the electromagnetic and weak forces. The [[W and Z bosons]] are the elementary particles that mediate the [[weak interaction]], while the [[photon]] mediates the [[electromagnetic interaction]]. At energies much greater than 100 GeV, all these particles behave in a similar manner. The [[Unified field theory#Modern progress|Weinberg–Salam theory]] predicts that, at lower energies, this symmetry is broken so that the photon and the massive W and Z bosons emerge.<ref>A Brief History of Time, Stephen Hawking, Bantam; 10th anniversary edition (1998). pp. 73–74.{{ISBN?}}</ref> In addition, fermions develop mass consistently.<br />
<br />
在粒子物理的标准模型中,与电弱力相关的SU(2) × U(1)规范对称性自发破缺产生多种粒子的质量,并将电磁力和弱相互作用分离。W玻色子和Z玻色子是介导弱相互作用的基本粒子,而光子介导电磁相互作用。当能量远远大于100 GeV时,所有这些粒子的行为都相似。Weinberg-Salam理论预测,在较低的能量下,这种对称性被打破,光子和大质量的W和Z玻色子就会出现。此外,费米子不断地发展质量。<br />
<br />
Without spontaneous symmetry breaking, the [[Standard Model]] of elementary particle interactions requires the existence of a number of particles. However, some particles (the [[W and Z bosons]]) would then be predicted to be massless, when, in reality, they are observed to have mass. To overcome this, spontaneous symmetry breaking is augmented by the [[Higgs mechanism]] to give these particles mass. It also suggests the presence of a new particle, the [[Higgs boson]], detected in 2012.<br />
<br />
在没有自发对称性破缺的情况下,基本粒子相互作用的标准模型要求存在多种粒子。然而,一些粒子(W玻色子和Z玻色子)将被预测为无质量的,而实际上它们被观察到有质量。为了克服这个问题,希格斯机制增强了自发对称破缺,从而赋予这些粒子质量。它还表明一种新粒子——希格斯玻色子——的存在,它在2012年被实验探测到。<br />
<br />
[[Superconductivity]] of metals is a condensed-matter analog of the Higgs phenomena, in which a condensate of Cooper pairs of electrons spontaneously breaks the U(1) gauge symmetry associated with light and electromagnetism.<br />
<br />
金属的超导性是一种类似于希格斯现象的凝聚态物质,其中库珀电子对的凝聚会自发地打破与光和电磁相关的U(1)规范对称。<br />
<br />
===Condensed matter physics===<br />
Most phases of matter can be understood through the lens of spontaneous symmetry breaking. For example, crystals are periodic arrays of atoms that are not invariant under all translations (only under a small subset of translations by a lattice vector). Magnets have north and south poles that are oriented in a specific direction, breaking [[rotational symmetry]]. In addition to these examples, there are a whole host of other symmetry-breaking phases of matter — including nematic phases of liquid crystals, charge- and spin-density waves, superfluids, and many others.<br />
<br />
There are several known examples of matter that cannot be described by spontaneous symmetry breaking, including: topologically ordered phases of matter, such as [[Fractional quantum Hall effect|fractional quantum Hall liquids]], and [[Quantum spin liquid|spin-liquids]]. These states do not break any symmetry, but are distinct phases of matter. Unlike the case of spontaneous symmetry breaking, there is not a general framework for describing such states.<ref name=chen>{{cite journal | last1 = Chen | first1 = Xie | author-link3 = Xiao-Gang Wen | last2 = Gu | first2 = Zheng-Cheng | last3 = Wen | first3 = Xiao-Gang | year = 2010 | title = Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order | journal = Phys. Rev. B | volume = 82 | issue = 15| page = 155138 | doi=10.1103/physrevb.82.155138|arxiv = 1004.3835 |bibcode = 2010PhRvB..82o5138C | s2cid = 14593420 }}</ref><br />
<br />
====Continuous symmetry====<br />
The ferromagnet is the canonical system that spontaneously breaks the continuous symmetry of the spins below the [[Curie temperature]] and at {{nowrap|1=''h'' = 0}}, where ''h'' is the external magnetic field. Below the [[Curie temperature]], the energy of the system is invariant under inversion of the magnetization ''m''('''x''') such that {{nowrap|1=''m''('''x''') = −''m''(−'''x''')}}. The symmetry is spontaneously broken as {{nowrap|''h'' → 0}} when the Hamiltonian becomes invariant under the inversion transformation, but the expectation value is not invariant.<br />
<br />
Spontaneously-symmetry-broken phases of matter are characterized by an order parameter that describes the quantity which breaks the symmetry under consideration. For example, in a magnet, the order parameter is the local magnetization.<br />
<br />
Spontaneous breaking of a continuous symmetry is inevitably accompanied by gapless (meaning that these modes do not cost any energy to excite) Nambu–Goldstone modes associated with slow, long-wavelength fluctuations of the order parameter. For example, vibrational modes in a crystal, known as phonons, are associated with slow density fluctuations of the crystal's atoms. The associated Goldstone mode for magnets are oscillating waves of spin known as spin-waves. For symmetry-breaking states, whose order parameter is not a conserved quantity, Nambu–Goldstone modes are typically massless and propagate at a constant velocity.<br />
<br />
An important theorem, due to Mermin and Wagner, states that, at finite temperature, thermally activated fluctuations of Nambu–Goldstone modes destroy the long-range order, and prevent spontaneous symmetry breaking in one- and two-dimensional systems. Similarly, quantum fluctuations of the order parameter prevent most types of continuous symmetry breaking in one-dimensional systems even at zero temperature. (An important exception is ferromagnets, whose order parameter, magnetization, is an exactly conserved quantity and does not have any quantum fluctuations.)<br />
<br />
Other long-range interacting systems, such as cylindrical curved surfaces interacting via the [[Coulomb potential]] or [[Yukawa potential]], have been shown to break translational and rotational symmetries.<ref><br />
{{cite journal<br />
|last1=Kohlstedt |first1=K.L.<br />
|last2=Vernizzi |first2=G.<br />
|last3=Solis |first3=F.J.<br />
|last4=Olvera de la Cruz |first4=M.<br />
|year=2007<br />
|title=Spontaneous Chirality via Long-range Electrostatic Forces<br />
|journal=[[Physical Review Letters]]<br />
|volume=99 |issue=3<br />
|page=030602<br />
|doi=10.1103/PhysRevLett.99.030602<br />
|arxiv = 0704.3435 |bibcode = 2007PhRvL..99c0602K |pmid=17678276|s2cid=37983980<br />
}}</ref> It was shown, in the presence of a symmetric Hamiltonian, and in the limit of infinite volume, the system spontaneously adopts a chiral configuration — i.e., breaks [[mirror plane]] [[symmetry]].<br />
<br />
===Dynamical symmetry breaking 动力学对称性破缺===<br />
Dynamical symmetry breaking (DSB) is a special form of spontaneous symmetry breaking in which the ground state of the system has reduced symmetry properties compared to its theoretical description (i.e., [[Lagrangian (field theory)|Lagrangian]]).<br />
<br />
动力学对称性破缺(DSB)是自发对称性破缺的一种特殊形式,在这种情况下,系统的基态比理论描述(例如拉格朗日量)的对称性降低。<br />
<br />
Dynamical breaking of a global symmetry is a spontaneous symmetry breaking, which happens not at the (classical) tree level (i.e., at the level of the bare action), but due to quantum corrections (i.e., at the level of the [[effective action]]).<br />
<br />
全局对称性的动力学破缺是自发对称性破缺,它不是发生在(经典)树的水平(例如在bare作用的水平),而是由于量子修正(例如在有效作用的水平)。<br />
<br />
Dynamical breaking of a gauge symmetry {{ref|note1}} is subtler. In the conventional spontaneous gauge symmetry breaking, there exists an unstable [[Higgs particle]] in the theory, which drives the vacuum to a symmetry-broken phase. (See, for example, [[electroweak interaction]].) In dynamical gauge symmetry breaking, however, no unstable Higgs particle operates in the theory, but the bound states of the system itself provide the unstable fields that render the phase transition. For example, Bardeen, Hill, and Lindner published a paper that attempts to replace the conventional [[Higgs mechanism]] in the [[standard model]] by a DSB that is driven by a bound state of top-antitop quarks. (Such models, in which a composite particle plays the role of the Higgs boson, are often referred to as "Composite Higgs models".)<ref><br />
{{cite journal<br />
|author1=William A. Bardeen<br />
|author2-link=Christopher T. Hill<br />
|author2=Christopher T. Hill<br />
|author3-link=Manfred Lindner<br />
|author3=Manfred Lindner<br />
|year=1990<br />
|title=Minimal dynamical symmetry breaking of the standard model<br />
|journal=[[Physical Review D]]<br />
|volume=41 |issue=5 |pages=1647–1660<br />
|bibcode=1990PhRvD..41.1647B<br />
|doi=10.1103/PhysRevD.41.1647<br />
|pmid=10012522<br />
|author1-link=William A. Bardeen<br />
}}</ref> Dynamical breaking of gauge symmetries is often due to creation of a [[fermionic condensate]] — e.g., the [[quark condensate]], which is connected to the [[Chiral symmetry breaking|dynamical breaking of chiral symmetry]] in [[quantum chromodynamics]]. Conventional [[superconductivity]] is the paradigmatic example from the condensed matter side, where phonon-mediated attractions lead electrons to become bound in pairs and then condense, thereby breaking the electromagnetic gauge symmetry.<br />
<br />
规范对称性动力学破缺更加微妙。在常规规范对称自发破缺理论中,存在一个不稳定的希格斯粒子,希格斯粒子驱动真空进入对称破缺相。(例如,参见弱电相互作用。)然而,在规范对称性动力学破缺中,不存在不稳定的希格斯粒子,但系统本身的束缚态提供了导致相变的不稳定场。例如,巴丁、希尔和林德纳发表了一篇论文,试图用一个由顶-反顶夸克束缚状态驱动的DSB来取代标准模型中的传统希格斯机制。(在这种模型中,复合粒子扮演希格斯玻色子的角色,通常被称为“复合希格斯模型”。)规范对称性动力学破缺通常是由于费米凝聚的产生,例如夸克凝聚,它与量子色动力学中手性对称的动力学破缺有关。传统的超导性是凝聚态物质方面的典型例子,声子的吸引导致电子成对结合然后凝聚,从而打破电磁规范对称性。<br />
<br />
==Generalisation and technical usage==<br />
For spontaneous symmetry breaking to occur, there must be a system in which there are several equally likely outcomes. The system as a whole is therefore [[Symmetry (physics)|symmetric]] with respect to these outcomes. However, if the system is sampled (i.e. if the system is actually used or interacted with in any way), a specific outcome must occur. Though the system as a whole is symmetric, it is never encountered with this symmetry, but only in one specific asymmetric state. Hence, the symmetry is said to be spontaneously broken in that theory. Nevertheless, the fact that each outcome is equally likely is a reflection of the underlying symmetry, which is thus often dubbed "hidden symmetry", and has crucial formal consequences. (See the article on the [[Nambu–Goldstone boson|Goldstone boson]].)<br />
<br />
When a theory is symmetric with respect to a [[symmetry group]], but requires that one element of the group be distinct, then spontaneous symmetry breaking has occurred. The theory must not dictate ''which'' member is distinct, only that ''one is''. From this point on, the theory can be treated as if this element actually is distinct, with the proviso that any results found in this way must be resymmetrized, by taking the average of each of the elements of the group being the distinct one.<br />
<br />
The crucial concept in physics theories is the [[order parameter]]. If there is a field (often a background field) which acquires an expectation value (not necessarily a [[vacuum expectation value|''vacuum'' expectation value]]) which is not invariant under the symmetry in question, we say that the system is in the [[ordered phase]], and the symmetry is spontaneously broken. This is because other subsystems interact with the order parameter, which specifies a "frame of reference" to be measured against. In that case, the [[vacuum state]] does not obey the initial symmetry (which would keep it invariant, in the linearly realized '''Wigner mode''' in which it would be a singlet), and, instead changes under the (hidden) symmetry, now implemented in the (nonlinear) '''Nambu–Goldstone mode'''. Normally, in the absence of the Higgs mechanism, massless [[Goldstone boson]]s arise.<br />
<br />
The symmetry group can be discrete, such as the [[space group]] of a crystal, or continuous (e.g., a [[Lie group]]), such as the rotational symmetry of space. However, if the system contains only a single spatial dimension, then only discrete symmetries may be broken in a [[vacuum state]] of the full [[Quantum mechanics|quantum theory]], although a classical solution may break a continuous symmetry.<br />
<br />
==Nobel Prize==<br />
On October 7, 2008, the [[Royal Swedish Academy of Sciences]] awarded the 2008 [[Nobel Prize in Physics]] to three scientists for their work in subatomic physics symmetry breaking. [[Yoichiro Nambu]], of the [[University of Chicago]], won half of the prize for the discovery of the mechanism of spontaneous broken symmetry in the context of the strong interactions, specifically [[chiral symmetry breaking]]. Physicists [[Makoto Kobayashi (physicist)|Makoto Kobayashi]] and [[Toshihide Maskawa]], of [[Kyoto University]], shared the other half of the prize for discovering the origin of the [[Explicit symmetry breaking|explicit breaking]] of CP symmetry in the weak interactions.<ref>{{cite web|author=The Nobel Foundation|title=The Nobel Prize in Physics 2008|url=http://nobelprize.org/nobel_prizes/physics/laureates/2008/index.html|work=nobelprize.org|access-date=January 15, 2008}}</ref> This origin is ultimately reliant on the Higgs mechanism, but, so far understood as a "just so" feature of Higgs couplings, not a spontaneously broken symmetry phenomenon.<br />
<br />
==See also==<br />
{{div col|colwidth=24em}}<br />
* [[Autocatalytic reactions and order creation]]<br />
* [[Catastrophe theory]]<br />
* [[Chiral symmetry breaking]]<br />
* [[CP-violation]]<br />
* [[Fermi ball]]<br />
* [[Gauge gravitation theory]]<br />
* [[Goldstone boson]]<br />
* [[Grand unified theory]]<br />
* [[Higgs mechanism]]<br />
* [[Higgs boson]]<br />
* [[Higgs field (classical)]]<br />
* [[Irreversibility]]<br />
* [[Magnetic catalysis]] of chiral symmetry breaking<br />
* [[Mermin–Wagner theorem]]<br />
* [[Norton's dome]]<br />
* [[Second-order phase transition]]<br />
* [[Spontaneous absolute asymmetric synthesis]] in chemistry<br />
* [[Symmetry breaking]]<br />
* [[Tachyon condensation]]<br />
* [[1964 PRL symmetry breaking papers]]<br />
{{div col end}}<br />
<br />
==Notes==<br />
* {{note|note1}} Note that (as in fundamental Higgs driven spontaneous gauge symmetry breaking) the term "symmetry breaking" is a misnomer when applied to gauge symmetries.<br />
<br />
==References==<br />
{{Reflist}}<br />
<br />
==External links==<br />
{{wikiquote}}<br />
* For a pedagogic introduction to electroweak symmetry breaking with step by step derivations, not found in texts, of many key relations, see http://www.quantumfieldtheory.info/Electroweak_Sym_breaking.pdf<br />
* [http://hyperphysics.phy-astr.gsu.edu/hbase/forces/unify.html#c2 Spontaneous symmetry breaking]<br />
* [http://prl.aps.org/50years/milestones#1964 Physical Review Letters – 50th Anniversary Milestone Papers]<br />
* [http://cerncourier.com/cws/article/cern/32522 In CERN Courier, Steven Weinberg reflects on spontaneous symmetry breaking]<br />
* [http://www.scholarpedia.org/article/Englert-Brout-Higgs-Guralnik-Hagen-Kibble_mechanism Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism on Scholarpedia]<br />
* [http://www.scholarpedia.org/article/Englert-Brout-Higgs-Guralnik-Hagen-Kibble_mechanism_%28history%29 History of Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism on Scholarpedia]<br />
* [https://arxiv.org/abs/0907.3466 The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles]<br />
* [http://www.worldscinet.com/ijmpa/24/2414/S0217751X09045431.html International Journal of Modern Physics A: The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles]<br />
* [http://www.datafilehost.com/download-7d512618.html Guralnik, G S; Hagen, C R and Kibble, T W B (1967). Broken Symmetries and the Goldstone Theorem. Advances in Physics, vol. 2 Interscience Publishers, New York. pp. 567–708] {{ISBN|0-470-17057-3}}<br />
* [http://lanl.arxiv.org/abs/hep-th/9802142 Spontaneous Symmetry Breaking in Gauge Theories: a Historical Survey]<br />
<br />
{{Standard model of physics}}<br />
{{Quantum mechanics topics}}<br />
<br />
{{DEFAULTSORT:Spontaneous Symmetry Breaking}}<br />
[[Category:Theoretical physics]]<br />
[[Category:Quantum field theory]]<br />
[[Category:Standard Model]]<br />
[[Category:Quantum chromodynamics]]<br />
[[Category:Symmetry]]<br />
[[Category:Quantum phases]]<br />
<br />
==实例==<br />
<br />
对称性破缺可以涵盖以下任何一种情况:<ref>{{cite web|url=http://www.angelfire.com/stars5/astroinfo/gloss/s.html|title=Astronomical Glossary|author=|date=|website=www.angelfire.com}}</ref><br />
* 某些结构的随机形成破坏了物理学基本定律的精确对称性;<br />
* 物理学中最小能量状态的对称性比系统本身少的情形;<br />
* 系统的实际状态由于明显对称的状态不稳定而不能反映动力学的基本对称性的情况(稳定性是以局部不对称为代价的);<br />
* 理论方程具有某种对称性,但其解可能没有(对称性是“隐藏的”)的情况。<br />
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在物理学文献中讨论的首批对称性破缺案例之一,与不可压缩流体在重力和流体静力平衡中均匀旋转的形式有关。在1834年,Jacobi <ref>{{cite journal| last=Jacobi | first=C.G.J. | title=Über die figur des gleichgewichts | journal=[[Annalen der Physik und Chemie]] | volume=109 | issue=33| pages=229–238 | year=1834| doi=10.1002/andp.18341090808 | bibcode=1834AnP...109..229J | url=https://zenodo.org/record/2027349 }}</ref>和后来的 Liouville <ref>{{cite journal| last=Liouville | first=J. | title=Sur la figure d'une masse fluide homogène, en équilibre et douée d'un mouvement de rotation| journal=Journal de l'École Polytechnique | issue=14| pages=289–296 | year=1834}}</ref>讨论了这样一个事实: 当旋转物体的动能相对于引力势能超过一定的临界值时,这个问题的平衡解是三轴椭球。在这个分叉点上,麦克劳林椭球体的轴对称性被破坏。此外,在这个分叉点之上,对于常数角动量,使动能最小化的解是非轴对称的 Jacobi 椭球,而不是 Maclaurin 椭球。<br />
==另请参阅==<br />
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*[[Higgs mechanism]]<br />
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*[[QCD vacuum]]<br />
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*[[Goldstone boson]]<br />
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*[[1964 PRL symmetry breaking papers]]<br />
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*[[希格斯机制]]<br />
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*[[QCD真空]]<br />
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*[[戈德斯通玻色子]]<br />
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*[[1964年PRL对称性破缺论文]]<br />
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==参考文献==<br />
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{{reflist|colwidth=30em}}<br />
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{{DEFAULTSORT:Symmetry Breaking}}<br />
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范畴: 对称<br />
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类别: 模式形成<br />
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本中文词条由XXX编译,XXX审校,XXX总审校,西瓜编辑,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''<br />
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[[Category:对称性破缺]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%AF%B9%E7%A7%B0%E6%80%A7%E7%A0%B4%E7%BC%BA&diff=24770对称性破缺2021-07-27T03:07:54Z<p>Jxzhou:/* Higgs mechanism 希格斯机制 */</p>
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[[图一:一个小球位于中央山丘的山峰处(C)。这是一种不稳定平衡:一个很小的扰动会使它落到左边(L)或右边(R)稳定点。尽管山丘是对称的,没有理由让球落在哪一侧,但观察到的最终状态仍然是不对称的,它总会落到某一侧]]。<br />
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在物理学中,一个作用于系统的(无限)小扰动使系统跨过临界点,通过决定去向分叉的哪个分支来决定系统的命运,这种现象叫做'''<font color="#ff8000">对称性破缺</font>'''。对于一个观测不到扰动(或“噪声”)的外部观察者来说,这个选择看起来是任意的。这个过程被称为对称性破缺,因为这种转变通常使系统从一个对称但无序的状态进入一个或多个确定的状态。在'''<font color="#ff8000">斑图生成</font>'''中对称性破缺起着重要作用。<br />
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1972年,诺贝尔奖得主P·W·安德森(P.W.Anderson)在《科学》(Science)杂志上发表了一篇名为《多即不同》的论文<ref>{{cite journal | last=Anderson | first=P.W. | title=More is Different | journal=Science | volume=177 | issue=4047| pages=393–396 | year=1972 | url=http://robotics.cs.tamu.edu/dshell/cs689/papers/anderson72more_is_different.pdf | doi=10.1126/science.177.4047.393 | pmid=17796623 | format=|bibcode = 1972Sci...177..393A }}</ref>,文中使用对称性破缺的思想表明,即使'''<font color="#ff8000">还原论</font>'''是正确的,但它的逆命题'''<font color="#ff8000">建构主义</font>'''是错误的。建构主义认为,在给出描述各组成部分的理论的情况下科学家可以轻易地预测复杂现象。<br />
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对称性破缺可以分为'''<font color="#ff8000">显性对称性破缺</font>'''和'''<font color="#ff8000">自发对称性破缺</font>'''两种类型,二者的区别是,在破缺对称性下系统的运动方程是否不变或者基态是否保持不变。<br />
==显性对称性破缺==<br />
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在'''<font color="#ff8000">显性对称性破缺</font>'''中,描述系统的运动方程在破缺对称下是不同的。在哈密顿力学或拉格朗日力学中,假若系统的哈密顿量(或拉格朗日量)中至少一项显性地打破了给定的对称性,就发生了显性对称性破缺。<br />
==自发对称性破缺==<br />
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在'''<font color="#ff8000">自发对称性破缺</font>'''中,系统的运动方程是不变的,但系统发生了变化。这是因为系统的背景(时空)——真空态——是非恒定的。这种对称性破缺可以用一个序参量进行参数化。这类对称破缺的一个特殊情况是'''<font color="#ff8000">动力学对称性破缺</font>'''。<br />
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Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state ends up in an asymmetric state.[1][2][3] In particular, it can describe systems where the equations of motion or the Lagrangian obey symmetries, but the lowest-energy vacuum solutions do not exhibit that same symmetry. When the system goes to one of those vacuum solutions, the symmetry is broken for perturbations around that vacuum even though the entire Lagrangian retains that symmetry.<br />
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自发对称破缺是一个自发的对称破缺过程,它使处于对称状态的物理系统最终处于非对称状态。特别地,它可以描述运动方程或拉格朗日方程服从某种对称性,但最低能量真空解不具有该对称性的系统。当系统进入其中一个真空解时,真空解周围的扰动会破坏系统对称性,尽管整个拉格朗日方程仍然保持了对称性。<br />
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==Overview==<br />
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In [[explicit symmetry breaking]], if two outcomes are considered, the probability of a pair of outcomes can be different. By definition, spontaneous symmetry breaking requires the existence of a symmetric probability distribution—any pair of outcomes has the same probability. In other words, the underlying laws{{clarify|date=December 2016}} are [[Invariant (physics)|invariant]] under a [[Symmetry (physics)|symmetry]] transformation.<br />
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The system, as a whole{{clarify|date=December 2016}}, changes under such transformations.<br />
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Phases of matter, such as crystals, magnets, and conventional superconductors, as well as simple phase transitions can be described by spontaneous symmetry breaking. Notable exceptions include topological phases of matter like the [[fractional quantum Hall effect]].<br />
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==Examples 例子==<br />
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===Sombrero potential===<br />
Consider a symmetric upward dome with a trough circling the bottom. If a ball is put at the very peak of the dome, the system is symmetric with respect to a rotation around the center axis. But the ball may ''spontaneously break'' this symmetry by rolling down the dome into the trough, a point of lowest energy. Afterward, the ball has come to a rest at some fixed point on the perimeter. The dome and the ball retain their individual symmetry, but the system does not.<ref>{{cite book |first=Gerald M. |last=Edelman |title=Bright Air, Brilliant Fire: On the Matter of the Mind |location=New York |publisher=BasicBooks |year=1992 |url=https://archive.org/details/brightairbrillia00gera |url-access=registration |page=[https://archive.org/details/brightairbrillia00gera/page/203 203] }}</ref><br />
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考虑一个对称向上的圆顶,底部环绕着一个槽。如果把一个球放在圆顶的最顶端,这个系统是围绕中心轴旋转对称的。但球体可能会自发地打破这种对称性,因为它会沿着穹顶滚动到能量最低的槽中。然后,球在圆周上某个固定的点上停下来。圆顶和球保持了各自的对称,但系统却没有保持对称性。<br />
[[Image:Mexican hat potential polar.svg|270px|thumb|left|Graph of Goldstone's "[[sombrero]]" potential function <math>V(\phi)</math>.|链接=Special:FilePath/Mexican_hat_potential_polar.svg]]<br />
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In the simplest idealized relativistic model, the spontaneously broken symmetry is summarized through an illustrative [[scalar field theory]]. The relevant [[Lagrangian (field theory)|Lagrangian]] of a scalar field <math>\phi</math>, which essentially dictates how a system behaves, can be split up into kinetic and potential terms,<br />
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在最简单的理想相对论模型中,可以用一个解释性的标量场理论总结自发破对称性。一个标量场 <math>\phi</math>的拉格朗日量从本质上决定了系统的行为,它可以分解成动能项和势能项:<br />
{{NumBlk|::|<math>\mathcal{L} = \partial^\mu \phi \partial_\mu \phi - V(\phi).</math>|{{EquationRef|1}}}}<br />
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It is in this potential term <math>V(\phi)</math> that the symmetry breaking is triggered. An example of a potential, due to [[Jeffrey Goldstone]]<ref>{{Cite journal | last1 = Goldstone | first1 = J. | doi = 10.1007/BF02812722 | title = Field theories with " Superconductor " solutions | journal = Il Nuovo Cimento | volume = 19 | issue = 1 | pages = 154–164 | year = 1961 | bibcode = 1961NCim...19..154G | s2cid = 120409034 | url = http://cds.cern.ch/record/343400 }}</ref> is illustrated in the graph at the left.<br />
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正是在势能项 <math>V(\phi)</math> 中触发了对称性破缺。例如左图所示的 [[Jeffrey Goldstone]] 给出的势能函数:<br />
{{NumBlk|::|<math>V(\phi) = -5|\phi|^2 + |\phi|^4 \,</math>.|{{EquationRef|2}}}}<br />
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This potential has an infinite number of possible [[minimum|minima]] (vacuum states) given by<br />
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该是函数具有无穷数量的最小值点(真空态)当<br />
{{NumBlk|::|<math>\phi = \sqrt{5} e^{i\theta} </math>.|{{EquationRef|3}}}}<br />
for any real ''θ'' between 0 and 2''π''. The system also has an unstable vacuum state corresponding to {{nowrap|1=''Φ'' = 0}}. This state has a [[Unitary group|U(1)]] symmetry. However, once the system falls into a specific stable vacuum state (amounting to a choice of ''θ''), this symmetry will appear to be lost, or "spontaneously broken".<br />
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对于0到2π之间的任何实数θ。系统也有一个不稳定的真空状态,对应于Φ = 0。这个状态具有U(1)对称。然而,一旦系统落入某个稳定真空状态(相当于选择θ),这种对称性就会消失,或者说“自发破缺”。<br />
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In fact, any other choice of ''θ'' would have exactly the same energy, implying the existence of a massless [[Goldstone boson|Nambu–Goldstone boson]], the mode running around the circle at the minimum of this potential, and indicating there is some memory of the original symmetry in the Lagrangian.<br />
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事实上,任何其他θ的选择都将具有完全相同的能量,这意味着无质量的南部-戈德斯通玻色子的存在,这种模式在势能的最小值绕圆运动,并表明存在拉格朗日方程中原始对称性的一些记忆。<br />
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===Other examples===<br />
* For [[ferromagnet]]ic materials, the underlying laws are invariant under spatial rotations. Here, the order parameter is the [[magnetization]], which measures the magnetic dipole density. Above the [[Curie temperature]], the order parameter is zero, which is spatially invariant, and there is no symmetry breaking. Below the Curie temperature, however, the magnetization acquires a constant nonvanishing value, which points in a certain direction (in the idealized situation where we have full equilibrium; otherwise, translational symmetry gets broken as well). The residual rotational symmetries which leave the orientation of this vector invariant remain unbroken, unlike the other rotations which do not and are thus spontaneously broken.<br />
* 对于铁磁性材料,其基本定律在空间旋转下是不变的。在这里,序参量是衡量磁偶极子密度的磁化强度。在居里温度以上,序参量为零,具有空间不变性,不存在对称性破缺。然而,在居里温度以下,磁化强度变成一个恒定的非零值,指向一个特定的方向(在有充分平衡的理想情况下;否则,平移对称性也会破缺)。使该向量方向不变的旋转对称性仍然保留,而其他旋转对称性自发破缺。<br />
* The laws describing a solid are invariant under the full [[Euclidean group]], but the solid itself spontaneously breaks this group down to a [[space group]]. The displacement and the orientation are the order parameters.<br />
* 描述固体的定律在完整的欧几里得群下是不变的,但固体本身会自发地将这个群分解为一个空间群。其中位移和方向是序参量。<br />
* General relativity has a Lorentz symmetry, but in [[Friedmann–Lemaître–Robertson–Walker metric|FRW cosmological models]], the mean 4-velocity field defined by averaging over the velocities of the galaxies (the galaxies act like gas particles at cosmological scales) acts as an order parameter breaking this symmetry. Similar comments can be made about the cosmic microwave background.<br />
* 广义相对论具有洛伦兹对称性,但在FRW宇宙模型中,定义为星系速度的平均值(星系在宇宙尺度上的行为就像气体粒子) 的平均 4-速度场,作为序参量会打破这种对称性。对于宇宙微波背景辐射也有类似的评论。<br />
* For the [[electroweak]] model, as explained earlier, a component of the Higgs field provides the order parameter breaking the electroweak gauge symmetry to the electromagnetic gauge symmetry. Like the ferromagnetic example, there is a phase transition at the electroweak temperature. The same comment about us not tending to notice broken symmetries suggests why it took so long for us to discover electroweak unification.<br />
* 对于电弱模型,如前面所解释的,希格斯场的一个分量提供了将电弱规范对称性破缺到电磁规范对称性的序参量。和铁磁的例子一样,在电弱温度下也有相变。同样的关于我们不倾向于注意破缺对称性的评论,也说明了为什么我们花了这么长时间才发现电弱统一。<br />
* In superconductors, there is a condensed-matter collective field ψ, which acts as the order parameter breaking the electromagnetic gauge symmetry.<br />
* 在超导体中有一个凝聚态集体场ψ,它是打破电磁规范对称性的序参量。<br />
* Take a thin cylindrical plastic rod and push both ends together. Before buckling, the system is symmetric under rotation, and so visibly cylindrically symmetric. But after buckling, it looks different, and asymmetric. Nevertheless, features of the cylindrical symmetry are still there: ignoring friction, it would take no force to freely spin the rod around, displacing the ground state in time, and amounting to an oscillation of vanishing frequency, unlike the radial oscillations in the direction of the buckle. This spinning mode is effectively the requisite [[Goldstone boson|Nambu–Goldstone boson]].<br />
* 拿一个细长的圆柱形塑料杆,把两端推到一起。在屈曲之前,系统在旋转下是对称的,因此可见圆柱对称性。但在弯曲之后,它看起来就不同了,而且是不对称的。然而,圆柱对称性的特征仍然存在:忽略摩擦,杆可以不受外力自由地自旋,在时间上取代基态,等于一个频率趋于零的振荡,而不是沿屈曲方向的径向振荡。这种自旋模式实际上是必需的南部-戈德斯通玻色子。<br />
* Consider a uniform layer of [[fluid]] over an infinite horizontal plane. This system has all the symmetries of the Euclidean plane. But now heat the bottom surface uniformly so that it becomes much hotter than the upper surface. When the temperature gradient becomes large enough, [[convection cell]]s will form, breaking the Euclidean symmetry.<br />
* 考虑无限水平面上的一层均匀的流体。这个系统具有欧几里得平面的所有对称性。但是现在均匀地加热底部表面,使它变得比上表面热得多。当温度梯度足够大时,就会形成对流单元,打破了欧几里得对称。<br />
* Consider a bead on a circular hoop that is rotated about a vertical [[diameter]]. As the [[rotational velocity]] is increased gradually from rest, the bead will initially stay at its initial [[equilibrium point]] at the bottom of the hoop (intuitively stable, lowest [[gravitational potential]]). At a certain critical rotational velocity, this point will become unstable and the bead will jump to one of two other newly created equilibria, [[equidistant]] from the center. Initially, the system is symmetric with respect to the diameter, yet after passing the critical velocity, the bead ends up in one of the two new equilibrium points, thus breaking the symmetry.<br />
* 考虑一个围绕某个竖直的直径旋转的圆形箍上的珠子。当旋转速度从静止逐渐增加时,珠子最初会停留在环底部的初始平衡点(直观上稳定,重力势最低)。在一定的临界旋转速度下,这一点将变得不稳定,珠子将跳到另外两个新创建的离中心等距离的平衡点中的一个。起初,系统相对直径是对称的,但在通过临界速度后,珠子最终停留在两个新的平衡点中的一个,从而打破了对称性。<br />
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==Spontaneous symmetry breaking in physics 物理学中的自发对称性破缺==<br />
[[File:Spontaneous symmetry breaking (explanatory diagram).png|thumb|right|250px|''Spontaneous symmetry breaking illustrated'': At high energy levels (''left''), the ball settles in the center, and the result is symmetric. At lower energy levels (''right''), the overall "rules" remain symmetric, but the symmetric "[[sombrero|Sombrero]]" enforces an asymmetric outcome, since eventually the ball must rest at some random spot on the bottom, "spontaneously", and not all others.|链接=Special:FilePath/Spontaneous_symmetry_breaking_(explanatory_diagram).png]]<br />
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===Particle physics 粒子物理===<br />
In [[particle physics]], the [[force carrier]] particles are normally specified by field equations with [[gauge symmetry]]; their equations predict that certain measurements will be the same at any point in the field. For instance, field equations might predict that the mass of two quarks is constant. Solving the equations to find the mass of each quark might give two solutions. In one solution, quark A is heavier than quark B. In the second solution, quark B is heavier than quark A ''by the same amount''. The symmetry of the equations is not reflected by the individual solutions, but it is reflected by the range of solutions.<br />
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在粒子物理学中,载力子通常由规范对称的场方程表示;它们的方程预测到某些测量值在场的任何点上都是相同的。例如,场方程可以预测两个夸克的质量是常数。通过求解方程来求每个夸克的质量可能会得到两个解。在一个解中,夸克A比夸克B重;在第二个解中,夸克B比夸克A重相同的量。方程的对称性不是由单个解来反映的,而是由解的范围来反映的。<br />
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An actual measurement reflects only one solution, representing a breakdown in the symmetry of the underlying theory. "Hidden" is a better term than "broken", because the symmetry is always there in these equations. This phenomenon is called [[Spontaneous magnetization|''spontaneous'']] symmetry breaking (SSB) because ''nothing'' (that we know of) breaks the symmetry in the equations.<ref name="Weinberg2011">{{cite book|author=Steven Weinberg|title=Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature|url=https://books.google.com/books?id=Rsg3PE_9_ccC|date=20 April 2011|publisher=Knopf Doubleday Publishing Group|isbn=978-0-307-78786-6}}</ref>{{rp|194–195}}<br />
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一个实际的测量只反映了一个解,代表了其潜在理论的对称性的破缺。在这里“隐藏”是比“破坏”更好的术语,因为对称性总是存在于这些方程中。这种现象被称为自发对称破缺(SSB),因为(我们所知道的)没有任何东西会打破方程中的对称性。<br />
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====Chiral symmetry 手性对称性====<br />
{{Main article|Chiral symmetry breaking}}<br />
Chiral symmetry breaking is an example of spontaneous symmetry breaking affecting the [[chiral symmetry]] of the [[strong interactions]] in particle physics. It is a property of [[quantum chromodynamics]], the [[quantum field theory]] describing these interactions, and is responsible for the bulk of the mass (over 99%) of the [[nucleons]], and thus of all common matter, as it converts very light bound [[quarks]] into 100 times heavier constituents of [[baryons]]. The approximate [[Nambu–Goldstone boson]]s in this spontaneous symmetry breaking process are the [[pions]], whose mass is an order of magnitude lighter than the mass of the nucleons. It served as the prototype and significant ingredient of the Higgs mechanism underlying the electroweak symmetry breaking.<br />
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手性对称破缺是粒子物理中影响强相互作用手性对称的自发对称破缺的一个例子。手性对称性破缺是量子色动力学(描述这些相互作用的量子场理论)的一种特性,它是核子的大部分质量(超过99%)的成因,因此也是所有普通物质的主要成因,因为它将非常轻的束缚夸克转化为100倍重量的重子的成分。在这个自发对称破缺过程中,近似的南部-戈德斯通玻色子是介子,其质量比核子的质量轻一个数量级。它是电弱对称破缺的希格斯机制的原型和重要组成部分。<br />
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====Higgs mechanism 希格斯机制====<br />
{{Main article|Higgs mechanism|Yukawa interaction}}<br />
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The strong, weak, and electromagnetic forces can all be understood as arising from [[gauge symmetry|gauge symmetries]]. The [[Higgs mechanism]], the spontaneous symmetry breaking of gauge symmetries, is an important component in understanding the [[superconductivity]] of metals and the origin of particle masses in the standard model of particle physics. One important consequence of the distinction between true symmetries and ''gauge symmetries'', is that the spontaneous breaking of a gauge symmetry does not give rise to characteristic massless Nambu–Goldstone physical modes, but only massive modes, like the plasma mode in a superconductor, or the Higgs mode observed in particle physics.<br />
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强、弱和电磁力都可以理解为来自规范对称。希格斯机制,即规范对称的自发对称破缺机制,是理解金属超导性和粒子物理标准模型中粒子质量起源的重要组成部分。区分真正的对称性和规范对称性的一个重要的结果,是规范对称性的自发破缺不产生典型的无质量Nambu-Goldstone物理模式,而是只产生有质量的模式,像超导体中的等离子体模式,或者粒子物理学中观察到的希格斯模式。<br />
<br />
In the standard model of particle physics, spontaneous symmetry breaking of the {{nowrap|SU(2) × U(1)}} gauge symmetry associated with the electro-weak force generates masses for several particles, and separates the electromagnetic and weak forces. The [[W and Z bosons]] are the elementary particles that mediate the [[weak interaction]], while the [[photon]] mediates the [[electromagnetic interaction]]. At energies much greater than 100 GeV, all these particles behave in a similar manner. The [[Unified field theory#Modern progress|Weinberg–Salam theory]] predicts that, at lower energies, this symmetry is broken so that the photon and the massive W and Z bosons emerge.<ref>A Brief History of Time, Stephen Hawking, Bantam; 10th anniversary edition (1998). pp. 73–74.{{ISBN?}}</ref> In addition, fermions develop mass consistently.<br />
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在粒子物理的标准模型中,与电弱力相关的SU(2) × U(1)规范对称性自发破缺产生多种粒子的质量,并将电磁力和弱相互作用分离。W玻色子和Z玻色子是介导弱相互作用的基本粒子,而光子介导电磁相互作用。当能量远远大于100 GeV时,所有这些粒子的行为都相似。Weinberg-Salam理论预测,在较低的能量下,这种对称性被打破,光子和大质量的W和Z玻色子就会出现。此外,费米子不断地发展质量。<br />
<br />
Without spontaneous symmetry breaking, the [[Standard Model]] of elementary particle interactions requires the existence of a number of particles. However, some particles (the [[W and Z bosons]]) would then be predicted to be massless, when, in reality, they are observed to have mass. To overcome this, spontaneous symmetry breaking is augmented by the [[Higgs mechanism]] to give these particles mass. It also suggests the presence of a new particle, the [[Higgs boson]], detected in 2012.<br />
<br />
在没有自发对称性破缺的情况下,基本粒子相互作用的标准模型要求存在多种粒子。然而,一些粒子(W玻色子和Z玻色子)将被预测为无质量的,而实际上它们被观察到有质量。为了克服这个问题,希格斯机制增强了自发对称破缺,从而赋予这些粒子质量。它还表明一种新粒子——希格斯玻色子——的存在,它在2012年被实验探测到。<br />
<br />
[[Superconductivity]] of metals is a condensed-matter analog of the Higgs phenomena, in which a condensate of Cooper pairs of electrons spontaneously breaks the U(1) gauge symmetry associated with light and electromagnetism.<br />
<br />
金属的超导性是一种类似于希格斯现象的凝聚态物质,其中库珀电子对的凝聚会自发地打破与光和电磁相关的U(1)规范对称。<br />
<br />
===Condensed matter physics===<br />
Most phases of matter can be understood through the lens of spontaneous symmetry breaking. For example, crystals are periodic arrays of atoms that are not invariant under all translations (only under a small subset of translations by a lattice vector). Magnets have north and south poles that are oriented in a specific direction, breaking [[rotational symmetry]]. In addition to these examples, there are a whole host of other symmetry-breaking phases of matter — including nematic phases of liquid crystals, charge- and spin-density waves, superfluids, and many others.<br />
<br />
There are several known examples of matter that cannot be described by spontaneous symmetry breaking, including: topologically ordered phases of matter, such as [[Fractional quantum Hall effect|fractional quantum Hall liquids]], and [[Quantum spin liquid|spin-liquids]]. These states do not break any symmetry, but are distinct phases of matter. Unlike the case of spontaneous symmetry breaking, there is not a general framework for describing such states.<ref name=chen>{{cite journal | last1 = Chen | first1 = Xie | author-link3 = Xiao-Gang Wen | last2 = Gu | first2 = Zheng-Cheng | last3 = Wen | first3 = Xiao-Gang | year = 2010 | title = Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order | journal = Phys. Rev. B | volume = 82 | issue = 15| page = 155138 | doi=10.1103/physrevb.82.155138|arxiv = 1004.3835 |bibcode = 2010PhRvB..82o5138C | s2cid = 14593420 }}</ref><br />
<br />
====Continuous symmetry====<br />
The ferromagnet is the canonical system that spontaneously breaks the continuous symmetry of the spins below the [[Curie temperature]] and at {{nowrap|1=''h'' = 0}}, where ''h'' is the external magnetic field. Below the [[Curie temperature]], the energy of the system is invariant under inversion of the magnetization ''m''('''x''') such that {{nowrap|1=''m''('''x''') = −''m''(−'''x''')}}. The symmetry is spontaneously broken as {{nowrap|''h'' → 0}} when the Hamiltonian becomes invariant under the inversion transformation, but the expectation value is not invariant.<br />
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Spontaneously-symmetry-broken phases of matter are characterized by an order parameter that describes the quantity which breaks the symmetry under consideration. For example, in a magnet, the order parameter is the local magnetization.<br />
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Spontaneous breaking of a continuous symmetry is inevitably accompanied by gapless (meaning that these modes do not cost any energy to excite) Nambu–Goldstone modes associated with slow, long-wavelength fluctuations of the order parameter. For example, vibrational modes in a crystal, known as phonons, are associated with slow density fluctuations of the crystal's atoms. The associated Goldstone mode for magnets are oscillating waves of spin known as spin-waves. For symmetry-breaking states, whose order parameter is not a conserved quantity, Nambu–Goldstone modes are typically massless and propagate at a constant velocity.<br />
<br />
An important theorem, due to Mermin and Wagner, states that, at finite temperature, thermally activated fluctuations of Nambu–Goldstone modes destroy the long-range order, and prevent spontaneous symmetry breaking in one- and two-dimensional systems. Similarly, quantum fluctuations of the order parameter prevent most types of continuous symmetry breaking in one-dimensional systems even at zero temperature. (An important exception is ferromagnets, whose order parameter, magnetization, is an exactly conserved quantity and does not have any quantum fluctuations.)<br />
<br />
Other long-range interacting systems, such as cylindrical curved surfaces interacting via the [[Coulomb potential]] or [[Yukawa potential]], have been shown to break translational and rotational symmetries.<ref><br />
{{cite journal<br />
|last1=Kohlstedt |first1=K.L.<br />
|last2=Vernizzi |first2=G.<br />
|last3=Solis |first3=F.J.<br />
|last4=Olvera de la Cruz |first4=M.<br />
|year=2007<br />
|title=Spontaneous Chirality via Long-range Electrostatic Forces<br />
|journal=[[Physical Review Letters]]<br />
|volume=99 |issue=3<br />
|page=030602<br />
|doi=10.1103/PhysRevLett.99.030602<br />
|arxiv = 0704.3435 |bibcode = 2007PhRvL..99c0602K |pmid=17678276|s2cid=37983980<br />
}}</ref> It was shown, in the presence of a symmetric Hamiltonian, and in the limit of infinite volume, the system spontaneously adopts a chiral configuration — i.e., breaks [[mirror plane]] [[symmetry]].<br />
<br />
===Dynamical symmetry breaking===<br />
Dynamical symmetry breaking (DSB) is a special form of spontaneous symmetry breaking in which the ground state of the system has reduced symmetry properties compared to its theoretical description (i.e., [[Lagrangian (field theory)|Lagrangian]]).<br />
<br />
Dynamical breaking of a global symmetry is a spontaneous symmetry breaking, which happens not at the (classical) tree level (i.e., at the level of the bare action), but due to quantum corrections (i.e., at the level of the [[effective action]]).<br />
<br />
Dynamical breaking of a gauge symmetry {{ref|note1}} is subtler. In the conventional spontaneous gauge symmetry breaking, there exists an unstable [[Higgs particle]] in the theory, which drives the vacuum to a symmetry-broken phase. (See, for example, [[electroweak interaction]].) In dynamical gauge symmetry breaking, however, no unstable Higgs particle operates in the theory, but the bound states of the system itself provide the unstable fields that render the phase transition. For example, Bardeen, Hill, and Lindner published a paper that attempts to replace the conventional [[Higgs mechanism]] in the [[standard model]] by a DSB that is driven by a bound state of top-antitop quarks. (Such models, in which a composite particle plays the role of the Higgs boson, are often referred to as "Composite Higgs models".)<ref><br />
{{cite journal<br />
|author1=William A. Bardeen<br />
|author2-link=Christopher T. Hill<br />
|author2=Christopher T. Hill<br />
|author3-link=Manfred Lindner<br />
|author3=Manfred Lindner<br />
|year=1990<br />
|title=Minimal dynamical symmetry breaking of the standard model<br />
|journal=[[Physical Review D]]<br />
|volume=41 |issue=5 |pages=1647–1660<br />
|bibcode=1990PhRvD..41.1647B<br />
|doi=10.1103/PhysRevD.41.1647<br />
|pmid=10012522<br />
|author1-link=William A. Bardeen<br />
}}</ref> Dynamical breaking of gauge symmetries is often due to creation of a [[fermionic condensate]] — e.g., the [[quark condensate]], which is connected to the [[Chiral symmetry breaking|dynamical breaking of chiral symmetry]] in [[quantum chromodynamics]]. Conventional [[superconductivity]] is the paradigmatic example from the condensed matter side, where phonon-mediated attractions lead electrons to become bound in pairs and then condense, thereby breaking the electromagnetic gauge symmetry.<br />
<br />
==Generalisation and technical usage==<br />
For spontaneous symmetry breaking to occur, there must be a system in which there are several equally likely outcomes. The system as a whole is therefore [[Symmetry (physics)|symmetric]] with respect to these outcomes. However, if the system is sampled (i.e. if the system is actually used or interacted with in any way), a specific outcome must occur. Though the system as a whole is symmetric, it is never encountered with this symmetry, but only in one specific asymmetric state. Hence, the symmetry is said to be spontaneously broken in that theory. Nevertheless, the fact that each outcome is equally likely is a reflection of the underlying symmetry, which is thus often dubbed "hidden symmetry", and has crucial formal consequences. (See the article on the [[Nambu–Goldstone boson|Goldstone boson]].)<br />
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When a theory is symmetric with respect to a [[symmetry group]], but requires that one element of the group be distinct, then spontaneous symmetry breaking has occurred. The theory must not dictate ''which'' member is distinct, only that ''one is''. From this point on, the theory can be treated as if this element actually is distinct, with the proviso that any results found in this way must be resymmetrized, by taking the average of each of the elements of the group being the distinct one.<br />
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The crucial concept in physics theories is the [[order parameter]]. If there is a field (often a background field) which acquires an expectation value (not necessarily a [[vacuum expectation value|''vacuum'' expectation value]]) which is not invariant under the symmetry in question, we say that the system is in the [[ordered phase]], and the symmetry is spontaneously broken. This is because other subsystems interact with the order parameter, which specifies a "frame of reference" to be measured against. In that case, the [[vacuum state]] does not obey the initial symmetry (which would keep it invariant, in the linearly realized '''Wigner mode''' in which it would be a singlet), and, instead changes under the (hidden) symmetry, now implemented in the (nonlinear) '''Nambu–Goldstone mode'''. Normally, in the absence of the Higgs mechanism, massless [[Goldstone boson]]s arise.<br />
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The symmetry group can be discrete, such as the [[space group]] of a crystal, or continuous (e.g., a [[Lie group]]), such as the rotational symmetry of space. However, if the system contains only a single spatial dimension, then only discrete symmetries may be broken in a [[vacuum state]] of the full [[Quantum mechanics|quantum theory]], although a classical solution may break a continuous symmetry.<br />
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==Nobel Prize==<br />
On October 7, 2008, the [[Royal Swedish Academy of Sciences]] awarded the 2008 [[Nobel Prize in Physics]] to three scientists for their work in subatomic physics symmetry breaking. [[Yoichiro Nambu]], of the [[University of Chicago]], won half of the prize for the discovery of the mechanism of spontaneous broken symmetry in the context of the strong interactions, specifically [[chiral symmetry breaking]]. Physicists [[Makoto Kobayashi (physicist)|Makoto Kobayashi]] and [[Toshihide Maskawa]], of [[Kyoto University]], shared the other half of the prize for discovering the origin of the [[Explicit symmetry breaking|explicit breaking]] of CP symmetry in the weak interactions.<ref>{{cite web|author=The Nobel Foundation|title=The Nobel Prize in Physics 2008|url=http://nobelprize.org/nobel_prizes/physics/laureates/2008/index.html|work=nobelprize.org|access-date=January 15, 2008}}</ref> This origin is ultimately reliant on the Higgs mechanism, but, so far understood as a "just so" feature of Higgs couplings, not a spontaneously broken symmetry phenomenon.<br />
<br />
==See also==<br />
{{div col|colwidth=24em}}<br />
* [[Autocatalytic reactions and order creation]]<br />
* [[Catastrophe theory]]<br />
* [[Chiral symmetry breaking]]<br />
* [[CP-violation]]<br />
* [[Fermi ball]]<br />
* [[Gauge gravitation theory]]<br />
* [[Goldstone boson]]<br />
* [[Grand unified theory]]<br />
* [[Higgs mechanism]]<br />
* [[Higgs boson]]<br />
* [[Higgs field (classical)]]<br />
* [[Irreversibility]]<br />
* [[Magnetic catalysis]] of chiral symmetry breaking<br />
* [[Mermin–Wagner theorem]]<br />
* [[Norton's dome]]<br />
* [[Second-order phase transition]]<br />
* [[Spontaneous absolute asymmetric synthesis]] in chemistry<br />
* [[Symmetry breaking]]<br />
* [[Tachyon condensation]]<br />
* [[1964 PRL symmetry breaking papers]]<br />
{{div col end}}<br />
<br />
==Notes==<br />
* {{note|note1}} Note that (as in fundamental Higgs driven spontaneous gauge symmetry breaking) the term "symmetry breaking" is a misnomer when applied to gauge symmetries.<br />
<br />
==References==<br />
{{Reflist}}<br />
<br />
==External links==<br />
{{wikiquote}}<br />
* For a pedagogic introduction to electroweak symmetry breaking with step by step derivations, not found in texts, of many key relations, see http://www.quantumfieldtheory.info/Electroweak_Sym_breaking.pdf<br />
* [http://hyperphysics.phy-astr.gsu.edu/hbase/forces/unify.html#c2 Spontaneous symmetry breaking]<br />
* [http://prl.aps.org/50years/milestones#1964 Physical Review Letters – 50th Anniversary Milestone Papers]<br />
* [http://cerncourier.com/cws/article/cern/32522 In CERN Courier, Steven Weinberg reflects on spontaneous symmetry breaking]<br />
* [http://www.scholarpedia.org/article/Englert-Brout-Higgs-Guralnik-Hagen-Kibble_mechanism Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism on Scholarpedia]<br />
* [http://www.scholarpedia.org/article/Englert-Brout-Higgs-Guralnik-Hagen-Kibble_mechanism_%28history%29 History of Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism on Scholarpedia]<br />
* [https://arxiv.org/abs/0907.3466 The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles]<br />
* [http://www.worldscinet.com/ijmpa/24/2414/S0217751X09045431.html International Journal of Modern Physics A: The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles]<br />
* [http://www.datafilehost.com/download-7d512618.html Guralnik, G S; Hagen, C R and Kibble, T W B (1967). Broken Symmetries and the Goldstone Theorem. Advances in Physics, vol. 2 Interscience Publishers, New York. pp. 567–708] {{ISBN|0-470-17057-3}}<br />
* [http://lanl.arxiv.org/abs/hep-th/9802142 Spontaneous Symmetry Breaking in Gauge Theories: a Historical Survey]<br />
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{{Standard model of physics}}<br />
{{Quantum mechanics topics}}<br />
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{{DEFAULTSORT:Spontaneous Symmetry Breaking}}<br />
[[Category:Theoretical physics]]<br />
[[Category:Quantum field theory]]<br />
[[Category:Standard Model]]<br />
[[Category:Quantum chromodynamics]]<br />
[[Category:Symmetry]]<br />
[[Category:Quantum phases]]<br />
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==实例==<br />
<br />
对称性破缺可以涵盖以下任何一种情况:<ref>{{cite web|url=http://www.angelfire.com/stars5/astroinfo/gloss/s.html|title=Astronomical Glossary|author=|date=|website=www.angelfire.com}}</ref><br />
* 某些结构的随机形成破坏了物理学基本定律的精确对称性;<br />
* 物理学中最小能量状态的对称性比系统本身少的情形;<br />
* 系统的实际状态由于明显对称的状态不稳定而不能反映动力学的基本对称性的情况(稳定性是以局部不对称为代价的);<br />
* 理论方程具有某种对称性,但其解可能没有(对称性是“隐藏的”)的情况。<br />
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在物理学文献中讨论的首批对称性破缺案例之一,与不可压缩流体在重力和流体静力平衡中均匀旋转的形式有关。在1834年,Jacobi <ref>{{cite journal| last=Jacobi | first=C.G.J. | title=Über die figur des gleichgewichts | journal=[[Annalen der Physik und Chemie]] | volume=109 | issue=33| pages=229–238 | year=1834| doi=10.1002/andp.18341090808 | bibcode=1834AnP...109..229J | url=https://zenodo.org/record/2027349 }}</ref>和后来的 Liouville <ref>{{cite journal| last=Liouville | first=J. | title=Sur la figure d'une masse fluide homogène, en équilibre et douée d'un mouvement de rotation| journal=Journal de l'École Polytechnique | issue=14| pages=289–296 | year=1834}}</ref>讨论了这样一个事实: 当旋转物体的动能相对于引力势能超过一定的临界值时,这个问题的平衡解是三轴椭球。在这个分叉点上,麦克劳林椭球体的轴对称性被破坏。此外,在这个分叉点之上,对于常数角动量,使动能最小化的解是非轴对称的 Jacobi 椭球,而不是 Maclaurin 椭球。<br />
==另请参阅==<br />
<br />
*[[Higgs mechanism]]<br />
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*[[QCD vacuum]]<br />
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*[[Goldstone boson]]<br />
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*[[1964 PRL symmetry breaking papers]]<br />
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*[[希格斯机制]]<br />
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*[[QCD真空]]<br />
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*[[戈德斯通玻色子]]<br />
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*[[1964年PRL对称性破缺论文]]<br />
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==参考文献==<br />
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{{reflist|colwidth=30em}}<br />
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{{DEFAULTSORT:Symmetry Breaking}}<br />
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范畴: 对称<br />
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类别: 模式形成<br />
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本中文词条由XXX编译,XXX审校,XXX总审校,西瓜编辑,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''<br />
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<noinclude><br />
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[[Category:对称性破缺]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%AF%B9%E7%A7%B0%E6%80%A7%E7%A0%B4%E7%BC%BA&diff=24763对称性破缺2021-07-26T09:53:32Z<p>Jxzhou:/* Chiral symmetry */</p>
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[[图一:一个小球位于中央山丘的山峰处(C)。这是一种不稳定平衡:一个很小的扰动会使它落到左边(L)或右边(R)稳定点。尽管山丘是对称的,没有理由让球落在哪一侧,但观察到的最终状态仍然是不对称的,它总会落到某一侧]]。<br />
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在物理学中,一个作用于系统的(无限)小扰动使系统跨过临界点,通过决定去向分叉的哪个分支来决定系统的命运,这种现象叫做'''<font color="#ff8000">对称性破缺</font>'''。对于一个观测不到扰动(或“噪声”)的外部观察者来说,这个选择看起来是任意的。这个过程被称为对称性破缺,因为这种转变通常使系统从一个对称但无序的状态进入一个或多个确定的状态。在'''<font color="#ff8000">斑图生成</font>'''中对称性破缺起着重要作用。<br />
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1972年,诺贝尔奖得主P·W·安德森(P.W.Anderson)在《科学》(Science)杂志上发表了一篇名为《多即不同》的论文<ref>{{cite journal | last=Anderson | first=P.W. | title=More is Different | journal=Science | volume=177 | issue=4047| pages=393–396 | year=1972 | url=http://robotics.cs.tamu.edu/dshell/cs689/papers/anderson72more_is_different.pdf | doi=10.1126/science.177.4047.393 | pmid=17796623 | format=|bibcode = 1972Sci...177..393A }}</ref>,文中使用对称性破缺的思想表明,即使'''<font color="#ff8000">还原论</font>'''是正确的,但它的逆命题'''<font color="#ff8000">建构主义</font>'''是错误的。建构主义认为,在给出描述各组成部分的理论的情况下科学家可以轻易地预测复杂现象。<br />
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对称性破缺可以分为'''<font color="#ff8000">显性对称性破缺</font>'''和'''<font color="#ff8000">自发对称性破缺</font>'''两种类型,二者的区别是,在破缺对称性下系统的运动方程是否不变或者基态是否保持不变。<br />
==显性对称性破缺==<br />
<br />
在'''<font color="#ff8000">显性对称性破缺</font>'''中,描述系统的运动方程在破缺对称下是不同的。在哈密顿力学或拉格朗日力学中,假若系统的哈密顿量(或拉格朗日量)中至少一项显性地打破了给定的对称性,就发生了显性对称性破缺。<br />
==自发对称性破缺==<br />
<br />
在'''<font color="#ff8000">自发对称性破缺</font>'''中,系统的运动方程是不变的,但系统发生了变化。这是因为系统的背景(时空)——真空态——是非恒定的。这种对称性破缺可以用一个序参量进行参数化。这类对称破缺的一个特殊情况是'''<font color="#ff8000">动力学对称性破缺</font>'''。<br />
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Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state ends up in an asymmetric state.[1][2][3] In particular, it can describe systems where the equations of motion or the Lagrangian obey symmetries, but the lowest-energy vacuum solutions do not exhibit that same symmetry. When the system goes to one of those vacuum solutions, the symmetry is broken for perturbations around that vacuum even though the entire Lagrangian retains that symmetry.<br />
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自发对称破缺是一个自发的对称破缺过程,它使处于对称状态的物理系统最终处于非对称状态。特别地,它可以描述运动方程或拉格朗日方程服从某种对称性,但最低能量真空解不具有该对称性的系统。当系统进入其中一个真空解时,真空解周围的扰动会破坏系统对称性,尽管整个拉格朗日方程仍然保持了对称性。<br />
<br />
==Overview==<br />
<br />
In [[explicit symmetry breaking]], if two outcomes are considered, the probability of a pair of outcomes can be different. By definition, spontaneous symmetry breaking requires the existence of a symmetric probability distribution—any pair of outcomes has the same probability. In other words, the underlying laws{{clarify|date=December 2016}} are [[Invariant (physics)|invariant]] under a [[Symmetry (physics)|symmetry]] transformation.<br />
<br />
The system, as a whole{{clarify|date=December 2016}}, changes under such transformations.<br />
<br />
Phases of matter, such as crystals, magnets, and conventional superconductors, as well as simple phase transitions can be described by spontaneous symmetry breaking. Notable exceptions include topological phases of matter like the [[fractional quantum Hall effect]].<br />
<br />
==Examples 例子==<br />
<br />
===Sombrero potential===<br />
Consider a symmetric upward dome with a trough circling the bottom. If a ball is put at the very peak of the dome, the system is symmetric with respect to a rotation around the center axis. But the ball may ''spontaneously break'' this symmetry by rolling down the dome into the trough, a point of lowest energy. Afterward, the ball has come to a rest at some fixed point on the perimeter. The dome and the ball retain their individual symmetry, but the system does not.<ref>{{cite book |first=Gerald M. |last=Edelman |title=Bright Air, Brilliant Fire: On the Matter of the Mind |location=New York |publisher=BasicBooks |year=1992 |url=https://archive.org/details/brightairbrillia00gera |url-access=registration |page=[https://archive.org/details/brightairbrillia00gera/page/203 203] }}</ref><br />
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考虑一个对称向上的圆顶,底部环绕着一个槽。如果把一个球放在圆顶的最顶端,这个系统是围绕中心轴旋转对称的。但球体可能会自发地打破这种对称性,因为它会沿着穹顶滚动到能量最低的槽中。然后,球在圆周上某个固定的点上停下来。圆顶和球保持了各自的对称,但系统却没有保持对称性。<br />
[[Image:Mexican hat potential polar.svg|270px|thumb|left|Graph of Goldstone's "[[sombrero]]" potential function <math>V(\phi)</math>.|链接=Special:FilePath/Mexican_hat_potential_polar.svg]]<br />
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In the simplest idealized relativistic model, the spontaneously broken symmetry is summarized through an illustrative [[scalar field theory]]. The relevant [[Lagrangian (field theory)|Lagrangian]] of a scalar field <math>\phi</math>, which essentially dictates how a system behaves, can be split up into kinetic and potential terms,<br />
<br />
在最简单的理想相对论模型中,可以用一个解释性的标量场理论总结自发破对称性。一个标量场 <math>\phi</math>的拉格朗日量从本质上决定了系统的行为,它可以分解成动能项和势能项:<br />
{{NumBlk|::|<math>\mathcal{L} = \partial^\mu \phi \partial_\mu \phi - V(\phi).</math>|{{EquationRef|1}}}}<br />
<br />
It is in this potential term <math>V(\phi)</math> that the symmetry breaking is triggered. An example of a potential, due to [[Jeffrey Goldstone]]<ref>{{Cite journal | last1 = Goldstone | first1 = J. | doi = 10.1007/BF02812722 | title = Field theories with " Superconductor " solutions | journal = Il Nuovo Cimento | volume = 19 | issue = 1 | pages = 154–164 | year = 1961 | bibcode = 1961NCim...19..154G | s2cid = 120409034 | url = http://cds.cern.ch/record/343400 }}</ref> is illustrated in the graph at the left.<br />
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正是在势能项 <math>V(\phi)</math> 中触发了对称性破缺。例如左图所示的 [[Jeffrey Goldstone]] 给出的势能函数:<br />
{{NumBlk|::|<math>V(\phi) = -5|\phi|^2 + |\phi|^4 \,</math>.|{{EquationRef|2}}}}<br />
<br />
This potential has an infinite number of possible [[minimum|minima]] (vacuum states) given by<br />
<br />
该是函数具有无穷数量的最小值点(真空态)当<br />
{{NumBlk|::|<math>\phi = \sqrt{5} e^{i\theta} </math>.|{{EquationRef|3}}}}<br />
for any real ''θ'' between 0 and 2''π''. The system also has an unstable vacuum state corresponding to {{nowrap|1=''Φ'' = 0}}. This state has a [[Unitary group|U(1)]] symmetry. However, once the system falls into a specific stable vacuum state (amounting to a choice of ''θ''), this symmetry will appear to be lost, or "spontaneously broken".<br />
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对于0到2π之间的任何实数θ。系统也有一个不稳定的真空状态,对应于Φ = 0。这个状态具有U(1)对称。然而,一旦系统落入某个稳定真空状态(相当于选择θ),这种对称性就会消失,或者说“自发破缺”。<br />
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In fact, any other choice of ''θ'' would have exactly the same energy, implying the existence of a massless [[Goldstone boson|Nambu–Goldstone boson]], the mode running around the circle at the minimum of this potential, and indicating there is some memory of the original symmetry in the Lagrangian.<br />
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事实上,任何其他θ的选择都将具有完全相同的能量,这意味着无质量的南部-戈德斯通玻色子的存在,这种模式在势能的最小值绕圆运动,并表明存在拉格朗日方程中原始对称性的一些记忆。<br />
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===Other examples===<br />
* For [[ferromagnet]]ic materials, the underlying laws are invariant under spatial rotations. Here, the order parameter is the [[magnetization]], which measures the magnetic dipole density. Above the [[Curie temperature]], the order parameter is zero, which is spatially invariant, and there is no symmetry breaking. Below the Curie temperature, however, the magnetization acquires a constant nonvanishing value, which points in a certain direction (in the idealized situation where we have full equilibrium; otherwise, translational symmetry gets broken as well). The residual rotational symmetries which leave the orientation of this vector invariant remain unbroken, unlike the other rotations which do not and are thus spontaneously broken.<br />
* 对于铁磁性材料,其基本定律在空间旋转下是不变的。在这里,序参量是衡量磁偶极子密度的磁化强度。在居里温度以上,序参量为零,具有空间不变性,不存在对称性破缺。然而,在居里温度以下,磁化强度变成一个恒定的非零值,指向一个特定的方向(在有充分平衡的理想情况下;否则,平移对称性也会破缺)。使该向量方向不变的旋转对称性仍然保留,而其他旋转对称性自发破缺。<br />
* The laws describing a solid are invariant under the full [[Euclidean group]], but the solid itself spontaneously breaks this group down to a [[space group]]. The displacement and the orientation are the order parameters.<br />
* 描述固体的定律在完整的欧几里得群下是不变的,但固体本身会自发地将这个群分解为一个空间群。其中位移和方向是序参量。<br />
* General relativity has a Lorentz symmetry, but in [[Friedmann–Lemaître–Robertson–Walker metric|FRW cosmological models]], the mean 4-velocity field defined by averaging over the velocities of the galaxies (the galaxies act like gas particles at cosmological scales) acts as an order parameter breaking this symmetry. Similar comments can be made about the cosmic microwave background.<br />
* 广义相对论具有洛伦兹对称性,但在FRW宇宙模型中,定义为星系速度的平均值(星系在宇宙尺度上的行为就像气体粒子) 的平均 4-速度场,作为序参量会打破这种对称性。对于宇宙微波背景辐射也有类似的评论。<br />
* For the [[electroweak]] model, as explained earlier, a component of the Higgs field provides the order parameter breaking the electroweak gauge symmetry to the electromagnetic gauge symmetry. Like the ferromagnetic example, there is a phase transition at the electroweak temperature. The same comment about us not tending to notice broken symmetries suggests why it took so long for us to discover electroweak unification.<br />
* 对于电弱模型,如前面所解释的,希格斯场的一个分量提供了将电弱规范对称性破缺到电磁规范对称性的序参量。和铁磁的例子一样,在电弱温度下也有相变。同样的关于我们不倾向于注意破缺对称性的评论,也说明了为什么我们花了这么长时间才发现电弱统一。<br />
* In superconductors, there is a condensed-matter collective field ψ, which acts as the order parameter breaking the electromagnetic gauge symmetry.<br />
* 在超导体中有一个凝聚态集体场ψ,它是打破电磁规范对称性的序参量。<br />
* Take a thin cylindrical plastic rod and push both ends together. Before buckling, the system is symmetric under rotation, and so visibly cylindrically symmetric. But after buckling, it looks different, and asymmetric. Nevertheless, features of the cylindrical symmetry are still there: ignoring friction, it would take no force to freely spin the rod around, displacing the ground state in time, and amounting to an oscillation of vanishing frequency, unlike the radial oscillations in the direction of the buckle. This spinning mode is effectively the requisite [[Goldstone boson|Nambu–Goldstone boson]].<br />
* 拿一个细长的圆柱形塑料杆,把两端推到一起。在屈曲之前,系统在旋转下是对称的,因此可见圆柱对称性。但在弯曲之后,它看起来就不同了,而且是不对称的。然而,圆柱对称性的特征仍然存在:忽略摩擦,杆可以不受外力自由地自旋,在时间上取代基态,等于一个频率趋于零的振荡,而不是沿屈曲方向的径向振荡。这种自旋模式实际上是必需的南部-戈德斯通玻色子。<br />
* Consider a uniform layer of [[fluid]] over an infinite horizontal plane. This system has all the symmetries of the Euclidean plane. But now heat the bottom surface uniformly so that it becomes much hotter than the upper surface. When the temperature gradient becomes large enough, [[convection cell]]s will form, breaking the Euclidean symmetry.<br />
* 考虑无限水平面上的一层均匀的流体。这个系统具有欧几里得平面的所有对称性。但是现在均匀地加热底部表面,使它变得比上表面热得多。当温度梯度足够大时,就会形成对流单元,打破了欧几里得对称。<br />
* Consider a bead on a circular hoop that is rotated about a vertical [[diameter]]. As the [[rotational velocity]] is increased gradually from rest, the bead will initially stay at its initial [[equilibrium point]] at the bottom of the hoop (intuitively stable, lowest [[gravitational potential]]). At a certain critical rotational velocity, this point will become unstable and the bead will jump to one of two other newly created equilibria, [[equidistant]] from the center. Initially, the system is symmetric with respect to the diameter, yet after passing the critical velocity, the bead ends up in one of the two new equilibrium points, thus breaking the symmetry.<br />
* 考虑一个围绕某个竖直的直径旋转的圆形箍上的珠子。当旋转速度从静止逐渐增加时,珠子最初会停留在环底部的初始平衡点(直观上稳定,重力势最低)。在一定的临界旋转速度下,这一点将变得不稳定,珠子将跳到另外两个新创建的离中心等距离的平衡点中的一个。起初,系统相对直径是对称的,但在通过临界速度后,珠子最终停留在两个新的平衡点中的一个,从而打破了对称性。<br />
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==Spontaneous symmetry breaking in physics 物理学中的自发对称性破缺==<br />
[[File:Spontaneous symmetry breaking (explanatory diagram).png|thumb|right|250px|''Spontaneous symmetry breaking illustrated'': At high energy levels (''left''), the ball settles in the center, and the result is symmetric. At lower energy levels (''right''), the overall "rules" remain symmetric, but the symmetric "[[sombrero|Sombrero]]" enforces an asymmetric outcome, since eventually the ball must rest at some random spot on the bottom, "spontaneously", and not all others.|链接=Special:FilePath/Spontaneous_symmetry_breaking_(explanatory_diagram).png]]<br />
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===Particle physics 粒子物理===<br />
In [[particle physics]], the [[force carrier]] particles are normally specified by field equations with [[gauge symmetry]]; their equations predict that certain measurements will be the same at any point in the field. For instance, field equations might predict that the mass of two quarks is constant. Solving the equations to find the mass of each quark might give two solutions. In one solution, quark A is heavier than quark B. In the second solution, quark B is heavier than quark A ''by the same amount''. The symmetry of the equations is not reflected by the individual solutions, but it is reflected by the range of solutions.<br />
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在粒子物理学中,载力子通常由规范对称的场方程表示;它们的方程预测到某些测量值在场的任何点上都是相同的。例如,场方程可以预测两个夸克的质量是常数。通过求解方程来求每个夸克的质量可能会得到两个解。在一个解中,夸克A比夸克B重;在第二个解中,夸克B比夸克A重相同的量。方程的对称性不是由单个解来反映的,而是由解的范围来反映的。<br />
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An actual measurement reflects only one solution, representing a breakdown in the symmetry of the underlying theory. "Hidden" is a better term than "broken", because the symmetry is always there in these equations. This phenomenon is called [[Spontaneous magnetization|''spontaneous'']] symmetry breaking (SSB) because ''nothing'' (that we know of) breaks the symmetry in the equations.<ref name="Weinberg2011">{{cite book|author=Steven Weinberg|title=Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature|url=https://books.google.com/books?id=Rsg3PE_9_ccC|date=20 April 2011|publisher=Knopf Doubleday Publishing Group|isbn=978-0-307-78786-6}}</ref>{{rp|194–195}}<br />
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一个实际的测量只反映了一个解,代表了其潜在理论的对称性的破缺。在这里“隐藏”是比“破坏”更好的术语,因为对称性总是存在于这些方程中。这种现象被称为自发对称破缺(SSB),因为(我们所知道的)没有任何东西会打破方程中的对称性。<br />
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====Chiral symmetry 手性对称性====<br />
{{Main article|Chiral symmetry breaking}}<br />
Chiral symmetry breaking is an example of spontaneous symmetry breaking affecting the [[chiral symmetry]] of the [[strong interactions]] in particle physics. It is a property of [[quantum chromodynamics]], the [[quantum field theory]] describing these interactions, and is responsible for the bulk of the mass (over 99%) of the [[nucleons]], and thus of all common matter, as it converts very light bound [[quarks]] into 100 times heavier constituents of [[baryons]]. The approximate [[Nambu–Goldstone boson]]s in this spontaneous symmetry breaking process are the [[pions]], whose mass is an order of magnitude lighter than the mass of the nucleons. It served as the prototype and significant ingredient of the Higgs mechanism underlying the electroweak symmetry breaking.<br />
<br />
手性对称破缺是粒子物理中影响强相互作用手性对称的自发对称破缺的一个例子。手性对称性破缺是量子色动力学(描述这些相互作用的量子场理论)的一种特性,它是核子的大部分质量(超过99%)的成因,因此也是所有普通物质的主要成因,因为它将非常轻的束缚夸克转化为100倍重量的重子的成分。在这个自发对称破缺过程中,近似的南部-戈德斯通玻色子是介子,其质量比核子的质量轻一个数量级。它是电弱对称破缺的希格斯机制的原型和重要组成部分。<br />
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====Higgs mechanism 希格斯机制====<br />
{{Main article|Higgs mechanism|Yukawa interaction}}<br />
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The strong, weak, and electromagnetic forces can all be understood as arising from [[gauge symmetry|gauge symmetries]]. The [[Higgs mechanism]], the spontaneous symmetry breaking of gauge symmetries, is an important component in understanding the [[superconductivity]] of metals and the origin of particle masses in the standard model of particle physics. One important consequence of the distinction between true symmetries and ''gauge symmetries'', is that the spontaneous breaking of a gauge symmetry does not give rise to characteristic massless Nambu–Goldstone physical modes, but only massive modes, like the plasma mode in a superconductor, or the Higgs mode observed in particle physics.<br />
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强、弱和电磁力都可以理解为来自规范对称。希格斯机制,即规范对称的自发对称破缺机制,是理解金属超导性和粒子物理标准模型中粒子质量起源的重要组成部分。区分真正的对称性和规范对称性的一个重要的结果,是规范对称性的自发破缺不产生典型的无质量Nambu-Goldstone物理模式,而是只产生有质量的模式,像超导体中的等离子体模式,或者粒子物理学中观察到的希格斯模式。<br />
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In the standard model of particle physics, spontaneous symmetry breaking of the {{nowrap|SU(2) × U(1)}} gauge symmetry associated with the electro-weak force generates masses for several particles, and separates the electromagnetic and weak forces. The [[W and Z bosons]] are the elementary particles that mediate the [[weak interaction]], while the [[photon]] mediates the [[electromagnetic interaction]]. At energies much greater than 100 GeV, all these particles behave in a similar manner. The [[Unified field theory#Modern progress|Weinberg–Salam theory]] predicts that, at lower energies, this symmetry is broken so that the photon and the massive W and Z bosons emerge.<ref>A Brief History of Time, Stephen Hawking, Bantam; 10th anniversary edition (1998). pp. 73–74.{{ISBN?}}</ref> In addition, fermions develop mass consistently.<br />
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Without spontaneous symmetry breaking, the [[Standard Model]] of elementary particle interactions requires the existence of a number of particles. However, some particles (the [[W and Z bosons]]) would then be predicted to be massless, when, in reality, they are observed to have mass. To overcome this, spontaneous symmetry breaking is augmented by the [[Higgs mechanism]] to give these particles mass. It also suggests the presence of a new particle, the [[Higgs boson]], detected in 2012.<br />
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[[Superconductivity]] of metals is a condensed-matter analog of the Higgs phenomena, in which a condensate of Cooper pairs of electrons spontaneously breaks the U(1) gauge symmetry associated with light and electromagnetism.<br />
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===Condensed matter physics===<br />
Most phases of matter can be understood through the lens of spontaneous symmetry breaking. For example, crystals are periodic arrays of atoms that are not invariant under all translations (only under a small subset of translations by a lattice vector). Magnets have north and south poles that are oriented in a specific direction, breaking [[rotational symmetry]]. In addition to these examples, there are a whole host of other symmetry-breaking phases of matter — including nematic phases of liquid crystals, charge- and spin-density waves, superfluids, and many others.<br />
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There are several known examples of matter that cannot be described by spontaneous symmetry breaking, including: topologically ordered phases of matter, such as [[Fractional quantum Hall effect|fractional quantum Hall liquids]], and [[Quantum spin liquid|spin-liquids]]. These states do not break any symmetry, but are distinct phases of matter. Unlike the case of spontaneous symmetry breaking, there is not a general framework for describing such states.<ref name=chen>{{cite journal | last1 = Chen | first1 = Xie | author-link3 = Xiao-Gang Wen | last2 = Gu | first2 = Zheng-Cheng | last3 = Wen | first3 = Xiao-Gang | year = 2010 | title = Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order | journal = Phys. Rev. B | volume = 82 | issue = 15| page = 155138 | doi=10.1103/physrevb.82.155138|arxiv = 1004.3835 |bibcode = 2010PhRvB..82o5138C | s2cid = 14593420 }}</ref><br />
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====Continuous symmetry====<br />
The ferromagnet is the canonical system that spontaneously breaks the continuous symmetry of the spins below the [[Curie temperature]] and at {{nowrap|1=''h'' = 0}}, where ''h'' is the external magnetic field. Below the [[Curie temperature]], the energy of the system is invariant under inversion of the magnetization ''m''('''x''') such that {{nowrap|1=''m''('''x''') = −''m''(−'''x''')}}. The symmetry is spontaneously broken as {{nowrap|''h'' → 0}} when the Hamiltonian becomes invariant under the inversion transformation, but the expectation value is not invariant.<br />
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Spontaneously-symmetry-broken phases of matter are characterized by an order parameter that describes the quantity which breaks the symmetry under consideration. For example, in a magnet, the order parameter is the local magnetization.<br />
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Spontaneous breaking of a continuous symmetry is inevitably accompanied by gapless (meaning that these modes do not cost any energy to excite) Nambu–Goldstone modes associated with slow, long-wavelength fluctuations of the order parameter. For example, vibrational modes in a crystal, known as phonons, are associated with slow density fluctuations of the crystal's atoms. The associated Goldstone mode for magnets are oscillating waves of spin known as spin-waves. For symmetry-breaking states, whose order parameter is not a conserved quantity, Nambu–Goldstone modes are typically massless and propagate at a constant velocity.<br />
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An important theorem, due to Mermin and Wagner, states that, at finite temperature, thermally activated fluctuations of Nambu–Goldstone modes destroy the long-range order, and prevent spontaneous symmetry breaking in one- and two-dimensional systems. Similarly, quantum fluctuations of the order parameter prevent most types of continuous symmetry breaking in one-dimensional systems even at zero temperature. (An important exception is ferromagnets, whose order parameter, magnetization, is an exactly conserved quantity and does not have any quantum fluctuations.)<br />
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Other long-range interacting systems, such as cylindrical curved surfaces interacting via the [[Coulomb potential]] or [[Yukawa potential]], have been shown to break translational and rotational symmetries.<ref><br />
{{cite journal<br />
|last1=Kohlstedt |first1=K.L.<br />
|last2=Vernizzi |first2=G.<br />
|last3=Solis |first3=F.J.<br />
|last4=Olvera de la Cruz |first4=M.<br />
|year=2007<br />
|title=Spontaneous Chirality via Long-range Electrostatic Forces<br />
|journal=[[Physical Review Letters]]<br />
|volume=99 |issue=3<br />
|page=030602<br />
|doi=10.1103/PhysRevLett.99.030602<br />
|arxiv = 0704.3435 |bibcode = 2007PhRvL..99c0602K |pmid=17678276|s2cid=37983980<br />
}}</ref> It was shown, in the presence of a symmetric Hamiltonian, and in the limit of infinite volume, the system spontaneously adopts a chiral configuration — i.e., breaks [[mirror plane]] [[symmetry]].<br />
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===Dynamical symmetry breaking===<br />
Dynamical symmetry breaking (DSB) is a special form of spontaneous symmetry breaking in which the ground state of the system has reduced symmetry properties compared to its theoretical description (i.e., [[Lagrangian (field theory)|Lagrangian]]).<br />
<br />
Dynamical breaking of a global symmetry is a spontaneous symmetry breaking, which happens not at the (classical) tree level (i.e., at the level of the bare action), but due to quantum corrections (i.e., at the level of the [[effective action]]).<br />
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Dynamical breaking of a gauge symmetry {{ref|note1}} is subtler. In the conventional spontaneous gauge symmetry breaking, there exists an unstable [[Higgs particle]] in the theory, which drives the vacuum to a symmetry-broken phase. (See, for example, [[electroweak interaction]].) In dynamical gauge symmetry breaking, however, no unstable Higgs particle operates in the theory, but the bound states of the system itself provide the unstable fields that render the phase transition. For example, Bardeen, Hill, and Lindner published a paper that attempts to replace the conventional [[Higgs mechanism]] in the [[standard model]] by a DSB that is driven by a bound state of top-antitop quarks. (Such models, in which a composite particle plays the role of the Higgs boson, are often referred to as "Composite Higgs models".)<ref><br />
{{cite journal<br />
|author1=William A. Bardeen<br />
|author2-link=Christopher T. Hill<br />
|author2=Christopher T. Hill<br />
|author3-link=Manfred Lindner<br />
|author3=Manfred Lindner<br />
|year=1990<br />
|title=Minimal dynamical symmetry breaking of the standard model<br />
|journal=[[Physical Review D]]<br />
|volume=41 |issue=5 |pages=1647–1660<br />
|bibcode=1990PhRvD..41.1647B<br />
|doi=10.1103/PhysRevD.41.1647<br />
|pmid=10012522<br />
|author1-link=William A. Bardeen<br />
}}</ref> Dynamical breaking of gauge symmetries is often due to creation of a [[fermionic condensate]] — e.g., the [[quark condensate]], which is connected to the [[Chiral symmetry breaking|dynamical breaking of chiral symmetry]] in [[quantum chromodynamics]]. Conventional [[superconductivity]] is the paradigmatic example from the condensed matter side, where phonon-mediated attractions lead electrons to become bound in pairs and then condense, thereby breaking the electromagnetic gauge symmetry.<br />
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==Generalisation and technical usage==<br />
For spontaneous symmetry breaking to occur, there must be a system in which there are several equally likely outcomes. The system as a whole is therefore [[Symmetry (physics)|symmetric]] with respect to these outcomes. However, if the system is sampled (i.e. if the system is actually used or interacted with in any way), a specific outcome must occur. Though the system as a whole is symmetric, it is never encountered with this symmetry, but only in one specific asymmetric state. Hence, the symmetry is said to be spontaneously broken in that theory. Nevertheless, the fact that each outcome is equally likely is a reflection of the underlying symmetry, which is thus often dubbed "hidden symmetry", and has crucial formal consequences. (See the article on the [[Nambu–Goldstone boson|Goldstone boson]].)<br />
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When a theory is symmetric with respect to a [[symmetry group]], but requires that one element of the group be distinct, then spontaneous symmetry breaking has occurred. The theory must not dictate ''which'' member is distinct, only that ''one is''. From this point on, the theory can be treated as if this element actually is distinct, with the proviso that any results found in this way must be resymmetrized, by taking the average of each of the elements of the group being the distinct one.<br />
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The crucial concept in physics theories is the [[order parameter]]. If there is a field (often a background field) which acquires an expectation value (not necessarily a [[vacuum expectation value|''vacuum'' expectation value]]) which is not invariant under the symmetry in question, we say that the system is in the [[ordered phase]], and the symmetry is spontaneously broken. This is because other subsystems interact with the order parameter, which specifies a "frame of reference" to be measured against. In that case, the [[vacuum state]] does not obey the initial symmetry (which would keep it invariant, in the linearly realized '''Wigner mode''' in which it would be a singlet), and, instead changes under the (hidden) symmetry, now implemented in the (nonlinear) '''Nambu–Goldstone mode'''. Normally, in the absence of the Higgs mechanism, massless [[Goldstone boson]]s arise.<br />
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The symmetry group can be discrete, such as the [[space group]] of a crystal, or continuous (e.g., a [[Lie group]]), such as the rotational symmetry of space. However, if the system contains only a single spatial dimension, then only discrete symmetries may be broken in a [[vacuum state]] of the full [[Quantum mechanics|quantum theory]], although a classical solution may break a continuous symmetry.<br />
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==Nobel Prize==<br />
On October 7, 2008, the [[Royal Swedish Academy of Sciences]] awarded the 2008 [[Nobel Prize in Physics]] to three scientists for their work in subatomic physics symmetry breaking. [[Yoichiro Nambu]], of the [[University of Chicago]], won half of the prize for the discovery of the mechanism of spontaneous broken symmetry in the context of the strong interactions, specifically [[chiral symmetry breaking]]. Physicists [[Makoto Kobayashi (physicist)|Makoto Kobayashi]] and [[Toshihide Maskawa]], of [[Kyoto University]], shared the other half of the prize for discovering the origin of the [[Explicit symmetry breaking|explicit breaking]] of CP symmetry in the weak interactions.<ref>{{cite web|author=The Nobel Foundation|title=The Nobel Prize in Physics 2008|url=http://nobelprize.org/nobel_prizes/physics/laureates/2008/index.html|work=nobelprize.org|access-date=January 15, 2008}}</ref> This origin is ultimately reliant on the Higgs mechanism, but, so far understood as a "just so" feature of Higgs couplings, not a spontaneously broken symmetry phenomenon.<br />
<br />
==See also==<br />
{{div col|colwidth=24em}}<br />
* [[Autocatalytic reactions and order creation]]<br />
* [[Catastrophe theory]]<br />
* [[Chiral symmetry breaking]]<br />
* [[CP-violation]]<br />
* [[Fermi ball]]<br />
* [[Gauge gravitation theory]]<br />
* [[Goldstone boson]]<br />
* [[Grand unified theory]]<br />
* [[Higgs mechanism]]<br />
* [[Higgs boson]]<br />
* [[Higgs field (classical)]]<br />
* [[Irreversibility]]<br />
* [[Magnetic catalysis]] of chiral symmetry breaking<br />
* [[Mermin–Wagner theorem]]<br />
* [[Norton's dome]]<br />
* [[Second-order phase transition]]<br />
* [[Spontaneous absolute asymmetric synthesis]] in chemistry<br />
* [[Symmetry breaking]]<br />
* [[Tachyon condensation]]<br />
* [[1964 PRL symmetry breaking papers]]<br />
{{div col end}}<br />
<br />
==Notes==<br />
* {{note|note1}} Note that (as in fundamental Higgs driven spontaneous gauge symmetry breaking) the term "symmetry breaking" is a misnomer when applied to gauge symmetries.<br />
<br />
==References==<br />
{{Reflist}}<br />
<br />
==External links==<br />
{{wikiquote}}<br />
* For a pedagogic introduction to electroweak symmetry breaking with step by step derivations, not found in texts, of many key relations, see http://www.quantumfieldtheory.info/Electroweak_Sym_breaking.pdf<br />
* [http://hyperphysics.phy-astr.gsu.edu/hbase/forces/unify.html#c2 Spontaneous symmetry breaking]<br />
* [http://prl.aps.org/50years/milestones#1964 Physical Review Letters – 50th Anniversary Milestone Papers]<br />
* [http://cerncourier.com/cws/article/cern/32522 In CERN Courier, Steven Weinberg reflects on spontaneous symmetry breaking]<br />
* [http://www.scholarpedia.org/article/Englert-Brout-Higgs-Guralnik-Hagen-Kibble_mechanism Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism on Scholarpedia]<br />
* [http://www.scholarpedia.org/article/Englert-Brout-Higgs-Guralnik-Hagen-Kibble_mechanism_%28history%29 History of Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism on Scholarpedia]<br />
* [https://arxiv.org/abs/0907.3466 The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles]<br />
* [http://www.worldscinet.com/ijmpa/24/2414/S0217751X09045431.html International Journal of Modern Physics A: The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles]<br />
* [http://www.datafilehost.com/download-7d512618.html Guralnik, G S; Hagen, C R and Kibble, T W B (1967). Broken Symmetries and the Goldstone Theorem. Advances in Physics, vol. 2 Interscience Publishers, New York. pp. 567–708] {{ISBN|0-470-17057-3}}<br />
* [http://lanl.arxiv.org/abs/hep-th/9802142 Spontaneous Symmetry Breaking in Gauge Theories: a Historical Survey]<br />
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{{Standard model of physics}}<br />
{{Quantum mechanics topics}}<br />
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{{DEFAULTSORT:Spontaneous Symmetry Breaking}}<br />
[[Category:Theoretical physics]]<br />
[[Category:Quantum field theory]]<br />
[[Category:Standard Model]]<br />
[[Category:Quantum chromodynamics]]<br />
[[Category:Symmetry]]<br />
[[Category:Quantum phases]]<br />
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==实例==<br />
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对称性破缺可以涵盖以下任何一种情况:<ref>{{cite web|url=http://www.angelfire.com/stars5/astroinfo/gloss/s.html|title=Astronomical Glossary|author=|date=|website=www.angelfire.com}}</ref><br />
* 某些结构的随机形成破坏了物理学基本定律的精确对称性;<br />
* 物理学中最小能量状态的对称性比系统本身少的情形;<br />
* 系统的实际状态由于明显对称的状态不稳定而不能反映动力学的基本对称性的情况(稳定性是以局部不对称为代价的);<br />
* 理论方程具有某种对称性,但其解可能没有(对称性是“隐藏的”)的情况。<br />
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在物理学文献中讨论的首批对称性破缺案例之一,与不可压缩流体在重力和流体静力平衡中均匀旋转的形式有关。在1834年,Jacobi <ref>{{cite journal| last=Jacobi | first=C.G.J. | title=Über die figur des gleichgewichts | journal=[[Annalen der Physik und Chemie]] | volume=109 | issue=33| pages=229–238 | year=1834| doi=10.1002/andp.18341090808 | bibcode=1834AnP...109..229J | url=https://zenodo.org/record/2027349 }}</ref>和后来的 Liouville <ref>{{cite journal| last=Liouville | first=J. | title=Sur la figure d'une masse fluide homogène, en équilibre et douée d'un mouvement de rotation| journal=Journal de l'École Polytechnique | issue=14| pages=289–296 | year=1834}}</ref>讨论了这样一个事实: 当旋转物体的动能相对于引力势能超过一定的临界值时,这个问题的平衡解是三轴椭球。在这个分叉点上,麦克劳林椭球体的轴对称性被破坏。此外,在这个分叉点之上,对于常数角动量,使动能最小化的解是非轴对称的 Jacobi 椭球,而不是 Maclaurin 椭球。<br />
==另请参阅==<br />
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*[[Higgs mechanism]]<br />
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*[[QCD vacuum]]<br />
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*[[Goldstone boson]]<br />
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*[[1964 PRL symmetry breaking papers]]<br />
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*[[希格斯机制]]<br />
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*[[QCD真空]]<br />
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*[[戈德斯通玻色子]]<br />
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*[[1964年PRL对称性破缺论文]]<br />
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==参考文献==<br />
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{{reflist|colwidth=30em}}<br />
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{{DEFAULTSORT:Symmetry Breaking}}<br />
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范畴: 对称<br />
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类别: 模式形成<br />
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本中文词条由XXX编译,XXX审校,XXX总审校,西瓜编辑,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''<br />
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<noinclude><br />
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[[Category:对称性破缺]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%AF%B9%E7%A7%B0%E6%80%A7%E7%A0%B4%E7%BC%BA&diff=24761对称性破缺2021-07-26T08:54:55Z<p>Jxzhou:/* Spontaneous symmetry breaking in physics */</p>
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<div><br />
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[[图一:一个小球位于中央山丘的山峰处(C)。这是一种不稳定平衡:一个很小的扰动会使它落到左边(L)或右边(R)稳定点。尽管山丘是对称的,没有理由让球落在哪一侧,但观察到的最终状态仍然是不对称的,它总会落到某一侧]]。<br />
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在物理学中,一个作用于系统的(无限)小扰动使系统跨过临界点,通过决定去向分叉的哪个分支来决定系统的命运,这种现象叫做'''<font color="#ff8000">对称性破缺</font>'''。对于一个观测不到扰动(或“噪声”)的外部观察者来说,这个选择看起来是任意的。这个过程被称为对称性破缺,因为这种转变通常使系统从一个对称但无序的状态进入一个或多个确定的状态。在'''<font color="#ff8000">斑图生成</font>'''中对称性破缺起着重要作用。<br />
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1972年,诺贝尔奖得主P·W·安德森(P.W.Anderson)在《科学》(Science)杂志上发表了一篇名为《多即不同》的论文<ref>{{cite journal | last=Anderson | first=P.W. | title=More is Different | journal=Science | volume=177 | issue=4047| pages=393–396 | year=1972 | url=http://robotics.cs.tamu.edu/dshell/cs689/papers/anderson72more_is_different.pdf | doi=10.1126/science.177.4047.393 | pmid=17796623 | format=|bibcode = 1972Sci...177..393A }}</ref>,文中使用对称性破缺的思想表明,即使'''<font color="#ff8000">还原论</font>'''是正确的,但它的逆命题'''<font color="#ff8000">建构主义</font>'''是错误的。建构主义认为,在给出描述各组成部分的理论的情况下科学家可以轻易地预测复杂现象。<br />
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对称性破缺可以分为'''<font color="#ff8000">显性对称性破缺</font>'''和'''<font color="#ff8000">自发对称性破缺</font>'''两种类型,二者的区别是,在破缺对称性下系统的运动方程是否不变或者基态是否保持不变。<br />
==显性对称性破缺==<br />
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在'''<font color="#ff8000">显性对称性破缺</font>'''中,描述系统的运动方程在破缺对称下是不同的。在哈密顿力学或拉格朗日力学中,假若系统的哈密顿量(或拉格朗日量)中至少一项显性地打破了给定的对称性,就发生了显性对称性破缺。<br />
==自发对称性破缺==<br />
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在'''<font color="#ff8000">自发对称性破缺</font>'''中,系统的运动方程是不变的,但系统发生了变化。这是因为系统的背景(时空)——真空态——是非恒定的。这种对称性破缺可以用一个序参量进行参数化。这类对称破缺的一个特殊情况是'''<font color="#ff8000">动力学对称性破缺</font>'''。<br />
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Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state ends up in an asymmetric state.[1][2][3] In particular, it can describe systems where the equations of motion or the Lagrangian obey symmetries, but the lowest-energy vacuum solutions do not exhibit that same symmetry. When the system goes to one of those vacuum solutions, the symmetry is broken for perturbations around that vacuum even though the entire Lagrangian retains that symmetry.<br />
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自发对称破缺是一个自发的对称破缺过程,它使处于对称状态的物理系统最终处于非对称状态。特别地,它可以描述运动方程或拉格朗日方程服从某种对称性,但最低能量真空解不具有该对称性的系统。当系统进入其中一个真空解时,真空解周围的扰动会破坏系统对称性,尽管整个拉格朗日方程仍然保持了对称性。<br />
<br />
==Overview==<br />
<br />
In [[explicit symmetry breaking]], if two outcomes are considered, the probability of a pair of outcomes can be different. By definition, spontaneous symmetry breaking requires the existence of a symmetric probability distribution—any pair of outcomes has the same probability. In other words, the underlying laws{{clarify|date=December 2016}} are [[Invariant (physics)|invariant]] under a [[Symmetry (physics)|symmetry]] transformation.<br />
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The system, as a whole{{clarify|date=December 2016}}, changes under such transformations.<br />
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Phases of matter, such as crystals, magnets, and conventional superconductors, as well as simple phase transitions can be described by spontaneous symmetry breaking. Notable exceptions include topological phases of matter like the [[fractional quantum Hall effect]].<br />
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==Examples 例子==<br />
<br />
===Sombrero potential===<br />
Consider a symmetric upward dome with a trough circling the bottom. If a ball is put at the very peak of the dome, the system is symmetric with respect to a rotation around the center axis. But the ball may ''spontaneously break'' this symmetry by rolling down the dome into the trough, a point of lowest energy. Afterward, the ball has come to a rest at some fixed point on the perimeter. The dome and the ball retain their individual symmetry, but the system does not.<ref>{{cite book |first=Gerald M. |last=Edelman |title=Bright Air, Brilliant Fire: On the Matter of the Mind |location=New York |publisher=BasicBooks |year=1992 |url=https://archive.org/details/brightairbrillia00gera |url-access=registration |page=[https://archive.org/details/brightairbrillia00gera/page/203 203] }}</ref><br />
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考虑一个对称向上的圆顶,底部环绕着一个槽。如果把一个球放在圆顶的最顶端,这个系统是围绕中心轴旋转对称的。但球体可能会自发地打破这种对称性,因为它会沿着穹顶滚动到能量最低的槽中。然后,球在圆周上某个固定的点上停下来。圆顶和球保持了各自的对称,但系统却没有保持对称性。<br />
[[Image:Mexican hat potential polar.svg|270px|thumb|left|Graph of Goldstone's "[[sombrero]]" potential function <math>V(\phi)</math>.|链接=Special:FilePath/Mexican_hat_potential_polar.svg]]<br />
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In the simplest idealized relativistic model, the spontaneously broken symmetry is summarized through an illustrative [[scalar field theory]]. The relevant [[Lagrangian (field theory)|Lagrangian]] of a scalar field <math>\phi</math>, which essentially dictates how a system behaves, can be split up into kinetic and potential terms,<br />
<br />
在最简单的理想相对论模型中,可以用一个解释性的标量场理论总结自发破对称性。一个标量场 <math>\phi</math>的拉格朗日量从本质上决定了系统的行为,它可以分解成动能项和势能项:<br />
{{NumBlk|::|<math>\mathcal{L} = \partial^\mu \phi \partial_\mu \phi - V(\phi).</math>|{{EquationRef|1}}}}<br />
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It is in this potential term <math>V(\phi)</math> that the symmetry breaking is triggered. An example of a potential, due to [[Jeffrey Goldstone]]<ref>{{Cite journal | last1 = Goldstone | first1 = J. | doi = 10.1007/BF02812722 | title = Field theories with " Superconductor " solutions | journal = Il Nuovo Cimento | volume = 19 | issue = 1 | pages = 154–164 | year = 1961 | bibcode = 1961NCim...19..154G | s2cid = 120409034 | url = http://cds.cern.ch/record/343400 }}</ref> is illustrated in the graph at the left.<br />
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正是在势能项 <math>V(\phi)</math> 中触发了对称性破缺。例如左图所示的 [[Jeffrey Goldstone]] 给出的势能函数:<br />
{{NumBlk|::|<math>V(\phi) = -5|\phi|^2 + |\phi|^4 \,</math>.|{{EquationRef|2}}}}<br />
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This potential has an infinite number of possible [[minimum|minima]] (vacuum states) given by<br />
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该是函数具有无穷数量的最小值点(真空态)当<br />
{{NumBlk|::|<math>\phi = \sqrt{5} e^{i\theta} </math>.|{{EquationRef|3}}}}<br />
for any real ''θ'' between 0 and 2''π''. The system also has an unstable vacuum state corresponding to {{nowrap|1=''Φ'' = 0}}. This state has a [[Unitary group|U(1)]] symmetry. However, once the system falls into a specific stable vacuum state (amounting to a choice of ''θ''), this symmetry will appear to be lost, or "spontaneously broken".<br />
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对于0到2π之间的任何实数θ。系统也有一个不稳定的真空状态,对应于Φ = 0。这个状态具有U(1)对称。然而,一旦系统落入某个稳定真空状态(相当于选择θ),这种对称性就会消失,或者说“自发破缺”。<br />
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In fact, any other choice of ''θ'' would have exactly the same energy, implying the existence of a massless [[Goldstone boson|Nambu–Goldstone boson]], the mode running around the circle at the minimum of this potential, and indicating there is some memory of the original symmetry in the Lagrangian.<br />
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事实上,任何其他θ的选择都将具有完全相同的能量,这意味着无质量的南部-戈德斯通玻色子的存在,这种模式在势能的最小值绕圆运动,并表明存在拉格朗日方程中原始对称性的一些记忆。<br />
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===Other examples===<br />
* For [[ferromagnet]]ic materials, the underlying laws are invariant under spatial rotations. Here, the order parameter is the [[magnetization]], which measures the magnetic dipole density. Above the [[Curie temperature]], the order parameter is zero, which is spatially invariant, and there is no symmetry breaking. Below the Curie temperature, however, the magnetization acquires a constant nonvanishing value, which points in a certain direction (in the idealized situation where we have full equilibrium; otherwise, translational symmetry gets broken as well). The residual rotational symmetries which leave the orientation of this vector invariant remain unbroken, unlike the other rotations which do not and are thus spontaneously broken.<br />
* 对于铁磁性材料,其基本定律在空间旋转下是不变的。在这里,序参量是衡量磁偶极子密度的磁化强度。在居里温度以上,序参量为零,具有空间不变性,不存在对称性破缺。然而,在居里温度以下,磁化强度变成一个恒定的非零值,指向一个特定的方向(在有充分平衡的理想情况下;否则,平移对称性也会破缺)。使该向量方向不变的旋转对称性仍然保留,而其他旋转对称性自发破缺。<br />
* The laws describing a solid are invariant under the full [[Euclidean group]], but the solid itself spontaneously breaks this group down to a [[space group]]. The displacement and the orientation are the order parameters.<br />
* 描述固体的定律在完整的欧几里得群下是不变的,但固体本身会自发地将这个群分解为一个空间群。其中位移和方向是序参量。<br />
* General relativity has a Lorentz symmetry, but in [[Friedmann–Lemaître–Robertson–Walker metric|FRW cosmological models]], the mean 4-velocity field defined by averaging over the velocities of the galaxies (the galaxies act like gas particles at cosmological scales) acts as an order parameter breaking this symmetry. Similar comments can be made about the cosmic microwave background.<br />
* 广义相对论具有洛伦兹对称性,但在FRW宇宙模型中,定义为星系速度的平均值(星系在宇宙尺度上的行为就像气体粒子) 的平均 4-速度场,作为序参量会打破这种对称性。对于宇宙微波背景辐射也有类似的评论。<br />
* For the [[electroweak]] model, as explained earlier, a component of the Higgs field provides the order parameter breaking the electroweak gauge symmetry to the electromagnetic gauge symmetry. Like the ferromagnetic example, there is a phase transition at the electroweak temperature. The same comment about us not tending to notice broken symmetries suggests why it took so long for us to discover electroweak unification.<br />
* 对于电弱模型,如前面所解释的,希格斯场的一个分量提供了将电弱规范对称性破缺到电磁规范对称性的序参量。和铁磁的例子一样,在电弱温度下也有相变。同样的关于我们不倾向于注意破缺对称性的评论,也说明了为什么我们花了这么长时间才发现电弱统一。<br />
* In superconductors, there is a condensed-matter collective field ψ, which acts as the order parameter breaking the electromagnetic gauge symmetry.<br />
* 在超导体中有一个凝聚态集体场ψ,它是打破电磁规范对称性的序参量。<br />
* Take a thin cylindrical plastic rod and push both ends together. Before buckling, the system is symmetric under rotation, and so visibly cylindrically symmetric. But after buckling, it looks different, and asymmetric. Nevertheless, features of the cylindrical symmetry are still there: ignoring friction, it would take no force to freely spin the rod around, displacing the ground state in time, and amounting to an oscillation of vanishing frequency, unlike the radial oscillations in the direction of the buckle. This spinning mode is effectively the requisite [[Goldstone boson|Nambu–Goldstone boson]].<br />
* 拿一个细长的圆柱形塑料杆,把两端推到一起。在屈曲之前,系统在旋转下是对称的,因此可见圆柱对称性。但在弯曲之后,它看起来就不同了,而且是不对称的。然而,圆柱对称性的特征仍然存在:忽略摩擦,杆可以不受外力自由地自旋,在时间上取代基态,等于一个频率趋于零的振荡,而不是沿屈曲方向的径向振荡。这种自旋模式实际上是必需的南部-戈德斯通玻色子。<br />
* Consider a uniform layer of [[fluid]] over an infinite horizontal plane. This system has all the symmetries of the Euclidean plane. But now heat the bottom surface uniformly so that it becomes much hotter than the upper surface. When the temperature gradient becomes large enough, [[convection cell]]s will form, breaking the Euclidean symmetry.<br />
* 考虑无限水平面上的一层均匀的流体。这个系统具有欧几里得平面的所有对称性。但是现在均匀地加热底部表面,使它变得比上表面热得多。当温度梯度足够大时,就会形成对流单元,打破了欧几里得对称。<br />
* Consider a bead on a circular hoop that is rotated about a vertical [[diameter]]. As the [[rotational velocity]] is increased gradually from rest, the bead will initially stay at its initial [[equilibrium point]] at the bottom of the hoop (intuitively stable, lowest [[gravitational potential]]). At a certain critical rotational velocity, this point will become unstable and the bead will jump to one of two other newly created equilibria, [[equidistant]] from the center. Initially, the system is symmetric with respect to the diameter, yet after passing the critical velocity, the bead ends up in one of the two new equilibrium points, thus breaking the symmetry.<br />
* 考虑一个围绕某个竖直的直径旋转的圆形箍上的珠子。当旋转速度从静止逐渐增加时,珠子最初会停留在环底部的初始平衡点(直观上稳定,重力势最低)。在一定的临界旋转速度下,这一点将变得不稳定,珠子将跳到另外两个新创建的离中心等距离的平衡点中的一个。起初,系统相对直径是对称的,但在通过临界速度后,珠子最终停留在两个新的平衡点中的一个,从而打破了对称性。<br />
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==Spontaneous symmetry breaking in physics 物理学中的自发对称性破缺==<br />
[[File:Spontaneous symmetry breaking (explanatory diagram).png|thumb|right|250px|''Spontaneous symmetry breaking illustrated'': At high energy levels (''left''), the ball settles in the center, and the result is symmetric. At lower energy levels (''right''), the overall "rules" remain symmetric, but the symmetric "[[sombrero|Sombrero]]" enforces an asymmetric outcome, since eventually the ball must rest at some random spot on the bottom, "spontaneously", and not all others.|链接=Special:FilePath/Spontaneous_symmetry_breaking_(explanatory_diagram).png]]<br />
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===Particle physics 粒子物理===<br />
In [[particle physics]], the [[force carrier]] particles are normally specified by field equations with [[gauge symmetry]]; their equations predict that certain measurements will be the same at any point in the field. For instance, field equations might predict that the mass of two quarks is constant. Solving the equations to find the mass of each quark might give two solutions. In one solution, quark A is heavier than quark B. In the second solution, quark B is heavier than quark A ''by the same amount''. The symmetry of the equations is not reflected by the individual solutions, but it is reflected by the range of solutions.<br />
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在粒子物理学中,载力子通常由规范对称的场方程表示;它们的方程预测到某些测量值在场的任何点上都是相同的。例如,场方程可以预测两个夸克的质量是常数。通过求解方程来求每个夸克的质量可能会得到两个解。在一个解中,夸克A比夸克B重;在第二个解中,夸克B比夸克A重相同的量。方程的对称性不是由单个解来反映的,而是由解的范围来反映的。<br />
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An actual measurement reflects only one solution, representing a breakdown in the symmetry of the underlying theory. "Hidden" is a better term than "broken", because the symmetry is always there in these equations. This phenomenon is called [[Spontaneous magnetization|''spontaneous'']] symmetry breaking (SSB) because ''nothing'' (that we know of) breaks the symmetry in the equations.<ref name="Weinberg2011">{{cite book|author=Steven Weinberg|title=Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature|url=https://books.google.com/books?id=Rsg3PE_9_ccC|date=20 April 2011|publisher=Knopf Doubleday Publishing Group|isbn=978-0-307-78786-6}}</ref>{{rp|194–195}}<br />
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一个实际的测量只反映了一个解,代表了其潜在理论的对称性的破缺。在这里“隐藏”是比“破坏”更好的术语,因为对称性总是存在于这些方程中。这种现象被称为自发对称破缺(SSB),因为(我们所知道的)没有任何东西会打破方程中的对称性。<br />
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====Chiral symmetry====<br />
{{Main article|Chiral symmetry breaking}}<br />
Chiral symmetry breaking is an example of spontaneous symmetry breaking affecting the [[chiral symmetry]] of the [[strong interactions]] in particle physics. It is a property of [[quantum chromodynamics]], the [[quantum field theory]] describing these interactions, and is responsible for the bulk of the mass (over 99%) of the [[nucleons]], and thus of all common matter, as it converts very light bound [[quarks]] into 100 times heavier constituents of [[baryons]]. The approximate [[Nambu–Goldstone boson]]s in this spontaneous symmetry breaking process are the [[pions]], whose mass is an order of magnitude lighter than the mass of the nucleons. It served as the prototype and significant ingredient of the Higgs mechanism underlying the electroweak symmetry breaking.<br />
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====Higgs mechanism====<br />
{{Main article|Higgs mechanism|Yukawa interaction}}<br />
<br />
The strong, weak, and electromagnetic forces can all be understood as arising from [[gauge symmetry|gauge symmetries]]. The [[Higgs mechanism]], the spontaneous symmetry breaking of gauge symmetries, is an important component in understanding the [[superconductivity]] of metals and the origin of particle masses in the standard model of particle physics. One important consequence of the distinction between true symmetries and ''gauge symmetries'', is that the spontaneous breaking of a gauge symmetry does not give rise to characteristic massless Nambu–Goldstone physical modes, but only massive modes, like the plasma mode in a superconductor, or the Higgs mode observed in particle physics.<br />
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In the standard model of particle physics, spontaneous symmetry breaking of the {{nowrap|SU(2) × U(1)}} gauge symmetry associated with the electro-weak force generates masses for several particles, and separates the electromagnetic and weak forces. The [[W and Z bosons]] are the elementary particles that mediate the [[weak interaction]], while the [[photon]] mediates the [[electromagnetic interaction]]. At energies much greater than 100 GeV, all these particles behave in a similar manner. The [[Unified field theory#Modern progress|Weinberg–Salam theory]] predicts that, at lower energies, this symmetry is broken so that the photon and the massive W and Z bosons emerge.<ref>A Brief History of Time, Stephen Hawking, Bantam; 10th anniversary edition (1998). pp. 73–74.{{ISBN?}}</ref> In addition, fermions develop mass consistently.<br />
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Without spontaneous symmetry breaking, the [[Standard Model]] of elementary particle interactions requires the existence of a number of particles. However, some particles (the [[W and Z bosons]]) would then be predicted to be massless, when, in reality, they are observed to have mass. To overcome this, spontaneous symmetry breaking is augmented by the [[Higgs mechanism]] to give these particles mass. It also suggests the presence of a new particle, the [[Higgs boson]], detected in 2012.<br />
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[[Superconductivity]] of metals is a condensed-matter analog of the Higgs phenomena, in which a condensate of Cooper pairs of electrons spontaneously breaks the U(1) gauge symmetry associated with light and electromagnetism.<br />
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===Condensed matter physics===<br />
Most phases of matter can be understood through the lens of spontaneous symmetry breaking. For example, crystals are periodic arrays of atoms that are not invariant under all translations (only under a small subset of translations by a lattice vector). Magnets have north and south poles that are oriented in a specific direction, breaking [[rotational symmetry]]. In addition to these examples, there are a whole host of other symmetry-breaking phases of matter — including nematic phases of liquid crystals, charge- and spin-density waves, superfluids, and many others.<br />
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There are several known examples of matter that cannot be described by spontaneous symmetry breaking, including: topologically ordered phases of matter, such as [[Fractional quantum Hall effect|fractional quantum Hall liquids]], and [[Quantum spin liquid|spin-liquids]]. These states do not break any symmetry, but are distinct phases of matter. Unlike the case of spontaneous symmetry breaking, there is not a general framework for describing such states.<ref name=chen>{{cite journal | last1 = Chen | first1 = Xie | author-link3 = Xiao-Gang Wen | last2 = Gu | first2 = Zheng-Cheng | last3 = Wen | first3 = Xiao-Gang | year = 2010 | title = Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order | journal = Phys. Rev. B | volume = 82 | issue = 15| page = 155138 | doi=10.1103/physrevb.82.155138|arxiv = 1004.3835 |bibcode = 2010PhRvB..82o5138C | s2cid = 14593420 }}</ref><br />
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====Continuous symmetry====<br />
The ferromagnet is the canonical system that spontaneously breaks the continuous symmetry of the spins below the [[Curie temperature]] and at {{nowrap|1=''h'' = 0}}, where ''h'' is the external magnetic field. Below the [[Curie temperature]], the energy of the system is invariant under inversion of the magnetization ''m''('''x''') such that {{nowrap|1=''m''('''x''') = −''m''(−'''x''')}}. The symmetry is spontaneously broken as {{nowrap|''h'' → 0}} when the Hamiltonian becomes invariant under the inversion transformation, but the expectation value is not invariant.<br />
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Spontaneously-symmetry-broken phases of matter are characterized by an order parameter that describes the quantity which breaks the symmetry under consideration. For example, in a magnet, the order parameter is the local magnetization.<br />
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Spontaneous breaking of a continuous symmetry is inevitably accompanied by gapless (meaning that these modes do not cost any energy to excite) Nambu–Goldstone modes associated with slow, long-wavelength fluctuations of the order parameter. For example, vibrational modes in a crystal, known as phonons, are associated with slow density fluctuations of the crystal's atoms. The associated Goldstone mode for magnets are oscillating waves of spin known as spin-waves. For symmetry-breaking states, whose order parameter is not a conserved quantity, Nambu–Goldstone modes are typically massless and propagate at a constant velocity.<br />
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An important theorem, due to Mermin and Wagner, states that, at finite temperature, thermally activated fluctuations of Nambu–Goldstone modes destroy the long-range order, and prevent spontaneous symmetry breaking in one- and two-dimensional systems. Similarly, quantum fluctuations of the order parameter prevent most types of continuous symmetry breaking in one-dimensional systems even at zero temperature. (An important exception is ferromagnets, whose order parameter, magnetization, is an exactly conserved quantity and does not have any quantum fluctuations.)<br />
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Other long-range interacting systems, such as cylindrical curved surfaces interacting via the [[Coulomb potential]] or [[Yukawa potential]], have been shown to break translational and rotational symmetries.<ref><br />
{{cite journal<br />
|last1=Kohlstedt |first1=K.L.<br />
|last2=Vernizzi |first2=G.<br />
|last3=Solis |first3=F.J.<br />
|last4=Olvera de la Cruz |first4=M.<br />
|year=2007<br />
|title=Spontaneous Chirality via Long-range Electrostatic Forces<br />
|journal=[[Physical Review Letters]]<br />
|volume=99 |issue=3<br />
|page=030602<br />
|doi=10.1103/PhysRevLett.99.030602<br />
|arxiv = 0704.3435 |bibcode = 2007PhRvL..99c0602K |pmid=17678276|s2cid=37983980<br />
}}</ref> It was shown, in the presence of a symmetric Hamiltonian, and in the limit of infinite volume, the system spontaneously adopts a chiral configuration — i.e., breaks [[mirror plane]] [[symmetry]].<br />
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===Dynamical symmetry breaking===<br />
Dynamical symmetry breaking (DSB) is a special form of spontaneous symmetry breaking in which the ground state of the system has reduced symmetry properties compared to its theoretical description (i.e., [[Lagrangian (field theory)|Lagrangian]]).<br />
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Dynamical breaking of a global symmetry is a spontaneous symmetry breaking, which happens not at the (classical) tree level (i.e., at the level of the bare action), but due to quantum corrections (i.e., at the level of the [[effective action]]).<br />
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Dynamical breaking of a gauge symmetry {{ref|note1}} is subtler. In the conventional spontaneous gauge symmetry breaking, there exists an unstable [[Higgs particle]] in the theory, which drives the vacuum to a symmetry-broken phase. (See, for example, [[electroweak interaction]].) In dynamical gauge symmetry breaking, however, no unstable Higgs particle operates in the theory, but the bound states of the system itself provide the unstable fields that render the phase transition. For example, Bardeen, Hill, and Lindner published a paper that attempts to replace the conventional [[Higgs mechanism]] in the [[standard model]] by a DSB that is driven by a bound state of top-antitop quarks. (Such models, in which a composite particle plays the role of the Higgs boson, are often referred to as "Composite Higgs models".)<ref><br />
{{cite journal<br />
|author1=William A. Bardeen<br />
|author2-link=Christopher T. Hill<br />
|author2=Christopher T. Hill<br />
|author3-link=Manfred Lindner<br />
|author3=Manfred Lindner<br />
|year=1990<br />
|title=Minimal dynamical symmetry breaking of the standard model<br />
|journal=[[Physical Review D]]<br />
|volume=41 |issue=5 |pages=1647–1660<br />
|bibcode=1990PhRvD..41.1647B<br />
|doi=10.1103/PhysRevD.41.1647<br />
|pmid=10012522<br />
|author1-link=William A. Bardeen<br />
}}</ref> Dynamical breaking of gauge symmetries is often due to creation of a [[fermionic condensate]] — e.g., the [[quark condensate]], which is connected to the [[Chiral symmetry breaking|dynamical breaking of chiral symmetry]] in [[quantum chromodynamics]]. Conventional [[superconductivity]] is the paradigmatic example from the condensed matter side, where phonon-mediated attractions lead electrons to become bound in pairs and then condense, thereby breaking the electromagnetic gauge symmetry.<br />
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==Generalisation and technical usage==<br />
For spontaneous symmetry breaking to occur, there must be a system in which there are several equally likely outcomes. The system as a whole is therefore [[Symmetry (physics)|symmetric]] with respect to these outcomes. However, if the system is sampled (i.e. if the system is actually used or interacted with in any way), a specific outcome must occur. Though the system as a whole is symmetric, it is never encountered with this symmetry, but only in one specific asymmetric state. Hence, the symmetry is said to be spontaneously broken in that theory. Nevertheless, the fact that each outcome is equally likely is a reflection of the underlying symmetry, which is thus often dubbed "hidden symmetry", and has crucial formal consequences. (See the article on the [[Nambu–Goldstone boson|Goldstone boson]].)<br />
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When a theory is symmetric with respect to a [[symmetry group]], but requires that one element of the group be distinct, then spontaneous symmetry breaking has occurred. The theory must not dictate ''which'' member is distinct, only that ''one is''. From this point on, the theory can be treated as if this element actually is distinct, with the proviso that any results found in this way must be resymmetrized, by taking the average of each of the elements of the group being the distinct one.<br />
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The crucial concept in physics theories is the [[order parameter]]. If there is a field (often a background field) which acquires an expectation value (not necessarily a [[vacuum expectation value|''vacuum'' expectation value]]) which is not invariant under the symmetry in question, we say that the system is in the [[ordered phase]], and the symmetry is spontaneously broken. This is because other subsystems interact with the order parameter, which specifies a "frame of reference" to be measured against. In that case, the [[vacuum state]] does not obey the initial symmetry (which would keep it invariant, in the linearly realized '''Wigner mode''' in which it would be a singlet), and, instead changes under the (hidden) symmetry, now implemented in the (nonlinear) '''Nambu–Goldstone mode'''. Normally, in the absence of the Higgs mechanism, massless [[Goldstone boson]]s arise.<br />
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The symmetry group can be discrete, such as the [[space group]] of a crystal, or continuous (e.g., a [[Lie group]]), such as the rotational symmetry of space. However, if the system contains only a single spatial dimension, then only discrete symmetries may be broken in a [[vacuum state]] of the full [[Quantum mechanics|quantum theory]], although a classical solution may break a continuous symmetry.<br />
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==Nobel Prize==<br />
On October 7, 2008, the [[Royal Swedish Academy of Sciences]] awarded the 2008 [[Nobel Prize in Physics]] to three scientists for their work in subatomic physics symmetry breaking. [[Yoichiro Nambu]], of the [[University of Chicago]], won half of the prize for the discovery of the mechanism of spontaneous broken symmetry in the context of the strong interactions, specifically [[chiral symmetry breaking]]. Physicists [[Makoto Kobayashi (physicist)|Makoto Kobayashi]] and [[Toshihide Maskawa]], of [[Kyoto University]], shared the other half of the prize for discovering the origin of the [[Explicit symmetry breaking|explicit breaking]] of CP symmetry in the weak interactions.<ref>{{cite web|author=The Nobel Foundation|title=The Nobel Prize in Physics 2008|url=http://nobelprize.org/nobel_prizes/physics/laureates/2008/index.html|work=nobelprize.org|access-date=January 15, 2008}}</ref> This origin is ultimately reliant on the Higgs mechanism, but, so far understood as a "just so" feature of Higgs couplings, not a spontaneously broken symmetry phenomenon.<br />
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==See also==<br />
{{div col|colwidth=24em}}<br />
* [[Autocatalytic reactions and order creation]]<br />
* [[Catastrophe theory]]<br />
* [[Chiral symmetry breaking]]<br />
* [[CP-violation]]<br />
* [[Fermi ball]]<br />
* [[Gauge gravitation theory]]<br />
* [[Goldstone boson]]<br />
* [[Grand unified theory]]<br />
* [[Higgs mechanism]]<br />
* [[Higgs boson]]<br />
* [[Higgs field (classical)]]<br />
* [[Irreversibility]]<br />
* [[Magnetic catalysis]] of chiral symmetry breaking<br />
* [[Mermin–Wagner theorem]]<br />
* [[Norton's dome]]<br />
* [[Second-order phase transition]]<br />
* [[Spontaneous absolute asymmetric synthesis]] in chemistry<br />
* [[Symmetry breaking]]<br />
* [[Tachyon condensation]]<br />
* [[1964 PRL symmetry breaking papers]]<br />
{{div col end}}<br />
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==Notes==<br />
* {{note|note1}} Note that (as in fundamental Higgs driven spontaneous gauge symmetry breaking) the term "symmetry breaking" is a misnomer when applied to gauge symmetries.<br />
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==References==<br />
{{Reflist}}<br />
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==External links==<br />
{{wikiquote}}<br />
* For a pedagogic introduction to electroweak symmetry breaking with step by step derivations, not found in texts, of many key relations, see http://www.quantumfieldtheory.info/Electroweak_Sym_breaking.pdf<br />
* [http://hyperphysics.phy-astr.gsu.edu/hbase/forces/unify.html#c2 Spontaneous symmetry breaking]<br />
* [http://prl.aps.org/50years/milestones#1964 Physical Review Letters – 50th Anniversary Milestone Papers]<br />
* [http://cerncourier.com/cws/article/cern/32522 In CERN Courier, Steven Weinberg reflects on spontaneous symmetry breaking]<br />
* [http://www.scholarpedia.org/article/Englert-Brout-Higgs-Guralnik-Hagen-Kibble_mechanism Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism on Scholarpedia]<br />
* [http://www.scholarpedia.org/article/Englert-Brout-Higgs-Guralnik-Hagen-Kibble_mechanism_%28history%29 History of Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism on Scholarpedia]<br />
* [https://arxiv.org/abs/0907.3466 The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles]<br />
* [http://www.worldscinet.com/ijmpa/24/2414/S0217751X09045431.html International Journal of Modern Physics A: The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles]<br />
* [http://www.datafilehost.com/download-7d512618.html Guralnik, G S; Hagen, C R and Kibble, T W B (1967). Broken Symmetries and the Goldstone Theorem. Advances in Physics, vol. 2 Interscience Publishers, New York. pp. 567–708] {{ISBN|0-470-17057-3}}<br />
* [http://lanl.arxiv.org/abs/hep-th/9802142 Spontaneous Symmetry Breaking in Gauge Theories: a Historical Survey]<br />
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{{Standard model of physics}}<br />
{{Quantum mechanics topics}}<br />
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{{DEFAULTSORT:Spontaneous Symmetry Breaking}}<br />
[[Category:Theoretical physics]]<br />
[[Category:Quantum field theory]]<br />
[[Category:Standard Model]]<br />
[[Category:Quantum chromodynamics]]<br />
[[Category:Symmetry]]<br />
[[Category:Quantum phases]]<br />
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==实例==<br />
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对称性破缺可以涵盖以下任何一种情况:<ref>{{cite web|url=http://www.angelfire.com/stars5/astroinfo/gloss/s.html|title=Astronomical Glossary|author=|date=|website=www.angelfire.com}}</ref><br />
* 某些结构的随机形成破坏了物理学基本定律的精确对称性;<br />
* 物理学中最小能量状态的对称性比系统本身少的情形;<br />
* 系统的实际状态由于明显对称的状态不稳定而不能反映动力学的基本对称性的情况(稳定性是以局部不对称为代价的);<br />
* 理论方程具有某种对称性,但其解可能没有(对称性是“隐藏的”)的情况。<br />
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在物理学文献中讨论的首批对称性破缺案例之一,与不可压缩流体在重力和流体静力平衡中均匀旋转的形式有关。在1834年,Jacobi <ref>{{cite journal| last=Jacobi | first=C.G.J. | title=Über die figur des gleichgewichts | journal=[[Annalen der Physik und Chemie]] | volume=109 | issue=33| pages=229–238 | year=1834| doi=10.1002/andp.18341090808 | bibcode=1834AnP...109..229J | url=https://zenodo.org/record/2027349 }}</ref>和后来的 Liouville <ref>{{cite journal| last=Liouville | first=J. | title=Sur la figure d'une masse fluide homogène, en équilibre et douée d'un mouvement de rotation| journal=Journal de l'École Polytechnique | issue=14| pages=289–296 | year=1834}}</ref>讨论了这样一个事实: 当旋转物体的动能相对于引力势能超过一定的临界值时,这个问题的平衡解是三轴椭球。在这个分叉点上,麦克劳林椭球体的轴对称性被破坏。此外,在这个分叉点之上,对于常数角动量,使动能最小化的解是非轴对称的 Jacobi 椭球,而不是 Maclaurin 椭球。<br />
==另请参阅==<br />
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*[[Higgs mechanism]]<br />
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*[[QCD vacuum]]<br />
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*[[Goldstone boson]]<br />
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*[[1964 PRL symmetry breaking papers]]<br />
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*[[希格斯机制]]<br />
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*[[QCD真空]]<br />
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*[[戈德斯通玻色子]]<br />
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*[[1964年PRL对称性破缺论文]]<br />
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==参考文献==<br />
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{{reflist|colwidth=30em}}<br />
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{{DEFAULTSORT:Symmetry Breaking}}<br />
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范畴: 对称<br />
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类别: 模式形成<br />
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本中文词条由XXX编译,XXX审校,XXX总审校,西瓜编辑,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''<br />
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<noinclude><br />
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[[Category:对称性破缺]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%AF%B9%E7%A7%B0%E6%80%A7%E7%A0%B4%E7%BC%BA&diff=24760对称性破缺2021-07-26T08:23:00Z<p>Jxzhou:/* Other examples */</p>
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[[图一:一个小球位于中央山丘的山峰处(C)。这是一种不稳定平衡:一个很小的扰动会使它落到左边(L)或右边(R)稳定点。尽管山丘是对称的,没有理由让球落在哪一侧,但观察到的最终状态仍然是不对称的,它总会落到某一侧]]。<br />
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在物理学中,一个作用于系统的(无限)小扰动使系统跨过临界点,通过决定去向分叉的哪个分支来决定系统的命运,这种现象叫做'''<font color="#ff8000">对称性破缺</font>'''。对于一个观测不到扰动(或“噪声”)的外部观察者来说,这个选择看起来是任意的。这个过程被称为对称性破缺,因为这种转变通常使系统从一个对称但无序的状态进入一个或多个确定的状态。在'''<font color="#ff8000">斑图生成</font>'''中对称性破缺起着重要作用。<br />
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1972年,诺贝尔奖得主P·W·安德森(P.W.Anderson)在《科学》(Science)杂志上发表了一篇名为《多即不同》的论文<ref>{{cite journal | last=Anderson | first=P.W. | title=More is Different | journal=Science | volume=177 | issue=4047| pages=393–396 | year=1972 | url=http://robotics.cs.tamu.edu/dshell/cs689/papers/anderson72more_is_different.pdf | doi=10.1126/science.177.4047.393 | pmid=17796623 | format=|bibcode = 1972Sci...177..393A }}</ref>,文中使用对称性破缺的思想表明,即使'''<font color="#ff8000">还原论</font>'''是正确的,但它的逆命题'''<font color="#ff8000">建构主义</font>'''是错误的。建构主义认为,在给出描述各组成部分的理论的情况下科学家可以轻易地预测复杂现象。<br />
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对称性破缺可以分为'''<font color="#ff8000">显性对称性破缺</font>'''和'''<font color="#ff8000">自发对称性破缺</font>'''两种类型,二者的区别是,在破缺对称性下系统的运动方程是否不变或者基态是否保持不变。<br />
==显性对称性破缺==<br />
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在'''<font color="#ff8000">显性对称性破缺</font>'''中,描述系统的运动方程在破缺对称下是不同的。在哈密顿力学或拉格朗日力学中,假若系统的哈密顿量(或拉格朗日量)中至少一项显性地打破了给定的对称性,就发生了显性对称性破缺。<br />
==自发对称性破缺==<br />
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在'''<font color="#ff8000">自发对称性破缺</font>'''中,系统的运动方程是不变的,但系统发生了变化。这是因为系统的背景(时空)——真空态——是非恒定的。这种对称性破缺可以用一个序参量进行参数化。这类对称破缺的一个特殊情况是'''<font color="#ff8000">动力学对称性破缺</font>'''。<br />
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Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state ends up in an asymmetric state.[1][2][3] In particular, it can describe systems where the equations of motion or the Lagrangian obey symmetries, but the lowest-energy vacuum solutions do not exhibit that same symmetry. When the system goes to one of those vacuum solutions, the symmetry is broken for perturbations around that vacuum even though the entire Lagrangian retains that symmetry.<br />
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自发对称破缺是一个自发的对称破缺过程,它使处于对称状态的物理系统最终处于非对称状态。特别地,它可以描述运动方程或拉格朗日方程服从某种对称性,但最低能量真空解不具有该对称性的系统。当系统进入其中一个真空解时,真空解周围的扰动会破坏系统对称性,尽管整个拉格朗日方程仍然保持了对称性。<br />
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==Overview==<br />
<br />
In [[explicit symmetry breaking]], if two outcomes are considered, the probability of a pair of outcomes can be different. By definition, spontaneous symmetry breaking requires the existence of a symmetric probability distribution—any pair of outcomes has the same probability. In other words, the underlying laws{{clarify|date=December 2016}} are [[Invariant (physics)|invariant]] under a [[Symmetry (physics)|symmetry]] transformation.<br />
<br />
The system, as a whole{{clarify|date=December 2016}}, changes under such transformations.<br />
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Phases of matter, such as crystals, magnets, and conventional superconductors, as well as simple phase transitions can be described by spontaneous symmetry breaking. Notable exceptions include topological phases of matter like the [[fractional quantum Hall effect]].<br />
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==Examples 例子==<br />
<br />
===Sombrero potential===<br />
Consider a symmetric upward dome with a trough circling the bottom. If a ball is put at the very peak of the dome, the system is symmetric with respect to a rotation around the center axis. But the ball may ''spontaneously break'' this symmetry by rolling down the dome into the trough, a point of lowest energy. Afterward, the ball has come to a rest at some fixed point on the perimeter. The dome and the ball retain their individual symmetry, but the system does not.<ref>{{cite book |first=Gerald M. |last=Edelman |title=Bright Air, Brilliant Fire: On the Matter of the Mind |location=New York |publisher=BasicBooks |year=1992 |url=https://archive.org/details/brightairbrillia00gera |url-access=registration |page=[https://archive.org/details/brightairbrillia00gera/page/203 203] }}</ref><br />
<br />
考虑一个对称向上的圆顶,底部环绕着一个槽。如果把一个球放在圆顶的最顶端,这个系统是围绕中心轴旋转对称的。但球体可能会自发地打破这种对称性,因为它会沿着穹顶滚动到能量最低的槽中。然后,球在圆周上某个固定的点上停下来。圆顶和球保持了各自的对称,但系统却没有保持对称性。<br />
[[Image:Mexican hat potential polar.svg|270px|thumb|left|Graph of Goldstone's "[[sombrero]]" potential function <math>V(\phi)</math>.|链接=Special:FilePath/Mexican_hat_potential_polar.svg]]<br />
<br />
In the simplest idealized relativistic model, the spontaneously broken symmetry is summarized through an illustrative [[scalar field theory]]. The relevant [[Lagrangian (field theory)|Lagrangian]] of a scalar field <math>\phi</math>, which essentially dictates how a system behaves, can be split up into kinetic and potential terms,<br />
<br />
在最简单的理想相对论模型中,可以用一个解释性的标量场理论总结自发破对称性。一个标量场 <math>\phi</math>的拉格朗日量从本质上决定了系统的行为,它可以分解成动能项和势能项:<br />
{{NumBlk|::|<math>\mathcal{L} = \partial^\mu \phi \partial_\mu \phi - V(\phi).</math>|{{EquationRef|1}}}}<br />
<br />
It is in this potential term <math>V(\phi)</math> that the symmetry breaking is triggered. An example of a potential, due to [[Jeffrey Goldstone]]<ref>{{Cite journal | last1 = Goldstone | first1 = J. | doi = 10.1007/BF02812722 | title = Field theories with " Superconductor " solutions | journal = Il Nuovo Cimento | volume = 19 | issue = 1 | pages = 154–164 | year = 1961 | bibcode = 1961NCim...19..154G | s2cid = 120409034 | url = http://cds.cern.ch/record/343400 }}</ref> is illustrated in the graph at the left.<br />
<br />
正是在势能项 <math>V(\phi)</math> 中触发了对称性破缺。例如左图所示的 [[Jeffrey Goldstone]] 给出的势能函数:<br />
{{NumBlk|::|<math>V(\phi) = -5|\phi|^2 + |\phi|^4 \,</math>.|{{EquationRef|2}}}}<br />
<br />
This potential has an infinite number of possible [[minimum|minima]] (vacuum states) given by<br />
<br />
该是函数具有无穷数量的最小值点(真空态)当<br />
{{NumBlk|::|<math>\phi = \sqrt{5} e^{i\theta} </math>.|{{EquationRef|3}}}}<br />
for any real ''θ'' between 0 and 2''π''. The system also has an unstable vacuum state corresponding to {{nowrap|1=''Φ'' = 0}}. This state has a [[Unitary group|U(1)]] symmetry. However, once the system falls into a specific stable vacuum state (amounting to a choice of ''θ''), this symmetry will appear to be lost, or "spontaneously broken".<br />
<br />
对于0到2π之间的任何实数θ。系统也有一个不稳定的真空状态,对应于Φ = 0。这个状态具有U(1)对称。然而,一旦系统落入某个稳定真空状态(相当于选择θ),这种对称性就会消失,或者说“自发破缺”。<br />
<br />
In fact, any other choice of ''θ'' would have exactly the same energy, implying the existence of a massless [[Goldstone boson|Nambu–Goldstone boson]], the mode running around the circle at the minimum of this potential, and indicating there is some memory of the original symmetry in the Lagrangian.<br />
<br />
事实上,任何其他θ的选择都将具有完全相同的能量,这意味着无质量的南部-戈德斯通玻色子的存在,这种模式在势能的最小值绕圆运动,并表明存在拉格朗日方程中原始对称性的一些记忆。<br />
<br />
===Other examples===<br />
* For [[ferromagnet]]ic materials, the underlying laws are invariant under spatial rotations. Here, the order parameter is the [[magnetization]], which measures the magnetic dipole density. Above the [[Curie temperature]], the order parameter is zero, which is spatially invariant, and there is no symmetry breaking. Below the Curie temperature, however, the magnetization acquires a constant nonvanishing value, which points in a certain direction (in the idealized situation where we have full equilibrium; otherwise, translational symmetry gets broken as well). The residual rotational symmetries which leave the orientation of this vector invariant remain unbroken, unlike the other rotations which do not and are thus spontaneously broken.<br />
* 对于铁磁性材料,其基本定律在空间旋转下是不变的。在这里,序参量是衡量磁偶极子密度的磁化强度。在居里温度以上,序参量为零,具有空间不变性,不存在对称性破缺。然而,在居里温度以下,磁化强度变成一个恒定的非零值,指向一个特定的方向(在有充分平衡的理想情况下;否则,平移对称性也会破缺)。使该向量方向不变的旋转对称性仍然保留,而其他旋转对称性自发破缺。<br />
* The laws describing a solid are invariant under the full [[Euclidean group]], but the solid itself spontaneously breaks this group down to a [[space group]]. The displacement and the orientation are the order parameters.<br />
* 描述固体的定律在完整的欧几里得群下是不变的,但固体本身会自发地将这个群分解为一个空间群。其中位移和方向是序参量。<br />
* General relativity has a Lorentz symmetry, but in [[Friedmann–Lemaître–Robertson–Walker metric|FRW cosmological models]], the mean 4-velocity field defined by averaging over the velocities of the galaxies (the galaxies act like gas particles at cosmological scales) acts as an order parameter breaking this symmetry. Similar comments can be made about the cosmic microwave background.<br />
* 广义相对论具有洛伦兹对称性,但在FRW宇宙模型中,定义为星系速度的平均值(星系在宇宙尺度上的行为就像气体粒子) 的平均 4-速度场,作为序参量会打破这种对称性。对于宇宙微波背景辐射也有类似的评论。<br />
* For the [[electroweak]] model, as explained earlier, a component of the Higgs field provides the order parameter breaking the electroweak gauge symmetry to the electromagnetic gauge symmetry. Like the ferromagnetic example, there is a phase transition at the electroweak temperature. The same comment about us not tending to notice broken symmetries suggests why it took so long for us to discover electroweak unification.<br />
* 对于电弱模型,如前面所解释的,希格斯场的一个分量提供了将电弱规范对称性破缺到电磁规范对称性的序参量。和铁磁的例子一样,在电弱温度下也有相变。同样的关于我们不倾向于注意破缺对称性的评论,也说明了为什么我们花了这么长时间才发现电弱统一。<br />
* In superconductors, there is a condensed-matter collective field ψ, which acts as the order parameter breaking the electromagnetic gauge symmetry.<br />
* 在超导体中有一个凝聚态集体场ψ,它是打破电磁规范对称性的序参量。<br />
* Take a thin cylindrical plastic rod and push both ends together. Before buckling, the system is symmetric under rotation, and so visibly cylindrically symmetric. But after buckling, it looks different, and asymmetric. Nevertheless, features of the cylindrical symmetry are still there: ignoring friction, it would take no force to freely spin the rod around, displacing the ground state in time, and amounting to an oscillation of vanishing frequency, unlike the radial oscillations in the direction of the buckle. This spinning mode is effectively the requisite [[Goldstone boson|Nambu–Goldstone boson]].<br />
* 拿一个细长的圆柱形塑料杆,把两端推到一起。在屈曲之前,系统在旋转下是对称的,因此可见圆柱对称性。但在弯曲之后,它看起来就不同了,而且是不对称的。然而,圆柱对称性的特征仍然存在:忽略摩擦,杆可以不受外力自由地自旋,在时间上取代基态,等于一个频率趋于零的振荡,而不是沿屈曲方向的径向振荡。这种自旋模式实际上是必需的南部-戈德斯通玻色子。<br />
* Consider a uniform layer of [[fluid]] over an infinite horizontal plane. This system has all the symmetries of the Euclidean plane. But now heat the bottom surface uniformly so that it becomes much hotter than the upper surface. When the temperature gradient becomes large enough, [[convection cell]]s will form, breaking the Euclidean symmetry.<br />
* 考虑无限水平面上的一层均匀的流体。这个系统具有欧几里得平面的所有对称性。但是现在均匀地加热底部表面,使它变得比上表面热得多。当温度梯度足够大时,就会形成对流单元,打破了欧几里得对称。<br />
* Consider a bead on a circular hoop that is rotated about a vertical [[diameter]]. As the [[rotational velocity]] is increased gradually from rest, the bead will initially stay at its initial [[equilibrium point]] at the bottom of the hoop (intuitively stable, lowest [[gravitational potential]]). At a certain critical rotational velocity, this point will become unstable and the bead will jump to one of two other newly created equilibria, [[equidistant]] from the center. Initially, the system is symmetric with respect to the diameter, yet after passing the critical velocity, the bead ends up in one of the two new equilibrium points, thus breaking the symmetry.<br />
* 考虑一个围绕某个竖直的直径旋转的圆形箍上的珠子。当旋转速度从静止逐渐增加时,珠子最初会停留在环底部的初始平衡点(直观上稳定,重力势最低)。在一定的临界旋转速度下,这一点将变得不稳定,珠子将跳到另外两个新创建的离中心等距离的平衡点中的一个。起初,系统相对直径是对称的,但在通过临界速度后,珠子最终停留在两个新的平衡点中的一个,从而打破了对称性。<br />
<br />
==Spontaneous symmetry breaking in physics==<br />
[[File:Spontaneous symmetry breaking (explanatory diagram).png|thumb|right|250px|''Spontaneous symmetry breaking illustrated'': At high energy levels (''left''), the ball settles in the center, and the result is symmetric. At lower energy levels (''right''), the overall "rules" remain symmetric, but the symmetric "[[sombrero|Sombrero]]" enforces an asymmetric outcome, since eventually the ball must rest at some random spot on the bottom, "spontaneously", and not all others.|链接=Special:FilePath/Spontaneous_symmetry_breaking_(explanatory_diagram).png]]<br />
<br />
===Particle physics===<br />
In [[particle physics]], the [[force carrier]] particles are normally specified by field equations with [[gauge symmetry]]; their equations predict that certain measurements will be the same at any point in the field. For instance, field equations might predict that the mass of two quarks is constant. Solving the equations to find the mass of each quark might give two solutions. In one solution, quark A is heavier than quark B. In the second solution, quark B is heavier than quark A ''by the same amount''. The symmetry of the equations is not reflected by the individual solutions, but it is reflected by the range of solutions.<br />
<br />
An actual measurement reflects only one solution, representing a breakdown in the symmetry of the underlying theory. "Hidden" is a better term than "broken", because the symmetry is always there in these equations. This phenomenon is called [[Spontaneous magnetization|''spontaneous'']] symmetry breaking (SSB) because ''nothing'' (that we know of) breaks the symmetry in the equations.<ref name="Weinberg2011">{{cite book|author=Steven Weinberg|title=Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature|url=https://books.google.com/books?id=Rsg3PE_9_ccC|date=20 April 2011|publisher=Knopf Doubleday Publishing Group|isbn=978-0-307-78786-6}}</ref>{{rp|194–195}}<br />
<br />
====Chiral symmetry====<br />
{{Main article|Chiral symmetry breaking}}<br />
Chiral symmetry breaking is an example of spontaneous symmetry breaking affecting the [[chiral symmetry]] of the [[strong interactions]] in particle physics. It is a property of [[quantum chromodynamics]], the [[quantum field theory]] describing these interactions, and is responsible for the bulk of the mass (over 99%) of the [[nucleons]], and thus of all common matter, as it converts very light bound [[quarks]] into 100 times heavier constituents of [[baryons]]. The approximate [[Nambu–Goldstone boson]]s in this spontaneous symmetry breaking process are the [[pions]], whose mass is an order of magnitude lighter than the mass of the nucleons. It served as the prototype and significant ingredient of the Higgs mechanism underlying the electroweak symmetry breaking.<br />
<br />
====Higgs mechanism====<br />
{{Main article|Higgs mechanism|Yukawa interaction}}<br />
<br />
The strong, weak, and electromagnetic forces can all be understood as arising from [[gauge symmetry|gauge symmetries]]. The [[Higgs mechanism]], the spontaneous symmetry breaking of gauge symmetries, is an important component in understanding the [[superconductivity]] of metals and the origin of particle masses in the standard model of particle physics. One important consequence of the distinction between true symmetries and ''gauge symmetries'', is that the spontaneous breaking of a gauge symmetry does not give rise to characteristic massless Nambu–Goldstone physical modes, but only massive modes, like the plasma mode in a superconductor, or the Higgs mode observed in particle physics.<br />
<br />
In the standard model of particle physics, spontaneous symmetry breaking of the {{nowrap|SU(2) × U(1)}} gauge symmetry associated with the electro-weak force generates masses for several particles, and separates the electromagnetic and weak forces. The [[W and Z bosons]] are the elementary particles that mediate the [[weak interaction]], while the [[photon]] mediates the [[electromagnetic interaction]]. At energies much greater than 100 GeV, all these particles behave in a similar manner. The [[Unified field theory#Modern progress|Weinberg–Salam theory]] predicts that, at lower energies, this symmetry is broken so that the photon and the massive W and Z bosons emerge.<ref>A Brief History of Time, Stephen Hawking, Bantam; 10th anniversary edition (1998). pp. 73–74.{{ISBN?}}</ref> In addition, fermions develop mass consistently.<br />
<br />
Without spontaneous symmetry breaking, the [[Standard Model]] of elementary particle interactions requires the existence of a number of particles. However, some particles (the [[W and Z bosons]]) would then be predicted to be massless, when, in reality, they are observed to have mass. To overcome this, spontaneous symmetry breaking is augmented by the [[Higgs mechanism]] to give these particles mass. It also suggests the presence of a new particle, the [[Higgs boson]], detected in 2012.<br />
<br />
[[Superconductivity]] of metals is a condensed-matter analog of the Higgs phenomena, in which a condensate of Cooper pairs of electrons spontaneously breaks the U(1) gauge symmetry associated with light and electromagnetism.<br />
<br />
===Condensed matter physics===<br />
Most phases of matter can be understood through the lens of spontaneous symmetry breaking. For example, crystals are periodic arrays of atoms that are not invariant under all translations (only under a small subset of translations by a lattice vector). Magnets have north and south poles that are oriented in a specific direction, breaking [[rotational symmetry]]. In addition to these examples, there are a whole host of other symmetry-breaking phases of matter — including nematic phases of liquid crystals, charge- and spin-density waves, superfluids, and many others.<br />
<br />
There are several known examples of matter that cannot be described by spontaneous symmetry breaking, including: topologically ordered phases of matter, such as [[Fractional quantum Hall effect|fractional quantum Hall liquids]], and [[Quantum spin liquid|spin-liquids]]. These states do not break any symmetry, but are distinct phases of matter. Unlike the case of spontaneous symmetry breaking, there is not a general framework for describing such states.<ref name=chen>{{cite journal | last1 = Chen | first1 = Xie | author-link3 = Xiao-Gang Wen | last2 = Gu | first2 = Zheng-Cheng | last3 = Wen | first3 = Xiao-Gang | year = 2010 | title = Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order | journal = Phys. Rev. B | volume = 82 | issue = 15| page = 155138 | doi=10.1103/physrevb.82.155138|arxiv = 1004.3835 |bibcode = 2010PhRvB..82o5138C | s2cid = 14593420 }}</ref><br />
<br />
====Continuous symmetry====<br />
The ferromagnet is the canonical system that spontaneously breaks the continuous symmetry of the spins below the [[Curie temperature]] and at {{nowrap|1=''h'' = 0}}, where ''h'' is the external magnetic field. Below the [[Curie temperature]], the energy of the system is invariant under inversion of the magnetization ''m''('''x''') such that {{nowrap|1=''m''('''x''') = −''m''(−'''x''')}}. The symmetry is spontaneously broken as {{nowrap|''h'' → 0}} when the Hamiltonian becomes invariant under the inversion transformation, but the expectation value is not invariant.<br />
<br />
Spontaneously-symmetry-broken phases of matter are characterized by an order parameter that describes the quantity which breaks the symmetry under consideration. For example, in a magnet, the order parameter is the local magnetization.<br />
<br />
Spontaneous breaking of a continuous symmetry is inevitably accompanied by gapless (meaning that these modes do not cost any energy to excite) Nambu–Goldstone modes associated with slow, long-wavelength fluctuations of the order parameter. For example, vibrational modes in a crystal, known as phonons, are associated with slow density fluctuations of the crystal's atoms. The associated Goldstone mode for magnets are oscillating waves of spin known as spin-waves. For symmetry-breaking states, whose order parameter is not a conserved quantity, Nambu–Goldstone modes are typically massless and propagate at a constant velocity.<br />
<br />
An important theorem, due to Mermin and Wagner, states that, at finite temperature, thermally activated fluctuations of Nambu–Goldstone modes destroy the long-range order, and prevent spontaneous symmetry breaking in one- and two-dimensional systems. Similarly, quantum fluctuations of the order parameter prevent most types of continuous symmetry breaking in one-dimensional systems even at zero temperature. (An important exception is ferromagnets, whose order parameter, magnetization, is an exactly conserved quantity and does not have any quantum fluctuations.)<br />
<br />
Other long-range interacting systems, such as cylindrical curved surfaces interacting via the [[Coulomb potential]] or [[Yukawa potential]], have been shown to break translational and rotational symmetries.<ref><br />
{{cite journal<br />
|last1=Kohlstedt |first1=K.L.<br />
|last2=Vernizzi |first2=G.<br />
|last3=Solis |first3=F.J.<br />
|last4=Olvera de la Cruz |first4=M.<br />
|year=2007<br />
|title=Spontaneous Chirality via Long-range Electrostatic Forces<br />
|journal=[[Physical Review Letters]]<br />
|volume=99 |issue=3<br />
|page=030602<br />
|doi=10.1103/PhysRevLett.99.030602<br />
|arxiv = 0704.3435 |bibcode = 2007PhRvL..99c0602K |pmid=17678276|s2cid=37983980<br />
}}</ref> It was shown, in the presence of a symmetric Hamiltonian, and in the limit of infinite volume, the system spontaneously adopts a chiral configuration — i.e., breaks [[mirror plane]] [[symmetry]].<br />
<br />
===Dynamical symmetry breaking===<br />
Dynamical symmetry breaking (DSB) is a special form of spontaneous symmetry breaking in which the ground state of the system has reduced symmetry properties compared to its theoretical description (i.e., [[Lagrangian (field theory)|Lagrangian]]).<br />
<br />
Dynamical breaking of a global symmetry is a spontaneous symmetry breaking, which happens not at the (classical) tree level (i.e., at the level of the bare action), but due to quantum corrections (i.e., at the level of the [[effective action]]).<br />
<br />
Dynamical breaking of a gauge symmetry {{ref|note1}} is subtler. In the conventional spontaneous gauge symmetry breaking, there exists an unstable [[Higgs particle]] in the theory, which drives the vacuum to a symmetry-broken phase. (See, for example, [[electroweak interaction]].) In dynamical gauge symmetry breaking, however, no unstable Higgs particle operates in the theory, but the bound states of the system itself provide the unstable fields that render the phase transition. For example, Bardeen, Hill, and Lindner published a paper that attempts to replace the conventional [[Higgs mechanism]] in the [[standard model]] by a DSB that is driven by a bound state of top-antitop quarks. (Such models, in which a composite particle plays the role of the Higgs boson, are often referred to as "Composite Higgs models".)<ref><br />
{{cite journal<br />
|author1=William A. Bardeen<br />
|author2-link=Christopher T. Hill<br />
|author2=Christopher T. Hill<br />
|author3-link=Manfred Lindner<br />
|author3=Manfred Lindner<br />
|year=1990<br />
|title=Minimal dynamical symmetry breaking of the standard model<br />
|journal=[[Physical Review D]]<br />
|volume=41 |issue=5 |pages=1647–1660<br />
|bibcode=1990PhRvD..41.1647B<br />
|doi=10.1103/PhysRevD.41.1647<br />
|pmid=10012522<br />
|author1-link=William A. Bardeen<br />
}}</ref> Dynamical breaking of gauge symmetries is often due to creation of a [[fermionic condensate]] — e.g., the [[quark condensate]], which is connected to the [[Chiral symmetry breaking|dynamical breaking of chiral symmetry]] in [[quantum chromodynamics]]. Conventional [[superconductivity]] is the paradigmatic example from the condensed matter side, where phonon-mediated attractions lead electrons to become bound in pairs and then condense, thereby breaking the electromagnetic gauge symmetry.<br />
<br />
==Generalisation and technical usage==<br />
For spontaneous symmetry breaking to occur, there must be a system in which there are several equally likely outcomes. The system as a whole is therefore [[Symmetry (physics)|symmetric]] with respect to these outcomes. However, if the system is sampled (i.e. if the system is actually used or interacted with in any way), a specific outcome must occur. Though the system as a whole is symmetric, it is never encountered with this symmetry, but only in one specific asymmetric state. Hence, the symmetry is said to be spontaneously broken in that theory. Nevertheless, the fact that each outcome is equally likely is a reflection of the underlying symmetry, which is thus often dubbed "hidden symmetry", and has crucial formal consequences. (See the article on the [[Nambu–Goldstone boson|Goldstone boson]].)<br />
<br />
When a theory is symmetric with respect to a [[symmetry group]], but requires that one element of the group be distinct, then spontaneous symmetry breaking has occurred. The theory must not dictate ''which'' member is distinct, only that ''one is''. From this point on, the theory can be treated as if this element actually is distinct, with the proviso that any results found in this way must be resymmetrized, by taking the average of each of the elements of the group being the distinct one.<br />
<br />
The crucial concept in physics theories is the [[order parameter]]. If there is a field (often a background field) which acquires an expectation value (not necessarily a [[vacuum expectation value|''vacuum'' expectation value]]) which is not invariant under the symmetry in question, we say that the system is in the [[ordered phase]], and the symmetry is spontaneously broken. This is because other subsystems interact with the order parameter, which specifies a "frame of reference" to be measured against. In that case, the [[vacuum state]] does not obey the initial symmetry (which would keep it invariant, in the linearly realized '''Wigner mode''' in which it would be a singlet), and, instead changes under the (hidden) symmetry, now implemented in the (nonlinear) '''Nambu–Goldstone mode'''. Normally, in the absence of the Higgs mechanism, massless [[Goldstone boson]]s arise.<br />
<br />
The symmetry group can be discrete, such as the [[space group]] of a crystal, or continuous (e.g., a [[Lie group]]), such as the rotational symmetry of space. However, if the system contains only a single spatial dimension, then only discrete symmetries may be broken in a [[vacuum state]] of the full [[Quantum mechanics|quantum theory]], although a classical solution may break a continuous symmetry.<br />
<br />
==Nobel Prize==<br />
On October 7, 2008, the [[Royal Swedish Academy of Sciences]] awarded the 2008 [[Nobel Prize in Physics]] to three scientists for their work in subatomic physics symmetry breaking. [[Yoichiro Nambu]], of the [[University of Chicago]], won half of the prize for the discovery of the mechanism of spontaneous broken symmetry in the context of the strong interactions, specifically [[chiral symmetry breaking]]. Physicists [[Makoto Kobayashi (physicist)|Makoto Kobayashi]] and [[Toshihide Maskawa]], of [[Kyoto University]], shared the other half of the prize for discovering the origin of the [[Explicit symmetry breaking|explicit breaking]] of CP symmetry in the weak interactions.<ref>{{cite web|author=The Nobel Foundation|title=The Nobel Prize in Physics 2008|url=http://nobelprize.org/nobel_prizes/physics/laureates/2008/index.html|work=nobelprize.org|access-date=January 15, 2008}}</ref> This origin is ultimately reliant on the Higgs mechanism, but, so far understood as a "just so" feature of Higgs couplings, not a spontaneously broken symmetry phenomenon.<br />
<br />
==See also==<br />
{{div col|colwidth=24em}}<br />
* [[Autocatalytic reactions and order creation]]<br />
* [[Catastrophe theory]]<br />
* [[Chiral symmetry breaking]]<br />
* [[CP-violation]]<br />
* [[Fermi ball]]<br />
* [[Gauge gravitation theory]]<br />
* [[Goldstone boson]]<br />
* [[Grand unified theory]]<br />
* [[Higgs mechanism]]<br />
* [[Higgs boson]]<br />
* [[Higgs field (classical)]]<br />
* [[Irreversibility]]<br />
* [[Magnetic catalysis]] of chiral symmetry breaking<br />
* [[Mermin–Wagner theorem]]<br />
* [[Norton's dome]]<br />
* [[Second-order phase transition]]<br />
* [[Spontaneous absolute asymmetric synthesis]] in chemistry<br />
* [[Symmetry breaking]]<br />
* [[Tachyon condensation]]<br />
* [[1964 PRL symmetry breaking papers]]<br />
{{div col end}}<br />
<br />
==Notes==<br />
* {{note|note1}} Note that (as in fundamental Higgs driven spontaneous gauge symmetry breaking) the term "symmetry breaking" is a misnomer when applied to gauge symmetries.<br />
<br />
==References==<br />
{{Reflist}}<br />
<br />
==External links==<br />
{{wikiquote}}<br />
* For a pedagogic introduction to electroweak symmetry breaking with step by step derivations, not found in texts, of many key relations, see http://www.quantumfieldtheory.info/Electroweak_Sym_breaking.pdf<br />
* [http://hyperphysics.phy-astr.gsu.edu/hbase/forces/unify.html#c2 Spontaneous symmetry breaking]<br />
* [http://prl.aps.org/50years/milestones#1964 Physical Review Letters – 50th Anniversary Milestone Papers]<br />
* [http://cerncourier.com/cws/article/cern/32522 In CERN Courier, Steven Weinberg reflects on spontaneous symmetry breaking]<br />
* [http://www.scholarpedia.org/article/Englert-Brout-Higgs-Guralnik-Hagen-Kibble_mechanism Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism on Scholarpedia]<br />
* [http://www.scholarpedia.org/article/Englert-Brout-Higgs-Guralnik-Hagen-Kibble_mechanism_%28history%29 History of Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism on Scholarpedia]<br />
* [https://arxiv.org/abs/0907.3466 The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles]<br />
* [http://www.worldscinet.com/ijmpa/24/2414/S0217751X09045431.html International Journal of Modern Physics A: The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles]<br />
* [http://www.datafilehost.com/download-7d512618.html Guralnik, G S; Hagen, C R and Kibble, T W B (1967). Broken Symmetries and the Goldstone Theorem. Advances in Physics, vol. 2 Interscience Publishers, New York. pp. 567–708] {{ISBN|0-470-17057-3}}<br />
* [http://lanl.arxiv.org/abs/hep-th/9802142 Spontaneous Symmetry Breaking in Gauge Theories: a Historical Survey]<br />
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{{Standard model of physics}}<br />
{{Quantum mechanics topics}}<br />
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{{DEFAULTSORT:Spontaneous Symmetry Breaking}}<br />
[[Category:Theoretical physics]]<br />
[[Category:Quantum field theory]]<br />
[[Category:Standard Model]]<br />
[[Category:Quantum chromodynamics]]<br />
[[Category:Symmetry]]<br />
[[Category:Quantum phases]]<br />
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==实例==<br />
<br />
对称性破缺可以涵盖以下任何一种情况:<ref>{{cite web|url=http://www.angelfire.com/stars5/astroinfo/gloss/s.html|title=Astronomical Glossary|author=|date=|website=www.angelfire.com}}</ref><br />
* 某些结构的随机形成破坏了物理学基本定律的精确对称性;<br />
* 物理学中最小能量状态的对称性比系统本身少的情形;<br />
* 系统的实际状态由于明显对称的状态不稳定而不能反映动力学的基本对称性的情况(稳定性是以局部不对称为代价的);<br />
* 理论方程具有某种对称性,但其解可能没有(对称性是“隐藏的”)的情况。<br />
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在物理学文献中讨论的首批对称性破缺案例之一,与不可压缩流体在重力和流体静力平衡中均匀旋转的形式有关。在1834年,Jacobi <ref>{{cite journal| last=Jacobi | first=C.G.J. | title=Über die figur des gleichgewichts | journal=[[Annalen der Physik und Chemie]] | volume=109 | issue=33| pages=229–238 | year=1834| doi=10.1002/andp.18341090808 | bibcode=1834AnP...109..229J | url=https://zenodo.org/record/2027349 }}</ref>和后来的 Liouville <ref>{{cite journal| last=Liouville | first=J. | title=Sur la figure d'une masse fluide homogène, en équilibre et douée d'un mouvement de rotation| journal=Journal de l'École Polytechnique | issue=14| pages=289–296 | year=1834}}</ref>讨论了这样一个事实: 当旋转物体的动能相对于引力势能超过一定的临界值时,这个问题的平衡解是三轴椭球。在这个分叉点上,麦克劳林椭球体的轴对称性被破坏。此外,在这个分叉点之上,对于常数角动量,使动能最小化的解是非轴对称的 Jacobi 椭球,而不是 Maclaurin 椭球。<br />
==另请参阅==<br />
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*[[Higgs mechanism]]<br />
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*[[QCD vacuum]]<br />
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*[[Goldstone boson]]<br />
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*[[1964 PRL symmetry breaking papers]]<br />
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*[[希格斯机制]]<br />
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*[[QCD真空]]<br />
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*[[戈德斯通玻色子]]<br />
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*[[1964年PRL对称性破缺论文]]<br />
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==参考文献==<br />
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{{reflist|colwidth=30em}}<br />
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{{DEFAULTSORT:Symmetry Breaking}}<br />
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范畴: 对称<br />
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类别: 模式形成<br />
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本中文词条由XXX编译,XXX审校,XXX总审校,西瓜编辑,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''<br />
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<noinclude><br />
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[[Category:对称性破缺]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%AF%B9%E7%A7%B0%E6%80%A7%E7%A0%B4%E7%BC%BA&diff=24741对称性破缺2021-07-26T07:27:48Z<p>Jxzhou:/* Sombrero potential */</p>
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[[图一:一个小球位于中央山丘的山峰处(C)。这是一种不稳定平衡:一个很小的扰动会使它落到左边(L)或右边(R)稳定点。尽管山丘是对称的,没有理由让球落在哪一侧,但观察到的最终状态仍然是不对称的,它总会落到某一侧]]。<br />
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在物理学中,一个作用于系统的(无限)小扰动使系统跨过临界点,通过决定去向分叉的哪个分支来决定系统的命运,这种现象叫做'''<font color="#ff8000">对称性破缺</font>'''。对于一个观测不到扰动(或“噪声”)的外部观察者来说,这个选择看起来是任意的。这个过程被称为对称性破缺,因为这种转变通常使系统从一个对称但无序的状态进入一个或多个确定的状态。在'''<font color="#ff8000">斑图生成</font>'''中对称性破缺起着重要作用。<br />
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1972年,诺贝尔奖得主P·W·安德森(P.W.Anderson)在《科学》(Science)杂志上发表了一篇名为《多即不同》的论文<ref>{{cite journal | last=Anderson | first=P.W. | title=More is Different | journal=Science | volume=177 | issue=4047| pages=393–396 | year=1972 | url=http://robotics.cs.tamu.edu/dshell/cs689/papers/anderson72more_is_different.pdf | doi=10.1126/science.177.4047.393 | pmid=17796623 | format=|bibcode = 1972Sci...177..393A }}</ref>,文中使用对称性破缺的思想表明,即使'''<font color="#ff8000">还原论</font>'''是正确的,但它的逆命题'''<font color="#ff8000">建构主义</font>'''是错误的。建构主义认为,在给出描述各组成部分的理论的情况下科学家可以轻易地预测复杂现象。<br />
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对称性破缺可以分为'''<font color="#ff8000">显性对称性破缺</font>'''和'''<font color="#ff8000">自发对称性破缺</font>'''两种类型,二者的区别是,在破缺对称性下系统的运动方程是否不变或者基态是否保持不变。<br />
==显性对称性破缺==<br />
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在'''<font color="#ff8000">显性对称性破缺</font>'''中,描述系统的运动方程在破缺对称下是不同的。在哈密顿力学或拉格朗日力学中,假若系统的哈密顿量(或拉格朗日量)中至少一项显性地打破了给定的对称性,就发生了显性对称性破缺。<br />
==自发对称性破缺==<br />
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在'''<font color="#ff8000">自发对称性破缺</font>'''中,系统的运动方程是不变的,但系统发生了变化。这是因为系统的背景(时空)——真空态——是非恒定的。这种对称性破缺可以用一个序参量进行参数化。这类对称破缺的一个特殊情况是'''<font color="#ff8000">动力学对称性破缺</font>'''。<br />
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Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state ends up in an asymmetric state.[1][2][3] In particular, it can describe systems where the equations of motion or the Lagrangian obey symmetries, but the lowest-energy vacuum solutions do not exhibit that same symmetry. When the system goes to one of those vacuum solutions, the symmetry is broken for perturbations around that vacuum even though the entire Lagrangian retains that symmetry.<br />
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自发对称破缺是一个自发的对称破缺过程,它使处于对称状态的物理系统最终处于非对称状态。特别地,它可以描述运动方程或拉格朗日方程服从某种对称性,但最低能量真空解不具有该对称性的系统。当系统进入其中一个真空解时,真空解周围的扰动会破坏系统对称性,尽管整个拉格朗日方程仍然保持了对称性。<br />
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==Overview==<br />
<br />
In [[explicit symmetry breaking]], if two outcomes are considered, the probability of a pair of outcomes can be different. By definition, spontaneous symmetry breaking requires the existence of a symmetric probability distribution—any pair of outcomes has the same probability. In other words, the underlying laws{{clarify|date=December 2016}} are [[Invariant (physics)|invariant]] under a [[Symmetry (physics)|symmetry]] transformation.<br />
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The system, as a whole{{clarify|date=December 2016}}, changes under such transformations.<br />
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Phases of matter, such as crystals, magnets, and conventional superconductors, as well as simple phase transitions can be described by spontaneous symmetry breaking. Notable exceptions include topological phases of matter like the [[fractional quantum Hall effect]].<br />
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==Examples 例子==<br />
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===Sombrero potential===<br />
Consider a symmetric upward dome with a trough circling the bottom. If a ball is put at the very peak of the dome, the system is symmetric with respect to a rotation around the center axis. But the ball may ''spontaneously break'' this symmetry by rolling down the dome into the trough, a point of lowest energy. Afterward, the ball has come to a rest at some fixed point on the perimeter. The dome and the ball retain their individual symmetry, but the system does not.<ref>{{cite book |first=Gerald M. |last=Edelman |title=Bright Air, Brilliant Fire: On the Matter of the Mind |location=New York |publisher=BasicBooks |year=1992 |url=https://archive.org/details/brightairbrillia00gera |url-access=registration |page=[https://archive.org/details/brightairbrillia00gera/page/203 203] }}</ref><br />
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考虑一个对称向上的圆顶,底部环绕着一个槽。如果把一个球放在圆顶的最顶端,这个系统是围绕中心轴旋转对称的。但球体可能会自发地打破这种对称性,因为它会沿着穹顶滚动到能量最低的槽中。然后,球在圆周上某个固定的点上停下来。圆顶和球保持了各自的对称,但系统却没有保持对称性。<br />
[[Image:Mexican hat potential polar.svg|270px|thumb|left|Graph of Goldstone's "[[sombrero]]" potential function <math>V(\phi)</math>.|链接=Special:FilePath/Mexican_hat_potential_polar.svg]]<br />
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In the simplest idealized relativistic model, the spontaneously broken symmetry is summarized through an illustrative [[scalar field theory]]. The relevant [[Lagrangian (field theory)|Lagrangian]] of a scalar field <math>\phi</math>, which essentially dictates how a system behaves, can be split up into kinetic and potential terms,<br />
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在最简单的理想相对论模型中,可以用一个解释性的标量场理论总结自发破对称性。一个标量场 <math>\phi</math>的拉格朗日量从本质上决定了系统的行为,它可以分解成动能项和势能项:<br />
{{NumBlk|::|<math>\mathcal{L} = \partial^\mu \phi \partial_\mu \phi - V(\phi).</math>|{{EquationRef|1}}}}<br />
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It is in this potential term <math>V(\phi)</math> that the symmetry breaking is triggered. An example of a potential, due to [[Jeffrey Goldstone]]<ref>{{Cite journal | last1 = Goldstone | first1 = J. | doi = 10.1007/BF02812722 | title = Field theories with " Superconductor " solutions | journal = Il Nuovo Cimento | volume = 19 | issue = 1 | pages = 154–164 | year = 1961 | bibcode = 1961NCim...19..154G | s2cid = 120409034 | url = http://cds.cern.ch/record/343400 }}</ref> is illustrated in the graph at the left.<br />
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正是在势能项 <math>V(\phi)</math> 中触发了对称性破缺。例如左图所示的 [[Jeffrey Goldstone]] 给出的势能函数:<br />
{{NumBlk|::|<math>V(\phi) = -5|\phi|^2 + |\phi|^4 \,</math>.|{{EquationRef|2}}}}<br />
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This potential has an infinite number of possible [[minimum|minima]] (vacuum states) given by<br />
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该是函数具有无穷数量的最小值点(真空态)当<br />
{{NumBlk|::|<math>\phi = \sqrt{5} e^{i\theta} </math>.|{{EquationRef|3}}}}<br />
for any real ''θ'' between 0 and 2''π''. The system also has an unstable vacuum state corresponding to {{nowrap|1=''Φ'' = 0}}. This state has a [[Unitary group|U(1)]] symmetry. However, once the system falls into a specific stable vacuum state (amounting to a choice of ''θ''), this symmetry will appear to be lost, or "spontaneously broken".<br />
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对于0到2π之间的任何实数θ。系统也有一个不稳定的真空状态,对应于Φ = 0。这个状态具有U(1)对称。然而,一旦系统落入某个稳定真空状态(相当于选择θ),这种对称性就会消失,或者说“自发破缺”。<br />
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In fact, any other choice of ''θ'' would have exactly the same energy, implying the existence of a massless [[Goldstone boson|Nambu–Goldstone boson]], the mode running around the circle at the minimum of this potential, and indicating there is some memory of the original symmetry in the Lagrangian.<br />
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事实上,任何其他θ的选择都将具有完全相同的能量,这意味着无质量的南部-戈德斯通玻色子的存在,这种模式在势能的最小值绕圆运动,并表明存在拉格朗日方程中原始对称性的一些记忆。<br />
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===Other examples===<br />
* For [[ferromagnet]]ic materials, the underlying laws are invariant under spatial rotations. Here, the order parameter is the [[magnetization]], which measures the magnetic dipole density. Above the [[Curie temperature]], the order parameter is zero, which is spatially invariant, and there is no symmetry breaking. Below the Curie temperature, however, the magnetization acquires a constant nonvanishing value, which points in a certain direction (in the idealized situation where we have full equilibrium; otherwise, translational symmetry gets broken as well). The residual rotational symmetries which leave the orientation of this vector invariant remain unbroken, unlike the other rotations which do not and are thus spontaneously broken.<br />
* The laws describing a solid are invariant under the full [[Euclidean group]], but the solid itself spontaneously breaks this group down to a [[space group]]. The displacement and the orientation are the order parameters.<br />
* General relativity has a Lorentz symmetry, but in [[Friedmann–Lemaître–Robertson–Walker metric|FRW cosmological models]], the mean 4-velocity field defined by averaging over the velocities of the galaxies (the galaxies act like gas particles at cosmological scales) acts as an order parameter breaking this symmetry. Similar comments can be made about the cosmic microwave background.<br />
* For the [[electroweak]] model, as explained earlier, a component of the Higgs field provides the order parameter breaking the electroweak gauge symmetry to the electromagnetic gauge symmetry. Like the ferromagnetic example, there is a phase transition at the electroweak temperature. The same comment about us not tending to notice broken symmetries suggests why it took so long for us to discover electroweak unification.<br />
* In superconductors, there is a condensed-matter collective field ψ, which acts as the order parameter breaking the electromagnetic gauge symmetry.<br />
* Take a thin cylindrical plastic rod and push both ends together. Before buckling, the system is symmetric under rotation, and so visibly cylindrically symmetric. But after buckling, it looks different, and asymmetric. Nevertheless, features of the cylindrical symmetry are still there: ignoring friction, it would take no force to freely spin the rod around, displacing the ground state in time, and amounting to an oscillation of vanishing frequency, unlike the radial oscillations in the direction of the buckle. This spinning mode is effectively the requisite [[Goldstone boson|Nambu–Goldstone boson]].<br />
* Consider a uniform layer of [[fluid]] over an infinite horizontal plane. This system has all the symmetries of the Euclidean plane. But now heat the bottom surface uniformly so that it becomes much hotter than the upper surface. When the temperature gradient becomes large enough, [[convection cell]]s will form, breaking the Euclidean symmetry.<br />
* Consider a bead on a circular hoop that is rotated about a vertical [[diameter]]. As the [[rotational velocity]] is increased gradually from rest, the bead will initially stay at its initial [[equilibrium point]] at the bottom of the hoop (intuitively stable, lowest [[gravitational potential]]). At a certain critical rotational velocity, this point will become unstable and the bead will jump to one of two other newly created equilibria, [[equidistant]] from the center. Initially, the system is symmetric with respect to the diameter, yet after passing the critical velocity, the bead ends up in one of the two new equilibrium points, thus breaking the symmetry.<br />
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==Spontaneous symmetry breaking in physics==<br />
[[File:Spontaneous symmetry breaking (explanatory diagram).png|thumb|right|250px|''Spontaneous symmetry breaking illustrated'': At high energy levels (''left''), the ball settles in the center, and the result is symmetric. At lower energy levels (''right''), the overall "rules" remain symmetric, but the symmetric "[[sombrero|Sombrero]]" enforces an asymmetric outcome, since eventually the ball must rest at some random spot on the bottom, "spontaneously", and not all others.|链接=Special:FilePath/Spontaneous_symmetry_breaking_(explanatory_diagram).png]]<br />
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===Particle physics===<br />
In [[particle physics]], the [[force carrier]] particles are normally specified by field equations with [[gauge symmetry]]; their equations predict that certain measurements will be the same at any point in the field. For instance, field equations might predict that the mass of two quarks is constant. Solving the equations to find the mass of each quark might give two solutions. In one solution, quark A is heavier than quark B. In the second solution, quark B is heavier than quark A ''by the same amount''. The symmetry of the equations is not reflected by the individual solutions, but it is reflected by the range of solutions.<br />
<br />
An actual measurement reflects only one solution, representing a breakdown in the symmetry of the underlying theory. "Hidden" is a better term than "broken", because the symmetry is always there in these equations. This phenomenon is called [[Spontaneous magnetization|''spontaneous'']] symmetry breaking (SSB) because ''nothing'' (that we know of) breaks the symmetry in the equations.<ref name="Weinberg2011">{{cite book|author=Steven Weinberg|title=Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature|url=https://books.google.com/books?id=Rsg3PE_9_ccC|date=20 April 2011|publisher=Knopf Doubleday Publishing Group|isbn=978-0-307-78786-6}}</ref>{{rp|194–195}}<br />
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====Chiral symmetry====<br />
{{Main article|Chiral symmetry breaking}}<br />
Chiral symmetry breaking is an example of spontaneous symmetry breaking affecting the [[chiral symmetry]] of the [[strong interactions]] in particle physics. It is a property of [[quantum chromodynamics]], the [[quantum field theory]] describing these interactions, and is responsible for the bulk of the mass (over 99%) of the [[nucleons]], and thus of all common matter, as it converts very light bound [[quarks]] into 100 times heavier constituents of [[baryons]]. The approximate [[Nambu–Goldstone boson]]s in this spontaneous symmetry breaking process are the [[pions]], whose mass is an order of magnitude lighter than the mass of the nucleons. It served as the prototype and significant ingredient of the Higgs mechanism underlying the electroweak symmetry breaking.<br />
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====Higgs mechanism====<br />
{{Main article|Higgs mechanism|Yukawa interaction}}<br />
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The strong, weak, and electromagnetic forces can all be understood as arising from [[gauge symmetry|gauge symmetries]]. The [[Higgs mechanism]], the spontaneous symmetry breaking of gauge symmetries, is an important component in understanding the [[superconductivity]] of metals and the origin of particle masses in the standard model of particle physics. One important consequence of the distinction between true symmetries and ''gauge symmetries'', is that the spontaneous breaking of a gauge symmetry does not give rise to characteristic massless Nambu–Goldstone physical modes, but only massive modes, like the plasma mode in a superconductor, or the Higgs mode observed in particle physics.<br />
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In the standard model of particle physics, spontaneous symmetry breaking of the {{nowrap|SU(2) × U(1)}} gauge symmetry associated with the electro-weak force generates masses for several particles, and separates the electromagnetic and weak forces. The [[W and Z bosons]] are the elementary particles that mediate the [[weak interaction]], while the [[photon]] mediates the [[electromagnetic interaction]]. At energies much greater than 100 GeV, all these particles behave in a similar manner. The [[Unified field theory#Modern progress|Weinberg–Salam theory]] predicts that, at lower energies, this symmetry is broken so that the photon and the massive W and Z bosons emerge.<ref>A Brief History of Time, Stephen Hawking, Bantam; 10th anniversary edition (1998). pp. 73–74.{{ISBN?}}</ref> In addition, fermions develop mass consistently.<br />
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Without spontaneous symmetry breaking, the [[Standard Model]] of elementary particle interactions requires the existence of a number of particles. However, some particles (the [[W and Z bosons]]) would then be predicted to be massless, when, in reality, they are observed to have mass. To overcome this, spontaneous symmetry breaking is augmented by the [[Higgs mechanism]] to give these particles mass. It also suggests the presence of a new particle, the [[Higgs boson]], detected in 2012.<br />
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[[Superconductivity]] of metals is a condensed-matter analog of the Higgs phenomena, in which a condensate of Cooper pairs of electrons spontaneously breaks the U(1) gauge symmetry associated with light and electromagnetism.<br />
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===Condensed matter physics===<br />
Most phases of matter can be understood through the lens of spontaneous symmetry breaking. For example, crystals are periodic arrays of atoms that are not invariant under all translations (only under a small subset of translations by a lattice vector). Magnets have north and south poles that are oriented in a specific direction, breaking [[rotational symmetry]]. In addition to these examples, there are a whole host of other symmetry-breaking phases of matter — including nematic phases of liquid crystals, charge- and spin-density waves, superfluids, and many others.<br />
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There are several known examples of matter that cannot be described by spontaneous symmetry breaking, including: topologically ordered phases of matter, such as [[Fractional quantum Hall effect|fractional quantum Hall liquids]], and [[Quantum spin liquid|spin-liquids]]. These states do not break any symmetry, but are distinct phases of matter. Unlike the case of spontaneous symmetry breaking, there is not a general framework for describing such states.<ref name=chen>{{cite journal | last1 = Chen | first1 = Xie | author-link3 = Xiao-Gang Wen | last2 = Gu | first2 = Zheng-Cheng | last3 = Wen | first3 = Xiao-Gang | year = 2010 | title = Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order | journal = Phys. Rev. B | volume = 82 | issue = 15| page = 155138 | doi=10.1103/physrevb.82.155138|arxiv = 1004.3835 |bibcode = 2010PhRvB..82o5138C | s2cid = 14593420 }}</ref><br />
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====Continuous symmetry====<br />
The ferromagnet is the canonical system that spontaneously breaks the continuous symmetry of the spins below the [[Curie temperature]] and at {{nowrap|1=''h'' = 0}}, where ''h'' is the external magnetic field. Below the [[Curie temperature]], the energy of the system is invariant under inversion of the magnetization ''m''('''x''') such that {{nowrap|1=''m''('''x''') = −''m''(−'''x''')}}. The symmetry is spontaneously broken as {{nowrap|''h'' → 0}} when the Hamiltonian becomes invariant under the inversion transformation, but the expectation value is not invariant.<br />
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Spontaneously-symmetry-broken phases of matter are characterized by an order parameter that describes the quantity which breaks the symmetry under consideration. For example, in a magnet, the order parameter is the local magnetization.<br />
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Spontaneous breaking of a continuous symmetry is inevitably accompanied by gapless (meaning that these modes do not cost any energy to excite) Nambu–Goldstone modes associated with slow, long-wavelength fluctuations of the order parameter. For example, vibrational modes in a crystal, known as phonons, are associated with slow density fluctuations of the crystal's atoms. The associated Goldstone mode for magnets are oscillating waves of spin known as spin-waves. For symmetry-breaking states, whose order parameter is not a conserved quantity, Nambu–Goldstone modes are typically massless and propagate at a constant velocity.<br />
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An important theorem, due to Mermin and Wagner, states that, at finite temperature, thermally activated fluctuations of Nambu–Goldstone modes destroy the long-range order, and prevent spontaneous symmetry breaking in one- and two-dimensional systems. Similarly, quantum fluctuations of the order parameter prevent most types of continuous symmetry breaking in one-dimensional systems even at zero temperature. (An important exception is ferromagnets, whose order parameter, magnetization, is an exactly conserved quantity and does not have any quantum fluctuations.)<br />
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Other long-range interacting systems, such as cylindrical curved surfaces interacting via the [[Coulomb potential]] or [[Yukawa potential]], have been shown to break translational and rotational symmetries.<ref><br />
{{cite journal<br />
|last1=Kohlstedt |first1=K.L.<br />
|last2=Vernizzi |first2=G.<br />
|last3=Solis |first3=F.J.<br />
|last4=Olvera de la Cruz |first4=M.<br />
|year=2007<br />
|title=Spontaneous Chirality via Long-range Electrostatic Forces<br />
|journal=[[Physical Review Letters]]<br />
|volume=99 |issue=3<br />
|page=030602<br />
|doi=10.1103/PhysRevLett.99.030602<br />
|arxiv = 0704.3435 |bibcode = 2007PhRvL..99c0602K |pmid=17678276|s2cid=37983980<br />
}}</ref> It was shown, in the presence of a symmetric Hamiltonian, and in the limit of infinite volume, the system spontaneously adopts a chiral configuration — i.e., breaks [[mirror plane]] [[symmetry]].<br />
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===Dynamical symmetry breaking===<br />
Dynamical symmetry breaking (DSB) is a special form of spontaneous symmetry breaking in which the ground state of the system has reduced symmetry properties compared to its theoretical description (i.e., [[Lagrangian (field theory)|Lagrangian]]).<br />
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Dynamical breaking of a global symmetry is a spontaneous symmetry breaking, which happens not at the (classical) tree level (i.e., at the level of the bare action), but due to quantum corrections (i.e., at the level of the [[effective action]]).<br />
<br />
Dynamical breaking of a gauge symmetry {{ref|note1}} is subtler. In the conventional spontaneous gauge symmetry breaking, there exists an unstable [[Higgs particle]] in the theory, which drives the vacuum to a symmetry-broken phase. (See, for example, [[electroweak interaction]].) In dynamical gauge symmetry breaking, however, no unstable Higgs particle operates in the theory, but the bound states of the system itself provide the unstable fields that render the phase transition. For example, Bardeen, Hill, and Lindner published a paper that attempts to replace the conventional [[Higgs mechanism]] in the [[standard model]] by a DSB that is driven by a bound state of top-antitop quarks. (Such models, in which a composite particle plays the role of the Higgs boson, are often referred to as "Composite Higgs models".)<ref><br />
{{cite journal<br />
|author1=William A. Bardeen<br />
|author2-link=Christopher T. Hill<br />
|author2=Christopher T. Hill<br />
|author3-link=Manfred Lindner<br />
|author3=Manfred Lindner<br />
|year=1990<br />
|title=Minimal dynamical symmetry breaking of the standard model<br />
|journal=[[Physical Review D]]<br />
|volume=41 |issue=5 |pages=1647–1660<br />
|bibcode=1990PhRvD..41.1647B<br />
|doi=10.1103/PhysRevD.41.1647<br />
|pmid=10012522<br />
|author1-link=William A. Bardeen<br />
}}</ref> Dynamical breaking of gauge symmetries is often due to creation of a [[fermionic condensate]] — e.g., the [[quark condensate]], which is connected to the [[Chiral symmetry breaking|dynamical breaking of chiral symmetry]] in [[quantum chromodynamics]]. Conventional [[superconductivity]] is the paradigmatic example from the condensed matter side, where phonon-mediated attractions lead electrons to become bound in pairs and then condense, thereby breaking the electromagnetic gauge symmetry.<br />
<br />
==Generalisation and technical usage==<br />
For spontaneous symmetry breaking to occur, there must be a system in which there are several equally likely outcomes. The system as a whole is therefore [[Symmetry (physics)|symmetric]] with respect to these outcomes. However, if the system is sampled (i.e. if the system is actually used or interacted with in any way), a specific outcome must occur. Though the system as a whole is symmetric, it is never encountered with this symmetry, but only in one specific asymmetric state. Hence, the symmetry is said to be spontaneously broken in that theory. Nevertheless, the fact that each outcome is equally likely is a reflection of the underlying symmetry, which is thus often dubbed "hidden symmetry", and has crucial formal consequences. (See the article on the [[Nambu–Goldstone boson|Goldstone boson]].)<br />
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When a theory is symmetric with respect to a [[symmetry group]], but requires that one element of the group be distinct, then spontaneous symmetry breaking has occurred. The theory must not dictate ''which'' member is distinct, only that ''one is''. From this point on, the theory can be treated as if this element actually is distinct, with the proviso that any results found in this way must be resymmetrized, by taking the average of each of the elements of the group being the distinct one.<br />
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The crucial concept in physics theories is the [[order parameter]]. If there is a field (often a background field) which acquires an expectation value (not necessarily a [[vacuum expectation value|''vacuum'' expectation value]]) which is not invariant under the symmetry in question, we say that the system is in the [[ordered phase]], and the symmetry is spontaneously broken. This is because other subsystems interact with the order parameter, which specifies a "frame of reference" to be measured against. In that case, the [[vacuum state]] does not obey the initial symmetry (which would keep it invariant, in the linearly realized '''Wigner mode''' in which it would be a singlet), and, instead changes under the (hidden) symmetry, now implemented in the (nonlinear) '''Nambu–Goldstone mode'''. Normally, in the absence of the Higgs mechanism, massless [[Goldstone boson]]s arise.<br />
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The symmetry group can be discrete, such as the [[space group]] of a crystal, or continuous (e.g., a [[Lie group]]), such as the rotational symmetry of space. However, if the system contains only a single spatial dimension, then only discrete symmetries may be broken in a [[vacuum state]] of the full [[Quantum mechanics|quantum theory]], although a classical solution may break a continuous symmetry.<br />
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==Nobel Prize==<br />
On October 7, 2008, the [[Royal Swedish Academy of Sciences]] awarded the 2008 [[Nobel Prize in Physics]] to three scientists for their work in subatomic physics symmetry breaking. [[Yoichiro Nambu]], of the [[University of Chicago]], won half of the prize for the discovery of the mechanism of spontaneous broken symmetry in the context of the strong interactions, specifically [[chiral symmetry breaking]]. Physicists [[Makoto Kobayashi (physicist)|Makoto Kobayashi]] and [[Toshihide Maskawa]], of [[Kyoto University]], shared the other half of the prize for discovering the origin of the [[Explicit symmetry breaking|explicit breaking]] of CP symmetry in the weak interactions.<ref>{{cite web|author=The Nobel Foundation|title=The Nobel Prize in Physics 2008|url=http://nobelprize.org/nobel_prizes/physics/laureates/2008/index.html|work=nobelprize.org|access-date=January 15, 2008}}</ref> This origin is ultimately reliant on the Higgs mechanism, but, so far understood as a "just so" feature of Higgs couplings, not a spontaneously broken symmetry phenomenon.<br />
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==See also==<br />
{{div col|colwidth=24em}}<br />
* [[Autocatalytic reactions and order creation]]<br />
* [[Catastrophe theory]]<br />
* [[Chiral symmetry breaking]]<br />
* [[CP-violation]]<br />
* [[Fermi ball]]<br />
* [[Gauge gravitation theory]]<br />
* [[Goldstone boson]]<br />
* [[Grand unified theory]]<br />
* [[Higgs mechanism]]<br />
* [[Higgs boson]]<br />
* [[Higgs field (classical)]]<br />
* [[Irreversibility]]<br />
* [[Magnetic catalysis]] of chiral symmetry breaking<br />
* [[Mermin–Wagner theorem]]<br />
* [[Norton's dome]]<br />
* [[Second-order phase transition]]<br />
* [[Spontaneous absolute asymmetric synthesis]] in chemistry<br />
* [[Symmetry breaking]]<br />
* [[Tachyon condensation]]<br />
* [[1964 PRL symmetry breaking papers]]<br />
{{div col end}}<br />
<br />
==Notes==<br />
* {{note|note1}} Note that (as in fundamental Higgs driven spontaneous gauge symmetry breaking) the term "symmetry breaking" is a misnomer when applied to gauge symmetries.<br />
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==References==<br />
{{Reflist}}<br />
<br />
==External links==<br />
{{wikiquote}}<br />
* For a pedagogic introduction to electroweak symmetry breaking with step by step derivations, not found in texts, of many key relations, see http://www.quantumfieldtheory.info/Electroweak_Sym_breaking.pdf<br />
* [http://hyperphysics.phy-astr.gsu.edu/hbase/forces/unify.html#c2 Spontaneous symmetry breaking]<br />
* [http://prl.aps.org/50years/milestones#1964 Physical Review Letters – 50th Anniversary Milestone Papers]<br />
* [http://cerncourier.com/cws/article/cern/32522 In CERN Courier, Steven Weinberg reflects on spontaneous symmetry breaking]<br />
* [http://www.scholarpedia.org/article/Englert-Brout-Higgs-Guralnik-Hagen-Kibble_mechanism Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism on Scholarpedia]<br />
* [http://www.scholarpedia.org/article/Englert-Brout-Higgs-Guralnik-Hagen-Kibble_mechanism_%28history%29 History of Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism on Scholarpedia]<br />
* [https://arxiv.org/abs/0907.3466 The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles]<br />
* [http://www.worldscinet.com/ijmpa/24/2414/S0217751X09045431.html International Journal of Modern Physics A: The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles]<br />
* [http://www.datafilehost.com/download-7d512618.html Guralnik, G S; Hagen, C R and Kibble, T W B (1967). Broken Symmetries and the Goldstone Theorem. Advances in Physics, vol. 2 Interscience Publishers, New York. pp. 567–708] {{ISBN|0-470-17057-3}}<br />
* [http://lanl.arxiv.org/abs/hep-th/9802142 Spontaneous Symmetry Breaking in Gauge Theories: a Historical Survey]<br />
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{{Standard model of physics}}<br />
{{Quantum mechanics topics}}<br />
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{{DEFAULTSORT:Spontaneous Symmetry Breaking}}<br />
[[Category:Theoretical physics]]<br />
[[Category:Quantum field theory]]<br />
[[Category:Standard Model]]<br />
[[Category:Quantum chromodynamics]]<br />
[[Category:Symmetry]]<br />
[[Category:Quantum phases]]<br />
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==实例==<br />
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对称性破缺可以涵盖以下任何一种情况:<ref>{{cite web|url=http://www.angelfire.com/stars5/astroinfo/gloss/s.html|title=Astronomical Glossary|author=|date=|website=www.angelfire.com}}</ref><br />
* 某些结构的随机形成破坏了物理学基本定律的精确对称性;<br />
* 物理学中最小能量状态的对称性比系统本身少的情形;<br />
* 系统的实际状态由于明显对称的状态不稳定而不能反映动力学的基本对称性的情况(稳定性是以局部不对称为代价的);<br />
* 理论方程具有某种对称性,但其解可能没有(对称性是“隐藏的”)的情况。<br />
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在物理学文献中讨论的首批对称性破缺案例之一,与不可压缩流体在重力和流体静力平衡中均匀旋转的形式有关。在1834年,Jacobi <ref>{{cite journal| last=Jacobi | first=C.G.J. | title=Über die figur des gleichgewichts | journal=[[Annalen der Physik und Chemie]] | volume=109 | issue=33| pages=229–238 | year=1834| doi=10.1002/andp.18341090808 | bibcode=1834AnP...109..229J | url=https://zenodo.org/record/2027349 }}</ref>和后来的 Liouville <ref>{{cite journal| last=Liouville | first=J. | title=Sur la figure d'une masse fluide homogène, en équilibre et douée d'un mouvement de rotation| journal=Journal de l'École Polytechnique | issue=14| pages=289–296 | year=1834}}</ref>讨论了这样一个事实: 当旋转物体的动能相对于引力势能超过一定的临界值时,这个问题的平衡解是三轴椭球。在这个分叉点上,麦克劳林椭球体的轴对称性被破坏。此外,在这个分叉点之上,对于常数角动量,使动能最小化的解是非轴对称的 Jacobi 椭球,而不是 Maclaurin 椭球。<br />
==另请参阅==<br />
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*[[Higgs mechanism]]<br />
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*[[QCD vacuum]]<br />
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*[[Goldstone boson]]<br />
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*[[1964 PRL symmetry breaking papers]]<br />
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*[[希格斯机制]]<br />
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*[[QCD真空]]<br />
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*[[戈德斯通玻色子]]<br />
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*[[1964年PRL对称性破缺论文]]<br />
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==参考文献==<br />
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{{reflist|colwidth=30em}}<br />
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{{DEFAULTSORT:Symmetry Breaking}}<br />
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范畴: 对称<br />
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类别: 模式形成<br />
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本中文词条由XXX编译,XXX审校,XXX总审校,西瓜编辑,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''<br />
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<noinclude><br />
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[[Category:对称性破缺]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%AF%B9%E7%A7%B0%E6%80%A7%E7%A0%B4%E7%BC%BA&diff=24740对称性破缺2021-07-26T07:27:06Z<p>Jxzhou:</p>
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[[图一:一个小球位于中央山丘的山峰处(C)。这是一种不稳定平衡:一个很小的扰动会使它落到左边(L)或右边(R)稳定点。尽管山丘是对称的,没有理由让球落在哪一侧,但观察到的最终状态仍然是不对称的,它总会落到某一侧]]。<br />
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在物理学中,一个作用于系统的(无限)小扰动使系统跨过临界点,通过决定去向分叉的哪个分支来决定系统的命运,这种现象叫做'''<font color="#ff8000">对称性破缺</font>'''。对于一个观测不到扰动(或“噪声”)的外部观察者来说,这个选择看起来是任意的。这个过程被称为对称性破缺,因为这种转变通常使系统从一个对称但无序的状态进入一个或多个确定的状态。在'''<font color="#ff8000">斑图生成</font>'''中对称性破缺起着重要作用。<br />
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1972年,诺贝尔奖得主P·W·安德森(P.W.Anderson)在《科学》(Science)杂志上发表了一篇名为《多即不同》的论文<ref>{{cite journal | last=Anderson | first=P.W. | title=More is Different | journal=Science | volume=177 | issue=4047| pages=393–396 | year=1972 | url=http://robotics.cs.tamu.edu/dshell/cs689/papers/anderson72more_is_different.pdf | doi=10.1126/science.177.4047.393 | pmid=17796623 | format=|bibcode = 1972Sci...177..393A }}</ref>,文中使用对称性破缺的思想表明,即使'''<font color="#ff8000">还原论</font>'''是正确的,但它的逆命题'''<font color="#ff8000">建构主义</font>'''是错误的。建构主义认为,在给出描述各组成部分的理论的情况下科学家可以轻易地预测复杂现象。<br />
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对称性破缺可以分为'''<font color="#ff8000">显性对称性破缺</font>'''和'''<font color="#ff8000">自发对称性破缺</font>'''两种类型,二者的区别是,在破缺对称性下系统的运动方程是否不变或者基态是否保持不变。<br />
==显性对称性破缺==<br />
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在'''<font color="#ff8000">显性对称性破缺</font>'''中,描述系统的运动方程在破缺对称下是不同的。在哈密顿力学或拉格朗日力学中,假若系统的哈密顿量(或拉格朗日量)中至少一项显性地打破了给定的对称性,就发生了显性对称性破缺。<br />
==自发对称性破缺==<br />
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在'''<font color="#ff8000">自发对称性破缺</font>'''中,系统的运动方程是不变的,但系统发生了变化。这是因为系统的背景(时空)——真空态——是非恒定的。这种对称性破缺可以用一个序参量进行参数化。这类对称破缺的一个特殊情况是'''<font color="#ff8000">动力学对称性破缺</font>'''。<br />
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Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state ends up in an asymmetric state.[1][2][3] In particular, it can describe systems where the equations of motion or the Lagrangian obey symmetries, but the lowest-energy vacuum solutions do not exhibit that same symmetry. When the system goes to one of those vacuum solutions, the symmetry is broken for perturbations around that vacuum even though the entire Lagrangian retains that symmetry.<br />
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自发对称破缺是一个自发的对称破缺过程,它使处于对称状态的物理系统最终处于非对称状态。特别地,它可以描述运动方程或拉格朗日方程服从某种对称性,但最低能量真空解不具有该对称性的系统。当系统进入其中一个真空解时,真空解周围的扰动会破坏系统对称性,尽管整个拉格朗日方程仍然保持了对称性。<br />
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==Overview==<br />
<br />
In [[explicit symmetry breaking]], if two outcomes are considered, the probability of a pair of outcomes can be different. By definition, spontaneous symmetry breaking requires the existence of a symmetric probability distribution—any pair of outcomes has the same probability. In other words, the underlying laws{{clarify|date=December 2016}} are [[Invariant (physics)|invariant]] under a [[Symmetry (physics)|symmetry]] transformation.<br />
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The system, as a whole{{clarify|date=December 2016}}, changes under such transformations.<br />
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Phases of matter, such as crystals, magnets, and conventional superconductors, as well as simple phase transitions can be described by spontaneous symmetry breaking. Notable exceptions include topological phases of matter like the [[fractional quantum Hall effect]].<br />
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==Examples 例子==<br />
<br />
===Sombrero potential===<br />
Consider a symmetric upward dome with a trough circling the bottom. If a ball is put at the very peak of the dome, the system is symmetric with respect to a rotation around the center axis. But the ball may ''spontaneously break'' this symmetry by rolling down the dome into the trough, a point of lowest energy. Afterward, the ball has come to a rest at some fixed point on the perimeter. The dome and the ball retain their individual symmetry, but the system does not.<ref>{{cite book |first=Gerald M. |last=Edelman |title=Bright Air, Brilliant Fire: On the Matter of the Mind |location=New York |publisher=BasicBooks |year=1992 |url=https://archive.org/details/brightairbrillia00gera |url-access=registration |page=[https://archive.org/details/brightairbrillia00gera/page/203 203] }}</ref><br />
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考虑一个对称向上的圆顶,底部环绕着一个槽。如果把一个球放在圆顶的最顶端,这个系统是围绕中心轴旋转对称的。但球体可能会自发地打破这种对称性,因为它会沿着穹顶滚动到能量最低的槽中。然后,球在圆周上某个固定的点上停下来。圆顶和球保持了各自的对称,但系统却没有保持对称性。<br />
[[Image:Mexican hat potential polar.svg|270px|thumb|left|Graph of Goldstone's "[[sombrero]]" potential function <math>V(\phi)</math>.|链接=Special:FilePath/Mexican_hat_potential_polar.svg]]<br />
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In the simplest idealized relativistic model, the spontaneously broken symmetry is summarized through an illustrative [[scalar field theory]]. The relevant [[Lagrangian (field theory)|Lagrangian]] of a scalar field <math>\phi</math>, which essentially dictates how a system behaves, can be split up into kinetic and potential terms,<br />
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在最简单的理想相对论模型中,可以用一个解释性的标量场理论总结自发破对称性。一个标量场 <math>\phi</math>的拉格朗日量从本质上决定了系统的行为,它可以分解成动能项和势能项:<br />
{{NumBlk|::|<math>\mathcal{L} = \partial^\mu \phi \partial_\mu \phi - V(\phi).</math>|{{EquationRef|1}}}}<br />
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It is in this potential term <math>V(\phi)</math> that the symmetry breaking is triggered. An example of a potential, due to [[Jeffrey Goldstone]]<ref>{{Cite journal | last1 = Goldstone | first1 = J. | doi = 10.1007/BF02812722 | title = Field theories with " Superconductor " solutions | journal = Il Nuovo Cimento | volume = 19 | issue = 1 | pages = 154–164 | year = 1961 | bibcode = 1961NCim...19..154G | s2cid = 120409034 | url = http://cds.cern.ch/record/343400 }}</ref> is illustrated in the graph at the left.<br />
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正是在势能项 <math>V(\phi)</math> 中触发了对称性破缺。例如作图所示的 [[Jeffrey Goldstone]] 给出的势能函数:<br />
{{NumBlk|::|<math>V(\phi) = -5|\phi|^2 + |\phi|^4 \,</math>.|{{EquationRef|2}}}}<br />
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This potential has an infinite number of possible [[minimum|minima]] (vacuum states) given by<br />
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该是函数具有无穷数量的最小值点(真空态)当<br />
{{NumBlk|::|<math>\phi = \sqrt{5} e^{i\theta} </math>.|{{EquationRef|3}}}}<br />
for any real ''θ'' between 0 and 2''π''. The system also has an unstable vacuum state corresponding to {{nowrap|1=''Φ'' = 0}}. This state has a [[Unitary group|U(1)]] symmetry. However, once the system falls into a specific stable vacuum state (amounting to a choice of ''θ''), this symmetry will appear to be lost, or "spontaneously broken".<br />
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对于0到2π之间的任何实数θ。系统也有一个不稳定的真空状态,对应于Φ = 0。这个状态具有U(1)对称。然而,一旦系统落入某个稳定真空状态(相当于选择θ),这种对称性就会消失,或者说“自发破缺”。<br />
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In fact, any other choice of ''θ'' would have exactly the same energy, implying the existence of a massless [[Goldstone boson|Nambu–Goldstone boson]], the mode running around the circle at the minimum of this potential, and indicating there is some memory of the original symmetry in the Lagrangian.<br />
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事实上,任何其他θ的选择都将具有完全相同的能量,这意味着无质量的南部-戈德斯通玻色子的存在,这种模式在势能的最小值绕圆运动,并表明存在拉格朗日方程中原始对称性的一些记忆。<br />
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===Other examples===<br />
* For [[ferromagnet]]ic materials, the underlying laws are invariant under spatial rotations. Here, the order parameter is the [[magnetization]], which measures the magnetic dipole density. Above the [[Curie temperature]], the order parameter is zero, which is spatially invariant, and there is no symmetry breaking. Below the Curie temperature, however, the magnetization acquires a constant nonvanishing value, which points in a certain direction (in the idealized situation where we have full equilibrium; otherwise, translational symmetry gets broken as well). The residual rotational symmetries which leave the orientation of this vector invariant remain unbroken, unlike the other rotations which do not and are thus spontaneously broken.<br />
* The laws describing a solid are invariant under the full [[Euclidean group]], but the solid itself spontaneously breaks this group down to a [[space group]]. The displacement and the orientation are the order parameters.<br />
* General relativity has a Lorentz symmetry, but in [[Friedmann–Lemaître–Robertson–Walker metric|FRW cosmological models]], the mean 4-velocity field defined by averaging over the velocities of the galaxies (the galaxies act like gas particles at cosmological scales) acts as an order parameter breaking this symmetry. Similar comments can be made about the cosmic microwave background.<br />
* For the [[electroweak]] model, as explained earlier, a component of the Higgs field provides the order parameter breaking the electroweak gauge symmetry to the electromagnetic gauge symmetry. Like the ferromagnetic example, there is a phase transition at the electroweak temperature. The same comment about us not tending to notice broken symmetries suggests why it took so long for us to discover electroweak unification.<br />
* In superconductors, there is a condensed-matter collective field ψ, which acts as the order parameter breaking the electromagnetic gauge symmetry.<br />
* Take a thin cylindrical plastic rod and push both ends together. Before buckling, the system is symmetric under rotation, and so visibly cylindrically symmetric. But after buckling, it looks different, and asymmetric. Nevertheless, features of the cylindrical symmetry are still there: ignoring friction, it would take no force to freely spin the rod around, displacing the ground state in time, and amounting to an oscillation of vanishing frequency, unlike the radial oscillations in the direction of the buckle. This spinning mode is effectively the requisite [[Goldstone boson|Nambu–Goldstone boson]].<br />
* Consider a uniform layer of [[fluid]] over an infinite horizontal plane. This system has all the symmetries of the Euclidean plane. But now heat the bottom surface uniformly so that it becomes much hotter than the upper surface. When the temperature gradient becomes large enough, [[convection cell]]s will form, breaking the Euclidean symmetry.<br />
* Consider a bead on a circular hoop that is rotated about a vertical [[diameter]]. As the [[rotational velocity]] is increased gradually from rest, the bead will initially stay at its initial [[equilibrium point]] at the bottom of the hoop (intuitively stable, lowest [[gravitational potential]]). At a certain critical rotational velocity, this point will become unstable and the bead will jump to one of two other newly created equilibria, [[equidistant]] from the center. Initially, the system is symmetric with respect to the diameter, yet after passing the critical velocity, the bead ends up in one of the two new equilibrium points, thus breaking the symmetry.<br />
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==Spontaneous symmetry breaking in physics==<br />
[[File:Spontaneous symmetry breaking (explanatory diagram).png|thumb|right|250px|''Spontaneous symmetry breaking illustrated'': At high energy levels (''left''), the ball settles in the center, and the result is symmetric. At lower energy levels (''right''), the overall "rules" remain symmetric, but the symmetric "[[sombrero|Sombrero]]" enforces an asymmetric outcome, since eventually the ball must rest at some random spot on the bottom, "spontaneously", and not all others.|链接=Special:FilePath/Spontaneous_symmetry_breaking_(explanatory_diagram).png]]<br />
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===Particle physics===<br />
In [[particle physics]], the [[force carrier]] particles are normally specified by field equations with [[gauge symmetry]]; their equations predict that certain measurements will be the same at any point in the field. For instance, field equations might predict that the mass of two quarks is constant. Solving the equations to find the mass of each quark might give two solutions. In one solution, quark A is heavier than quark B. In the second solution, quark B is heavier than quark A ''by the same amount''. The symmetry of the equations is not reflected by the individual solutions, but it is reflected by the range of solutions.<br />
<br />
An actual measurement reflects only one solution, representing a breakdown in the symmetry of the underlying theory. "Hidden" is a better term than "broken", because the symmetry is always there in these equations. This phenomenon is called [[Spontaneous magnetization|''spontaneous'']] symmetry breaking (SSB) because ''nothing'' (that we know of) breaks the symmetry in the equations.<ref name="Weinberg2011">{{cite book|author=Steven Weinberg|title=Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature|url=https://books.google.com/books?id=Rsg3PE_9_ccC|date=20 April 2011|publisher=Knopf Doubleday Publishing Group|isbn=978-0-307-78786-6}}</ref>{{rp|194–195}}<br />
<br />
====Chiral symmetry====<br />
{{Main article|Chiral symmetry breaking}}<br />
Chiral symmetry breaking is an example of spontaneous symmetry breaking affecting the [[chiral symmetry]] of the [[strong interactions]] in particle physics. It is a property of [[quantum chromodynamics]], the [[quantum field theory]] describing these interactions, and is responsible for the bulk of the mass (over 99%) of the [[nucleons]], and thus of all common matter, as it converts very light bound [[quarks]] into 100 times heavier constituents of [[baryons]]. The approximate [[Nambu–Goldstone boson]]s in this spontaneous symmetry breaking process are the [[pions]], whose mass is an order of magnitude lighter than the mass of the nucleons. It served as the prototype and significant ingredient of the Higgs mechanism underlying the electroweak symmetry breaking.<br />
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====Higgs mechanism====<br />
{{Main article|Higgs mechanism|Yukawa interaction}}<br />
<br />
The strong, weak, and electromagnetic forces can all be understood as arising from [[gauge symmetry|gauge symmetries]]. The [[Higgs mechanism]], the spontaneous symmetry breaking of gauge symmetries, is an important component in understanding the [[superconductivity]] of metals and the origin of particle masses in the standard model of particle physics. One important consequence of the distinction between true symmetries and ''gauge symmetries'', is that the spontaneous breaking of a gauge symmetry does not give rise to characteristic massless Nambu–Goldstone physical modes, but only massive modes, like the plasma mode in a superconductor, or the Higgs mode observed in particle physics.<br />
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In the standard model of particle physics, spontaneous symmetry breaking of the {{nowrap|SU(2) × U(1)}} gauge symmetry associated with the electro-weak force generates masses for several particles, and separates the electromagnetic and weak forces. The [[W and Z bosons]] are the elementary particles that mediate the [[weak interaction]], while the [[photon]] mediates the [[electromagnetic interaction]]. At energies much greater than 100 GeV, all these particles behave in a similar manner. The [[Unified field theory#Modern progress|Weinberg–Salam theory]] predicts that, at lower energies, this symmetry is broken so that the photon and the massive W and Z bosons emerge.<ref>A Brief History of Time, Stephen Hawking, Bantam; 10th anniversary edition (1998). pp. 73–74.{{ISBN?}}</ref> In addition, fermions develop mass consistently.<br />
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Without spontaneous symmetry breaking, the [[Standard Model]] of elementary particle interactions requires the existence of a number of particles. However, some particles (the [[W and Z bosons]]) would then be predicted to be massless, when, in reality, they are observed to have mass. To overcome this, spontaneous symmetry breaking is augmented by the [[Higgs mechanism]] to give these particles mass. It also suggests the presence of a new particle, the [[Higgs boson]], detected in 2012.<br />
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[[Superconductivity]] of metals is a condensed-matter analog of the Higgs phenomena, in which a condensate of Cooper pairs of electrons spontaneously breaks the U(1) gauge symmetry associated with light and electromagnetism.<br />
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===Condensed matter physics===<br />
Most phases of matter can be understood through the lens of spontaneous symmetry breaking. For example, crystals are periodic arrays of atoms that are not invariant under all translations (only under a small subset of translations by a lattice vector). Magnets have north and south poles that are oriented in a specific direction, breaking [[rotational symmetry]]. In addition to these examples, there are a whole host of other symmetry-breaking phases of matter — including nematic phases of liquid crystals, charge- and spin-density waves, superfluids, and many others.<br />
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There are several known examples of matter that cannot be described by spontaneous symmetry breaking, including: topologically ordered phases of matter, such as [[Fractional quantum Hall effect|fractional quantum Hall liquids]], and [[Quantum spin liquid|spin-liquids]]. These states do not break any symmetry, but are distinct phases of matter. Unlike the case of spontaneous symmetry breaking, there is not a general framework for describing such states.<ref name=chen>{{cite journal | last1 = Chen | first1 = Xie | author-link3 = Xiao-Gang Wen | last2 = Gu | first2 = Zheng-Cheng | last3 = Wen | first3 = Xiao-Gang | year = 2010 | title = Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order | journal = Phys. Rev. B | volume = 82 | issue = 15| page = 155138 | doi=10.1103/physrevb.82.155138|arxiv = 1004.3835 |bibcode = 2010PhRvB..82o5138C | s2cid = 14593420 }}</ref><br />
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====Continuous symmetry====<br />
The ferromagnet is the canonical system that spontaneously breaks the continuous symmetry of the spins below the [[Curie temperature]] and at {{nowrap|1=''h'' = 0}}, where ''h'' is the external magnetic field. Below the [[Curie temperature]], the energy of the system is invariant under inversion of the magnetization ''m''('''x''') such that {{nowrap|1=''m''('''x''') = −''m''(−'''x''')}}. The symmetry is spontaneously broken as {{nowrap|''h'' → 0}} when the Hamiltonian becomes invariant under the inversion transformation, but the expectation value is not invariant.<br />
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Spontaneously-symmetry-broken phases of matter are characterized by an order parameter that describes the quantity which breaks the symmetry under consideration. For example, in a magnet, the order parameter is the local magnetization.<br />
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Spontaneous breaking of a continuous symmetry is inevitably accompanied by gapless (meaning that these modes do not cost any energy to excite) Nambu–Goldstone modes associated with slow, long-wavelength fluctuations of the order parameter. For example, vibrational modes in a crystal, known as phonons, are associated with slow density fluctuations of the crystal's atoms. The associated Goldstone mode for magnets are oscillating waves of spin known as spin-waves. For symmetry-breaking states, whose order parameter is not a conserved quantity, Nambu–Goldstone modes are typically massless and propagate at a constant velocity.<br />
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An important theorem, due to Mermin and Wagner, states that, at finite temperature, thermally activated fluctuations of Nambu–Goldstone modes destroy the long-range order, and prevent spontaneous symmetry breaking in one- and two-dimensional systems. Similarly, quantum fluctuations of the order parameter prevent most types of continuous symmetry breaking in one-dimensional systems even at zero temperature. (An important exception is ferromagnets, whose order parameter, magnetization, is an exactly conserved quantity and does not have any quantum fluctuations.)<br />
<br />
Other long-range interacting systems, such as cylindrical curved surfaces interacting via the [[Coulomb potential]] or [[Yukawa potential]], have been shown to break translational and rotational symmetries.<ref><br />
{{cite journal<br />
|last1=Kohlstedt |first1=K.L.<br />
|last2=Vernizzi |first2=G.<br />
|last3=Solis |first3=F.J.<br />
|last4=Olvera de la Cruz |first4=M.<br />
|year=2007<br />
|title=Spontaneous Chirality via Long-range Electrostatic Forces<br />
|journal=[[Physical Review Letters]]<br />
|volume=99 |issue=3<br />
|page=030602<br />
|doi=10.1103/PhysRevLett.99.030602<br />
|arxiv = 0704.3435 |bibcode = 2007PhRvL..99c0602K |pmid=17678276|s2cid=37983980<br />
}}</ref> It was shown, in the presence of a symmetric Hamiltonian, and in the limit of infinite volume, the system spontaneously adopts a chiral configuration — i.e., breaks [[mirror plane]] [[symmetry]].<br />
<br />
===Dynamical symmetry breaking===<br />
Dynamical symmetry breaking (DSB) is a special form of spontaneous symmetry breaking in which the ground state of the system has reduced symmetry properties compared to its theoretical description (i.e., [[Lagrangian (field theory)|Lagrangian]]).<br />
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Dynamical breaking of a global symmetry is a spontaneous symmetry breaking, which happens not at the (classical) tree level (i.e., at the level of the bare action), but due to quantum corrections (i.e., at the level of the [[effective action]]).<br />
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Dynamical breaking of a gauge symmetry {{ref|note1}} is subtler. In the conventional spontaneous gauge symmetry breaking, there exists an unstable [[Higgs particle]] in the theory, which drives the vacuum to a symmetry-broken phase. (See, for example, [[electroweak interaction]].) In dynamical gauge symmetry breaking, however, no unstable Higgs particle operates in the theory, but the bound states of the system itself provide the unstable fields that render the phase transition. For example, Bardeen, Hill, and Lindner published a paper that attempts to replace the conventional [[Higgs mechanism]] in the [[standard model]] by a DSB that is driven by a bound state of top-antitop quarks. (Such models, in which a composite particle plays the role of the Higgs boson, are often referred to as "Composite Higgs models".)<ref><br />
{{cite journal<br />
|author1=William A. Bardeen<br />
|author2-link=Christopher T. Hill<br />
|author2=Christopher T. Hill<br />
|author3-link=Manfred Lindner<br />
|author3=Manfred Lindner<br />
|year=1990<br />
|title=Minimal dynamical symmetry breaking of the standard model<br />
|journal=[[Physical Review D]]<br />
|volume=41 |issue=5 |pages=1647–1660<br />
|bibcode=1990PhRvD..41.1647B<br />
|doi=10.1103/PhysRevD.41.1647<br />
|pmid=10012522<br />
|author1-link=William A. Bardeen<br />
}}</ref> Dynamical breaking of gauge symmetries is often due to creation of a [[fermionic condensate]] — e.g., the [[quark condensate]], which is connected to the [[Chiral symmetry breaking|dynamical breaking of chiral symmetry]] in [[quantum chromodynamics]]. Conventional [[superconductivity]] is the paradigmatic example from the condensed matter side, where phonon-mediated attractions lead electrons to become bound in pairs and then condense, thereby breaking the electromagnetic gauge symmetry.<br />
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==Generalisation and technical usage==<br />
For spontaneous symmetry breaking to occur, there must be a system in which there are several equally likely outcomes. The system as a whole is therefore [[Symmetry (physics)|symmetric]] with respect to these outcomes. However, if the system is sampled (i.e. if the system is actually used or interacted with in any way), a specific outcome must occur. Though the system as a whole is symmetric, it is never encountered with this symmetry, but only in one specific asymmetric state. Hence, the symmetry is said to be spontaneously broken in that theory. Nevertheless, the fact that each outcome is equally likely is a reflection of the underlying symmetry, which is thus often dubbed "hidden symmetry", and has crucial formal consequences. (See the article on the [[Nambu–Goldstone boson|Goldstone boson]].)<br />
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When a theory is symmetric with respect to a [[symmetry group]], but requires that one element of the group be distinct, then spontaneous symmetry breaking has occurred. The theory must not dictate ''which'' member is distinct, only that ''one is''. From this point on, the theory can be treated as if this element actually is distinct, with the proviso that any results found in this way must be resymmetrized, by taking the average of each of the elements of the group being the distinct one.<br />
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The crucial concept in physics theories is the [[order parameter]]. If there is a field (often a background field) which acquires an expectation value (not necessarily a [[vacuum expectation value|''vacuum'' expectation value]]) which is not invariant under the symmetry in question, we say that the system is in the [[ordered phase]], and the symmetry is spontaneously broken. This is because other subsystems interact with the order parameter, which specifies a "frame of reference" to be measured against. In that case, the [[vacuum state]] does not obey the initial symmetry (which would keep it invariant, in the linearly realized '''Wigner mode''' in which it would be a singlet), and, instead changes under the (hidden) symmetry, now implemented in the (nonlinear) '''Nambu–Goldstone mode'''. Normally, in the absence of the Higgs mechanism, massless [[Goldstone boson]]s arise.<br />
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The symmetry group can be discrete, such as the [[space group]] of a crystal, or continuous (e.g., a [[Lie group]]), such as the rotational symmetry of space. However, if the system contains only a single spatial dimension, then only discrete symmetries may be broken in a [[vacuum state]] of the full [[Quantum mechanics|quantum theory]], although a classical solution may break a continuous symmetry.<br />
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==Nobel Prize==<br />
On October 7, 2008, the [[Royal Swedish Academy of Sciences]] awarded the 2008 [[Nobel Prize in Physics]] to three scientists for their work in subatomic physics symmetry breaking. [[Yoichiro Nambu]], of the [[University of Chicago]], won half of the prize for the discovery of the mechanism of spontaneous broken symmetry in the context of the strong interactions, specifically [[chiral symmetry breaking]]. Physicists [[Makoto Kobayashi (physicist)|Makoto Kobayashi]] and [[Toshihide Maskawa]], of [[Kyoto University]], shared the other half of the prize for discovering the origin of the [[Explicit symmetry breaking|explicit breaking]] of CP symmetry in the weak interactions.<ref>{{cite web|author=The Nobel Foundation|title=The Nobel Prize in Physics 2008|url=http://nobelprize.org/nobel_prizes/physics/laureates/2008/index.html|work=nobelprize.org|access-date=January 15, 2008}}</ref> This origin is ultimately reliant on the Higgs mechanism, but, so far understood as a "just so" feature of Higgs couplings, not a spontaneously broken symmetry phenomenon.<br />
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==See also==<br />
{{div col|colwidth=24em}}<br />
* [[Autocatalytic reactions and order creation]]<br />
* [[Catastrophe theory]]<br />
* [[Chiral symmetry breaking]]<br />
* [[CP-violation]]<br />
* [[Fermi ball]]<br />
* [[Gauge gravitation theory]]<br />
* [[Goldstone boson]]<br />
* [[Grand unified theory]]<br />
* [[Higgs mechanism]]<br />
* [[Higgs boson]]<br />
* [[Higgs field (classical)]]<br />
* [[Irreversibility]]<br />
* [[Magnetic catalysis]] of chiral symmetry breaking<br />
* [[Mermin–Wagner theorem]]<br />
* [[Norton's dome]]<br />
* [[Second-order phase transition]]<br />
* [[Spontaneous absolute asymmetric synthesis]] in chemistry<br />
* [[Symmetry breaking]]<br />
* [[Tachyon condensation]]<br />
* [[1964 PRL symmetry breaking papers]]<br />
{{div col end}}<br />
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==Notes==<br />
* {{note|note1}} Note that (as in fundamental Higgs driven spontaneous gauge symmetry breaking) the term "symmetry breaking" is a misnomer when applied to gauge symmetries.<br />
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==References==<br />
{{Reflist}}<br />
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==External links==<br />
{{wikiquote}}<br />
* For a pedagogic introduction to electroweak symmetry breaking with step by step derivations, not found in texts, of many key relations, see http://www.quantumfieldtheory.info/Electroweak_Sym_breaking.pdf<br />
* [http://hyperphysics.phy-astr.gsu.edu/hbase/forces/unify.html#c2 Spontaneous symmetry breaking]<br />
* [http://prl.aps.org/50years/milestones#1964 Physical Review Letters – 50th Anniversary Milestone Papers]<br />
* [http://cerncourier.com/cws/article/cern/32522 In CERN Courier, Steven Weinberg reflects on spontaneous symmetry breaking]<br />
* [http://www.scholarpedia.org/article/Englert-Brout-Higgs-Guralnik-Hagen-Kibble_mechanism Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism on Scholarpedia]<br />
* [http://www.scholarpedia.org/article/Englert-Brout-Higgs-Guralnik-Hagen-Kibble_mechanism_%28history%29 History of Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism on Scholarpedia]<br />
* [https://arxiv.org/abs/0907.3466 The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles]<br />
* [http://www.worldscinet.com/ijmpa/24/2414/S0217751X09045431.html International Journal of Modern Physics A: The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles]<br />
* [http://www.datafilehost.com/download-7d512618.html Guralnik, G S; Hagen, C R and Kibble, T W B (1967). Broken Symmetries and the Goldstone Theorem. Advances in Physics, vol. 2 Interscience Publishers, New York. pp. 567–708] {{ISBN|0-470-17057-3}}<br />
* [http://lanl.arxiv.org/abs/hep-th/9802142 Spontaneous Symmetry Breaking in Gauge Theories: a Historical Survey]<br />
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{{Standard model of physics}}<br />
{{Quantum mechanics topics}}<br />
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{{DEFAULTSORT:Spontaneous Symmetry Breaking}}<br />
[[Category:Theoretical physics]]<br />
[[Category:Quantum field theory]]<br />
[[Category:Standard Model]]<br />
[[Category:Quantum chromodynamics]]<br />
[[Category:Symmetry]]<br />
[[Category:Quantum phases]]<br />
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==实例==<br />
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对称性破缺可以涵盖以下任何一种情况:<ref>{{cite web|url=http://www.angelfire.com/stars5/astroinfo/gloss/s.html|title=Astronomical Glossary|author=|date=|website=www.angelfire.com}}</ref><br />
* 某些结构的随机形成破坏了物理学基本定律的精确对称性;<br />
* 物理学中最小能量状态的对称性比系统本身少的情形;<br />
* 系统的实际状态由于明显对称的状态不稳定而不能反映动力学的基本对称性的情况(稳定性是以局部不对称为代价的);<br />
* 理论方程具有某种对称性,但其解可能没有(对称性是“隐藏的”)的情况。<br />
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在物理学文献中讨论的首批对称性破缺案例之一,与不可压缩流体在重力和流体静力平衡中均匀旋转的形式有关。在1834年,Jacobi <ref>{{cite journal| last=Jacobi | first=C.G.J. | title=Über die figur des gleichgewichts | journal=[[Annalen der Physik und Chemie]] | volume=109 | issue=33| pages=229–238 | year=1834| doi=10.1002/andp.18341090808 | bibcode=1834AnP...109..229J | url=https://zenodo.org/record/2027349 }}</ref>和后来的 Liouville <ref>{{cite journal| last=Liouville | first=J. | title=Sur la figure d'une masse fluide homogène, en équilibre et douée d'un mouvement de rotation| journal=Journal de l'École Polytechnique | issue=14| pages=289–296 | year=1834}}</ref>讨论了这样一个事实: 当旋转物体的动能相对于引力势能超过一定的临界值时,这个问题的平衡解是三轴椭球。在这个分叉点上,麦克劳林椭球体的轴对称性被破坏。此外,在这个分叉点之上,对于常数角动量,使动能最小化的解是非轴对称的 Jacobi 椭球,而不是 Maclaurin 椭球。<br />
==另请参阅==<br />
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*[[Higgs mechanism]]<br />
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*[[QCD vacuum]]<br />
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*[[Goldstone boson]]<br />
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*[[1964 PRL symmetry breaking papers]]<br />
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*[[希格斯机制]]<br />
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*[[QCD真空]]<br />
<br />
*[[戈德斯通玻色子]]<br />
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*[[1964年PRL对称性破缺论文]]<br />
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==参考文献==<br />
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{{reflist|colwidth=30em}}<br />
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{{DEFAULTSORT:Symmetry Breaking}}<br />
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范畴: 对称<br />
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类别: 模式形成<br />
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本中文词条由XXX编译,XXX审校,XXX总审校,西瓜编辑,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''<br />
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[[Category:对称性破缺]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%AF%B9%E7%A7%B0%E6%80%A7%E7%A0%B4%E7%BC%BA&diff=24656对称性破缺2021-07-25T09:31:03Z<p>Jxzhou:</p>
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[[图一:一个小球位于中央山丘的山峰处(C)。这是一种不稳定平衡:一个很小的扰动会使它落到左边(L)或右边(R)稳定点。尽管山丘是对称的,没有理由让球落在哪一侧,但观察到的最终状态仍然是不对称的,它总会落到某一侧]]。<br />
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在物理学中,一个作用于系统的(无限)小扰动使系统跨过临界点,通过决定去向分叉的哪个分支来决定系统的命运,这种现象叫做'''<font color="#ff8000">对称性破缺</font>'''。对于一个观测不到扰动(或“噪声”)的外部观察者来说,这个选择看起来是任意的。这个过程被称为对称性破缺,因为这种转变通常使系统从一个对称但无序的状态进入一个或多个确定的状态。在'''<font color="#ff8000">斑图生成</font>'''中对称性破缺起着重要作用。<br />
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1972年,诺贝尔奖得主P·W·安德森(P.W.Anderson)在《科学》(Science)杂志上发表了一篇名为《多即不同》的论文<ref>{{cite journal | last=Anderson | first=P.W. | title=More is Different | journal=Science | volume=177 | issue=4047| pages=393–396 | year=1972 | url=http://robotics.cs.tamu.edu/dshell/cs689/papers/anderson72more_is_different.pdf | doi=10.1126/science.177.4047.393 | pmid=17796623 | format=|bibcode = 1972Sci...177..393A }}</ref>,文中使用对称性破缺的思想表明,即使'''<font color="#ff8000">还原论</font>'''是正确的,但它的逆命题'''<font color="#ff8000">建构主义</font>'''是错误的。建构主义认为,在给出描述各组成部分的理论的情况下科学家可以轻易地预测复杂现象。<br />
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对称性破缺可以分为'''<font color="#ff8000">显性对称性破缺</font>'''和'''<font color="#ff8000">自发对称性破缺</font>'''两种类型,二者的区别是,在破缺对称性下系统的运动方程是否不变或者基态是否保持不变。<br />
==显性对称性破缺==<br />
<br />
在'''<font color="#ff8000">显性对称性破缺</font>'''中,描述系统的运动方程在破缺对称下是不同的。在哈密顿力学或拉格朗日力学中,假若系统的哈密顿量(或拉格朗日量)中至少一项显性地打破了给定的对称性,就发生了显性对称性破缺。<br />
==自发对称性破缺==<br />
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在'''<font color="#ff8000">自发对称性破缺</font>'''中,系统的运动方程是不变的,但系统发生了变化。这是因为系统的背景(时空)——真空态——是非恒定的。这种对称性破缺可以用一个序参量进行参数化。这类对称破缺的一个特殊情况是'''<font color="#ff8000">动力学对称性破缺</font>'''。<br />
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Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state ends up in an asymmetric state.[1][2][3] In particular, it can describe systems where the equations of motion or the Lagrangian obey symmetries, but the lowest-energy vacuum solutions do not exhibit that same symmetry. When the system goes to one of those vacuum solutions, the symmetry is broken for perturbations around that vacuum even though the entire Lagrangian retains that symmetry.<br />
自发对称破缺是一个自发的对称破缺过程,它使处于对称状态的物理系统最终处于非对称状态。特别地,它可以描述运动方程或拉格朗日方程服从对称性的系统,但最低能量真空解不具有同样的对称性。当系统进入其中一个真空解时,由于真空周围的扰动对称性被打破了尽管整个拉格朗日方程保持了对称性。<br />
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==Overview==<br />
<br />
In [[explicit symmetry breaking]], if two outcomes are considered, the probability of a pair of outcomes can be different. By definition, spontaneous symmetry breaking requires the existence of a symmetric probability distribution—any pair of outcomes has the same probability. In other words, the underlying laws{{clarify|date=December 2016}} are [[Invariant (physics)|invariant]] under a [[Symmetry (physics)|symmetry]] transformation.<br />
<br />
The system, as a whole{{clarify|date=December 2016}}, changes under such transformations.<br />
<br />
Phases of matter, such as crystals, magnets, and conventional superconductors, as well as simple phase transitions can be described by spontaneous symmetry breaking. Notable exceptions include topological phases of matter like the [[fractional quantum Hall effect]].<br />
<br />
==Examples==<br />
<br />
===Sombrero potential===<br />
Consider a symmetric upward dome with a trough circling the bottom. If a ball is put at the very peak of the dome, the system is symmetric with respect to a rotation around the center axis. But the ball may ''spontaneously break'' this symmetry by rolling down the dome into the trough, a point of lowest energy. Afterward, the ball has come to a rest at some fixed point on the perimeter. The dome and the ball retain their individual symmetry, but the system does not.<ref>{{cite book |first=Gerald M. |last=Edelman |title=Bright Air, Brilliant Fire: On the Matter of the Mind |location=New York |publisher=BasicBooks |year=1992 |url=https://archive.org/details/brightairbrillia00gera |url-access=registration |page=[https://archive.org/details/brightairbrillia00gera/page/203 203] }}</ref><br />
[[Image:Mexican hat potential polar.svg|270px|thumb|left|Graph of Goldstone's "[[Sombrero|sombrero]]" potential function <math>V(\phi)</math>.]]<br />
<br />
In the simplest idealized relativistic model, the spontaneously broken symmetry is summarized through an illustrative [[scalar field theory]]. The relevant [[Lagrangian (field theory)|Lagrangian]] of a scalar field <math>\phi</math>, which essentially dictates how a system behaves, can be split up into kinetic and potential terms,<br />
{{NumBlk|::|<math>\mathcal{L} = \partial^\mu \phi \partial_\mu \phi - V(\phi).</math>|{{EquationRef|1}}}}<br />
<br />
It is in this potential term <math>V(\phi)</math> that the symmetry breaking is triggered. An example of a potential, due to [[Jeffrey Goldstone]]<ref>{{Cite journal | last1 = Goldstone | first1 = J. | doi = 10.1007/BF02812722 | title = Field theories with " Superconductor " solutions | journal = Il Nuovo Cimento | volume = 19 | issue = 1 | pages = 154–164 | year = 1961 | bibcode = 1961NCim...19..154G | s2cid = 120409034 | url = http://cds.cern.ch/record/343400 }}</ref> is illustrated in the graph at the left.<br />
{{NumBlk|::|<math>V(\phi) = -5|\phi|^2 + |\phi|^4 \,</math>.|{{EquationRef|2}}}}<br />
<br />
This potential has an infinite number of possible [[minimum|minima]] (vacuum states) given by<br />
{{NumBlk|::|<math>\phi = \sqrt{5} e^{i\theta} </math>.|{{EquationRef|3}}}}<br />
for any real ''θ'' between 0 and 2''π''. The system also has an unstable vacuum state corresponding to {{nowrap|1=''Φ'' = 0}}. This state has a [[Unitary group|U(1)]] symmetry. However, once the system falls into a specific stable vacuum state (amounting to a choice of ''θ''), this symmetry will appear to be lost, or "spontaneously broken".<br />
<br />
In fact, any other choice of ''θ'' would have exactly the same energy, implying the existence of a massless [[Goldstone boson|Nambu–Goldstone boson]], the mode running around the circle at the minimum of this potential, and indicating there is some memory of the original symmetry in the Lagrangian.<br />
<br />
===Other examples===<br />
* For [[ferromagnet]]ic materials, the underlying laws are invariant under spatial rotations. Here, the order parameter is the [[magnetization]], which measures the magnetic dipole density. Above the [[Curie temperature]], the order parameter is zero, which is spatially invariant, and there is no symmetry breaking. Below the Curie temperature, however, the magnetization acquires a constant nonvanishing value, which points in a certain direction (in the idealized situation where we have full equilibrium; otherwise, translational symmetry gets broken as well). The residual rotational symmetries which leave the orientation of this vector invariant remain unbroken, unlike the other rotations which do not and are thus spontaneously broken.<br />
* The laws describing a solid are invariant under the full [[Euclidean group]], but the solid itself spontaneously breaks this group down to a [[space group]]. The displacement and the orientation are the order parameters.<br />
* General relativity has a Lorentz symmetry, but in [[Friedmann–Lemaître–Robertson–Walker metric|FRW cosmological models]], the mean 4-velocity field defined by averaging over the velocities of the galaxies (the galaxies act like gas particles at cosmological scales) acts as an order parameter breaking this symmetry. Similar comments can be made about the cosmic microwave background.<br />
* For the [[electroweak]] model, as explained earlier, a component of the Higgs field provides the order parameter breaking the electroweak gauge symmetry to the electromagnetic gauge symmetry. Like the ferromagnetic example, there is a phase transition at the electroweak temperature. The same comment about us not tending to notice broken symmetries suggests why it took so long for us to discover electroweak unification.<br />
* In superconductors, there is a condensed-matter collective field ψ, which acts as the order parameter breaking the electromagnetic gauge symmetry.<br />
* Take a thin cylindrical plastic rod and push both ends together. Before buckling, the system is symmetric under rotation, and so visibly cylindrically symmetric. But after buckling, it looks different, and asymmetric. Nevertheless, features of the cylindrical symmetry are still there: ignoring friction, it would take no force to freely spin the rod around, displacing the ground state in time, and amounting to an oscillation of vanishing frequency, unlike the radial oscillations in the direction of the buckle. This spinning mode is effectively the requisite [[Goldstone boson|Nambu–Goldstone boson]].<br />
* Consider a uniform layer of [[fluid]] over an infinite horizontal plane. This system has all the symmetries of the Euclidean plane. But now heat the bottom surface uniformly so that it becomes much hotter than the upper surface. When the temperature gradient becomes large enough, [[convection cell]]s will form, breaking the Euclidean symmetry.<br />
* Consider a bead on a circular hoop that is rotated about a vertical [[diameter]]. As the [[rotational velocity]] is increased gradually from rest, the bead will initially stay at its initial [[equilibrium point]] at the bottom of the hoop (intuitively stable, lowest [[gravitational potential]]). At a certain critical rotational velocity, this point will become unstable and the bead will jump to one of two other newly created equilibria, [[equidistant]] from the center. Initially, the system is symmetric with respect to the diameter, yet after passing the critical velocity, the bead ends up in one of the two new equilibrium points, thus breaking the symmetry.<br />
<br />
==Spontaneous symmetry breaking in physics==<br />
[[File:Spontaneous symmetry breaking (explanatory diagram).png|thumb|right|250px|''Spontaneous symmetry breaking illustrated'': At high energy levels (''left''), the ball settles in the center, and the result is symmetric. At lower energy levels (''right''), the overall "rules" remain symmetric, but the symmetric "[[sombrero|Sombrero]]" enforces an asymmetric outcome, since eventually the ball must rest at some random spot on the bottom, "spontaneously", and not all others.]]<br />
<br />
===Particle physics===<br />
In [[particle physics]], the [[force carrier]] particles are normally specified by field equations with [[gauge symmetry]]; their equations predict that certain measurements will be the same at any point in the field. For instance, field equations might predict that the mass of two quarks is constant. Solving the equations to find the mass of each quark might give two solutions. In one solution, quark A is heavier than quark B. In the second solution, quark B is heavier than quark A ''by the same amount''. The symmetry of the equations is not reflected by the individual solutions, but it is reflected by the range of solutions.<br />
<br />
An actual measurement reflects only one solution, representing a breakdown in the symmetry of the underlying theory. "Hidden" is a better term than "broken", because the symmetry is always there in these equations. This phenomenon is called [[Spontaneous magnetization|''spontaneous'']] symmetry breaking (SSB) because ''nothing'' (that we know of) breaks the symmetry in the equations.<ref name="Weinberg2011">{{cite book|author=Steven Weinberg|title=Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature|url=https://books.google.com/books?id=Rsg3PE_9_ccC|date=20 April 2011|publisher=Knopf Doubleday Publishing Group|isbn=978-0-307-78786-6}}</ref>{{rp|194–195}}<br />
<br />
====Chiral symmetry====<br />
{{Main article|Chiral symmetry breaking}}<br />
Chiral symmetry breaking is an example of spontaneous symmetry breaking affecting the [[chiral symmetry]] of the [[strong interactions]] in particle physics. It is a property of [[quantum chromodynamics]], the [[quantum field theory]] describing these interactions, and is responsible for the bulk of the mass (over 99%) of the [[nucleons]], and thus of all common matter, as it converts very light bound [[quarks]] into 100 times heavier constituents of [[baryons]]. The approximate [[Nambu–Goldstone boson]]s in this spontaneous symmetry breaking process are the [[pions]], whose mass is an order of magnitude lighter than the mass of the nucleons. It served as the prototype and significant ingredient of the Higgs mechanism underlying the electroweak symmetry breaking.<br />
<br />
====Higgs mechanism====<br />
{{Main article|Higgs mechanism|Yukawa interaction}}<br />
<br />
The strong, weak, and electromagnetic forces can all be understood as arising from [[gauge symmetry|gauge symmetries]]. The [[Higgs mechanism]], the spontaneous symmetry breaking of gauge symmetries, is an important component in understanding the [[superconductivity]] of metals and the origin of particle masses in the standard model of particle physics. One important consequence of the distinction between true symmetries and ''gauge symmetries'', is that the spontaneous breaking of a gauge symmetry does not give rise to characteristic massless Nambu–Goldstone physical modes, but only massive modes, like the plasma mode in a superconductor, or the Higgs mode observed in particle physics.<br />
<br />
In the standard model of particle physics, spontaneous symmetry breaking of the {{nowrap|SU(2) × U(1)}} gauge symmetry associated with the electro-weak force generates masses for several particles, and separates the electromagnetic and weak forces. The [[W and Z bosons]] are the elementary particles that mediate the [[weak interaction]], while the [[photon]] mediates the [[electromagnetic interaction]]. At energies much greater than 100 GeV, all these particles behave in a similar manner. The [[Unified field theory#Modern progress|Weinberg–Salam theory]] predicts that, at lower energies, this symmetry is broken so that the photon and the massive W and Z bosons emerge.<ref>A Brief History of Time, Stephen Hawking, Bantam; 10th anniversary edition (1998). pp. 73–74.{{ISBN?}}</ref> In addition, fermions develop mass consistently.<br />
<br />
Without spontaneous symmetry breaking, the [[Standard Model]] of elementary particle interactions requires the existence of a number of particles. However, some particles (the [[W and Z bosons]]) would then be predicted to be massless, when, in reality, they are observed to have mass. To overcome this, spontaneous symmetry breaking is augmented by the [[Higgs mechanism]] to give these particles mass. It also suggests the presence of a new particle, the [[Higgs boson]], detected in 2012.<br />
<br />
[[Superconductivity]] of metals is a condensed-matter analog of the Higgs phenomena, in which a condensate of Cooper pairs of electrons spontaneously breaks the U(1) gauge symmetry associated with light and electromagnetism.<br />
<br />
===Condensed matter physics===<br />
Most phases of matter can be understood through the lens of spontaneous symmetry breaking. For example, crystals are periodic arrays of atoms that are not invariant under all translations (only under a small subset of translations by a lattice vector). Magnets have north and south poles that are oriented in a specific direction, breaking [[rotational symmetry]]. In addition to these examples, there are a whole host of other symmetry-breaking phases of matter — including nematic phases of liquid crystals, charge- and spin-density waves, superfluids, and many others.<br />
<br />
There are several known examples of matter that cannot be described by spontaneous symmetry breaking, including: topologically ordered phases of matter, such as [[Fractional quantum Hall effect|fractional quantum Hall liquids]], and [[Quantum spin liquid|spin-liquids]]. These states do not break any symmetry, but are distinct phases of matter. Unlike the case of spontaneous symmetry breaking, there is not a general framework for describing such states.<ref name=chen>{{cite journal | last1 = Chen | first1 = Xie | author-link3 = Xiao-Gang Wen | last2 = Gu | first2 = Zheng-Cheng | last3 = Wen | first3 = Xiao-Gang | year = 2010 | title = Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order | journal = Phys. Rev. B | volume = 82 | issue = 15| page = 155138 | doi=10.1103/physrevb.82.155138|arxiv = 1004.3835 |bibcode = 2010PhRvB..82o5138C | s2cid = 14593420 }}</ref><br />
<br />
====Continuous symmetry====<br />
The ferromagnet is the canonical system that spontaneously breaks the continuous symmetry of the spins below the [[Curie temperature]] and at {{nowrap|1=''h'' = 0}}, where ''h'' is the external magnetic field. Below the [[Curie temperature]], the energy of the system is invariant under inversion of the magnetization ''m''('''x''') such that {{nowrap|1=''m''('''x''') = −''m''(−'''x''')}}. The symmetry is spontaneously broken as {{nowrap|''h'' → 0}} when the Hamiltonian becomes invariant under the inversion transformation, but the expectation value is not invariant.<br />
<br />
Spontaneously-symmetry-broken phases of matter are characterized by an order parameter that describes the quantity which breaks the symmetry under consideration. For example, in a magnet, the order parameter is the local magnetization.<br />
<br />
Spontaneous breaking of a continuous symmetry is inevitably accompanied by gapless (meaning that these modes do not cost any energy to excite) Nambu–Goldstone modes associated with slow, long-wavelength fluctuations of the order parameter. For example, vibrational modes in a crystal, known as phonons, are associated with slow density fluctuations of the crystal's atoms. The associated Goldstone mode for magnets are oscillating waves of spin known as spin-waves. For symmetry-breaking states, whose order parameter is not a conserved quantity, Nambu–Goldstone modes are typically massless and propagate at a constant velocity.<br />
<br />
An important theorem, due to Mermin and Wagner, states that, at finite temperature, thermally activated fluctuations of Nambu–Goldstone modes destroy the long-range order, and prevent spontaneous symmetry breaking in one- and two-dimensional systems. Similarly, quantum fluctuations of the order parameter prevent most types of continuous symmetry breaking in one-dimensional systems even at zero temperature. (An important exception is ferromagnets, whose order parameter, magnetization, is an exactly conserved quantity and does not have any quantum fluctuations.)<br />
<br />
Other long-range interacting systems, such as cylindrical curved surfaces interacting via the [[Coulomb potential]] or [[Yukawa potential]], have been shown to break translational and rotational symmetries.<ref><br />
{{cite journal<br />
|last1=Kohlstedt |first1=K.L.<br />
|last2=Vernizzi |first2=G.<br />
|last3=Solis |first3=F.J.<br />
|last4=Olvera de la Cruz |first4=M.<br />
|year=2007<br />
|title=Spontaneous Chirality via Long-range Electrostatic Forces<br />
|journal=[[Physical Review Letters]]<br />
|volume=99 |issue=3<br />
|page=030602<br />
|doi=10.1103/PhysRevLett.99.030602<br />
|arxiv = 0704.3435 |bibcode = 2007PhRvL..99c0602K |pmid=17678276|s2cid=37983980<br />
}}</ref> It was shown, in the presence of a symmetric Hamiltonian, and in the limit of infinite volume, the system spontaneously adopts a chiral configuration — i.e., breaks [[mirror plane]] [[symmetry]].<br />
<br />
===Dynamical symmetry breaking===<br />
Dynamical symmetry breaking (DSB) is a special form of spontaneous symmetry breaking in which the ground state of the system has reduced symmetry properties compared to its theoretical description (i.e., [[Lagrangian (field theory)|Lagrangian]]).<br />
<br />
Dynamical breaking of a global symmetry is a spontaneous symmetry breaking, which happens not at the (classical) tree level (i.e., at the level of the bare action), but due to quantum corrections (i.e., at the level of the [[effective action]]).<br />
<br />
Dynamical breaking of a gauge symmetry {{ref|note1}} is subtler. In the conventional spontaneous gauge symmetry breaking, there exists an unstable [[Higgs particle]] in the theory, which drives the vacuum to a symmetry-broken phase. (See, for example, [[electroweak interaction]].) In dynamical gauge symmetry breaking, however, no unstable Higgs particle operates in the theory, but the bound states of the system itself provide the unstable fields that render the phase transition. For example, Bardeen, Hill, and Lindner published a paper that attempts to replace the conventional [[Higgs mechanism]] in the [[standard model]] by a DSB that is driven by a bound state of top-antitop quarks. (Such models, in which a composite particle plays the role of the Higgs boson, are often referred to as "Composite Higgs models".)<ref><br />
{{cite journal<br />
|author1=William A. Bardeen<br />
|author2-link=Christopher T. Hill<br />
|author2=Christopher T. Hill<br />
|author3-link=Manfred Lindner<br />
|author3=Manfred Lindner<br />
|year=1990<br />
|title=Minimal dynamical symmetry breaking of the standard model<br />
|journal=[[Physical Review D]]<br />
|volume=41 |issue=5 |pages=1647–1660<br />
|bibcode=1990PhRvD..41.1647B<br />
|doi=10.1103/PhysRevD.41.1647<br />
|pmid=10012522<br />
|author1-link=William A. Bardeen<br />
}}</ref> Dynamical breaking of gauge symmetries is often due to creation of a [[fermionic condensate]] — e.g., the [[quark condensate]], which is connected to the [[Chiral symmetry breaking|dynamical breaking of chiral symmetry]] in [[quantum chromodynamics]]. Conventional [[superconductivity]] is the paradigmatic example from the condensed matter side, where phonon-mediated attractions lead electrons to become bound in pairs and then condense, thereby breaking the electromagnetic gauge symmetry.<br />
<br />
==Generalisation and technical usage==<br />
For spontaneous symmetry breaking to occur, there must be a system in which there are several equally likely outcomes. The system as a whole is therefore [[Symmetry (physics)|symmetric]] with respect to these outcomes. However, if the system is sampled (i.e. if the system is actually used or interacted with in any way), a specific outcome must occur. Though the system as a whole is symmetric, it is never encountered with this symmetry, but only in one specific asymmetric state. Hence, the symmetry is said to be spontaneously broken in that theory. Nevertheless, the fact that each outcome is equally likely is a reflection of the underlying symmetry, which is thus often dubbed "hidden symmetry", and has crucial formal consequences. (See the article on the [[Nambu–Goldstone boson|Goldstone boson]].)<br />
<br />
When a theory is symmetric with respect to a [[symmetry group]], but requires that one element of the group be distinct, then spontaneous symmetry breaking has occurred. The theory must not dictate ''which'' member is distinct, only that ''one is''. From this point on, the theory can be treated as if this element actually is distinct, with the proviso that any results found in this way must be resymmetrized, by taking the average of each of the elements of the group being the distinct one.<br />
<br />
The crucial concept in physics theories is the [[order parameter]]. If there is a field (often a background field) which acquires an expectation value (not necessarily a [[vacuum expectation value|''vacuum'' expectation value]]) which is not invariant under the symmetry in question, we say that the system is in the [[ordered phase]], and the symmetry is spontaneously broken. This is because other subsystems interact with the order parameter, which specifies a "frame of reference" to be measured against. In that case, the [[vacuum state]] does not obey the initial symmetry (which would keep it invariant, in the linearly realized '''Wigner mode''' in which it would be a singlet), and, instead changes under the (hidden) symmetry, now implemented in the (nonlinear) '''Nambu–Goldstone mode'''. Normally, in the absence of the Higgs mechanism, massless [[Goldstone boson]]s arise.<br />
<br />
The symmetry group can be discrete, such as the [[space group]] of a crystal, or continuous (e.g., a [[Lie group]]), such as the rotational symmetry of space. However, if the system contains only a single spatial dimension, then only discrete symmetries may be broken in a [[vacuum state]] of the full [[Quantum mechanics|quantum theory]], although a classical solution may break a continuous symmetry.<br />
<br />
==Nobel Prize==<br />
On October 7, 2008, the [[Royal Swedish Academy of Sciences]] awarded the 2008 [[Nobel Prize in Physics]] to three scientists for their work in subatomic physics symmetry breaking. [[Yoichiro Nambu]], of the [[University of Chicago]], won half of the prize for the discovery of the mechanism of spontaneous broken symmetry in the context of the strong interactions, specifically [[chiral symmetry breaking]]. Physicists [[Makoto Kobayashi (physicist)|Makoto Kobayashi]] and [[Toshihide Maskawa]], of [[Kyoto University]], shared the other half of the prize for discovering the origin of the [[Explicit symmetry breaking|explicit breaking]] of CP symmetry in the weak interactions.<ref>{{cite web|author=The Nobel Foundation|title=The Nobel Prize in Physics 2008|url=http://nobelprize.org/nobel_prizes/physics/laureates/2008/index.html|work=nobelprize.org|access-date=January 15, 2008}}</ref> This origin is ultimately reliant on the Higgs mechanism, but, so far understood as a "just so" feature of Higgs couplings, not a spontaneously broken symmetry phenomenon.<br />
<br />
==See also==<br />
{{div col|colwidth=24em}}<br />
* [[Autocatalytic reactions and order creation]]<br />
* [[Catastrophe theory]]<br />
* [[Chiral symmetry breaking]]<br />
* [[CP-violation]]<br />
* [[Fermi ball]]<br />
* [[Gauge gravitation theory]]<br />
* [[Goldstone boson]]<br />
* [[Grand unified theory]]<br />
* [[Higgs mechanism]]<br />
* [[Higgs boson]]<br />
* [[Higgs field (classical)]]<br />
* [[Irreversibility]]<br />
* [[Magnetic catalysis]] of chiral symmetry breaking<br />
* [[Mermin–Wagner theorem]]<br />
* [[Norton's dome]]<br />
* [[Second-order phase transition]]<br />
* [[Spontaneous absolute asymmetric synthesis]] in chemistry<br />
* [[Symmetry breaking]]<br />
* [[Tachyon condensation]]<br />
* [[1964 PRL symmetry breaking papers]]<br />
{{div col end}}<br />
<br />
==Notes==<br />
* {{note|note1}} Note that (as in fundamental Higgs driven spontaneous gauge symmetry breaking) the term "symmetry breaking" is a misnomer when applied to gauge symmetries.<br />
<br />
==References==<br />
{{Reflist}}<br />
<br />
==External links==<br />
{{wikiquote}}<br />
* For a pedagogic introduction to electroweak symmetry breaking with step by step derivations, not found in texts, of many key relations, see http://www.quantumfieldtheory.info/Electroweak_Sym_breaking.pdf<br />
* [http://hyperphysics.phy-astr.gsu.edu/hbase/forces/unify.html#c2 Spontaneous symmetry breaking]<br />
* [http://prl.aps.org/50years/milestones#1964 Physical Review Letters – 50th Anniversary Milestone Papers]<br />
* [http://cerncourier.com/cws/article/cern/32522 In CERN Courier, Steven Weinberg reflects on spontaneous symmetry breaking]<br />
* [http://www.scholarpedia.org/article/Englert-Brout-Higgs-Guralnik-Hagen-Kibble_mechanism Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism on Scholarpedia]<br />
* [http://www.scholarpedia.org/article/Englert-Brout-Higgs-Guralnik-Hagen-Kibble_mechanism_%28history%29 History of Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism on Scholarpedia]<br />
* [https://arxiv.org/abs/0907.3466 The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles]<br />
* [http://www.worldscinet.com/ijmpa/24/2414/S0217751X09045431.html International Journal of Modern Physics A: The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles]<br />
* [http://www.datafilehost.com/download-7d512618.html Guralnik, G S; Hagen, C R and Kibble, T W B (1967). Broken Symmetries and the Goldstone Theorem. Advances in Physics, vol. 2 Interscience Publishers, New York. pp. 567–708] {{ISBN|0-470-17057-3}}<br />
* [http://lanl.arxiv.org/abs/hep-th/9802142 Spontaneous Symmetry Breaking in Gauge Theories: a Historical Survey]<br />
<br />
{{Standard model of physics}}<br />
{{Quantum mechanics topics}}<br />
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{{DEFAULTSORT:Spontaneous Symmetry Breaking}}<br />
[[Category:Theoretical physics]]<br />
[[Category:Quantum field theory]]<br />
[[Category:Standard Model]]<br />
[[Category:Quantum chromodynamics]]<br />
[[Category:Symmetry]]<br />
[[Category:Quantum phases]]<br />
<br />
==实例==<br />
<br />
对称性破缺可以涵盖以下任何一种情况:<ref>{{cite web|url=http://www.angelfire.com/stars5/astroinfo/gloss/s.html|title=Astronomical Glossary|author=|date=|website=www.angelfire.com}}</ref><br />
* 某些结构的随机形成破坏了物理学基本定律的精确对称性;<br />
* 物理学中最小能量状态的对称性比系统本身少的情形;<br />
* 系统的实际状态由于明显对称的状态不稳定而不能反映动力学的基本对称性的情况(稳定性是以局部不对称为代价的);<br />
* 理论方程具有某种对称性,但其解可能没有(对称性是“隐藏的”)的情况。<br />
<br />
<br />
在物理学文献中讨论的首批对称性破缺案例之一,与不可压缩流体在重力和流体静力平衡中均匀旋转的形式有关。在1834年,Jacobi <ref>{{cite journal| last=Jacobi | first=C.G.J. | title=Über die figur des gleichgewichts | journal=[[Annalen der Physik und Chemie]] | volume=109 | issue=33| pages=229–238 | year=1834| doi=10.1002/andp.18341090808 | bibcode=1834AnP...109..229J | url=https://zenodo.org/record/2027349 }}</ref>和后来的 Liouville <ref>{{cite journal| last=Liouville | first=J. | title=Sur la figure d'une masse fluide homogène, en équilibre et douée d'un mouvement de rotation| journal=Journal de l'École Polytechnique | issue=14| pages=289–296 | year=1834}}</ref>讨论了这样一个事实: 当旋转物体的动能相对于引力势能超过一定的临界值时,这个问题的平衡解是三轴椭球。在这个分叉点上,麦克劳林椭球体的轴对称性被破坏。此外,在这个分叉点之上,对于常数角动量,使动能最小化的解是非轴对称的 Jacobi 椭球,而不是 Maclaurin 椭球。<br />
==另请参阅==<br />
<br />
*[[Higgs mechanism]]<br />
<br />
*[[QCD vacuum]]<br />
<br />
*[[Goldstone boson]]<br />
<br />
*[[1964 PRL symmetry breaking papers]]<br />
<br />
*[[希格斯机制]]<br />
<br />
*[[QCD真空]]<br />
<br />
*[[戈德斯通玻色子]]<br />
<br />
*[[1964年PRL对称性破缺论文]]<br />
<br />
==参考文献==<br />
<br />
{{reflist|colwidth=30em}}<br />
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{{DEFAULTSORT:Symmetry Breaking}}<br />
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范畴: 对称<br />
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类别: 模式形成<br />
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本中文词条由XXX编译,XXX审校,XXX总审校,西瓜编辑,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''<br />
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<noinclude><br />
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[[Category:对称性破缺]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%AF%B9%E7%A7%B0%E6%80%A7%E7%A0%B4%E7%BC%BA&diff=24655对称性破缺2021-07-25T09:18:55Z<p>Jxzhou:</p>
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<div><br />
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[[图一:一个小球位于中央山丘的山峰处(C)。这是一种不稳定平衡:一个很小的扰动会使它落到左边(L)或右边(R)稳定点。尽管山丘是对称的,没有理由让球落在哪一侧,但观察到的最终状态仍然是不对称的,它总会落到某一侧]]。<br />
<br />
在物理学中,一个作用于系统的(无限)小扰动使系统跨过临界点,通过决定去向分叉的哪个分支来决定系统的命运,这种现象叫做'''<font color="#ff8000">对称性破缺</font>'''。对于一个观测不到扰动(或“噪声”)的外部观察者来说,这个选择看起来是任意的。这个过程被称为对称性破缺,因为这种转变通常使系统从一个对称但无序的状态进入一个或多个确定的状态。在'''<font color="#ff8000">斑图生成</font>'''中对称性破缺起着重要作用。<br />
<br />
1972年,诺贝尔奖得主P·W·安德森(P.W.Anderson)在《科学》(Science)杂志上发表了一篇名为《多即不同》的论文<ref>{{cite journal | last=Anderson | first=P.W. | title=More is Different | journal=Science | volume=177 | issue=4047| pages=393–396 | year=1972 | url=http://robotics.cs.tamu.edu/dshell/cs689/papers/anderson72more_is_different.pdf | doi=10.1126/science.177.4047.393 | pmid=17796623 | format=|bibcode = 1972Sci...177..393A }}</ref>,文中使用对称性破缺的思想表明,即使'''<font color="#ff8000">还原论</font>'''是正确的,但它的逆命题'''<font color="#ff8000">建构主义</font>'''是错误的。建构主义认为,在给出描述各组成部分的理论的情况下科学家可以轻易地预测复杂现象。<br />
<br />
对称性破缺可以分为'''<font color="#ff8000">显性对称性破缺</font>'''和'''<font color="#ff8000">自发对称性破缺</font>'''两种类型,二者的区别是,在破缺对称性下系统的运动方程是否不变或者基态是否保持不变。<br />
==显性对称性破缺==<br />
<br />
在'''<font color="#ff8000">显性对称性破缺</font>'''中,描述系统的运动方程在破缺对称下是不同的。在哈密顿力学或拉格朗日力学中,假若系统的哈密顿量(或拉格朗日量)中至少一项显性地打破了给定的对称性,就发生了显性对称性破缺。<br />
==自发对称性破缺==<br />
<br />
在'''<font color="#ff8000">自发对称性破缺</font>'''中,系统的运动方程是不变的,但系统发生了变化。这是因为系统的背景(时空)——真空态——是非恒定的。这种对称性破缺可以用一个序参量进行参数化。这类对称破缺的一个特殊情况是'''<font color="#ff8000">动力学对称性破缺</font>'''。<br />
<br />
==Overview==<br />
<br />
In [[explicit symmetry breaking]], if two outcomes are considered, the probability of a pair of outcomes can be different. By definition, spontaneous symmetry breaking requires the existence of a symmetric probability distribution—any pair of outcomes has the same probability. In other words, the underlying laws{{clarify|date=December 2016}} are [[Invariant (physics)|invariant]] under a [[Symmetry (physics)|symmetry]] transformation.<br />
<br />
The system, as a whole{{clarify|date=December 2016}}, changes under such transformations.<br />
<br />
Phases of matter, such as crystals, magnets, and conventional superconductors, as well as simple phase transitions can be described by spontaneous symmetry breaking. Notable exceptions include topological phases of matter like the [[fractional quantum Hall effect]].<br />
<br />
==Examples==<br />
<br />
===Sombrero potential===<br />
Consider a symmetric upward dome with a trough circling the bottom. If a ball is put at the very peak of the dome, the system is symmetric with respect to a rotation around the center axis. But the ball may ''spontaneously break'' this symmetry by rolling down the dome into the trough, a point of lowest energy. Afterward, the ball has come to a rest at some fixed point on the perimeter. The dome and the ball retain their individual symmetry, but the system does not.<ref>{{cite book |first=Gerald M. |last=Edelman |title=Bright Air, Brilliant Fire: On the Matter of the Mind |location=New York |publisher=BasicBooks |year=1992 |url=https://archive.org/details/brightairbrillia00gera |url-access=registration |page=[https://archive.org/details/brightairbrillia00gera/page/203 203] }}</ref><br />
[[Image:Mexican hat potential polar.svg|270px|thumb|left|Graph of Goldstone's "[[Sombrero|sombrero]]" potential function <math>V(\phi)</math>.]]<br />
<br />
In the simplest idealized relativistic model, the spontaneously broken symmetry is summarized through an illustrative [[scalar field theory]]. The relevant [[Lagrangian (field theory)|Lagrangian]] of a scalar field <math>\phi</math>, which essentially dictates how a system behaves, can be split up into kinetic and potential terms,<br />
{{NumBlk|::|<math>\mathcal{L} = \partial^\mu \phi \partial_\mu \phi - V(\phi).</math>|{{EquationRef|1}}}}<br />
<br />
It is in this potential term <math>V(\phi)</math> that the symmetry breaking is triggered. An example of a potential, due to [[Jeffrey Goldstone]]<ref>{{Cite journal | last1 = Goldstone | first1 = J. | doi = 10.1007/BF02812722 | title = Field theories with " Superconductor " solutions | journal = Il Nuovo Cimento | volume = 19 | issue = 1 | pages = 154–164 | year = 1961 | bibcode = 1961NCim...19..154G | s2cid = 120409034 | url = http://cds.cern.ch/record/343400 }}</ref> is illustrated in the graph at the left.<br />
{{NumBlk|::|<math>V(\phi) = -5|\phi|^2 + |\phi|^4 \,</math>.|{{EquationRef|2}}}}<br />
<br />
This potential has an infinite number of possible [[minimum|minima]] (vacuum states) given by<br />
{{NumBlk|::|<math>\phi = \sqrt{5} e^{i\theta} </math>.|{{EquationRef|3}}}}<br />
for any real ''θ'' between 0 and 2''π''. The system also has an unstable vacuum state corresponding to {{nowrap|1=''Φ'' = 0}}. This state has a [[Unitary group|U(1)]] symmetry. However, once the system falls into a specific stable vacuum state (amounting to a choice of ''θ''), this symmetry will appear to be lost, or "spontaneously broken".<br />
<br />
In fact, any other choice of ''θ'' would have exactly the same energy, implying the existence of a massless [[Goldstone boson|Nambu–Goldstone boson]], the mode running around the circle at the minimum of this potential, and indicating there is some memory of the original symmetry in the Lagrangian.<br />
<br />
===Other examples===<br />
* For [[ferromagnet]]ic materials, the underlying laws are invariant under spatial rotations. Here, the order parameter is the [[magnetization]], which measures the magnetic dipole density. Above the [[Curie temperature]], the order parameter is zero, which is spatially invariant, and there is no symmetry breaking. Below the Curie temperature, however, the magnetization acquires a constant nonvanishing value, which points in a certain direction (in the idealized situation where we have full equilibrium; otherwise, translational symmetry gets broken as well). The residual rotational symmetries which leave the orientation of this vector invariant remain unbroken, unlike the other rotations which do not and are thus spontaneously broken.<br />
* The laws describing a solid are invariant under the full [[Euclidean group]], but the solid itself spontaneously breaks this group down to a [[space group]]. The displacement and the orientation are the order parameters.<br />
* General relativity has a Lorentz symmetry, but in [[Friedmann–Lemaître–Robertson–Walker metric|FRW cosmological models]], the mean 4-velocity field defined by averaging over the velocities of the galaxies (the galaxies act like gas particles at cosmological scales) acts as an order parameter breaking this symmetry. Similar comments can be made about the cosmic microwave background.<br />
* For the [[electroweak]] model, as explained earlier, a component of the Higgs field provides the order parameter breaking the electroweak gauge symmetry to the electromagnetic gauge symmetry. Like the ferromagnetic example, there is a phase transition at the electroweak temperature. The same comment about us not tending to notice broken symmetries suggests why it took so long for us to discover electroweak unification.<br />
* In superconductors, there is a condensed-matter collective field ψ, which acts as the order parameter breaking the electromagnetic gauge symmetry.<br />
* Take a thin cylindrical plastic rod and push both ends together. Before buckling, the system is symmetric under rotation, and so visibly cylindrically symmetric. But after buckling, it looks different, and asymmetric. Nevertheless, features of the cylindrical symmetry are still there: ignoring friction, it would take no force to freely spin the rod around, displacing the ground state in time, and amounting to an oscillation of vanishing frequency, unlike the radial oscillations in the direction of the buckle. This spinning mode is effectively the requisite [[Goldstone boson|Nambu–Goldstone boson]].<br />
* Consider a uniform layer of [[fluid]] over an infinite horizontal plane. This system has all the symmetries of the Euclidean plane. But now heat the bottom surface uniformly so that it becomes much hotter than the upper surface. When the temperature gradient becomes large enough, [[convection cell]]s will form, breaking the Euclidean symmetry.<br />
* Consider a bead on a circular hoop that is rotated about a vertical [[diameter]]. As the [[rotational velocity]] is increased gradually from rest, the bead will initially stay at its initial [[equilibrium point]] at the bottom of the hoop (intuitively stable, lowest [[gravitational potential]]). At a certain critical rotational velocity, this point will become unstable and the bead will jump to one of two other newly created equilibria, [[equidistant]] from the center. Initially, the system is symmetric with respect to the diameter, yet after passing the critical velocity, the bead ends up in one of the two new equilibrium points, thus breaking the symmetry.<br />
<br />
==Spontaneous symmetry breaking in physics==<br />
[[File:Spontaneous symmetry breaking (explanatory diagram).png|thumb|right|250px|''Spontaneous symmetry breaking illustrated'': At high energy levels (''left''), the ball settles in the center, and the result is symmetric. At lower energy levels (''right''), the overall "rules" remain symmetric, but the symmetric "[[sombrero|Sombrero]]" enforces an asymmetric outcome, since eventually the ball must rest at some random spot on the bottom, "spontaneously", and not all others.]]<br />
<br />
===Particle physics===<br />
In [[particle physics]], the [[force carrier]] particles are normally specified by field equations with [[gauge symmetry]]; their equations predict that certain measurements will be the same at any point in the field. For instance, field equations might predict that the mass of two quarks is constant. Solving the equations to find the mass of each quark might give two solutions. In one solution, quark A is heavier than quark B. In the second solution, quark B is heavier than quark A ''by the same amount''. The symmetry of the equations is not reflected by the individual solutions, but it is reflected by the range of solutions.<br />
<br />
An actual measurement reflects only one solution, representing a breakdown in the symmetry of the underlying theory. "Hidden" is a better term than "broken", because the symmetry is always there in these equations. This phenomenon is called [[Spontaneous magnetization|''spontaneous'']] symmetry breaking (SSB) because ''nothing'' (that we know of) breaks the symmetry in the equations.<ref name="Weinberg2011">{{cite book|author=Steven Weinberg|title=Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature|url=https://books.google.com/books?id=Rsg3PE_9_ccC|date=20 April 2011|publisher=Knopf Doubleday Publishing Group|isbn=978-0-307-78786-6}}</ref>{{rp|194–195}}<br />
<br />
====Chiral symmetry====<br />
{{Main article|Chiral symmetry breaking}}<br />
Chiral symmetry breaking is an example of spontaneous symmetry breaking affecting the [[chiral symmetry]] of the [[strong interactions]] in particle physics. It is a property of [[quantum chromodynamics]], the [[quantum field theory]] describing these interactions, and is responsible for the bulk of the mass (over 99%) of the [[nucleons]], and thus of all common matter, as it converts very light bound [[quarks]] into 100 times heavier constituents of [[baryons]]. The approximate [[Nambu–Goldstone boson]]s in this spontaneous symmetry breaking process are the [[pions]], whose mass is an order of magnitude lighter than the mass of the nucleons. It served as the prototype and significant ingredient of the Higgs mechanism underlying the electroweak symmetry breaking.<br />
<br />
====Higgs mechanism====<br />
{{Main article|Higgs mechanism|Yukawa interaction}}<br />
<br />
The strong, weak, and electromagnetic forces can all be understood as arising from [[gauge symmetry|gauge symmetries]]. The [[Higgs mechanism]], the spontaneous symmetry breaking of gauge symmetries, is an important component in understanding the [[superconductivity]] of metals and the origin of particle masses in the standard model of particle physics. One important consequence of the distinction between true symmetries and ''gauge symmetries'', is that the spontaneous breaking of a gauge symmetry does not give rise to characteristic massless Nambu–Goldstone physical modes, but only massive modes, like the plasma mode in a superconductor, or the Higgs mode observed in particle physics.<br />
<br />
In the standard model of particle physics, spontaneous symmetry breaking of the {{nowrap|SU(2) × U(1)}} gauge symmetry associated with the electro-weak force generates masses for several particles, and separates the electromagnetic and weak forces. The [[W and Z bosons]] are the elementary particles that mediate the [[weak interaction]], while the [[photon]] mediates the [[electromagnetic interaction]]. At energies much greater than 100 GeV, all these particles behave in a similar manner. The [[Unified field theory#Modern progress|Weinberg–Salam theory]] predicts that, at lower energies, this symmetry is broken so that the photon and the massive W and Z bosons emerge.<ref>A Brief History of Time, Stephen Hawking, Bantam; 10th anniversary edition (1998). pp. 73–74.{{ISBN?}}</ref> In addition, fermions develop mass consistently.<br />
<br />
Without spontaneous symmetry breaking, the [[Standard Model]] of elementary particle interactions requires the existence of a number of particles. However, some particles (the [[W and Z bosons]]) would then be predicted to be massless, when, in reality, they are observed to have mass. To overcome this, spontaneous symmetry breaking is augmented by the [[Higgs mechanism]] to give these particles mass. It also suggests the presence of a new particle, the [[Higgs boson]], detected in 2012.<br />
<br />
[[Superconductivity]] of metals is a condensed-matter analog of the Higgs phenomena, in which a condensate of Cooper pairs of electrons spontaneously breaks the U(1) gauge symmetry associated with light and electromagnetism.<br />
<br />
===Condensed matter physics===<br />
Most phases of matter can be understood through the lens of spontaneous symmetry breaking. For example, crystals are periodic arrays of atoms that are not invariant under all translations (only under a small subset of translations by a lattice vector). Magnets have north and south poles that are oriented in a specific direction, breaking [[rotational symmetry]]. In addition to these examples, there are a whole host of other symmetry-breaking phases of matter — including nematic phases of liquid crystals, charge- and spin-density waves, superfluids, and many others.<br />
<br />
There are several known examples of matter that cannot be described by spontaneous symmetry breaking, including: topologically ordered phases of matter, such as [[Fractional quantum Hall effect|fractional quantum Hall liquids]], and [[Quantum spin liquid|spin-liquids]]. These states do not break any symmetry, but are distinct phases of matter. Unlike the case of spontaneous symmetry breaking, there is not a general framework for describing such states.<ref name=chen>{{cite journal | last1 = Chen | first1 = Xie | author-link3 = Xiao-Gang Wen | last2 = Gu | first2 = Zheng-Cheng | last3 = Wen | first3 = Xiao-Gang | year = 2010 | title = Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order | journal = Phys. Rev. B | volume = 82 | issue = 15| page = 155138 | doi=10.1103/physrevb.82.155138|arxiv = 1004.3835 |bibcode = 2010PhRvB..82o5138C | s2cid = 14593420 }}</ref><br />
<br />
====Continuous symmetry====<br />
The ferromagnet is the canonical system that spontaneously breaks the continuous symmetry of the spins below the [[Curie temperature]] and at {{nowrap|1=''h'' = 0}}, where ''h'' is the external magnetic field. Below the [[Curie temperature]], the energy of the system is invariant under inversion of the magnetization ''m''('''x''') such that {{nowrap|1=''m''('''x''') = −''m''(−'''x''')}}. The symmetry is spontaneously broken as {{nowrap|''h'' → 0}} when the Hamiltonian becomes invariant under the inversion transformation, but the expectation value is not invariant.<br />
<br />
Spontaneously-symmetry-broken phases of matter are characterized by an order parameter that describes the quantity which breaks the symmetry under consideration. For example, in a magnet, the order parameter is the local magnetization.<br />
<br />
Spontaneous breaking of a continuous symmetry is inevitably accompanied by gapless (meaning that these modes do not cost any energy to excite) Nambu–Goldstone modes associated with slow, long-wavelength fluctuations of the order parameter. For example, vibrational modes in a crystal, known as phonons, are associated with slow density fluctuations of the crystal's atoms. The associated Goldstone mode for magnets are oscillating waves of spin known as spin-waves. For symmetry-breaking states, whose order parameter is not a conserved quantity, Nambu–Goldstone modes are typically massless and propagate at a constant velocity.<br />
<br />
An important theorem, due to Mermin and Wagner, states that, at finite temperature, thermally activated fluctuations of Nambu–Goldstone modes destroy the long-range order, and prevent spontaneous symmetry breaking in one- and two-dimensional systems. Similarly, quantum fluctuations of the order parameter prevent most types of continuous symmetry breaking in one-dimensional systems even at zero temperature. (An important exception is ferromagnets, whose order parameter, magnetization, is an exactly conserved quantity and does not have any quantum fluctuations.)<br />
<br />
Other long-range interacting systems, such as cylindrical curved surfaces interacting via the [[Coulomb potential]] or [[Yukawa potential]], have been shown to break translational and rotational symmetries.<ref><br />
{{cite journal<br />
|last1=Kohlstedt |first1=K.L.<br />
|last2=Vernizzi |first2=G.<br />
|last3=Solis |first3=F.J.<br />
|last4=Olvera de la Cruz |first4=M.<br />
|year=2007<br />
|title=Spontaneous Chirality via Long-range Electrostatic Forces<br />
|journal=[[Physical Review Letters]]<br />
|volume=99 |issue=3<br />
|page=030602<br />
|doi=10.1103/PhysRevLett.99.030602<br />
|arxiv = 0704.3435 |bibcode = 2007PhRvL..99c0602K |pmid=17678276|s2cid=37983980<br />
}}</ref> It was shown, in the presence of a symmetric Hamiltonian, and in the limit of infinite volume, the system spontaneously adopts a chiral configuration — i.e., breaks [[mirror plane]] [[symmetry]].<br />
<br />
===Dynamical symmetry breaking===<br />
Dynamical symmetry breaking (DSB) is a special form of spontaneous symmetry breaking in which the ground state of the system has reduced symmetry properties compared to its theoretical description (i.e., [[Lagrangian (field theory)|Lagrangian]]).<br />
<br />
Dynamical breaking of a global symmetry is a spontaneous symmetry breaking, which happens not at the (classical) tree level (i.e., at the level of the bare action), but due to quantum corrections (i.e., at the level of the [[effective action]]).<br />
<br />
Dynamical breaking of a gauge symmetry {{ref|note1}} is subtler. In the conventional spontaneous gauge symmetry breaking, there exists an unstable [[Higgs particle]] in the theory, which drives the vacuum to a symmetry-broken phase. (See, for example, [[electroweak interaction]].) In dynamical gauge symmetry breaking, however, no unstable Higgs particle operates in the theory, but the bound states of the system itself provide the unstable fields that render the phase transition. For example, Bardeen, Hill, and Lindner published a paper that attempts to replace the conventional [[Higgs mechanism]] in the [[standard model]] by a DSB that is driven by a bound state of top-antitop quarks. (Such models, in which a composite particle plays the role of the Higgs boson, are often referred to as "Composite Higgs models".)<ref><br />
{{cite journal<br />
|author1=William A. Bardeen<br />
|author2-link=Christopher T. Hill<br />
|author2=Christopher T. Hill<br />
|author3-link=Manfred Lindner<br />
|author3=Manfred Lindner<br />
|year=1990<br />
|title=Minimal dynamical symmetry breaking of the standard model<br />
|journal=[[Physical Review D]]<br />
|volume=41 |issue=5 |pages=1647–1660<br />
|bibcode=1990PhRvD..41.1647B<br />
|doi=10.1103/PhysRevD.41.1647<br />
|pmid=10012522<br />
|author1-link=William A. Bardeen<br />
}}</ref> Dynamical breaking of gauge symmetries is often due to creation of a [[fermionic condensate]] — e.g., the [[quark condensate]], which is connected to the [[Chiral symmetry breaking|dynamical breaking of chiral symmetry]] in [[quantum chromodynamics]]. Conventional [[superconductivity]] is the paradigmatic example from the condensed matter side, where phonon-mediated attractions lead electrons to become bound in pairs and then condense, thereby breaking the electromagnetic gauge symmetry.<br />
<br />
==Generalisation and technical usage==<br />
For spontaneous symmetry breaking to occur, there must be a system in which there are several equally likely outcomes. The system as a whole is therefore [[Symmetry (physics)|symmetric]] with respect to these outcomes. However, if the system is sampled (i.e. if the system is actually used or interacted with in any way), a specific outcome must occur. Though the system as a whole is symmetric, it is never encountered with this symmetry, but only in one specific asymmetric state. Hence, the symmetry is said to be spontaneously broken in that theory. Nevertheless, the fact that each outcome is equally likely is a reflection of the underlying symmetry, which is thus often dubbed "hidden symmetry", and has crucial formal consequences. (See the article on the [[Nambu–Goldstone boson|Goldstone boson]].)<br />
<br />
When a theory is symmetric with respect to a [[symmetry group]], but requires that one element of the group be distinct, then spontaneous symmetry breaking has occurred. The theory must not dictate ''which'' member is distinct, only that ''one is''. From this point on, the theory can be treated as if this element actually is distinct, with the proviso that any results found in this way must be resymmetrized, by taking the average of each of the elements of the group being the distinct one.<br />
<br />
The crucial concept in physics theories is the [[order parameter]]. If there is a field (often a background field) which acquires an expectation value (not necessarily a [[vacuum expectation value|''vacuum'' expectation value]]) which is not invariant under the symmetry in question, we say that the system is in the [[ordered phase]], and the symmetry is spontaneously broken. This is because other subsystems interact with the order parameter, which specifies a "frame of reference" to be measured against. In that case, the [[vacuum state]] does not obey the initial symmetry (which would keep it invariant, in the linearly realized '''Wigner mode''' in which it would be a singlet), and, instead changes under the (hidden) symmetry, now implemented in the (nonlinear) '''Nambu–Goldstone mode'''. Normally, in the absence of the Higgs mechanism, massless [[Goldstone boson]]s arise.<br />
<br />
The symmetry group can be discrete, such as the [[space group]] of a crystal, or continuous (e.g., a [[Lie group]]), such as the rotational symmetry of space. However, if the system contains only a single spatial dimension, then only discrete symmetries may be broken in a [[vacuum state]] of the full [[Quantum mechanics|quantum theory]], although a classical solution may break a continuous symmetry.<br />
<br />
==Nobel Prize==<br />
On October 7, 2008, the [[Royal Swedish Academy of Sciences]] awarded the 2008 [[Nobel Prize in Physics]] to three scientists for their work in subatomic physics symmetry breaking. [[Yoichiro Nambu]], of the [[University of Chicago]], won half of the prize for the discovery of the mechanism of spontaneous broken symmetry in the context of the strong interactions, specifically [[chiral symmetry breaking]]. Physicists [[Makoto Kobayashi (physicist)|Makoto Kobayashi]] and [[Toshihide Maskawa]], of [[Kyoto University]], shared the other half of the prize for discovering the origin of the [[Explicit symmetry breaking|explicit breaking]] of CP symmetry in the weak interactions.<ref>{{cite web|author=The Nobel Foundation|title=The Nobel Prize in Physics 2008|url=http://nobelprize.org/nobel_prizes/physics/laureates/2008/index.html|work=nobelprize.org|access-date=January 15, 2008}}</ref> This origin is ultimately reliant on the Higgs mechanism, but, so far understood as a "just so" feature of Higgs couplings, not a spontaneously broken symmetry phenomenon.<br />
<br />
==See also==<br />
{{div col|colwidth=24em}}<br />
* [[Autocatalytic reactions and order creation]]<br />
* [[Catastrophe theory]]<br />
* [[Chiral symmetry breaking]]<br />
* [[CP-violation]]<br />
* [[Fermi ball]]<br />
* [[Gauge gravitation theory]]<br />
* [[Goldstone boson]]<br />
* [[Grand unified theory]]<br />
* [[Higgs mechanism]]<br />
* [[Higgs boson]]<br />
* [[Higgs field (classical)]]<br />
* [[Irreversibility]]<br />
* [[Magnetic catalysis]] of chiral symmetry breaking<br />
* [[Mermin–Wagner theorem]]<br />
* [[Norton's dome]]<br />
* [[Second-order phase transition]]<br />
* [[Spontaneous absolute asymmetric synthesis]] in chemistry<br />
* [[Symmetry breaking]]<br />
* [[Tachyon condensation]]<br />
* [[1964 PRL symmetry breaking papers]]<br />
{{div col end}}<br />
<br />
==Notes==<br />
* {{note|note1}} Note that (as in fundamental Higgs driven spontaneous gauge symmetry breaking) the term "symmetry breaking" is a misnomer when applied to gauge symmetries.<br />
<br />
==References==<br />
{{Reflist}}<br />
<br />
==External links==<br />
{{wikiquote}}<br />
* For a pedagogic introduction to electroweak symmetry breaking with step by step derivations, not found in texts, of many key relations, see http://www.quantumfieldtheory.info/Electroweak_Sym_breaking.pdf<br />
* [http://hyperphysics.phy-astr.gsu.edu/hbase/forces/unify.html#c2 Spontaneous symmetry breaking]<br />
* [http://prl.aps.org/50years/milestones#1964 Physical Review Letters – 50th Anniversary Milestone Papers]<br />
* [http://cerncourier.com/cws/article/cern/32522 In CERN Courier, Steven Weinberg reflects on spontaneous symmetry breaking]<br />
* [http://www.scholarpedia.org/article/Englert-Brout-Higgs-Guralnik-Hagen-Kibble_mechanism Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism on Scholarpedia]<br />
* [http://www.scholarpedia.org/article/Englert-Brout-Higgs-Guralnik-Hagen-Kibble_mechanism_%28history%29 History of Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism on Scholarpedia]<br />
* [https://arxiv.org/abs/0907.3466 The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles]<br />
* [http://www.worldscinet.com/ijmpa/24/2414/S0217751X09045431.html International Journal of Modern Physics A: The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles]<br />
* [http://www.datafilehost.com/download-7d512618.html Guralnik, G S; Hagen, C R and Kibble, T W B (1967). Broken Symmetries and the Goldstone Theorem. Advances in Physics, vol. 2 Interscience Publishers, New York. pp. 567–708] {{ISBN|0-470-17057-3}}<br />
* [http://lanl.arxiv.org/abs/hep-th/9802142 Spontaneous Symmetry Breaking in Gauge Theories: a Historical Survey]<br />
<br />
{{Standard model of physics}}<br />
{{Quantum mechanics topics}}<br />
<br />
{{DEFAULTSORT:Spontaneous Symmetry Breaking}}<br />
[[Category:Theoretical physics]]<br />
[[Category:Quantum field theory]]<br />
[[Category:Standard Model]]<br />
[[Category:Quantum chromodynamics]]<br />
[[Category:Symmetry]]<br />
[[Category:Quantum phases]]<br />
<br />
==实例==<br />
<br />
对称性破缺可以涵盖以下任何一种情况:<ref>{{cite web|url=http://www.angelfire.com/stars5/astroinfo/gloss/s.html|title=Astronomical Glossary|author=|date=|website=www.angelfire.com}}</ref><br />
* 某些结构的随机形成破坏了物理学基本定律的精确对称性;<br />
* 物理学中最小能量状态的对称性比系统本身少的情形;<br />
* 系统的实际状态由于明显对称的状态不稳定而不能反映动力学的基本对称性的情况(稳定性是以局部不对称为代价的);<br />
* 理论方程具有某种对称性,但其解可能没有(对称性是“隐藏的”)的情况。<br />
<br />
<br />
在物理学文献中讨论的首批对称性破缺案例之一,与不可压缩流体在重力和流体静力平衡中均匀旋转的形式有关。在1834年,Jacobi <ref>{{cite journal| last=Jacobi | first=C.G.J. | title=Über die figur des gleichgewichts | journal=[[Annalen der Physik und Chemie]] | volume=109 | issue=33| pages=229–238 | year=1834| doi=10.1002/andp.18341090808 | bibcode=1834AnP...109..229J | url=https://zenodo.org/record/2027349 }}</ref>和后来的 Liouville <ref>{{cite journal| last=Liouville | first=J. | title=Sur la figure d'une masse fluide homogène, en équilibre et douée d'un mouvement de rotation| journal=Journal de l'École Polytechnique | issue=14| pages=289–296 | year=1834}}</ref>讨论了这样一个事实: 当旋转物体的动能相对于引力势能超过一定的临界值时,这个问题的平衡解是三轴椭球。在这个分叉点上,麦克劳林椭球体的轴对称性被破坏。此外,在这个分叉点之上,对于常数角动量,使动能最小化的解是非轴对称的 Jacobi 椭球,而不是 Maclaurin 椭球。<br />
==另请参阅==<br />
<br />
*[[Higgs mechanism]]<br />
<br />
*[[QCD vacuum]]<br />
<br />
*[[Goldstone boson]]<br />
<br />
*[[1964 PRL symmetry breaking papers]]<br />
<br />
*[[希格斯机制]]<br />
<br />
*[[QCD真空]]<br />
<br />
*[[戈德斯通玻色子]]<br />
<br />
*[[1964年PRL对称性破缺论文]]<br />
<br />
==参考文献==<br />
<br />
{{reflist|colwidth=30em}}<br />
<br />
<br />
<br />
{{DEFAULTSORT:Symmetry Breaking}}<br />
<br />
范畴: 对称<br />
<br />
类别: 模式形成<br />
<br />
本中文词条由XXX编译,XXX审校,XXX总审校,西瓜编辑,欢迎在讨论页面留言。<br />
<br />
'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''<br />
<br />
<noinclude><br />
<br />
[[Category:对称性破缺]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%AF%B9%E7%A7%B0%E6%80%A7%E7%A0%B4%E7%BC%BA&diff=24521对称性破缺2021-07-19T01:23:29Z<p>Jxzhou:</p>
<hr />
<div><br />
<br />
<br />
<br />
[[图一:一个小球位于中央山丘的山峰处(C)。这是一种不稳定平衡:一个很小的扰动会使它落到左边(L)或右边(R)稳定点。尽管山丘是对称的,没有理由让球落在哪一侧,但观察到的最终状态仍然是不对称的,它总会落到某一侧]]。<br />
<br />
在物理学中,一个作用于系统的(无限)小扰动使系统跨过临界点,通过决定去向分叉的哪个分支来决定系统的命运,这种现象叫做'''<font color="#ff8000">对称性破缺</font>'''。对于一个观测不到扰动(或“噪声”)的外部观察者来说,这个选择看起来是任意的。这个过程被称为对称性破缺,因为这种转变通常使系统从一个对称但无序的状态进入一个或多个确定的状态。在'''<font color="#ff8000">斑图生成</font>'''中对称性破缺起着重要作用。<br />
<br />
1972年,诺贝尔奖得主P·W·安德森(P.W.Anderson)在《科学》(Science)杂志上发表了一篇名为《多即不同》的论文<ref>{{cite journal | last=Anderson | first=P.W. | title=More is Different | journal=Science | volume=177 | issue=4047| pages=393–396 | year=1972 | url=http://robotics.cs.tamu.edu/dshell/cs689/papers/anderson72more_is_different.pdf | doi=10.1126/science.177.4047.393 | pmid=17796623 | format=|bibcode = 1972Sci...177..393A }}</ref>,文中使用对称性破缺的思想表明,即使'''<font color="#ff8000">还原论</font>'''是正确的,但它的逆命题'''<font color="#ff8000">建构主义</font>'''是错误的。建构主义认为,在给出描述各组成部分的理论的情况下科学家可以轻易地预测复杂现象。<br />
<br />
对称性破缺可以分为'''<font color="#ff8000">显性对称性破缺</font>'''和'''<font color="#ff8000">自发对称性破缺</font>'''两种类型,二者的区别是,在破缺对称性下系统的运动方程是否不变或者基态是否保持不变。<br />
==显性对称性破缺==<br />
<br />
在'''<font color="#ff8000">显性对称性破缺</font>'''中,描述系统的运动方程在破缺对称下是不同的。在哈密顿力学或拉格朗日力学中,假若系统的哈密顿量(或拉格朗日量)中至少一项显性地打破了给定的对称性,就发生了显性对称性破缺。<br />
==自发对称性破缺==<br />
<br />
在'''<font color="#ff8000">自发对称性破缺</font>'''中,系统的运动方程是不变的,但系统发生了变化。这是因为系统的背景(时空)——真空态——是非恒定的。这种对称性破缺可以用一个序参量进行参数化。这类对称破缺的一个特殊情况是'''<font color="#ff8000">动力学对称性破缺</font>'''。<br />
==实例==<br />
<br />
对称性破缺可以涵盖以下任何一种情况:<ref>{{cite web|url=http://www.angelfire.com/stars5/astroinfo/gloss/s.html|title=Astronomical Glossary|author=|date=|website=www.angelfire.com}}</ref><br />
* 某些结构的随机形成破坏了物理学基本定律的精确对称性;<br />
* 物理学中最小能量状态的对称性比系统本身少的情形;<br />
* 系统的实际状态由于明显对称的状态不稳定而不能反映动力学的基本对称性的情况(稳定性是以局部不对称为代价的);<br />
* 理论方程具有某种对称性,但其解可能没有(对称性是“隐藏的”)的情况。<br />
<br />
<br />
在物理学文献中讨论的首批对称性破缺案例之一,与不可压缩流体在重力和流体静力平衡中均匀旋转的形式有关。在1834年,Jacobi <ref>{{cite journal| last=Jacobi | first=C.G.J. | title=Über die figur des gleichgewichts | journal=[[Annalen der Physik und Chemie]] | volume=109 | issue=33| pages=229–238 | year=1834| doi=10.1002/andp.18341090808 | bibcode=1834AnP...109..229J | url=https://zenodo.org/record/2027349 }}</ref>和后来的 Liouville <ref>{{cite journal| last=Liouville | first=J. | title=Sur la figure d'une masse fluide homogène, en équilibre et douée d'un mouvement de rotation| journal=Journal de l'École Polytechnique | issue=14| pages=289–296 | year=1834}}</ref>讨论了这样一个事实: 当旋转物体的动能相对于引力势能超过一定的临界值时,这个问题的平衡解是三轴椭球。在这个分叉点上,麦克劳林椭球体的轴对称性被破坏。此外,在这个分叉点之上,对于常数角动量,使动能最小化的解是非轴对称的 Jacobi 椭球,而不是 Maclaurin 椭球。<br />
==另请参阅==<br />
<br />
*[[Higgs mechanism]]<br />
<br />
*[[QCD vacuum]]<br />
<br />
*[[Goldstone boson]]<br />
<br />
*[[1964 PRL symmetry breaking papers]]<br />
<br />
*[[希格斯机制]]<br />
<br />
*[[QCD真空]]<br />
<br />
*[[戈德斯通玻色子]]<br />
<br />
*[[1964年PRL对称性破缺论文]]<br />
<br />
==参考文献==<br />
<br />
{{reflist|colwidth=30em}}<br />
<br />
<br />
<br />
{{DEFAULTSORT:Symmetry Breaking}}<br />
<br />
范畴: 对称<br />
<br />
类别: 模式形成<br />
<br />
本中文词条由XXX编译,XXX审校,XXX总审校,西瓜编辑,欢迎在讨论页面留言。<br />
<br />
'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''<br />
<br />
<noinclude><br />
<br />
[[Category:对称性破缺]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%AF%B9%E7%A7%B0%E6%80%A7%E7%A0%B4%E7%BC%BA&diff=24520对称性破缺2021-07-19T01:21:47Z<p>Jxzhou:</p>
<hr />
<div><br />
<br />
<br />
<br />
[[图一:一个小球位于中央山丘的山峰处(C)。这是一种不稳定平衡:一个很小的扰动会使它落到左边(L)或右边(R)稳定点。尽管山丘是对称的,没有理由让球落在哪一侧,但观察到的最终状态仍然是不对称的,它总会落到某一侧]]。<br />
<br />
在物理学中,一个作用于系统的(无限)小扰动使系统跨过临界点,通过决定去向分叉的哪个分支来决定系统的命运,这种现象叫做'''<font color="#ff8000">对称性破缺</font>'''。对于一个观测不到扰动(或“噪声”)的外部观察者来说,这个选择看起来是任意的。这个过程被称为对称性破缺,因为这种跃迁通常使系统从一个对称但无序的状态进入一个或多个确定的状态。在'''<font color="#ff8000">斑图生成</font>'''中对称性破缺起着重要作用。<br />
<br />
1972年,诺贝尔奖得主P·W·安德森(P.W.Anderson)在《科学》(Science)杂志上发表了一篇名为《多即不同》的论文<ref>{{cite journal | last=Anderson | first=P.W. | title=More is Different | journal=Science | volume=177 | issue=4047| pages=393–396 | year=1972 | url=http://robotics.cs.tamu.edu/dshell/cs689/papers/anderson72more_is_different.pdf | doi=10.1126/science.177.4047.393 | pmid=17796623 | format=|bibcode = 1972Sci...177..393A }}</ref>,文中使用对称性破缺的思想表明,即使'''<font color="#ff8000">还原论</font>'''是正确的,但它的逆命题'''<font color="#ff8000">建构主义</font>'''是错误的。建构主义认为,在给出描述各组成部分的理论的情况下科学家可以轻易地预测复杂现象。<br />
<br />
对称性破缺可以分为'''<font color="#ff8000">显性对称性破缺</font>'''和'''<font color="#ff8000">自发对称性破缺</font>'''两种类型,二者的区别是,在破缺对称性下系统的运动方程是否不变或者基态是否保持不变。<br />
==显性对称性破缺==<br />
<br />
在'''<font color="#ff8000">显性对称性破缺</font>'''中,描述系统的运动方程在破缺对称下是不同的。在哈密顿力学或拉格朗日力学中,假若系统的哈密顿量(或拉格朗日量)中至少一项显性地打破了给定的对称性,就发生了显性对称性破缺。<br />
==自发对称性破缺==<br />
<br />
在'''<font color="#ff8000">自发对称性破缺</font>'''中,系统的运动方程是不变的,但系统发生了变化。这是因为系统的背景(时空)——真空态——是非恒定的。这种对称性破缺可以用一个序参量进行参数化。这类对称破缺的一个特殊情况是'''<font color="#ff8000">动力学对称性破缺</font>'''。<br />
==实例==<br />
<br />
对称性破缺可以涵盖以下任何一种情况:<ref>{{cite web|url=http://www.angelfire.com/stars5/astroinfo/gloss/s.html|title=Astronomical Glossary|author=|date=|website=www.angelfire.com}}</ref><br />
* 某些结构的随机形成破坏了物理学基本定律的精确对称性;<br />
* 物理学中最小能量状态的对称性比系统本身少的情形;<br />
* 系统的实际状态由于明显对称的状态不稳定而不能反映动力学的基本对称性的情况(稳定性是以局部不对称为代价的);<br />
* 理论方程具有某种对称性,但其解可能没有(对称性是“隐藏的”)的情况。<br />
<br />
<br />
在物理学文献中讨论的首批对称性破缺案例之一,与不可压缩流体在重力和流体静力平衡中均匀旋转的形式有关。在1834年,Jacobi <ref>{{cite journal| last=Jacobi | first=C.G.J. | title=Über die figur des gleichgewichts | journal=[[Annalen der Physik und Chemie]] | volume=109 | issue=33| pages=229–238 | year=1834| doi=10.1002/andp.18341090808 | bibcode=1834AnP...109..229J | url=https://zenodo.org/record/2027349 }}</ref>和后来的 Liouville <ref>{{cite journal| last=Liouville | first=J. | title=Sur la figure d'une masse fluide homogène, en équilibre et douée d'un mouvement de rotation| journal=Journal de l'École Polytechnique | issue=14| pages=289–296 | year=1834}}</ref>讨论了这样一个事实: 当旋转物体的动能相对于引力势能超过一定的临界值时,这个问题的平衡解是三轴椭球。在这个分叉点上,麦克劳林椭球体的轴对称性被破坏。此外,在这个分叉点之上,对于常数角动量,使动能最小化的解是非轴对称的 Jacobi 椭球,而不是 Maclaurin 椭球。<br />
==另请参阅==<br />
<br />
*[[Higgs mechanism]]<br />
<br />
*[[QCD vacuum]]<br />
<br />
*[[Goldstone boson]]<br />
<br />
*[[1964 PRL symmetry breaking papers]]<br />
<br />
*[[希格斯机制]]<br />
<br />
*[[QCD真空]]<br />
<br />
*[[戈德斯通玻色子]]<br />
<br />
*[[1964年PRL对称性破缺论文]]<br />
<br />
==参考文献==<br />
<br />
{{reflist|colwidth=30em}}<br />
<br />
<br />
<br />
{{DEFAULTSORT:Symmetry Breaking}}<br />
<br />
范畴: 对称<br />
<br />
类别: 模式形成<br />
<br />
本中文词条由XXX编译,XXX审校,XXX总审校,西瓜编辑,欢迎在讨论页面留言。<br />
<br />
'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''<br />
<br />
<noinclude><br />
<br />
[[Category:对称性破缺]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%AF%B9%E7%A7%B0%E6%80%A7%E7%A0%B4%E7%BC%BA&diff=24485对称性破缺2021-07-18T12:03:49Z<p>Jxzhou:</p>
<hr />
<div><br />
<br />
<br />
<br />
[[图一:一个小球位于中央山丘的山峰处(C)。这是一种不稳定平衡:一个很小的扰动会使它落到左边(L)或右边(R)稳定点。尽管山丘是对称的,没有理由让球落在哪一侧,但观察到的最终状态仍然是不对称的,它总会落到某一侧]]。<br />
<br />
在物理学中,一个作用于系统的(无限)小扰动会使系统跨过临界点,通过决定去向分叉的哪个分支来决定系统的命运,这种现象叫做'''<font color="#ff8000">对称性破缺</font>'''。对于一个意识不到波动(或“噪音”)的外部观察者来说,这个选择看起来是任意的。这个过程被称为对称性破缺,因为这种跃迁通常使系统从一个对称但无序的状态进入一个或多个确定的状态。在'''<font color="#ff8000">斑图生成</font>'''中对称性破缺起着重要作用。<br />
<br />
1972年,诺贝尔奖得主P·W·安德森(P.W.Anderson)在《科学》(Science)杂志上发表了一篇名为《多即不同》的论文<ref>{{cite journal | last=Anderson | first=P.W. | title=More is Different | journal=Science | volume=177 | issue=4047| pages=393–396 | year=1972 | url=http://robotics.cs.tamu.edu/dshell/cs689/papers/anderson72more_is_different.pdf | doi=10.1126/science.177.4047.393 | pmid=17796623 | format=|bibcode = 1972Sci...177..393A }}</ref>,文中使用对称性破缺的概念表明,即使'''<font color="#ff8000">还原论</font>'''是正确的,但它的逆命题'''<font color="#ff8000">建构主义</font>'''是错误的。建构主义认为,在给出描述各组成部分的理论的情况下科学家可以轻易地预测复杂现象。<br />
<br />
对称性破缺可以分为'''<font color="#ff8000">显式对称性破缺</font>'''和'''<font color="#ff8000">自发对称性破缺</font>'''两种类型,其特征是运动方程或基态能否保持不变。<br />
==显式对称性破缺==<br />
<br />
在'''<font color="#ff8000">显式对称性破缺</font>'''中,系统的运动方程会发生变化。在哈密顿力学或拉格朗日力学中,假若系统的哈密顿量(或拉格朗日量)至少一项违反某种对称性,导致系统的物理行为不具备这种对称性,就发生了显式对称性破缺。该术语特别适用于大致具有对称性、违反对称项目很少的系统。<br />
==自发对称性破缺==<br />
<br />
在'''<font color="#ff8000">自发对称性破缺</font>'''中,系统的运动方程是不变的,但系统发生了变化。这是因为系统的背景(时空)是非恒定的。这种对称破缺用序参量进行参数化。这类对称破缺的一个特殊情况是'''<font color="#ff8000">动力学对称性破缺</font>'''。<br />
==实例==<br />
<br />
对称性破缺可以涵盖以下任何一种情况:<ref>{{cite web|url=http://www.angelfire.com/stars5/astroinfo/gloss/s.html|title=Astronomical Glossary|author=|date=|website=www.angelfire.com}}</ref><br />
* 某些结构的随机形成破坏了物理学基本定律的精确对称性;<br />
* 物理学中最小能量状态的对称性比系统本身少的情形;<br />
* 系统的实际状态由于明显对称的状态不稳定而不能反映动力学的基本对称性的情况(稳定性是以局部不对称为代价的);<br />
* 理论方程可能具有某种对称性,但其解可能没有(对称性是“隐藏的”)的情况。<br />
<br />
<br />
在物理学文献中讨论的首批对称性破缺案例之一,与不可压缩流体在重力和流体静力平衡中均匀旋转的形式有关。在1834年,Jacobi <ref>{{cite journal| last=Jacobi | first=C.G.J. | title=Über die figur des gleichgewichts | journal=[[Annalen der Physik und Chemie]] | volume=109 | issue=33| pages=229–238 | year=1834| doi=10.1002/andp.18341090808 | bibcode=1834AnP...109..229J | url=https://zenodo.org/record/2027349 }}</ref>和后来的 Liouville <ref>{{cite journal| last=Liouville | first=J. | title=Sur la figure d'une masse fluide homogène, en équilibre et douée d'un mouvement de rotation| journal=Journal de l'École Polytechnique | issue=14| pages=289–296 | year=1834}}</ref>讨论了这样一个事实: 当旋转物体的动能相对于引力势能超过一定的临界值时,这个问题的平衡解是三轴椭球。在这个分叉点上,麦克劳林椭球体的轴对称性被破坏。此外,在这个分叉点之上,对于常数角动量,使动能最小化的解是非轴对称的 Jacobi 椭球,而不是 Maclaurin 椭球。<br />
==另请参阅==<br />
<br />
*[[Higgs mechanism]]<br />
<br />
*[[QCD vacuum]]<br />
<br />
*[[Goldstone boson]]<br />
<br />
*[[1964 PRL symmetry breaking papers]]<br />
<br />
*[[希格斯机制]]<br />
<br />
*[[QCD真空]]<br />
<br />
*[[戈德斯通玻色子]]<br />
<br />
*[[1964年PRL对称性破缺论文]]<br />
<br />
==参考文献==<br />
<br />
{{reflist|colwidth=30em}}<br />
<br />
<br />
<br />
{{DEFAULTSORT:Symmetry Breaking}}<br />
<br />
范畴: 对称<br />
<br />
类别: 模式形成<br />
<br />
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[[Category:对称性破缺]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%AF%B9%E7%A7%B0%E6%80%A7%E7%A0%B4%E7%BC%BA&diff=24484对称性破缺2021-07-18T12:02:22Z<p>Jxzhou:</p>
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[[图一:一个小球位于中央山丘的山峰处(C)。这是一种不稳定平衡:一个很小的扰动会使它落到左边(L)或右边(R)稳定点。尽管山丘是对称的,没有理由让球落在哪一侧,但观察到的最终状态仍然是不对称的,它总会落到某一侧]]。<br />
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在物理学中,一个作用于系统的小扰动会使系统跨过临界点,通过决定去向分叉的哪个分支来决定系统的命运,这种现象叫做'''<font color="#ff8000">对称性破缺</font>'''。对于一个意识不到波动(或“噪音”)的外部观察者来说,这个选择看起来是任意的。这个过程被称为对称性破缺,因为这种跃迁通常使系统从一个对称但无序的状态进入一个或多个确定的状态。在'''<font color="#ff8000">斑图生成</font>'''中对称性破缺起着重要作用。<br />
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1972年,诺贝尔奖得主P·W·安德森(P.W.Anderson)在《科学》(Science)杂志上发表了一篇名为《多即不同》的论文<ref>{{cite journal | last=Anderson | first=P.W. | title=More is Different | journal=Science | volume=177 | issue=4047| pages=393–396 | year=1972 | url=http://robotics.cs.tamu.edu/dshell/cs689/papers/anderson72more_is_different.pdf | doi=10.1126/science.177.4047.393 | pmid=17796623 | format=|bibcode = 1972Sci...177..393A }}</ref>,文中使用对称性破缺的概念表明,即使'''<font color="#ff8000">还原论</font>'''是正确的,但它的逆命题'''<font color="#ff8000">建构主义</font>'''是错误的。建构主义认为,在给出描述各组成部分的理论的情况下科学家可以轻易地预测复杂现象。<br />
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对称性破缺可以分为'''<font color="#ff8000">显式对称性破缺</font>'''和'''<font color="#ff8000">自发对称性破缺</font>'''两种类型,其特征是运动方程或基态能否保持不变。<br />
==显式对称性破缺==<br />
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在'''<font color="#ff8000">显式对称性破缺</font>'''中,系统的运动方程会发生变化。在哈密顿力学或拉格朗日力学中,假若系统的哈密顿量(或拉格朗日量)至少一项违反某种对称性,导致系统的物理行为不具备这种对称性,就发生了显式对称性破缺。该术语特别适用于大致具有对称性、违反对称项目很少的系统。<br />
==自发对称性破缺==<br />
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在'''<font color="#ff8000">自发对称性破缺</font>'''中,系统的运动方程是不变的,但系统发生了变化。这是因为系统的背景(时空)是非恒定的。这种对称破缺用序参量进行参数化。这类对称破缺的一个特殊情况是'''<font color="#ff8000">动力学对称性破缺</font>'''。<br />
==实例==<br />
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对称性破缺可以涵盖以下任何一种情况:<ref>{{cite web|url=http://www.angelfire.com/stars5/astroinfo/gloss/s.html|title=Astronomical Glossary|author=|date=|website=www.angelfire.com}}</ref><br />
* 某些结构的随机形成破坏了物理学基本定律的精确对称性;<br />
* 物理学中最小能量状态的对称性比系统本身少的情形;<br />
* 系统的实际状态由于明显对称的状态不稳定而不能反映动力学的基本对称性的情况(稳定性是以局部不对称为代价的);<br />
* 理论方程可能具有某种对称性,但其解可能没有(对称性是“隐藏的”)的情况。<br />
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在物理学文献中讨论的首批对称性破缺案例之一,与不可压缩流体在重力和流体静力平衡中均匀旋转的形式有关。在1834年,Jacobi <ref>{{cite journal| last=Jacobi | first=C.G.J. | title=Über die figur des gleichgewichts | journal=[[Annalen der Physik und Chemie]] | volume=109 | issue=33| pages=229–238 | year=1834| doi=10.1002/andp.18341090808 | bibcode=1834AnP...109..229J | url=https://zenodo.org/record/2027349 }}</ref>和后来的 Liouville <ref>{{cite journal| last=Liouville | first=J. | title=Sur la figure d'une masse fluide homogène, en équilibre et douée d'un mouvement de rotation| journal=Journal de l'École Polytechnique | issue=14| pages=289–296 | year=1834}}</ref>讨论了这样一个事实: 当旋转物体的动能相对于引力势能超过一定的临界值时,这个问题的平衡解是三轴椭球。在这个分叉点上,麦克劳林椭球体的轴对称性被破坏。此外,在这个分叉点之上,对于常数角动量,使动能最小化的解是非轴对称的 Jacobi 椭球,而不是 Maclaurin 椭球。<br />
==另请参阅==<br />
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*[[Higgs mechanism]]<br />
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*[[QCD vacuum]]<br />
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*[[Goldstone boson]]<br />
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*[[1964 PRL symmetry breaking papers]]<br />
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*[[希格斯机制]]<br />
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*[[QCD真空]]<br />
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*[[戈德斯通玻色子]]<br />
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*[[1964年PRL对称性破缺论文]]<br />
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==参考文献==<br />
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{{reflist|colwidth=30em}}<br />
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{{DEFAULTSORT:Symmetry Breaking}}<br />
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范畴: 对称<br />
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类别: 模式形成<br />
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本中文词条由XXX编译,XXX审校,XXX总审校,西瓜编辑,欢迎在讨论页面留言。<br />
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[[Category:对称性破缺]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E7%83%AD%E5%8A%9B%E5%AD%A6&diff=21961热力学2021-02-23T09:46:16Z<p>Jxzhou:/* Introduction 引言 */</p>
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<div>此词条暂由jxzhou翻译,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{short description|Physics of heat, work, and temperature}}<br />
{{Use dmy dates|date=February 2016}}<br />
[[File:Carnot engine (hot body - working body - cold body).jpg|thumb|300px|right|Annotated color version of the original 1824 [[Carnot heat engine]] showing the hot body (boiler), working body (system, steam), and cold body (water), the letters labeled according to the stopping points in [[Carnot cycle]].]]<br />
{{Thermodynamics}}<br />
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'''Thermodynamics''' is a branch of [[physics]] that deals with [[heat]], [[Work (thermodynamics)|work]], and [[temperature]], and their relation to [[energy]], [[radiation]], and physical properties of [[matter]]. The behavior of these quantities is governed by the four [[laws of thermodynamics]] which convey a quantitative description using measurable macroscopic [[physical quantity|physical quantities]], but may be explained in terms of [[microscopic]] constituents by [[statistical mechanics]]. Thermodynamics applies to a wide variety of topics in [[science]] and [[engineering]], especially [[physical chemistry]], [[chemical engineering]] and [[mechanical engineering]], but also in other complex fields such as [[meteorology]].<br />
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热力学是物理学的一个分支,研究热、功和温度,以及它们与能量、辐射和物质物理性质的关系。这些量的行为遵循四个热力学定律,热力学定律用可测量的宏观物理量给出了一个定量描述,但是可以用统计力学以微观组成来解释。热力学适用于科学和工程中的各种各样的主题,尤其是物理化学、化学工程和机械工程,但也适用于气象学这样复杂的领域。<br />
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Historically, thermodynamics developed out of a desire to increase the [[thermodynamic efficiency|efficiency]] of early [[steam engine]]s, particularly through the work of French physicist [[Nicolas Léonard Sadi Carnot]] (1824) who believed that engine efficiency was the key that could help France win the [[Napoleonic Wars]].<ref>{{cite book | last = Clausius | first = Rudolf | title = On the Motive Power of Heat, and on the Laws which can be deduced from it for the Theory of Heat | publisher = Poggendorff's Annalen der Physik, LXXIX (Dover Reprint) | year = 1850 | isbn = 978-0-486-59065-3}}</ref> Scots-Irish physicist [[William Thomson, 1st Baron Kelvin|Lord Kelvin]] was the first to formulate a concise definition of thermodynamics in 1854<ref name=kelvin1854>{{cite book<br />
|title=Mathematical and Physical Papers<br />
|author= William Thomson, LL.D. D.C.L., F.R.S.<br />
|location=London, Cambridge<br />
|year=1882<br />
|volume=1<br />
|page=232<br />
|publisher=C.J. Clay, M.A. & Son, Cambridge University Press<br />
|url=https://books.google.com/books?id=nWMSAAAAIAAJ&q=On+an+Absolute+Thermometric+Scale+Founded+on+Carnot%E2%80%99s+Theory&pg=PA100<br />
}}</ref> which stated, "Thermo-dynamics is the subject of the relation of heat to forces acting between contiguous parts of bodies, and the relation of heat to electrical agency."<br />
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从历史上看,热力学是出于提高早期蒸汽机的热力学效率的愿望而发展的,特别是通过法国物理学家 NicolasLéonardSadi Carnot(1824)的工作,他认为发动机效率是帮助法国赢得拿破仑战争的关键。苏格兰裔爱尔兰物理学家开尔文勋爵(Lord Kelvin)于1854年首次提出了热力学的简明定义,其中指出:“热力学的主题是物体相邻部分之间热量与作用力的关系,以及热量与电能的关系。”<br />
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The initial application of thermodynamics to [[mechanical heat engine]]s was quickly extended to the study of chemical compounds and chemical reactions. [[Chemical thermodynamics]] studies the nature of the role of [[entropy]] in the process of [[chemical reaction]]s and has provided the bulk of expansion and knowledge of the field.<ref name="Gibbs 1876">{{cite book|author=Gibbs, Willard, J.|title=Transactions of the Connecticut Academy of Arts and Sciences|volume=III|pages=[https://archive.org/details/transactions03conn/page/108 108]–248, 343–524|year=1874–1878|url=https://archive.org/details/transactions03conn|publisher=New Haven}}</ref><ref name="Duhem 1886">Duhem, P.M.M. (1886). ''Le Potential Thermodynamique et ses Applications'', Hermann, Paris.</ref><ref name="Lewis Randall 1923">{{cite book | last1=Lewis | first1=Gilbert N. | last2=Randall | first2=Merle | title=Thermodynamics and the Free Energy of Chemical Substances | url=https://archive.org/details/thermodynamicsfr00gnle | publisher=McGraw-Hill Book Co. Inc. | year=1923}}</ref><ref name="Guggenheim 1933">Guggenheim, E.A. (1933). ''Modern Thermodynamics by the Methods of J.W. Gibbs'', Methuen, London.</ref><ref name="Guggenheim 1949/1967">Guggenheim, E.A. (1949/1967). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', 1st edition 1949, 5th edition 1967, North-Holland, Amsterdam.</ref><ref>{{cite book | author=Ilya Prigogine, I. & Defay, R., translated by D.H. Everett| title=Chemical Thermodynamics | year=1954 | publisher=Longmans, Green & Co., London. Includes classical non-equilibrium thermodynamics.}}<br />
</ref><ref name=Fermi>{{cite book<br />
|title=Thermodynamics<br />
|author=Enrico Fermi<br />
|url=https://books.google.com/books?id=VEZ1ljsT3IwC&q=thermodynamics<br />
|isbn=978-0486603612<br />
|publisher=Courier Dover Publications<br />
|year=1956<br />
|page=ix<br />
|oclc=230763036}}</ref><ref name="Perrot" >{{cite book | author=Perrot, Pierre | title=A to Z of Thermodynamics | publisher=Oxford University Press | year=1998 | isbn=978-0-19-856552-9 | oclc=123283342}}</ref><ref>{{cite book | author=Clark, John, O.E.| title=The Essential Dictionary of Science | publisher=Barnes & Noble Books | year=2004 | isbn=978-0-7607-4616-5 | oclc=58732844}}</ref> Other formulations of thermodynamics emerged. [[Statistical thermodynamics]], or statistical mechanics, concerns itself with [[statistics|statistical]] predictions of the collective motion of particles from their microscopic behavior. In 1909, [[Constantin Carathéodory]] presented a purely mathematical approach in an [[axiomatic]] formulation, a description often referred to as ''geometrical thermodynamics''.<br />
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热力学在机械热机上的最初应用很快扩展到了化学化合物和化学反应的研究。化学热力学研究了熵在化学反应过程中的作用性本质,并提供了更广阔的领域和知识。热力学的其他公式出现了。统计热力学,或称统计力学,从微观角度对粒子的集体运动进行统计预测。在1909年,康斯坦丁·卡拉西奥多在一个公理化形式里提出了一种纯粹的数学方法,通常被称为几何热力学。<br />
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==Introduction 引言==<br />
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A description of any thermodynamic system employs the four [[laws of thermodynamics]] that form an axiomatic basis. The first law specifies that energy can be exchanged between physical systems as [[heat]] and [[Mechanical work|work]].<ref>{{cite book | author=Van Ness, H.C. | title=Understanding Thermodynamics | publisher=Dover Publications, Inc. | year=1983 | origyear=1969 | isbn=9780486632773 | oclc=8846081 | url-access=registration | url=https://archive.org/details/understandingthe00vann }}</ref> The second law defines the existence of a quantity called [[entropy]], that describes the direction, thermodynamically, that a system can evolve and quantifies the state of order of a system and that can be used to quantify the useful work that can be extracted from the system.<ref>{{cite book | author=Dugdale, J.S. | title=Entropy and its Physical Meaning | publisher=Taylor and Francis | year=1998 | isbn=978-0-7484-0569-5 | oclc=36457809}}</ref><br />
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A description of any thermodynamic system employs the four laws of thermodynamics that form an axiomatic basis. The first law specifies that energy can be exchanged between physical systems as heat and work. The second law defines the existence of a quantity called entropy, that describes the direction, thermodynamically, that a system can evolve and quantifies the state of order of a system and that can be used to quantify the useful work that can be extracted from the system.<br />
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任何热力学系统的描述都使用了构成公理基础的四个热力学定律。第一定律规定能量可以在物理系统之间以热和功的形式进行交换。第二定律定义了一个叫做熵的量的存在,熵描述了一个系统在热力学上可以演化的方向,并且定量化一个系统有序的状态,用来量化可以从系统中提取的有用功。<br />
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In thermodynamics, interactions between large ensembles of objects are studied and categorized. Central to this are the concepts of the thermodynamic ''[[System (thermodynamics)|system]]'' and its ''[[Surroundings (thermodynamics)|surroundings]]''. A system is composed of particles, whose average motions define its properties, and those properties are in turn related to one another through [[Equation of state|equations of state]]. Properties can be combined to express [[internal energy]] and [[thermodynamic potential]]s, which are useful for determining conditions for [[Dynamic equilibrium|equilibrium]] and [[spontaneous process]]es.<br />
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In thermodynamics, interactions between large ensembles of objects are studied and categorized. Central to this are the concepts of the thermodynamic system and its surroundings. A system is composed of particles, whose average motions define its properties, and those properties are in turn related to one another through equations of state. Properties can be combined to express internal energy and thermodynamic potentials, which are useful for determining conditions for equilibrium and spontaneous processes.<br />
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热力学研究和分类了大量物体集合之间的相互作用。其核心是热力学系统及其周围环境的概念。一个系统是由粒子组成的,粒子的平均运动决定了它的性质,而这些性质又通过状态方程彼此相关。系统的性质可以结合起来表示内能和热力学势,这对于确定平衡和自发过程的条件是有用的。<br />
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With these tools, thermodynamics can be used to describe how systems respond to changes in their environment. This can be applied to a wide variety of topics in [[science]] and [[engineering]], such as [[engine]]s, [[phase transition]]s, [[chemical reaction]]s, [[transport phenomena]], and even [[black hole]]s. The results of thermodynamics are essential for other fields of [[physics]] and for [[chemistry]], [[chemical engineering]], [[corrosion engineering]], [[aerospace engineering]], [[mechanical engineering]], [[cell biology]], [[biomedical engineering]], [[materials science]], and [[economics]], to name a few.<ref>{{Cite book | last1=Smith | first1=J.M. | last2=Van Ness | first2=H.C. | last3=Abbott | first3=M.M. | title=Introduction to Chemical Engineering Thermodynamics | journal=Journal of Chemical Education | volume=27 | issue=10 | page=584 | year=2005 | isbn=978-0-07-310445-4 | oclc=56491111| bibcode=1950JChEd..27..584S | doi=10.1021/ed027p584.3 }}</ref><ref>{{cite book | author=Haynie, Donald, T. | title=Biological Thermodynamics | publisher=Cambridge University Press | year=2001 | isbn=978-0-521-79549-4 | oclc=43993556}}</ref><br />
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With these tools, thermodynamics can be used to describe how systems respond to changes in their environment. This can be applied to a wide variety of topics in science and engineering, such as engines, phase transitions, chemical reactions, transport phenomena, and even black holes. The results of thermodynamics are essential for other fields of physics and for chemistry, chemical engineering, corrosion engineering, aerospace engineering, mechanical engineering, cell biology, biomedical engineering, materials science, and economics, to name a few.<br />
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有了这些工具,热力学可以用来描述系统如何响应环境中的变化。这可以应用于科学和工程的各种主题,如引擎、相变、化学反应、输运现象、甚至黑洞。热力学的结果对于物理学其他领域、化学、化学工程、腐蚀工程、航空航天工程、机械工程、细胞生物学、生物医学工程、材料科学和经济学都是必不可少的。<br />
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This article is focused mainly on classical thermodynamics which primarily studies systems in [[thermodynamic equilibrium]]. [[Non-equilibrium thermodynamics]] is often treated as an extension of the classical treatment, but statistical mechanics has brought many advances to that field.<br />
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This article is focused mainly on classical thermodynamics which primarily studies systems in thermodynamic equilibrium. Non-equilibrium thermodynamics is often treated as an extension of the classical treatment, but statistical mechanics has brought many advances to that field.<br />
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这篇文章主要关注经典热力学,它主要研究热力学平衡中的系统。非平衡态热力学通常被视为经典方法的延伸,但是统计力学已经为这个领域带来了许多进步。<br />
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[[File:Eight founding schools.png|400px|thumb|The [[thermodynamicist]]s representative of the original eight founding schools of thermodynamics. The schools with the most-lasting effect in founding the modern versions of thermodynamics are the Berlin school, particularly as established in [[Rudolf Clausius]]’s 1865 textbook ''The Mechanical Theory of Heat'', the Vienna school, with the [[statistical mechanics]] of [[Ludwig Boltzmann]], and the Gibbsian school at Yale University, American engineer [[Willard Gibbs]]' 1876 ''[[On the Equilibrium of Heterogeneous Substances]]'' launching [[chemical thermodynamics]].<ref name="autogenerated1">[http://www.eoht.info/page/Schools+of+thermodynamics Schools of thermodynamics] – EoHT.info.</ref>]]<br />
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The [[thermodynamicists representative of the original eight founding schools of thermodynamics. The schools with the most-lasting effect in founding the modern versions of thermodynamics are the Berlin school, particularly as established in Rudolf Clausius’s 1865 textbook The Mechanical Theory of Heat, the Vienna school, with the statistical mechanics of Ludwig Boltzmann, and the Gibbsian school at Yale University, American engineer Willard Gibbs' 1876 On the Equilibrium of Heterogeneous Substances launching chemical thermodynamics.]]<br />
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代表热力学最初八个学派的热力学学者。在建立现代版本的热力学方面影响最深远的学校是柏林学派,特别是由 Rudolf Clausius 在1865年的教科书《热力学的机械理论》中建立的维也纳学派,与统计力学路德维希·玻尔兹曼合作的维也纳学派,以及耶鲁大学的 Gibbsian 学派,美国工程师 Willard Gibbs 在1876年建立的关于多相物质平衡化学热力学<br />
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==History==<br />
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==History==<br />
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历史<br />
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The [[history of thermodynamics]] as a scientific discipline generally begins with [[Otto von Guericke]] who, in 1650, built and designed the world's first [[vacuum pump]] and demonstrated a [[vacuum]] using his [[Magdeburg hemispheres]]. Guericke was driven to make a vacuum in order to disprove [[Aristotle]]'s long-held supposition that 'nature abhors a vacuum'. Shortly after Guericke, the English physicist and chemist [[Robert Boyle]] had learned of Guericke's designs and, in 1656, in coordination with English scientist [[Robert Hooke]], built an air pump.<ref>{{cite book | author=Partington, J.R. | title=A Short History of Chemistry | url=https://archive.org/details/shorthistoryofch0000part_q6h4 | url-access=registration | publisher=Dover | year=1989 | isbn= | oclc=19353301| author-link=J. R. Partington }}</ref> Using this pump, Boyle and Hooke noticed a correlation between [[pressure]], [[temperature]], and [[Volume (thermodynamics)|volume]]. In time, [[Boyle's Law]] was formulated, which states that pressure and volume are [[inverse proportion|inversely proportional]]. Then, in 1679, based on these concepts, an associate of Boyle's named [[Denis Papin]] built a [[steam digester]], which was a closed vessel with a tightly fitting lid that confined steam until a high pressure was generated.<br />
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The history of thermodynamics as a scientific discipline generally begins with Otto von Guericke who, in 1650, built and designed the world's first vacuum pump and demonstrated a vacuum using his Magdeburg hemispheres. Guericke was driven to make a vacuum in order to disprove Aristotle's long-held supposition that 'nature abhors a vacuum'. Shortly after Guericke, the English physicist and chemist Robert Boyle had learned of Guericke's designs and, in 1656, in coordination with English scientist Robert Hooke, built an air pump. Using this pump, Boyle and Hooke noticed a correlation between pressure, temperature, and volume. In time, Boyle's Law was formulated, which states that pressure and volume are inversely proportional. Then, in 1679, based on these concepts, an associate of Boyle's named Denis Papin built a steam digester, which was a closed vessel with a tightly fitting lid that confined steam until a high pressure was generated.<br />
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热力学史作为一门科学学科通常始于1650年的奥托·冯·格里克,他建造并设计了世界上第一台真空泵,并用他的马德堡半球展示了真空。格里克被迫制造一个真空,以反驳亚里士多德长期以来的假设,即“自然憎恶真空”。在格里克之后不久,英国物理学家和化学家罗伯特 · 波义耳听说了格里克的设计,并在1656年与英国科学家罗伯特 · 胡克合作制造了一个空气泵。波义耳和胡克利用这台泵,注意到了压力、温度和体积之间的关系。随着时间的推移,波义耳定律被公式化了,它指出压强和体积成反比。然后,在1679年,基于这些概念,波义耳的一位名叫丹尼斯 · 帕平的合伙人建造了一个蒸汽消化器,这是一个封闭的容器,有一个紧密的盖子,将蒸汽封闭起来,直到产生高压。<br />
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Later designs implemented a steam release valve that kept the machine from exploding. By watching the valve rhythmically move up and down, Papin conceived of the idea of a [[piston]] and a cylinder engine. He did not, however, follow through with his design. Nevertheless, in 1697, based on Papin's designs, engineer [[Thomas Savery]] built the first engine, followed by [[Thomas Newcomen]] in 1712. Although these early engines were crude and inefficient, they attracted the attention of the leading scientists of the time.<br />
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Later designs implemented a steam release valve that kept the machine from exploding. By watching the valve rhythmically move up and down, Papin conceived of the idea of a piston and a cylinder engine. He did not, however, follow through with his design. Nevertheless, in 1697, based on Papin's designs, engineer Thomas Savery built the first engine, followed by Thomas Newcomen in 1712. Although these early engines were crude and inefficient, they attracted the attention of the leading scientists of the time.<br />
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后来的设计实现了一个蒸汽释放阀,以防止机器爆炸。通过观察阀门有节奏地上下运动,帕平构思了活塞和汽缸发动机的概念。然而,他并没有坚持他的设计。然而,在1697年,根据帕平的设计,工程师托马斯 · 萨维里制造了第一台发动机,随后在1712年托马斯 · 纽科门制造了第一台发动机。虽然这些早期的发动机粗糙和低效,他们吸引了当时的主要科学家的注意。<br />
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The fundamental concepts of [[heat capacity]] and [[latent heat]], which were necessary for the development of thermodynamics, were developed by Professor [[Joseph Black]] at the University of Glasgow, where [[James Watt]] was employed as an instrument maker. Black and Watt performed experiments together, but it was Watt who conceived the idea of the [[Watt steam engine#Separate condenser|external condenser]] which resulted in a large increase in [[steam engine]] efficiency.<ref>The Newcomen engine was improved from 1711 until Watt's work, making the efficiency comparison subject to qualification, but the increase from the 1865 version was on the order of 100%.</ref> Drawing on all the previous work led [[Nicolas Léonard Sadi Carnot|Sadi Carnot]], the "father of thermodynamics", to publish ''[[Reflections on the Motive Power of Fire]]'' (1824), a discourse on heat, power, energy and engine efficiency. The book outlined the basic energetic relations between the [[Carnot engine]], the [[Carnot cycle]], and '''motive power'''. It marked the start of thermodynamics as a modern science.<ref name="Perrot" /><br />
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The fundamental concepts of heat capacity and latent heat, which were necessary for the development of thermodynamics, were developed by Professor Joseph Black at the University of Glasgow, where James Watt was employed as an instrument maker. Black and Watt performed experiments together, but it was Watt who conceived the idea of the external condenser which resulted in a large increase in steam engine efficiency. Drawing on all the previous work led Sadi Carnot, the "father of thermodynamics", to publish Reflections on the Motive Power of Fire (1824), a discourse on heat, power, energy and engine efficiency. The book outlined the basic energetic relations between the Carnot engine, the Carnot cycle, and motive power. It marked the start of thermodynamics as a modern science.<br />
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热容量和潜热的基本概念是热力学发展所必需的,是由格拉斯哥大学的 Joseph Black 教授提出来的,James Watt 是那里的一个仪器制造商。布莱克和瓦特一起进行实验,但是瓦特提出了外部冷凝器的概念,从而大大提高了蒸汽机的效率。根据以前所有的工作,“热力学之父”萨迪 · 卡诺发表了《论火的动力(1824年) ,一篇关于热、动力、能源和发动机效率的论文。这本书概述了卡诺发动机、卡诺循环和动力之间的基本能量关系。它标志着热力学作为一门现代科学的开始。<br />
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The first thermodynamic textbook was written in 1859 by [[William John Macquorn Rankine|William Rankine]], originally trained as a physicist and a civil and mechanical engineering professor at the [[University of Glasgow]].<ref>{{cite book |author1=Cengel, Yunus A. |author2=Boles, Michael A. | title=Thermodynamics – an Engineering Approach | publisher=McGraw-Hill | year=2005 | isbn=978-0-07-310768-4}}</ref> The first and second laws of thermodynamics emerged simultaneously in the 1850s, primarily out of the works of [[William John Macquorn Rankine|William Rankine]], [[Rudolf Clausius]], and [[William Thomson, 1st Baron Kelvin|William Thomson]] (Lord Kelvin).<ref name = "NKS note b">''[[A New Kind of Science]]'' [https://www.wolframscience.com/nks/notes-9-3--history-of-thermodynamics/ Note (b) for Irreversibility and the Second Law of Thermodynamics]</ref><br />
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The first thermodynamic textbook was written in 1859 by William Rankine, originally trained as a physicist and a civil and mechanical engineering professor at the University of Glasgow. The first and second laws of thermodynamics emerged simultaneously in the 1850s, primarily out of the works of William Rankine, Rudolf Clausius, and William Thomson (Lord Kelvin).<br />
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第一本热力学教科书是 William Rankine 在1859年写的,他最初是格拉斯哥大学的物理学家和土木机械工程教授。第一个和第二个热力学定律同时出现在19世纪50年代,主要出自 William Rankine,Rudolf Clausius 和 William Thomson (Lord Kelvin)的作品。<br />
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The foundations of statistical thermodynamics were set out by physicists such as [[James Clerk Maxwell]], [[Ludwig Boltzmann]], [[Max Planck]], [[Rudolf Clausius]] and [[Josiah Willard Gibbs|J. Willard Gibbs]].<br />
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The foundations of statistical thermodynamics were set out by physicists such as James Clerk Maxwell, Ludwig Boltzmann, Max Planck, Rudolf Clausius and J. Willard Gibbs.<br />
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统计热力学的基础是由物理学家建立的,如詹姆斯·克拉克·麦克斯韦,路德维希·玻尔兹曼,马克斯 · 普朗克,Rudolf Clausius 和 j. Willard Gibbs。<br />
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During the years 1873–76 the American mathematical physicist [[Josiah Willard Gibbs]] published a series of three papers, the most famous being ''[[On the Equilibrium of Heterogeneous Substances]]'',<ref name="Gibbs 1876"/> in which he showed how [[thermodynamic processes]], including [[chemical reaction]]s, could be graphically analyzed, by studying the [[energy]], [[entropy]], [[Volume (thermodynamics)|volume]], [[temperature]] and [[pressure]] of the [[thermodynamic system]] in such a manner, one can determine if a process would occur spontaneously.<ref>{{cite book | author=Gibbs, Willard | title=The Scientific Papers of J. Willard Gibbs, Volume One: Thermodynamics | publisher=Ox Bow Press | year=1993 | isbn=978-0-918024-77-0 | oclc=27974820}}</ref> Also [[Pierre Duhem]] in the 19th century wrote about chemical thermodynamics.<ref name="Duhem 1886"/> During the early 20th century, chemists such as [[Gilbert N. Lewis]], [[Merle Randall]],<ref name="Lewis Randall 1923"/> and [[E. A. Guggenheim]]<ref name="Guggenheim 1933"/><ref name="Guggenheim 1949/1967"/> applied the mathematical methods of Gibbs to the analysis of chemical processes.<br />
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During the years 1873–76 the American mathematical physicist Josiah Willard Gibbs published a series of three papers, the most famous being On the Equilibrium of Heterogeneous Substances, Also Pierre Duhem in the 19th century wrote about chemical thermodynamics. During the early 20th century, chemists such as Gilbert N. Lewis, Merle Randall, and E. A. Guggenheim applied the mathematical methods of Gibbs to the analysis of chemical processes.<br />
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在1873年至1876年间,美国数学物理学家约西亚·威拉德·吉布斯发表了一系列的3篇论文,其中最著名的是关于多相物质平衡,也是 Pierre Duhem 在19世纪写的关于化学热力学的论文。在20世纪早期,化学家如吉尔伯特·牛顿·路易斯,Merle Randall 和 e. a. Guggenheim 将吉布斯的数学方法应用于化学过程的分析。<br />
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==Etymology==<br />
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==Etymology==<br />
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词源学<br />
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这个术语的历史是丰富的,需要更多的补充<br />
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The etymology of ''thermodynamics'' has an intricate history.<ref name=eoht>{{cite web<br />
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The etymology of thermodynamics has an intricate history.<ref name=eoht>{{cite web<br />
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热力学的词源有一个错综复杂的历史<br />
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|url=http://www.eoht.info/page/Thermo-dynamics<br />
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|title=Thermodynamics (etymology)<br />
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| 题目: 热力学(词源)<br />
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出版商 EoHT.info<br />
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}}</ref> It was first spelled in a hyphenated form as an adjective (''thermo-dynamic'') and from 1854 to 1868 as the noun ''thermo-dynamics'' to represent the science of generalized heat engines.<ref name=eoht/><br />
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}}</ref> It was first spelled in a hyphenated form as an adjective (thermo-dynamic) and from 1854 to 1868 as the noun thermo-dynamics to represent the science of generalized heat engines.<br />
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它最初以连字符的形式作为形容词(热力学)拼写,从1854年到1868年作为名词热力学来代表广义热发动机的科学。<br />
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American [[Biophysics|biophysicist]] Donald Haynie claims that ''thermodynamics'' was coined in 1840 from the [[Greek language|Greek]] root [[wikt:θέρμη|θέρμη]] ''therme,'' meaning “heat”, and [[wikt:δύναμις|δύναμις]] ''dynamis,'' meaning “power”.<ref>{{cite book<br />
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American biophysicist Donald Haynie claims that thermodynamics was coined in 1840 from the Greek root θέρμη therme, meaning “heat”, and δύναμις dynamis, meaning “power”.<ref>{{cite book<br />
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美国生物物理学家唐纳德 · 海尼声称,热力学是在1840年从希腊词根 therme (意思是“热”)和 dynamis (意思是“力”)创造出来的。 文档{ cite book<br />
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生物热力学<br />
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作者唐纳德 · t · 海尼<br />
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剑桥大学出版社<br />
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Pierre Perrot claims that the term ''thermodynamics'' was coined by [[James Joule]] in 1858 to designate the science of relations between heat and power,<ref name="Perrot" /> however, Joule never used that term, but used instead the term ''perfect thermo-dynamic engine'' in reference to Thomson's 1849<ref name=kelvin1849/> phraseology.<ref name=eoht/><br />
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Pierre Perrot claims that the term thermodynamics was coined by James Joule in 1858 to designate the science of relations between heat and power, however, Joule never used that term, but used instead the term perfect thermo-dynamic engine in reference to Thomson's 1849 phraseology.<br />
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皮埃尔 · 佩罗声称,热力学这个术语是由詹姆斯 · 朱尔在1858年创造的,用来指代热量和能量之间关系的科学。然而,朱尔从来没有使用过这个术语,而是在汤姆森1849年的措辞中使用了完美热力学引擎这个术语。<br />
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By 1858, ''thermo-dynamics'', as a functional term, was used in [[William Thomson, 1st Baron Kelvin|William Thomson]]'s paper "An Account of Carnot's Theory of the Motive Power of Heat."<ref name=kelvin1849>Kelvin, William T. (1849) "An Account of Carnot's Theory of the Motive Power of Heat – with Numerical Results Deduced from Regnault's Experiments on Steam." ''Transactions of the Edinburg Royal Society, XVI. January 2.''[http://visualiseur.bnf.fr/Visualiseur?Destination=Gallica&O=NUMM-95118 Scanned Copy]</ref><br />
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By 1858, thermo-dynamics, as a functional term, was used in William Thomson's paper "An Account of Carnot's Theory of the Motive Power of Heat."<br />
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到1858年,热力学作为一个函数术语,被用于威廉 · 汤姆森的论文“卡诺的热动力理论的帐户。”<br />
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==Branches of thermodynamics==<br />
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==Branches of thermodynamics==<br />
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The study of thermodynamical systems has developed into several related branches, each using a different fundamental model as a theoretical or experimental basis, or applying the principles to varying types of systems.<br />
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The study of thermodynamical systems has developed into several related branches, each using a different fundamental model as a theoretical or experimental basis, or applying the principles to varying types of systems.<br />
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热力学系统的研究已经发展成为几个相关的分支,每个分支都使用不同的基本模型作为理论或实验基础,或者将这些原理应用于不同类型的系统。<br />
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===Classical thermodynamics===<br />
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===Classical thermodynamics===<br />
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Classical thermodynamics is the description of the states of thermodynamic systems at near-equilibrium, that uses macroscopic, measurable properties. It is used to model exchanges of energy, work and heat based on the [[laws of thermodynamics]]. The qualifier ''classical'' reflects the fact that it represents the first level of understanding of the subject as it developed in the 19th century and describes the changes of a system in terms of macroscopic empirical (large scale, and measurable) parameters. A microscopic interpretation of these concepts was later provided by the development of ''statistical mechanics''.<br />
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Classical thermodynamics is the description of the states of thermodynamic systems at near-equilibrium, that uses macroscopic, measurable properties. It is used to model exchanges of energy, work and heat based on the laws of thermodynamics. The qualifier classical reflects the fact that it represents the first level of understanding of the subject as it developed in the 19th century and describes the changes of a system in terms of macroscopic empirical (large scale, and measurable) parameters. A microscopic interpretation of these concepts was later provided by the development of statistical mechanics.<br />
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经典热力学是对近平衡态热力学系统状态的描述,它使用宏观的、可测量的性质。它被用来模拟能量、功和热量的交换,基于热力学定律。经典限定词反映了这样一个事实,即它代表了人们对这个学科在19世纪发展过程中的第一层次的理解,并且描述了一个系统在宏观经验(大尺度和可测量的)参数方面的变化。这些概念的微观解释后来由统计力学的发展提供。<br />
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===Statistical mechanics===<br />
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===Statistical mechanics===<br />
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[[Statistical mechanics]], also called statistical thermodynamics, emerged with the development of atomic and molecular theories in the late 19th century and early 20th century, and supplemented classical thermodynamics with an interpretation of the microscopic interactions between individual particles or quantum-mechanical states. This field relates the microscopic properties of individual atoms and molecules to the macroscopic, bulk properties of materials that can be observed on the human scale, thereby explaining classical thermodynamics as a natural result of statistics, classical mechanics, and [[Quantum mechanics|quantum theory]] at the microscopic level.<ref name= "NKS note b" /><br />
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Statistical mechanics, also called statistical thermodynamics, emerged with the development of atomic and molecular theories in the late 19th century and early 20th century, and supplemented classical thermodynamics with an interpretation of the microscopic interactions between individual particles or quantum-mechanical states. This field relates the microscopic properties of individual atoms and molecules to the macroscopic, bulk properties of materials that can be observed on the human scale, thereby explaining classical thermodynamics as a natural result of statistics, classical mechanics, and quantum theory at the microscopic level.<br />
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统计力学,又称统计热力学,在19世纪末20世纪初随着原子和分子理论的发展而出现,对单个粒子或量子力学状态之间的微观相互作用的解释补充了经典热力学。这个领域将单个原子和分子的微观属性与可以在人类尺度上观察到的物质的宏观体积属性联系起来,从而在微观层次上解释了经典热力学作为统计学、经典力学、量子理论的自然结果。<br />
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===Chemical thermodynamics===<br />
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[[Chemical thermodynamics]] is the study of the interrelation of [[energy]] with [[chemical reactions]] or with a physical change of [[thermodynamic state|state]] within the confines of the [[laws of thermodynamics]].<br />
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Chemical thermodynamics is the study of the interrelation of energy with chemical reactions or with a physical change of state within the confines of the laws of thermodynamics.<br />
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化学热力学是研究能量与化学反应或热力学定律范围内状态的物理变化之间的相互关系。<br />
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===Equilibrium thermodynamics===<br />
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===Equilibrium thermodynamics===<br />
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平衡热力学<br />
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[[Equilibrium thermodynamics]] is the study of transfers of matter and energy in systems or bodies that, by agencies in their surroundings, can be driven from one state of thermodynamic equilibrium to another. The term 'thermodynamic equilibrium' indicates a state of balance, in which all macroscopic flows are zero; in the case of the simplest systems or bodies, their intensive properties are homogeneous, and their pressures are perpendicular to their boundaries. In an equilibrium state there are no unbalanced potentials, or driving forces, between macroscopically distinct parts of the system. A central aim in equilibrium thermodynamics is: given a system in a well-defined initial equilibrium state, and given its surroundings, and given its constitutive walls, to calculate what will be the final equilibrium state of the system after a specified thermodynamic operation has changed its walls or surroundings.<br />
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Equilibrium thermodynamics is the study of transfers of matter and energy in systems or bodies that, by agencies in their surroundings, can be driven from one state of thermodynamic equilibrium to another. The term 'thermodynamic equilibrium' indicates a state of balance, in which all macroscopic flows are zero; in the case of the simplest systems or bodies, their intensive properties are homogeneous, and their pressures are perpendicular to their boundaries. In an equilibrium state there are no unbalanced potentials, or driving forces, between macroscopically distinct parts of the system. A central aim in equilibrium thermodynamics is: given a system in a well-defined initial equilibrium state, and given its surroundings, and given its constitutive walls, to calculate what will be the final equilibrium state of the system after a specified thermodynamic operation has changed its walls or surroundings.<br />
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平衡态热力学研究的是物质和能量在系统或物体中的转移,这些系统或物体在其周围的环境中,可以从一种热力学平衡状态转移到另一种状态。热力学平衡这个术语表示一种平衡状态,在这种状态下所有的宏观流动都是零; 对于最简单的系统或物体来说,它们的密集属性是均匀的,它们的压力垂直于它们的边界。在平衡状态下,系统宏观上截然不同的部分之间没有不平衡的势能或驱动力。平衡态热力学的一个中心目标是: 给定一个处于明确初始平衡状态的系统,给定其周围环境,给定其本构壁,计算在一个特定的热力学操作改变其周围或周围环境后,系统的最终平衡状态是什么。<br />
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[[Non-equilibrium thermodynamics]] is a branch of thermodynamics that deals with systems that are not in [[thermodynamic equilibrium]]. Most systems found in nature are not in thermodynamic equilibrium because they are not in stationary states, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are not in stationary states, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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非平衡态热力学是热力学的一个分支,主要研究非热力学平衡系统。自然界中发现的大多数系统都不在热力学平衡,因为它们不处于静止状态,并且不断不断地受到来自其他系统的物质和能量流动的影响。非平衡体系的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出目前已知的宏观热力学方法的范围。<br />
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--[[用户:厚朴|厚朴]]([[用户讨论:厚朴|讨论]]) 2020年7月20日 (一) 09:41 (CST)continuously and discontinuously的翻译是不是有些不恰当<br />
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==Laws of thermodynamics==<br />
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==Laws of thermodynamics==<br />
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热力学定律<br />
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{{Main|Laws of thermodynamics}}<br />
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Thermodynamics is principally based on a set of four laws which are universally valid when applied to systems that fall within the constraints implied by each. In the various theoretical descriptions of thermodynamics these laws may be expressed in seemingly differing forms, but the most prominent formulations are the following.<br />
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Thermodynamics is principally based on a set of four laws which are universally valid when applied to systems that fall within the constraints implied by each. In the various theoretical descriptions of thermodynamics these laws may be expressed in seemingly differing forms, but the most prominent formulations are the following.<br />
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热力学基本上是建立在一套四条定律的基础上的,这些定律在适用于每个定律所暗示的约束条件下的系统时是普遍有效的。在热力学的各种理论描述中,这些定律可能表现为看似不同的形式,但最突出的公式如下。<br />
--[[用户:厚朴|厚朴]]([[用户讨论:厚朴|讨论]]) 2020年7月20日 (一) 10:05 (CST) set翻译成一集 prominent翻译成著名?<br />
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===Zeroth Law===<br />
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===Zeroth Law===<br />
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第零定律<br />
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The [[zeroth law of thermodynamics]] states: ''If two systems are each in thermal equilibrium with a third, they are also in thermal equilibrium with each other.''<br />
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The zeroth law of thermodynamics states: If two systems are each in thermal equilibrium with a third, they are also in thermal equilibrium with each other.<br />
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美国热力学第零定律协会指出: 如果两个系统各有三分之一的热平衡,那么它们之间的热平衡也是一样的。<br />
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This statement implies that thermal equilibrium is an [[equivalence relation]] on the set of [[thermodynamic system]]s under consideration. Systems are said to be in equilibrium if the small, random exchanges between them (e.g. [[Brownian motion]]) do not lead to a net change in energy. This law is tacitly assumed in every measurement of temperature. Thus, if one seeks to decide whether two bodies are at the same [[temperature]], it is not necessary to bring them into contact and measure any changes of their observable properties in time.<ref>Moran, Michael J. and Howard N. Shapiro, 2008. ''Fundamentals of Engineering Thermodynamics''. 6th ed. Wiley and Sons: 16.</ref> The law provides an empirical definition of temperature, and justification for the construction of practical thermometers.<br />
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This statement implies that thermal equilibrium is an equivalence relation on the set of thermodynamic systems under consideration. Systems are said to be in equilibrium if the small, random exchanges between them (e.g. Brownian motion) do not lead to a net change in energy. This law is tacitly assumed in every measurement of temperature. Thus, if one seeks to decide whether two bodies are at the same temperature, it is not necessary to bring them into contact and measure any changes of their observable properties in time. The law provides an empirical definition of temperature, and justification for the construction of practical thermometers.<br />
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这种说法暗示了热平衡是热力学系统集合上的一个等价关系。如果系统之间的小的、随机的交换(例如:布朗运动)不会导致能量的净变化。这个定律在每次测量温度时都是默认的。因此,如果要确定两个物体是否处于同一温度,就没有必要使它们接触并及时测量它们可观测性质的任何变化。该定律提供了温度的经验定义,以及建造实用温度计的依据。<br />
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The zeroth law was not initially recognized as a separate law of thermodynamics, as its basis in thermodynamical equilibrium was implied in the other laws. The first, second, and third laws had been explicitly stated already, and found common acceptance in the physics community before the importance of the zeroth law for the definition of temperature was realized. As it was impractical to renumber the other laws, it was named the ''zeroth law''.<br />
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The zeroth law was not initially recognized as a separate law of thermodynamics, as its basis in thermodynamical equilibrium was implied in the other laws. The first, second, and third laws had been explicitly stated already, and found common acceptance in the physics community before the importance of the zeroth law for the definition of temperature was realized. As it was impractical to renumber the other laws, it was named the zeroth law.<br />
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第零定律最初并没有被认为是一个独立的热力学定律,因为它在热力学平衡中的基础在其他定律中也有暗示。第一定律、第二定律和第三定律在温度定义的第零定律的重要性被认识到之前已经被物理学界明确阐述,并且得到了普遍接受。由于对其他法律重新编号是不切实际的,因此将其命名为第零法律。<br />
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--[[用户:厚朴|厚朴]]([[用户讨论:厚朴|讨论]]) 2020年7月20日 (一) 10:05 (CST)法律 Law检查一遍<br />
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===First Law===<br />
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===First Law===<br />
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第一定律<br />
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The [[first law of thermodynamics]] states: ''In a process without transfer of matter, the change in [[internal energy]],'' {{math|Δ''U''}}'', of a [[thermodynamic system]] is equal to the energy gained as heat,'' {{math|''Q''}}'', less the thermodynamic work,'' {{math|''W''}}'', done by the system on its surroundings.''<ref>Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics, AIP Press, Woodbury NY, {{ISBN|0883187973}}, p. 79.</ref><ref group=nb>The sign convention (Q is heat supplied ''to'' the system as, W is work done ''by'' the system) is that of [[Rudolf Clausius]]. The opposite sign convention is customary in chemical thermodynamics.</ref><br />
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The first law of thermodynamics states: In a process without transfer of matter, the change in internal energy, , of a thermodynamic system is equal to the energy gained as heat, , less the thermodynamic work, , done by the system on its surroundings.<br />
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能量守恒定律指出: 在一个没有物质转移的过程中,一个热力学系统的内部能量的变化等于作为热量获得的能量,减去系统在其周围所做的热力学功。<br />
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:<math>\Delta U = Q - W</math>.<br />
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<math>\Delta U = Q - W</math>.<br />
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数学 Delta u q-w / 数学。<br />
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For processes that include transfer of matter, a further statement is needed: ''With due account of the respective fiducial reference states of the systems, when two systems, which may be of different chemical compositions, initially separated only by an impermeable wall, and otherwise isolated, are combined into a new system by the thermodynamic operation of removal of the wall, then''<br />
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For processes that include transfer of matter, a further statement is needed: With due account of the respective fiducial reference states of the systems, when two systems, which may be of different chemical compositions, initially separated only by an impermeable wall, and otherwise isolated, are combined into a new system by the thermodynamic operation of removal of the wall, then<br />
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对于包含物质转移的过程,需要进一步的陈述: 在适当考虑了系统各自的基准参考状态的情况下,当两个系统---- 它们可能是不同的化学成分,最初只是被不透水的墙隔开,或者是被隔离---- 通过移除热力学操作结合成一个新的系统时,那么<br />
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:<math>U_0 = U_1 + U_2</math>,<br />
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<math>U_0 = U_1 + U_2</math>,<br />
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数学 u 0 u 1 + u 2 / math,<br />
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''where'' {{math|''U''<sub>0</sub>}} ''denotes the internal energy of the combined system, and'' {{math|''U''<sub>1</sub>}} ''and'' {{math|''U''<sub>2</sub>}} ''denote the internal energies of the respective separated systems.''<br />
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where denotes the internal energy of the combined system, and and denote the internal energies of the respective separated systems.<br />
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其中表示组合系统的内能,并表示各自分离系统的内能。<br />
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Adapted for thermodynamics, this law is an expression of the principle of [[conservation of energy]], which states that energy can be transformed (changed from one form to another), but cannot be created or destroyed.<ref>Callen, H.B. (1960/1985).''Thermodynamics and an Introduction to Thermostatistics'', second edition, John Wiley & Sons, Hoboken NY, {{ISBN|9780471862567}}, pp. 11–13.</ref><br />
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Adapted for thermodynamics, this law is an expression of the principle of conservation of energy, which states that energy can be transformed (changed from one form to another), but cannot be created or destroyed.<br />
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这一定律适用于热力学,是能量守恒定律的一种表述,它指出能量可以转换(从一种形式转变为另一种形式) ,但不能被创造或破坏。<br />
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Internal energy is a principal property of the [[thermodynamic state]], while heat and work are modes of energy transfer by which a process may change this state. A change of internal energy of a system may be achieved by any combination of heat added or removed and work performed on or by the system. As a [[State function|function of state]], the internal energy does not depend on the manner, or on the path through intermediate steps, by which the system arrived at its state.<br />
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Internal energy is a principal property of the thermodynamic state, while heat and work are modes of energy transfer by which a process may change this state. A change of internal energy of a system may be achieved by any combination of heat added or removed and work performed on or by the system. As a function of state, the internal energy does not depend on the manner, or on the path through intermediate steps, by which the system arrived at its state.<br />
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内能是热力学状态的主要特性,而热和功是能量传递的方式,通过这种方式,一个过程可以改变这种状态。系统内部能量的变化可以通过加热或除热以及在系统上或由系统所做的功的任何组合来实现。作为状态的函数,内能并不依赖于系统到达其状态的方式或中间步骤的路径。<br />
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===Second Law===<br />
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===Second Law===<br />
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第二定律<br />
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The [[second law of thermodynamics]] states: ''Heat cannot spontaneously flow from a colder location to a hotter location.''<ref name= "NKS note b" /><br />
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The second law of thermodynamics states: Heat cannot spontaneously flow from a colder location to a hotter location.<br />
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热力学第二定律指出: 热量不能自发地从较冷的地方流向较热的地方。<br />
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This law is an expression of the universal principle of decay observable in nature. The second law is an observation of the fact that over time, differences in temperature, pressure, and chemical potential tend to even out in a physical system that is isolated from the outside world. [[Entropy]] is a measure of how much this process has progressed. The entropy of an isolated system which is not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium. However, principles guiding systems that are far from equilibrium are still debatable. One of such principles is the [[entropy production|maximum entropy production]] principle.<ref>{{cite journal|last1=Onsager|first1=Lars|title=Reciprocal Relations in Irreversible Processes|journal=Phys. Rev.|date=1931|volume=37|issue=405|pages=405–426|doi=10.1103/physrev.37.405|bibcode=1931PhRv...37..405O|doi-access=free}}</ref><ref>{{cite book|last1=Ziegler|first1=H.|title=An Introduction to Thermomechanics|date=1983|location=North Holland}}</ref> It states that non-equilibrium systems behave such a way as to maximize its entropy production.<ref>{{cite journal|last1=Belkin|first1=Andrey|last2=Hubler|first2=A.|last3=Bezryadin|first3=A.|title=Self-Assembled Wiggling Nano-Structures and the Principle of Maximum Entropy Production|journal=Sci. Rep.|date=2015|doi=10.1038/srep08323|pmid=25662746|pmc=4321171|bibcode=2015NatSR...5E8323B|volume=5|page=8323}}</ref><br />
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This law is an expression of the universal principle of decay observable in nature. The second law is an observation of the fact that over time, differences in temperature, pressure, and chemical potential tend to even out in a physical system that is isolated from the outside world. Entropy is a measure of how much this process has progressed. The entropy of an isolated system which is not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium. However, principles guiding systems that are far from equilibrium are still debatable. One of such principles is the maximum entropy production principle. It states that non-equilibrium systems behave such a way as to maximize its entropy production.<br />
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这个定律是可以在自然界观察到的衰变的普遍原理的一种表述。第二定律是对这样一个事实的观察: 随着时间的推移,在与外界隔绝的物理系统中,温度、压力和化学势的差异趋于均衡。熵是对这个过程进展程度的度量。不处于平衡状态的孤立系统的熵会随着时间的推移而增加,在平衡状态时达到最大值。然而,远离平衡的原则指导体系仍然是有争议的。其中一个原则就是最大产生熵原则。它指出,非平衡系统的行为方式使其产生熵最大化。<br />
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In classical thermodynamics, the second law is a basic postulate applicable to any system involving heat energy transfer; in statistical thermodynamics, the second law is a consequence of the assumed randomness of molecular chaos. There are many versions of the second law, but they all have the same effect, which is to explain the phenomenon of [[irreversibility]] in nature.<br />
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In classical thermodynamics, the second law is a basic postulate applicable to any system involving heat energy transfer; in statistical thermodynamics, the second law is a consequence of the assumed randomness of molecular chaos. There are many versions of the second law, but they all have the same effect, which is to explain the phenomenon of irreversibility in nature.<br />
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在经典热力学中,第二定律是适用于任何涉及热能传递的系统的基本假设; 在统计热力学中,第二定律是假定的分子混沌随机性的结果。第二定律有许多版本,但它们都具有同样的效果,即解释自然界中的不可逆现象。<br />
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===Third Law===<br />
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===Third Law===<br />
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第三定律<br />
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The [[third law of thermodynamics]] states: ''As the temperature of a system approaches absolute zero, all processes cease and the entropy of the system approaches a minimum value.''<br />
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The third law of thermodynamics states: As the temperature of a system approaches absolute zero, all processes cease and the entropy of the system approaches a minimum value.<br />
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热力学第三定律指出: 当一个系统的温度接近绝对零度时,所有的过程停止,系统的熵接近最小值。<br />
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This law of thermodynamics is a statistical law of nature regarding entropy and the impossibility of reaching [[absolute zero]] of temperature. This law provides an absolute reference point for the determination of entropy. The entropy determined relative to this point is the absolute entropy. Alternate definitions include "the entropy of all systems and of all states of a system is smallest at absolute zero," or equivalently "it is impossible to reach the absolute zero of temperature by any finite number of processes".<br />
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This law of thermodynamics is a statistical law of nature regarding entropy and the impossibility of reaching absolute zero of temperature. This law provides an absolute reference point for the determination of entropy. The entropy determined relative to this point is the absolute entropy. Alternate definitions include "the entropy of all systems and of all states of a system is smallest at absolute zero," or equivalently "it is impossible to reach the absolute zero of temperature by any finite number of processes".<br />
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这个热力学定律是关于熵和不可能达到绝对零度的自然统计法则。这个定律为确定熵提供了一个绝对的参考点。相对于这个点确定的熵就是绝对熵。替代定义包括”系统的所有系统和系统的所有状态的熵在绝对零度时最小” ,或相当于”任何有限数目的过程都不可能达到绝对零度”。<br />
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Absolute zero, at which all activity would stop if it were possible to achieve, is −273.15&nbsp;°C (degrees Celsius), or −459.67&nbsp;°F (degrees Fahrenheit), or 0 K (kelvin), or 0° R (degrees [[Rankine scale|Rankine]]).<br />
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Absolute zero, at which all activity would stop if it were possible to achieve, is −273.15&nbsp;°C (degrees Celsius), or −459.67&nbsp;°F (degrees Fahrenheit), or 0 K (kelvin), or 0° R (degrees Rankine).<br />
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绝对零度是-273.15摄氏度(摄氏度) ,或-459.67华氏度(华氏度) ,或0 k (开尔文) ,或0 r (朗肯度)。<br />
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==System models==<br />
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系统模型<br />
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[[File:system boundary.svg|200px|thumb|right|A diagram of a generic thermodynamic system]]<br />
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A diagram of a generic thermodynamic system<br />
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一个通用的热力学系统图表<br />
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An important concept in thermodynamics is the [[thermodynamic system]], which is a precisely defined region of the universe under study. Everything in the universe except the system is called the [[Environment (systems)|''surroundings'']]. A system is separated from the remainder of the universe by a [[Boundary (thermodynamic)|''boundary'']] which may be a physical boundary or notional, but which by convention defines a finite volume. Exchanges of [[Work (thermodynamics)|work]], [[heat]], or [[matter]] between the system and the surroundings take place across this boundary.<br />
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An important concept in thermodynamics is the thermodynamic system, which is a precisely defined region of the universe under study. Everything in the universe except the system is called the surroundings. A system is separated from the remainder of the universe by a boundary which may be a physical boundary or notional, but which by convention defines a finite volume. Exchanges of work, heat, or matter between the system and the surroundings take place across this boundary.<br />
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热力学中的一个重要概念是热力学系统,它是研究中的宇宙的一个精确定义的区域。除了这个系统之外,宇宙中的一切都被称为环境。一个系统通过一个边界从宇宙的其余部分中分离出来,这个边界可能是物理边界或者概念边界,但是按照惯例,它定义了一个有限的体积。系统和周围环境之间的功、热或物质的交换发生在这个边界上。<br />
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In practice, the boundary of a system is simply an imaginary dotted line drawn around a volume within which is going to be a change in the [[internal energy]] of that volume. Anything that passes across the boundary that effects a change in the internal energy of the system needs to be accounted for in the energy balance equation. The volume can be the region surrounding a single atom resonating energy, such as [[Max Planck]] defined in 1900; it can be a body of steam or air in a [[steam engine]], such as [[Nicolas Léonard Sadi Carnot|Sadi Carnot]] defined in 1824; it can be the body of a [[tropical cyclone]], such as [[Kerry Emanuel]] theorized in 1986 in the field of [[atmospheric thermodynamics]]; it could also be just one [[nuclide]] (i.e. a system of [[quark]]s) as hypothesized in [[quantum thermodynamics]], or the [[event horizon]] of a [[black hole thermodynamics|black hole]].<br />
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In practice, the boundary of a system is simply an imaginary dotted line drawn around a volume within which is going to be a change in the internal energy of that volume. Anything that passes across the boundary that effects a change in the internal energy of the system needs to be accounted for in the energy balance equation. The volume can be the region surrounding a single atom resonating energy, such as Max Planck defined in 1900; it can be a body of steam or air in a steam engine, such as Sadi Carnot defined in 1824; it can be the body of a tropical cyclone, such as Kerry Emanuel theorized in 1986 in the field of atmospheric thermodynamics; it could also be just one nuclide (i.e. a system of quarks) as hypothesized in quantum thermodynamics, or the event horizon of a black hole.<br />
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实际上,一个系统的边界只是一个虚构的虚线,它围绕着一个体积绘制,体积内部能量将发生变化。任何通过边界的影响系统内部能量的变化都需要在能量平衡方程中加以解释。体积可以是围绕单个原子共振能量的区域,如马克斯 · 普朗克在1900年定义的; 它可以是蒸汽机中的蒸汽体或空气体,如萨迪 · 卡诺在1824年定义的; 它可以是热带气旋的体,如 Kerry Emanuel 在1986年在大气热力学领域建立的理论; 它也可以只是一个核素(即:。量子热力学中假设的夸克系统,或黑洞的事件视界。<br />
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Boundaries are of four types: fixed, movable, real, and imaginary. For example, in an engine, a fixed boundary means the piston is locked at its position, within which a constant volume process might occur. If the piston is allowed to move that boundary is movable while the cylinder and cylinder head boundaries are fixed. For closed systems, boundaries are real while for open systems boundaries are often imaginary. In the case of a jet engine, a fixed imaginary boundary might be assumed at the intake of the engine, fixed boundaries along the surface of the case and a second fixed imaginary boundary across the exhaust nozzle.<br />
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Boundaries are of four types: fixed, movable, real, and imaginary. For example, in an engine, a fixed boundary means the piston is locked at its position, within which a constant volume process might occur. If the piston is allowed to move that boundary is movable while the cylinder and cylinder head boundaries are fixed. For closed systems, boundaries are real while for open systems boundaries are often imaginary. In the case of a jet engine, a fixed imaginary boundary might be assumed at the intake of the engine, fixed boundaries along the surface of the case and a second fixed imaginary boundary across the exhaust nozzle.<br />
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边界有四种类型: 固定的、可移动的、真实的和想象的。例如,在发动机中,一个固定的边界意味着活塞被锁定在它的位置,在那里可能发生一个定容过程。如果活塞允许移动,那么边界是可移动的,而气缸和气缸盖边界是固定的。对于封闭系统,边界是真实的,而对于开放系统,边界往往是虚构的。在喷气发动机的情况下,可以假定在发动机进气口处有一个固定的虚边界,沿着箱体表面有一个固定的边界,在排气喷嘴处有一个固定的虚边界。<br />
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Generally, thermodynamics distinguishes three classes of systems, defined in terms of what is allowed to cross their boundaries:<br />
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Generally, thermodynamics distinguishes three classes of systems, defined in terms of what is allowed to cross their boundaries:<br />
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一般来说,热力学区分了三类系统,根据允许什么跨越它们的边界来定义:<br />
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{{table of thermodynamic systems}}<br />
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As time passes in an isolated system, internal differences of pressures, densities, and temperatures tend to even out. A system in which all equalizing processes have gone to completion is said to be in a [[state (thermodynamic)|state]] of [[thermodynamic equilibrium]].<br />
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As time passes in an isolated system, internal differences of pressures, densities, and temperatures tend to even out. A system in which all equalizing processes have gone to completion is said to be in a state of thermodynamic equilibrium.<br />
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在一个孤立的系统中,随着时间的推移,压力、密度和温度的内部差异趋于平衡。一个所有均衡过程均已完成的系统被称为处于热力学平衡状态。<br />
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Once in thermodynamic equilibrium, a system's properties are, by definition, unchanging in time. Systems in equilibrium are much simpler and easier to understand than are systems which are not in equilibrium. Often, when analysing a dynamic thermodynamic process, the simplifying assumption is made that each intermediate state in the process is at equilibrium, producing thermodynamic processes which develop so slowly as to allow each intermediate step to be an equilibrium state and are said to be [[reversible process (thermodynamics)|reversible processes]].<br />
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Once in thermodynamic equilibrium, a system's properties are, by definition, unchanging in time. Systems in equilibrium are much simpler and easier to understand than are systems which are not in equilibrium. Often, when analysing a dynamic thermodynamic process, the simplifying assumption is made that each intermediate state in the process is at equilibrium, producing thermodynamic processes which develop so slowly as to allow each intermediate step to be an equilibrium state and are said to be reversible processes.<br />
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一旦进入热力学平衡,系统的属性,根据定义,在时间上是不变的。处于平衡状态的系统比不处于平衡状态的系统要简单得多,也更容易理解。通常,当分析一个动态热力学过程时,会做出这样的简化假设: 过程中的每一个居间态都处于平衡状态,产生的热力学过程发展得如此缓慢,以至于每一个中间步骤都是一个平衡状态,称之为可逆过程。<br />
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==States and processes==<br />
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==States and processes==<br />
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状态和过程<br />
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When a system is at equilibrium under a given set of conditions, it is said to be in a definite [[thermodynamic state]]. The state of the system can be described by a number of [[state function|state quantities]] that do not depend on the process by which the system arrived at its state. They are called [[intensive variable]]s or [[extensive variable]]s according to how they change when the size of the system changes. The properties of the system can be described by an [[equation of state]] which specifies the relationship between these variables. State may be thought of as the instantaneous quantitative description of a system with a set number of variables held constant.<br />
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When a system is at equilibrium under a given set of conditions, it is said to be in a definite thermodynamic state. The state of the system can be described by a number of state quantities that do not depend on the process by which the system arrived at its state. They are called intensive variables or extensive variables according to how they change when the size of the system changes. The properties of the system can be described by an equation of state which specifies the relationship between these variables. State may be thought of as the instantaneous quantitative description of a system with a set number of variables held constant.<br />
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当一个系统在一组给定的条件下处于平衡状态时,我们称之为处于一个确定的热力学状态。系统的状态可以用许多状态量来描述,这些状态量并不依赖于系统到达其状态的过程。它们被称为密集型变量或扩展型变量,这取决于它们在系统规模发生变化时的变化情况。系统的属性可以用一个状态方程来描述,它指定了这些变量之间的关系。状态可以被认为是一系列变量保持不变的系统的瞬时定量描述。<br />
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A [[thermodynamic process]] may be defined as the energetic evolution of a thermodynamic system proceeding from an initial state to a final state. It can be described by [[process function|process quantities]]. Typically, each thermodynamic process is distinguished from other processes in energetic character according to what parameters, such as temperature, pressure, or volume, etc., are held fixed; Furthermore, it is useful to group these processes into pairs, in which each variable held constant is one member of a [[conjugate variables (thermodynamics)|conjugate]] pair.<br />
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A thermodynamic process may be defined as the energetic evolution of a thermodynamic system proceeding from an initial state to a final state. It can be described by process quantities. Typically, each thermodynamic process is distinguished from other processes in energetic character according to what parameters, such as temperature, pressure, or volume, etc., are held fixed; Furthermore, it is useful to group these processes into pairs, in which each variable held constant is one member of a conjugate pair.<br />
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热力学过程可以被定义为热力学系统从初始状态到最终状态的能量演化。它可以用工艺量来描述。通常情况下,根据温度、压力、体积等参数的固定程度,每个热力学过程过程与能量特征中的其他过程是不同的; 此外,将这些过程分组成对也很有用,每个变量保持常数是一个共轭对的一个成员。<br />
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Several commonly studied thermodynamic processes are:<br />
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Several commonly studied thermodynamic processes are:<br />
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一些常见的研究热力学过程是:<br />
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* [[Adiabatic process]]: occurs without loss or gain of energy by [[heat]]<br />
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* [[Isenthalpic process]]: occurs at a constant [[enthalpy]]<br />
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* [[Isentropic process]]: a reversible adiabatic process, occurs at a constant [[entropy]]<br />
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* [[Isobaric process]]: occurs at constant [[pressure]]<br />
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* [[Isochoric process]]: occurs at constant [[Volume (thermodynamics)|volume]] (also called isometric/isovolumetric)<br />
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* [[Isothermal process]]: occurs at a constant [[temperature]]<br />
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* [[steady state|Steady state process]]: occurs without a change in the [[internal energy]]<br />
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== Instrumentation ==<br />
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== Instrumentation ==<br />
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仪器仪表<br />
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There are two types of [[thermodynamic instruments]], the '''meter''' and the '''reservoir'''. A thermodynamic meter is any device which measures any parameter of a [[thermodynamic system]]. In some cases, the thermodynamic parameter is actually defined in terms of an idealized measuring instrument. For example, the [[zeroth law of thermodynamics|zeroth law]] states that if two bodies are in thermal equilibrium with a third body, they are also in thermal equilibrium with each other. This principle, as noted by [[James Clerk Maxwell|James Maxwell]] in 1872, asserts that it is possible to measure temperature. An idealized [[thermometer]] is a sample of an ideal gas at constant pressure. From the [[ideal gas law]] ''pV=nRT'', the volume of such a sample can be used as an indicator of temperature; in this manner it defines temperature. Although pressure is defined mechanically, a pressure-measuring device, called a [[barometer]] may also be constructed from a sample of an ideal gas held at a constant temperature. A [[calorimeter]] is a device which is used to measure and define the internal energy of a system.<br />
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There are two types of thermodynamic instruments, the meter and the reservoir. A thermodynamic meter is any device which measures any parameter of a thermodynamic system. In some cases, the thermodynamic parameter is actually defined in terms of an idealized measuring instrument. For example, the zeroth law states that if two bodies are in thermal equilibrium with a third body, they are also in thermal equilibrium with each other. This principle, as noted by James Maxwell in 1872, asserts that it is possible to measure temperature. An idealized thermometer is a sample of an ideal gas at constant pressure. From the ideal gas law pV=nRT, the volume of such a sample can be used as an indicator of temperature; in this manner it defines temperature. Although pressure is defined mechanically, a pressure-measuring device, called a barometer may also be constructed from a sample of an ideal gas held at a constant temperature. A calorimeter is a device which is used to measure and define the internal energy of a system.<br />
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有两种类型的热力学设备,水表和水库。热力学仪表是测量热力学系统的任何参数的任何装置。在某些情况下,热力学参数实际上是用理想化的测量仪器来定义的。例如,第零定律指出,如果两个物体在热平衡中有第三个物体,那么它们也在热平衡中。正如詹姆斯 · 麦克斯韦尔在1872年指出的那样,这个原理断言测量温度是可能的。理想温度计是恒压下理想气体的样品。根据理想气体定律 pV nRT,这样一个样品的体积可以用作温度的指示器; 在这种方式下,它定义了温度。虽然压力是机械定义的,一个称为气压计的压力测量装置也可以由恒定温度下的理想气体样品构成。量热计是用来测量和定义系统内部能量的装置。<br />
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A thermodynamic reservoir is a system which is so large that its state parameters are not appreciably altered when it is brought into contact with the system of interest. When the reservoir is brought into contact with the system, the system is brought into equilibrium with the reservoir. For example, a pressure reservoir is a system at a particular pressure, which imposes that pressure upon the system to which it is mechanically connected. The Earth's atmosphere is often used as a pressure reservoir. If ocean water is used to cool a power plant, the ocean is often a temperature reservoir in the analysis of the power plant cycle.<br />
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A thermodynamic reservoir is a system which is so large that its state parameters are not appreciably altered when it is brought into contact with the system of interest. When the reservoir is brought into contact with the system, the system is brought into equilibrium with the reservoir. For example, a pressure reservoir is a system at a particular pressure, which imposes that pressure upon the system to which it is mechanically connected. The Earth's atmosphere is often used as a pressure reservoir. If ocean water is used to cool a power plant, the ocean is often a temperature reservoir in the analysis of the power plant cycle.<br />
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热力学储存器是这样一个系统,它的状态参数如此之大,当它与感兴趣的系统接触时,它的状态参数没有明显的改变。当油藏与系统接触时,系统与油藏达到平衡。例如,压力容器是一个处于特定压力下的系统,它对与之机械连接的系统施加压力。地球的大气层经常被用作压力储存器。如果用海水来冷却发电厂,在分析发电厂的循环过程中,海洋通常是一个温度储存库。<br />
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== Conjugate variables ==<br />
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== Conjugate variables ==<br />
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共轭变量<br />
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{{Main|Conjugate variables (thermodynamics)|l1=Conjugate variables}}<br />
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The central concept of thermodynamics is that of [[energy]], the ability to do [[Work (thermodynamics)|work]]. By the [[first law of thermodynamics|First Law]], the total energy of a system and its surroundings is conserved. Energy may be transferred into a system by heating, compression, or addition of matter, and extracted from a system by cooling, expansion, or extraction of matter. In [[mechanics]], for example, energy transfer equals the product of the force applied to a body and the resulting displacement.<br />
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The central concept of thermodynamics is that of energy, the ability to do work. By the First Law, the total energy of a system and its surroundings is conserved. Energy may be transferred into a system by heating, compression, or addition of matter, and extracted from a system by cooling, expansion, or extraction of matter. In mechanics, for example, energy transfer equals the product of the force applied to a body and the resulting displacement.<br />
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热力学的核心概念是能量,做功的能力。根据第一定律,系统及其周围环境的总能量是守恒的。能量可以通过加热、压缩或添加物质的方式转移到系统中,也可以通过冷却、膨胀或提取物质的方式从系统中提取。例如,在力学中,能量传递等于作用在物体上的力和由此产生的位移的乘积。<br />
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[[conjugate variables (thermodynamics)|Conjugate variables]] are pairs of thermodynamic concepts, with the first being akin to a "force" applied to some [[thermodynamic system]], the second being akin to the resulting "displacement," and the product of the two equalling the amount of energy transferred. The common conjugate variables are:<br />
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Conjugate variables are pairs of thermodynamic concepts, with the first being akin to a "force" applied to some thermodynamic system, the second being akin to the resulting "displacement," and the product of the two equalling the amount of energy transferred. The common conjugate variables are:<br />
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共轭变量是成对的热力学概念,第一个类似于施加在某些热力学系统上的“力” ,第二个类似于由此产生的“位移” ,两者的乘积等于所转移的能量。常见的共轭变量有:<br />
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* [[Pressure]]-[[Volume (thermodynamics)|volume]] (the [[Mechanics|mechanical]] parameters);<br />
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* [[Temperature]]-[[entropy]] (thermal parameters);<br />
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* [[Chemical potential]]-[[particle number]] (material parameters).<br />
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== Potentials ==<br />
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== Potentials ==<br />
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== Potentials ==<br />
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[[Thermodynamic potential]]s are different quantitative measures of the stored energy in a system. Potentials are used to measure the energy changes in systems as they evolve from an initial state to a final state. The potential used depends on the constraints of the system, such as constant temperature or pressure. For example, the Helmholtz and Gibbs energies are the energies available in a system to do useful work when the temperature and volume or the pressure and temperature are fixed, respectively.<br />
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Thermodynamic potentials are different quantitative measures of the stored energy in a system. Potentials are used to measure the energy changes in systems as they evolve from an initial state to a final state. The potential used depends on the constraints of the system, such as constant temperature or pressure. For example, the Helmholtz and Gibbs energies are the energies available in a system to do useful work when the temperature and volume or the pressure and temperature are fixed, respectively.<br />
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热力学势是体系中储存能量的不同定量度量。势能被用来测量系统从初始状态到最终状态的能量变化。所用的电位取决于系统的约束条件,如恒温或恒压。例如,亥姆霍兹能量和吉布斯能量是当温度和体积或压力和温度分别固定时,系统中可用于做有用功的能量。<br />
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The five most well known potentials are:<br />
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The five most well known potentials are:<br />
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五个最有名的潜力是:<br />
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{{table of thermodynamic potentials}}<br />
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where <math>T</math> is the [[thermodynamic temperature|temperature]], <math>S</math> the [[entropy]], <math>p</math> the [[pressure]], <math>V</math> the [[Volume (thermodynamics)|volume]], <math>\mu</math> the [[chemical potential]], <math>N</math> the number of particles in the system, and <math>i</math> is the count of particles types in the system.<br />
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where <math>T</math> is the temperature, <math>S</math> the entropy, <math>p</math> the pressure, <math>V</math> the volume, <math>\mu</math> the chemical potential, <math>N</math> the number of particles in the system, and <math>i</math> is the count of particles types in the system.<br />
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数学 t / math 是温度,数学 s / math 是熵,数学 p / math 是压力,数学 v / math 是体积,数学 mu / math 是化学势,数学 n / math 是系统中粒子的数量,数学 i / math 是系统中粒子类型的数量。<br />
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Thermodynamic potentials can be derived from the energy balance equation applied to a thermodynamic system. Other thermodynamic potentials can also be obtained through [[Legendre transformation]].<br />
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Thermodynamic potentials can be derived from the energy balance equation applied to a thermodynamic system. Other thermodynamic potentials can also be obtained through Legendre transformation.<br />
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热力学势可以从应用于热力学系统的能量平衡方程推导出来。其他热力学势也可以通过勒壤得转换得到。<br />
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== Applied fields ==<br />
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== Applied fields ==<br />
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应用领域<br />
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{{columns-list|colwidth=22em|<br />
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{{columns-list|colwidth=22em|<br />
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{ columns-list | colwidth 22em | <br />
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* [[Atmospheric thermodynamics]]<br />
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* [[Biological thermodynamics]]<br />
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* [[Black hole thermodynamics]]<br />
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* [[Chemical thermodynamics]]<br />
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* [[Classical thermodynamics]]<br />
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* [[Thermodynamic equilibrium|Equilibrium thermodynamics]]<br />
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* [[Industrial ecology]] (re: [[Exergy]])<br />
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* [[Maximum entropy thermodynamics]]<br />
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* [[Non-equilibrium thermodynamics]]<br />
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* [[Philosophy of thermal and statistical physics]]<br />
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* [[Psychrometrics]]<br />
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* [[Quantum thermodynamics]]<br />
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* [[Statistical thermodynamics]]<br />
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* [[Thermoeconomics]]<br />
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}}<br />
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}}<br />
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}}<br />
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== See also ==<br />
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== See also ==<br />
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参见<br />
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{{portal|Physics}}<br />
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* [[Thermodynamic process path]]<br />
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===Lists and timelines===<br />
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===Lists and timelines===<br />
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清单和时间线<br />
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* [[List of important publications in physics#Thermodynamics|List of important publications in thermodynamics]]<br />
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* [[List of textbooks in statistical mechanics|List of textbooks on thermodynamics and statistical mechanics]]<br />
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* [[List of thermal conductivities]]<br />
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* [[List of thermodynamic properties]]<br />
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* [[Table of thermodynamic equations]]<br />
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* [[Timeline of thermodynamics]]<br />
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== Notes ==<br />
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== Notes ==<br />
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注释<br />
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{{reflist|group=nb}}<br />
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==References==<br />
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==References==<br />
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参考资料<br />
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{{Reflist|35em}}<br />
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==Further reading==<br />
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==Further reading==<br />
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进一步阅读<br />
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* {{cite book|author1=Goldstein, Martin|author2=Inge F.|lastauthoramp=yes|title=The Refrigerator and the Universe|url=https://archive.org/details/refrigeratoruniv0000gold|url-access=registration|publisher=Harvard University Press|year=1993|isbn=978-0-674-75325-9|location=|pages=|oclc=32826343}} A nontechnical introduction, good on historical and interpretive matters.<br />
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* {{cite journal |last1=Kazakov |first1=Andrei |last2=Muzny |first2=Chris D. |last3=Chirico |first3=Robert D. |last4=Diky |first4=Vladimir V. |last5=Frenkel |first5=Michael |title=Web Thermo Tables – an On-Line Version of the TRC Thermodynamic Tables |journal=Journal of Research of the National Institute of Standards and Technology |volume=113 |issue=4 |year=2008 |pages=209–220 |issn=1044-677X |doi=10.6028/jres.113.016 |pmc=4651616 |pmid=27096122}}<br />
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* {{cite book|author=Gibbs J.W.|title=The Collected Works of J. Willard Gibbs Thermodynamics.|publisher=Longmans, Green and Co.|year=1928|isbn=|location=New York|pages=|oclc=}} Vol. 1, pp. 55–349.<br />
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* {{cite book|author=Guggenheim E.A.|title=Modern thermodynamics by the methods of Willard Gibbs|publisher=Methuen & co. ltd.|year=1933|isbn=|location=London|pages=|oclc=}}<br />
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* {{cite book|author=Denbigh K.|title=The Principles of Chemical Equilibrium: With Applications in Chemistry and Chemical Engineering.|publisher=Cambridge University Press|year=1981|isbn=|location=London|pages=|oclc=}}<br />
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* {{cite book|author=Stull, D.R., Westrum Jr., E.F. and Sinke, G.C.|title=The Chemical Thermodynamics of Organic Compounds.|publisher=John Wiley and Sons, Inc.|year=1969|isbn=|location=London|pages=|oclc=}}<br />
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* {{cite book|author=Bazarov I.P.|title=Thermodynamics: Textbook.|publisher=Lan publishing house|year=2010|isbn=978-5-8114-1003-3|location=St. Petersburg|page=384|oclc=}} 5th ed. (in Russian)<br />
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* {{cite book|author=Bawendi Moungi G., Alberty Robert A. and Silbey Robert J.|title=Physical Chemistry|publisher=J. Wiley & Sons, Incorporated|year=2004|isbn=|location=|pages=|oclc=}}<br />
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* {{cite book|author=Alberty Robert A.|title=Thermodynamics of Biochemical Reactions|publisher=Wiley-Interscience|year=2003|isbn=|location=|pages=|oclc=}}<br />
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* {{cite book|author=Alberty Robert A.|title=Biochemical Thermodynamics: Applications of Mathematica|journal=Methods of Biochemical Analysis|publisher=John Wiley & Sons, Inc.|year=2006|volume=48|isbn=978-0-471-75798-6|location=|pages=1–458|pmid=16878778|oclc=}}<br />
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The following titles are more technical:<br />
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The following titles are more technical:<br />
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下面的标题更具技术性:<br />
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* {{Cite book|title=Advanced Engineering Thermodynamics|last=Bejan|first=Adrian|publisher=Wiley|year=2016|isbn=978-1-119-05209-8|edition=4|location=|pages=}}<br />
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* {{cite book|author=Cengel, Yunus A., & Boles, Michael A.|title=Thermodynamics – an Engineering Approach|publisher=McGraw Hill|year=2002|isbn=978-0-07-238332-4|location=|pages=|oclc=45791449|url-access=registration|url=https://archive.org/details/thermodynamicsen00ceng_0}}<br />
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* {{cite book|author=Dunning-Davies, Jeremy|title=Concise Thermodynamics: Principles and Applications|publisher=Horwood Publishing|year=1997|isbn=978-1-8985-6315-0|location=|pages=|oclc=36025958}}<br />
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* {{cite book|author1=Kroemer, Herbert|author2=Kittel, Charles|lastauthoramp=yes|title=Thermal Physics|publisher=W.H. Freeman Company|year=1980|isbn=978-0-7167-1088-2|location=|pages=|oclc=32932988}}<br />
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== External links ==<br />
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== External links ==<br />
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外部链接<br />
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{{Wikibooks|Engineering Thermodynamics}}<br />
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{{wikiquote|Thermodynamics}}<br />
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* {{cite EB1911 |title=Thermodynamics |volume=26 |pages=808–814 |short=x |url=https://archive.org/details/encyclopaediabri26chisrich/page/808}}<br />
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* [http://tigger.uic.edu/~mansoori/Thermodynamic.Data.and.Property_html Thermodynamics Data & Property Calculation Websites]<br />
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* [http://tigger.uic.edu/~mansoori/Thermodynamics.Educational.Sites_html Thermodynamics Educational Websites]<br />
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* [http://scienceworld.wolfram.com/physics/topics/Thermodynamics.html Thermodynamics at ''ScienceWorld'']<br />
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* [http://www.wiley.com/legacy/college/boyer/0470003790/reviews/thermo/thermo_intro.htm Biochemistry Thermodynamics]<br />
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* [http://farside.ph.utexas.edu/teaching/sm1/lectures/lectures.html Thermodynamics and Statistical Mechanics]<br />
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* [https://web.archive.org/web/20090430200028/http://www.ent.ohiou.edu/~thermo/ Engineering Thermodynamics – A Graphical Approach]<br />
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* [http://farside.ph.utexas.edu/teaching/sm1/statmech.pdf Thermodynamics and Statistical Mechanics] by Richard Fitzpatrick<br />
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<small>This page was moved from [[wikipedia:en:Thermodynamics]]. Its edit history can be viewed at [[热力学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E7%83%AD%E5%8A%9B%E5%AD%A6&diff=21960热力学2021-02-23T09:29:53Z<p>Jxzhou:</p>
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<div>此词条暂由jxzhou翻译,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{short description|Physics of heat, work, and temperature}}<br />
{{Use dmy dates|date=February 2016}}<br />
[[File:Carnot engine (hot body - working body - cold body).jpg|thumb|300px|right|Annotated color version of the original 1824 [[Carnot heat engine]] showing the hot body (boiler), working body (system, steam), and cold body (water), the letters labeled according to the stopping points in [[Carnot cycle]].]]<br />
{{Thermodynamics}}<br />
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'''Thermodynamics''' is a branch of [[physics]] that deals with [[heat]], [[Work (thermodynamics)|work]], and [[temperature]], and their relation to [[energy]], [[radiation]], and physical properties of [[matter]]. The behavior of these quantities is governed by the four [[laws of thermodynamics]] which convey a quantitative description using measurable macroscopic [[physical quantity|physical quantities]], but may be explained in terms of [[microscopic]] constituents by [[statistical mechanics]]. Thermodynamics applies to a wide variety of topics in [[science]] and [[engineering]], especially [[physical chemistry]], [[chemical engineering]] and [[mechanical engineering]], but also in other complex fields such as [[meteorology]].<br />
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热力学是物理学的一个分支,研究热、功和温度,以及它们与能量、辐射和物质物理性质的关系。这些量的行为遵循四个热力学定律,热力学定律用可测量的宏观物理量给出了一个定量描述,但是可以用统计力学以微观组成来解释。热力学适用于科学和工程中的各种各样的主题,尤其是物理化学、化学工程和机械工程,但也适用于气象学这样复杂的领域。<br />
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Historically, thermodynamics developed out of a desire to increase the [[thermodynamic efficiency|efficiency]] of early [[steam engine]]s, particularly through the work of French physicist [[Nicolas Léonard Sadi Carnot]] (1824) who believed that engine efficiency was the key that could help France win the [[Napoleonic Wars]].<ref>{{cite book | last = Clausius | first = Rudolf | title = On the Motive Power of Heat, and on the Laws which can be deduced from it for the Theory of Heat | publisher = Poggendorff's Annalen der Physik, LXXIX (Dover Reprint) | year = 1850 | isbn = 978-0-486-59065-3}}</ref> Scots-Irish physicist [[William Thomson, 1st Baron Kelvin|Lord Kelvin]] was the first to formulate a concise definition of thermodynamics in 1854<ref name=kelvin1854>{{cite book<br />
|title=Mathematical and Physical Papers<br />
|author= William Thomson, LL.D. D.C.L., F.R.S.<br />
|location=London, Cambridge<br />
|year=1882<br />
|volume=1<br />
|page=232<br />
|publisher=C.J. Clay, M.A. & Son, Cambridge University Press<br />
|url=https://books.google.com/books?id=nWMSAAAAIAAJ&q=On+an+Absolute+Thermometric+Scale+Founded+on+Carnot%E2%80%99s+Theory&pg=PA100<br />
}}</ref> which stated, "Thermo-dynamics is the subject of the relation of heat to forces acting between contiguous parts of bodies, and the relation of heat to electrical agency."<br />
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从历史上看,热力学是出于提高早期蒸汽机的热力学效率的愿望而发展的,特别是通过法国物理学家 NicolasLéonardSadi Carnot(1824)的工作,他认为发动机效率是帮助法国赢得拿破仑战争的关键。苏格兰裔爱尔兰物理学家开尔文勋爵(Lord Kelvin)于1854年首次提出了热力学的简明定义,其中指出:“热力学的主题是物体相邻部分之间热量与作用力的关系,以及热量与电能的关系。”<br />
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The initial application of thermodynamics to [[mechanical heat engine]]s was quickly extended to the study of chemical compounds and chemical reactions. [[Chemical thermodynamics]] studies the nature of the role of [[entropy]] in the process of [[chemical reaction]]s and has provided the bulk of expansion and knowledge of the field.<ref name="Gibbs 1876">{{cite book|author=Gibbs, Willard, J.|title=Transactions of the Connecticut Academy of Arts and Sciences|volume=III|pages=[https://archive.org/details/transactions03conn/page/108 108]–248, 343–524|year=1874–1878|url=https://archive.org/details/transactions03conn|publisher=New Haven}}</ref><ref name="Duhem 1886">Duhem, P.M.M. (1886). ''Le Potential Thermodynamique et ses Applications'', Hermann, Paris.</ref><ref name="Lewis Randall 1923">{{cite book | last1=Lewis | first1=Gilbert N. | last2=Randall | first2=Merle | title=Thermodynamics and the Free Energy of Chemical Substances | url=https://archive.org/details/thermodynamicsfr00gnle | publisher=McGraw-Hill Book Co. Inc. | year=1923}}</ref><ref name="Guggenheim 1933">Guggenheim, E.A. (1933). ''Modern Thermodynamics by the Methods of J.W. Gibbs'', Methuen, London.</ref><ref name="Guggenheim 1949/1967">Guggenheim, E.A. (1949/1967). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', 1st edition 1949, 5th edition 1967, North-Holland, Amsterdam.</ref><ref>{{cite book | author=Ilya Prigogine, I. & Defay, R., translated by D.H. Everett| title=Chemical Thermodynamics | year=1954 | publisher=Longmans, Green & Co., London. Includes classical non-equilibrium thermodynamics.}}<br />
</ref><ref name=Fermi>{{cite book<br />
|title=Thermodynamics<br />
|author=Enrico Fermi<br />
|url=https://books.google.com/books?id=VEZ1ljsT3IwC&q=thermodynamics<br />
|isbn=978-0486603612<br />
|publisher=Courier Dover Publications<br />
|year=1956<br />
|page=ix<br />
|oclc=230763036}}</ref><ref name="Perrot" >{{cite book | author=Perrot, Pierre | title=A to Z of Thermodynamics | publisher=Oxford University Press | year=1998 | isbn=978-0-19-856552-9 | oclc=123283342}}</ref><ref>{{cite book | author=Clark, John, O.E.| title=The Essential Dictionary of Science | publisher=Barnes & Noble Books | year=2004 | isbn=978-0-7607-4616-5 | oclc=58732844}}</ref> Other formulations of thermodynamics emerged. [[Statistical thermodynamics]], or statistical mechanics, concerns itself with [[statistics|statistical]] predictions of the collective motion of particles from their microscopic behavior. In 1909, [[Constantin Carathéodory]] presented a purely mathematical approach in an [[axiomatic]] formulation, a description often referred to as ''geometrical thermodynamics''.<br />
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热力学在机械热机上的最初应用很快扩展到了化学化合物和化学反应的研究。化学热力学研究了熵在化学反应过程中的作用性本质,并提供了更广阔的领域和知识。热力学的其他公式出现了。统计热力学,或称统计力学,从微观角度对粒子的集体运动进行统计预测。在1909年,康斯坦丁·卡拉西奥多在一个公理化形式里提出了一种纯粹的数学方法,通常被称为几何热力学。<br />
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==Introduction 引言==<br />
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A description of any thermodynamic system employs the four [[laws of thermodynamics]] that form an axiomatic basis. The first law specifies that energy can be exchanged between physical systems as [[heat]] and [[Mechanical work|work]].<ref>{{cite book | author=Van Ness, H.C. | title=Understanding Thermodynamics | publisher=Dover Publications, Inc. | year=1983 | origyear=1969 | isbn=9780486632773 | oclc=8846081 | url-access=registration | url=https://archive.org/details/understandingthe00vann }}</ref> The second law defines the existence of a quantity called [[entropy]], that describes the direction, thermodynamically, that a system can evolve and quantifies the state of order of a system and that can be used to quantify the useful work that can be extracted from the system.<ref>{{cite book | author=Dugdale, J.S. | title=Entropy and its Physical Meaning | publisher=Taylor and Francis | year=1998 | isbn=978-0-7484-0569-5 | oclc=36457809}}</ref><br />
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A description of any thermodynamic system employs the four laws of thermodynamics that form an axiomatic basis. The first law specifies that energy can be exchanged between physical systems as heat and work. The second law defines the existence of a quantity called entropy, that describes the direction, thermodynamically, that a system can evolve and quantifies the state of order of a system and that can be used to quantify the useful work that can be extracted from the system.<br />
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任何热力学系统的描述都采用了构成公理基础的4个热力学定律。第一定律规定能量可以在物理系统之间以热和功的形式进行交换。第二定律定义了一个叫做熵的量的存在,这个量描述了一个系统可以进化和量化一个系统的有序状态的方向,可以用来量化可以从系统中提取的有用功。<br />
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In thermodynamics, interactions between large ensembles of objects are studied and categorized. Central to this are the concepts of the thermodynamic ''[[System (thermodynamics)|system]]'' and its ''[[Surroundings (thermodynamics)|surroundings]]''. A system is composed of particles, whose average motions define its properties, and those properties are in turn related to one another through [[Equation of state|equations of state]]. Properties can be combined to express [[internal energy]] and [[thermodynamic potential]]s, which are useful for determining conditions for [[Dynamic equilibrium|equilibrium]] and [[spontaneous process]]es.<br />
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In thermodynamics, interactions between large ensembles of objects are studied and categorized. Central to this are the concepts of the thermodynamic system and its surroundings. A system is composed of particles, whose average motions define its properties, and those properties are in turn related to one another through equations of state. Properties can be combined to express internal energy and thermodynamic potentials, which are useful for determining conditions for equilibrium and spontaneous processes.<br />
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在热力学中,研究和分类了物体大系综之间的相互作用。其核心是热力学系统及其周围环境的概念。一个系统是由粒子组成的,粒子的平均运动决定了它的性质,而这些性质又通过状态方程彼此相关。性质可以结合起来表示内能和热力学势,这对于确定平衡和自发过程的条件是有用的。<br />
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With these tools, thermodynamics can be used to describe how systems respond to changes in their environment. This can be applied to a wide variety of topics in [[science]] and [[engineering]], such as [[engine]]s, [[phase transition]]s, [[chemical reaction]]s, [[transport phenomena]], and even [[black hole]]s. The results of thermodynamics are essential for other fields of [[physics]] and for [[chemistry]], [[chemical engineering]], [[corrosion engineering]], [[aerospace engineering]], [[mechanical engineering]], [[cell biology]], [[biomedical engineering]], [[materials science]], and [[economics]], to name a few.<ref>{{Cite book | last1=Smith | first1=J.M. | last2=Van Ness | first2=H.C. | last3=Abbott | first3=M.M. | title=Introduction to Chemical Engineering Thermodynamics | journal=Journal of Chemical Education | volume=27 | issue=10 | page=584 | year=2005 | isbn=978-0-07-310445-4 | oclc=56491111| bibcode=1950JChEd..27..584S | doi=10.1021/ed027p584.3 }}</ref><ref>{{cite book | author=Haynie, Donald, T. | title=Biological Thermodynamics | publisher=Cambridge University Press | year=2001 | isbn=978-0-521-79549-4 | oclc=43993556}}</ref><br />
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With these tools, thermodynamics can be used to describe how systems respond to changes in their environment. This can be applied to a wide variety of topics in science and engineering, such as engines, phase transitions, chemical reactions, transport phenomena, and even black holes. The results of thermodynamics are essential for other fields of physics and for chemistry, chemical engineering, corrosion engineering, aerospace engineering, mechanical engineering, cell biology, biomedical engineering, materials science, and economics, to name a few.<br />
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有了这些工具,热力学可以用来描述系统如何响应环境中的变化。这可以应用于科学和工程的各种主题,如引擎,相变,化学反应,传输现象,甚至黑洞。热力学的结果对于物理学、化学、化学工程、腐蚀工程、航空航天工业奖、机械工程、细胞生物学、生物医学工程、材料科学和经济学等其他领域都是必不可少的。<br />
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This article is focused mainly on classical thermodynamics which primarily studies systems in [[thermodynamic equilibrium]]. [[Non-equilibrium thermodynamics]] is often treated as an extension of the classical treatment, but statistical mechanics has brought many advances to that field.<br />
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This article is focused mainly on classical thermodynamics which primarily studies systems in thermodynamic equilibrium. Non-equilibrium thermodynamics is often treated as an extension of the classical treatment, but statistical mechanics has brought many advances to that field.<br />
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这篇文章主要关注经典热力学,它主要研究热力学平衡中的系统。非平衡态热力学通常被视为古典治疗的延伸,但是统计力学已经在这个领域带来了许多进步。<br />
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[[File:Eight founding schools.png|400px|thumb|The [[thermodynamicist]]s representative of the original eight founding schools of thermodynamics. The schools with the most-lasting effect in founding the modern versions of thermodynamics are the Berlin school, particularly as established in [[Rudolf Clausius]]’s 1865 textbook ''The Mechanical Theory of Heat'', the Vienna school, with the [[statistical mechanics]] of [[Ludwig Boltzmann]], and the Gibbsian school at Yale University, American engineer [[Willard Gibbs]]' 1876 ''[[On the Equilibrium of Heterogeneous Substances]]'' launching [[chemical thermodynamics]].<ref name="autogenerated1">[http://www.eoht.info/page/Schools+of+thermodynamics Schools of thermodynamics] – EoHT.info.</ref>]]<br />
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The [[thermodynamicists representative of the original eight founding schools of thermodynamics. The schools with the most-lasting effect in founding the modern versions of thermodynamics are the Berlin school, particularly as established in Rudolf Clausius’s 1865 textbook The Mechanical Theory of Heat, the Vienna school, with the statistical mechanics of Ludwig Boltzmann, and the Gibbsian school at Yale University, American engineer Willard Gibbs' 1876 On the Equilibrium of Heterogeneous Substances launching chemical thermodynamics.]]<br />
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代表热力学最初八个学派的热力学学者。在建立现代版本的热力学方面影响最深远的学校是柏林学派,特别是由 Rudolf Clausius 在1865年的教科书《热力学的机械理论》中建立的维也纳学派,与统计力学路德维希·玻尔兹曼合作的维也纳学派,以及耶鲁大学的 Gibbsian 学派,美国工程师 Willard Gibbs 在1876年建立的关于多相物质平衡化学热力学<br />
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==History==<br />
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==History==<br />
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历史<br />
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The [[history of thermodynamics]] as a scientific discipline generally begins with [[Otto von Guericke]] who, in 1650, built and designed the world's first [[vacuum pump]] and demonstrated a [[vacuum]] using his [[Magdeburg hemispheres]]. Guericke was driven to make a vacuum in order to disprove [[Aristotle]]'s long-held supposition that 'nature abhors a vacuum'. Shortly after Guericke, the English physicist and chemist [[Robert Boyle]] had learned of Guericke's designs and, in 1656, in coordination with English scientist [[Robert Hooke]], built an air pump.<ref>{{cite book | author=Partington, J.R. | title=A Short History of Chemistry | url=https://archive.org/details/shorthistoryofch0000part_q6h4 | url-access=registration | publisher=Dover | year=1989 | isbn= | oclc=19353301| author-link=J. R. Partington }}</ref> Using this pump, Boyle and Hooke noticed a correlation between [[pressure]], [[temperature]], and [[Volume (thermodynamics)|volume]]. In time, [[Boyle's Law]] was formulated, which states that pressure and volume are [[inverse proportion|inversely proportional]]. Then, in 1679, based on these concepts, an associate of Boyle's named [[Denis Papin]] built a [[steam digester]], which was a closed vessel with a tightly fitting lid that confined steam until a high pressure was generated.<br />
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The history of thermodynamics as a scientific discipline generally begins with Otto von Guericke who, in 1650, built and designed the world's first vacuum pump and demonstrated a vacuum using his Magdeburg hemispheres. Guericke was driven to make a vacuum in order to disprove Aristotle's long-held supposition that 'nature abhors a vacuum'. Shortly after Guericke, the English physicist and chemist Robert Boyle had learned of Guericke's designs and, in 1656, in coordination with English scientist Robert Hooke, built an air pump. Using this pump, Boyle and Hooke noticed a correlation between pressure, temperature, and volume. In time, Boyle's Law was formulated, which states that pressure and volume are inversely proportional. Then, in 1679, based on these concepts, an associate of Boyle's named Denis Papin built a steam digester, which was a closed vessel with a tightly fitting lid that confined steam until a high pressure was generated.<br />
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热力学史作为一门科学学科通常始于1650年的奥托·冯·格里克,他建造并设计了世界上第一台真空泵,并用他的马德堡半球展示了真空。格里克被迫制造一个真空,以反驳亚里士多德长期以来的假设,即“自然憎恶真空”。在格里克之后不久,英国物理学家和化学家罗伯特 · 波义耳听说了格里克的设计,并在1656年与英国科学家罗伯特 · 胡克合作制造了一个空气泵。波义耳和胡克利用这台泵,注意到了压力、温度和体积之间的关系。随着时间的推移,波义耳定律被公式化了,它指出压强和体积成反比。然后,在1679年,基于这些概念,波义耳的一位名叫丹尼斯 · 帕平的合伙人建造了一个蒸汽消化器,这是一个封闭的容器,有一个紧密的盖子,将蒸汽封闭起来,直到产生高压。<br />
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Later designs implemented a steam release valve that kept the machine from exploding. By watching the valve rhythmically move up and down, Papin conceived of the idea of a [[piston]] and a cylinder engine. He did not, however, follow through with his design. Nevertheless, in 1697, based on Papin's designs, engineer [[Thomas Savery]] built the first engine, followed by [[Thomas Newcomen]] in 1712. Although these early engines were crude and inefficient, they attracted the attention of the leading scientists of the time.<br />
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Later designs implemented a steam release valve that kept the machine from exploding. By watching the valve rhythmically move up and down, Papin conceived of the idea of a piston and a cylinder engine. He did not, however, follow through with his design. Nevertheless, in 1697, based on Papin's designs, engineer Thomas Savery built the first engine, followed by Thomas Newcomen in 1712. Although these early engines were crude and inefficient, they attracted the attention of the leading scientists of the time.<br />
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后来的设计实现了一个蒸汽释放阀,以防止机器爆炸。通过观察阀门有节奏地上下运动,帕平构思了活塞和汽缸发动机的概念。然而,他并没有坚持他的设计。然而,在1697年,根据帕平的设计,工程师托马斯 · 萨维里制造了第一台发动机,随后在1712年托马斯 · 纽科门制造了第一台发动机。虽然这些早期的发动机粗糙和低效,他们吸引了当时的主要科学家的注意。<br />
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The fundamental concepts of [[heat capacity]] and [[latent heat]], which were necessary for the development of thermodynamics, were developed by Professor [[Joseph Black]] at the University of Glasgow, where [[James Watt]] was employed as an instrument maker. Black and Watt performed experiments together, but it was Watt who conceived the idea of the [[Watt steam engine#Separate condenser|external condenser]] which resulted in a large increase in [[steam engine]] efficiency.<ref>The Newcomen engine was improved from 1711 until Watt's work, making the efficiency comparison subject to qualification, but the increase from the 1865 version was on the order of 100%.</ref> Drawing on all the previous work led [[Nicolas Léonard Sadi Carnot|Sadi Carnot]], the "father of thermodynamics", to publish ''[[Reflections on the Motive Power of Fire]]'' (1824), a discourse on heat, power, energy and engine efficiency. The book outlined the basic energetic relations between the [[Carnot engine]], the [[Carnot cycle]], and '''motive power'''. It marked the start of thermodynamics as a modern science.<ref name="Perrot" /><br />
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The fundamental concepts of heat capacity and latent heat, which were necessary for the development of thermodynamics, were developed by Professor Joseph Black at the University of Glasgow, where James Watt was employed as an instrument maker. Black and Watt performed experiments together, but it was Watt who conceived the idea of the external condenser which resulted in a large increase in steam engine efficiency. Drawing on all the previous work led Sadi Carnot, the "father of thermodynamics", to publish Reflections on the Motive Power of Fire (1824), a discourse on heat, power, energy and engine efficiency. The book outlined the basic energetic relations between the Carnot engine, the Carnot cycle, and motive power. It marked the start of thermodynamics as a modern science.<br />
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热容量和潜热的基本概念是热力学发展所必需的,是由格拉斯哥大学的 Joseph Black 教授提出来的,James Watt 是那里的一个仪器制造商。布莱克和瓦特一起进行实验,但是瓦特提出了外部冷凝器的概念,从而大大提高了蒸汽机的效率。根据以前所有的工作,“热力学之父”萨迪 · 卡诺发表了《论火的动力(1824年) ,一篇关于热、动力、能源和发动机效率的论文。这本书概述了卡诺发动机、卡诺循环和动力之间的基本能量关系。它标志着热力学作为一门现代科学的开始。<br />
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The first thermodynamic textbook was written in 1859 by [[William John Macquorn Rankine|William Rankine]], originally trained as a physicist and a civil and mechanical engineering professor at the [[University of Glasgow]].<ref>{{cite book |author1=Cengel, Yunus A. |author2=Boles, Michael A. | title=Thermodynamics – an Engineering Approach | publisher=McGraw-Hill | year=2005 | isbn=978-0-07-310768-4}}</ref> The first and second laws of thermodynamics emerged simultaneously in the 1850s, primarily out of the works of [[William John Macquorn Rankine|William Rankine]], [[Rudolf Clausius]], and [[William Thomson, 1st Baron Kelvin|William Thomson]] (Lord Kelvin).<ref name = "NKS note b">''[[A New Kind of Science]]'' [https://www.wolframscience.com/nks/notes-9-3--history-of-thermodynamics/ Note (b) for Irreversibility and the Second Law of Thermodynamics]</ref><br />
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The first thermodynamic textbook was written in 1859 by William Rankine, originally trained as a physicist and a civil and mechanical engineering professor at the University of Glasgow. The first and second laws of thermodynamics emerged simultaneously in the 1850s, primarily out of the works of William Rankine, Rudolf Clausius, and William Thomson (Lord Kelvin).<br />
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第一本热力学教科书是 William Rankine 在1859年写的,他最初是格拉斯哥大学的物理学家和土木机械工程教授。第一个和第二个热力学定律同时出现在19世纪50年代,主要出自 William Rankine,Rudolf Clausius 和 William Thomson (Lord Kelvin)的作品。<br />
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The foundations of statistical thermodynamics were set out by physicists such as [[James Clerk Maxwell]], [[Ludwig Boltzmann]], [[Max Planck]], [[Rudolf Clausius]] and [[Josiah Willard Gibbs|J. Willard Gibbs]].<br />
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The foundations of statistical thermodynamics were set out by physicists such as James Clerk Maxwell, Ludwig Boltzmann, Max Planck, Rudolf Clausius and J. Willard Gibbs.<br />
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统计热力学的基础是由物理学家建立的,如詹姆斯·克拉克·麦克斯韦,路德维希·玻尔兹曼,马克斯 · 普朗克,Rudolf Clausius 和 j. Willard Gibbs。<br />
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During the years 1873–76 the American mathematical physicist [[Josiah Willard Gibbs]] published a series of three papers, the most famous being ''[[On the Equilibrium of Heterogeneous Substances]]'',<ref name="Gibbs 1876"/> in which he showed how [[thermodynamic processes]], including [[chemical reaction]]s, could be graphically analyzed, by studying the [[energy]], [[entropy]], [[Volume (thermodynamics)|volume]], [[temperature]] and [[pressure]] of the [[thermodynamic system]] in such a manner, one can determine if a process would occur spontaneously.<ref>{{cite book | author=Gibbs, Willard | title=The Scientific Papers of J. Willard Gibbs, Volume One: Thermodynamics | publisher=Ox Bow Press | year=1993 | isbn=978-0-918024-77-0 | oclc=27974820}}</ref> Also [[Pierre Duhem]] in the 19th century wrote about chemical thermodynamics.<ref name="Duhem 1886"/> During the early 20th century, chemists such as [[Gilbert N. Lewis]], [[Merle Randall]],<ref name="Lewis Randall 1923"/> and [[E. A. Guggenheim]]<ref name="Guggenheim 1933"/><ref name="Guggenheim 1949/1967"/> applied the mathematical methods of Gibbs to the analysis of chemical processes.<br />
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During the years 1873–76 the American mathematical physicist Josiah Willard Gibbs published a series of three papers, the most famous being On the Equilibrium of Heterogeneous Substances, Also Pierre Duhem in the 19th century wrote about chemical thermodynamics. During the early 20th century, chemists such as Gilbert N. Lewis, Merle Randall, and E. A. Guggenheim applied the mathematical methods of Gibbs to the analysis of chemical processes.<br />
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在1873年至1876年间,美国数学物理学家约西亚·威拉德·吉布斯发表了一系列的3篇论文,其中最著名的是关于多相物质平衡,也是 Pierre Duhem 在19世纪写的关于化学热力学的论文。在20世纪早期,化学家如吉尔伯特·牛顿·路易斯,Merle Randall 和 e. a. Guggenheim 将吉布斯的数学方法应用于化学过程的分析。<br />
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==Etymology==<br />
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==Etymology==<br />
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词源学<br />
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这个术语的历史是丰富的,需要更多的补充<br />
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The etymology of ''thermodynamics'' has an intricate history.<ref name=eoht>{{cite web<br />
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The etymology of thermodynamics has an intricate history.<ref name=eoht>{{cite web<br />
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热力学的词源有一个错综复杂的历史<br />
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|url=http://www.eoht.info/page/Thermo-dynamics<br />
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|title=Thermodynamics (etymology)<br />
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|title=Thermodynamics (etymology)<br />
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| 题目: 热力学(词源)<br />
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出版商 EoHT.info<br />
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}}</ref> It was first spelled in a hyphenated form as an adjective (''thermo-dynamic'') and from 1854 to 1868 as the noun ''thermo-dynamics'' to represent the science of generalized heat engines.<ref name=eoht/><br />
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}}</ref> It was first spelled in a hyphenated form as an adjective (thermo-dynamic) and from 1854 to 1868 as the noun thermo-dynamics to represent the science of generalized heat engines.<br />
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它最初以连字符的形式作为形容词(热力学)拼写,从1854年到1868年作为名词热力学来代表广义热发动机的科学。<br />
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American [[Biophysics|biophysicist]] Donald Haynie claims that ''thermodynamics'' was coined in 1840 from the [[Greek language|Greek]] root [[wikt:θέρμη|θέρμη]] ''therme,'' meaning “heat”, and [[wikt:δύναμις|δύναμις]] ''dynamis,'' meaning “power”.<ref>{{cite book<br />
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American biophysicist Donald Haynie claims that thermodynamics was coined in 1840 from the Greek root θέρμη therme, meaning “heat”, and δύναμις dynamis, meaning “power”.<ref>{{cite book<br />
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美国生物物理学家唐纳德 · 海尼声称,热力学是在1840年从希腊词根 therme (意思是“热”)和 dynamis (意思是“力”)创造出来的。 文档{ cite book<br />
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生物热力学<br />
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第二版<br />
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作者唐纳德 · t · 海尼<br />
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剑桥大学出版社<br />
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2008年<br />
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|page=[https://archive.org/details/biologicalthermo0000hayn/page/26 26]<br />
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Pierre Perrot claims that the term ''thermodynamics'' was coined by [[James Joule]] in 1858 to designate the science of relations between heat and power,<ref name="Perrot" /> however, Joule never used that term, but used instead the term ''perfect thermo-dynamic engine'' in reference to Thomson's 1849<ref name=kelvin1849/> phraseology.<ref name=eoht/><br />
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Pierre Perrot claims that the term thermodynamics was coined by James Joule in 1858 to designate the science of relations between heat and power, however, Joule never used that term, but used instead the term perfect thermo-dynamic engine in reference to Thomson's 1849 phraseology.<br />
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皮埃尔 · 佩罗声称,热力学这个术语是由詹姆斯 · 朱尔在1858年创造的,用来指代热量和能量之间关系的科学。然而,朱尔从来没有使用过这个术语,而是在汤姆森1849年的措辞中使用了完美热力学引擎这个术语。<br />
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By 1858, ''thermo-dynamics'', as a functional term, was used in [[William Thomson, 1st Baron Kelvin|William Thomson]]'s paper "An Account of Carnot's Theory of the Motive Power of Heat."<ref name=kelvin1849>Kelvin, William T. (1849) "An Account of Carnot's Theory of the Motive Power of Heat – with Numerical Results Deduced from Regnault's Experiments on Steam." ''Transactions of the Edinburg Royal Society, XVI. January 2.''[http://visualiseur.bnf.fr/Visualiseur?Destination=Gallica&O=NUMM-95118 Scanned Copy]</ref><br />
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By 1858, thermo-dynamics, as a functional term, was used in William Thomson's paper "An Account of Carnot's Theory of the Motive Power of Heat."<br />
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到1858年,热力学作为一个函数术语,被用于威廉 · 汤姆森的论文“卡诺的热动力理论的帐户。”<br />
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==Branches of thermodynamics==<br />
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==Branches of thermodynamics==<br />
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The study of thermodynamical systems has developed into several related branches, each using a different fundamental model as a theoretical or experimental basis, or applying the principles to varying types of systems.<br />
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The study of thermodynamical systems has developed into several related branches, each using a different fundamental model as a theoretical or experimental basis, or applying the principles to varying types of systems.<br />
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热力学系统的研究已经发展成为几个相关的分支,每个分支都使用不同的基本模型作为理论或实验基础,或者将这些原理应用于不同类型的系统。<br />
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===Classical thermodynamics===<br />
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===Classical thermodynamics===<br />
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经典热力学<br />
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Classical thermodynamics is the description of the states of thermodynamic systems at near-equilibrium, that uses macroscopic, measurable properties. It is used to model exchanges of energy, work and heat based on the [[laws of thermodynamics]]. The qualifier ''classical'' reflects the fact that it represents the first level of understanding of the subject as it developed in the 19th century and describes the changes of a system in terms of macroscopic empirical (large scale, and measurable) parameters. A microscopic interpretation of these concepts was later provided by the development of ''statistical mechanics''.<br />
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Classical thermodynamics is the description of the states of thermodynamic systems at near-equilibrium, that uses macroscopic, measurable properties. It is used to model exchanges of energy, work and heat based on the laws of thermodynamics. The qualifier classical reflects the fact that it represents the first level of understanding of the subject as it developed in the 19th century and describes the changes of a system in terms of macroscopic empirical (large scale, and measurable) parameters. A microscopic interpretation of these concepts was later provided by the development of statistical mechanics.<br />
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经典热力学是对近平衡态热力学系统状态的描述,它使用宏观的、可测量的性质。它被用来模拟能量、功和热量的交换,基于热力学定律。经典限定词反映了这样一个事实,即它代表了人们对这个学科在19世纪发展过程中的第一层次的理解,并且描述了一个系统在宏观经验(大尺度和可测量的)参数方面的变化。这些概念的微观解释后来由统计力学的发展提供。<br />
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===Statistical mechanics===<br />
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===Statistical mechanics===<br />
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统计力学<br />
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[[Statistical mechanics]], also called statistical thermodynamics, emerged with the development of atomic and molecular theories in the late 19th century and early 20th century, and supplemented classical thermodynamics with an interpretation of the microscopic interactions between individual particles or quantum-mechanical states. This field relates the microscopic properties of individual atoms and molecules to the macroscopic, bulk properties of materials that can be observed on the human scale, thereby explaining classical thermodynamics as a natural result of statistics, classical mechanics, and [[Quantum mechanics|quantum theory]] at the microscopic level.<ref name= "NKS note b" /><br />
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Statistical mechanics, also called statistical thermodynamics, emerged with the development of atomic and molecular theories in the late 19th century and early 20th century, and supplemented classical thermodynamics with an interpretation of the microscopic interactions between individual particles or quantum-mechanical states. This field relates the microscopic properties of individual atoms and molecules to the macroscopic, bulk properties of materials that can be observed on the human scale, thereby explaining classical thermodynamics as a natural result of statistics, classical mechanics, and quantum theory at the microscopic level.<br />
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统计力学,又称统计热力学,在19世纪末20世纪初随着原子和分子理论的发展而出现,对单个粒子或量子力学状态之间的微观相互作用的解释补充了经典热力学。这个领域将单个原子和分子的微观属性与可以在人类尺度上观察到的物质的宏观体积属性联系起来,从而在微观层次上解释了经典热力学作为统计学、经典力学、量子理论的自然结果。<br />
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===Chemical thermodynamics===<br />
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化学热力学<br />
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[[Chemical thermodynamics]] is the study of the interrelation of [[energy]] with [[chemical reactions]] or with a physical change of [[thermodynamic state|state]] within the confines of the [[laws of thermodynamics]].<br />
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Chemical thermodynamics is the study of the interrelation of energy with chemical reactions or with a physical change of state within the confines of the laws of thermodynamics.<br />
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化学热力学是研究能量与化学反应或热力学定律范围内状态的物理变化之间的相互关系。<br />
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===Equilibrium thermodynamics===<br />
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===Equilibrium thermodynamics===<br />
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平衡热力学<br />
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[[Equilibrium thermodynamics]] is the study of transfers of matter and energy in systems or bodies that, by agencies in their surroundings, can be driven from one state of thermodynamic equilibrium to another. The term 'thermodynamic equilibrium' indicates a state of balance, in which all macroscopic flows are zero; in the case of the simplest systems or bodies, their intensive properties are homogeneous, and their pressures are perpendicular to their boundaries. In an equilibrium state there are no unbalanced potentials, or driving forces, between macroscopically distinct parts of the system. A central aim in equilibrium thermodynamics is: given a system in a well-defined initial equilibrium state, and given its surroundings, and given its constitutive walls, to calculate what will be the final equilibrium state of the system after a specified thermodynamic operation has changed its walls or surroundings.<br />
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Equilibrium thermodynamics is the study of transfers of matter and energy in systems or bodies that, by agencies in their surroundings, can be driven from one state of thermodynamic equilibrium to another. The term 'thermodynamic equilibrium' indicates a state of balance, in which all macroscopic flows are zero; in the case of the simplest systems or bodies, their intensive properties are homogeneous, and their pressures are perpendicular to their boundaries. In an equilibrium state there are no unbalanced potentials, or driving forces, between macroscopically distinct parts of the system. A central aim in equilibrium thermodynamics is: given a system in a well-defined initial equilibrium state, and given its surroundings, and given its constitutive walls, to calculate what will be the final equilibrium state of the system after a specified thermodynamic operation has changed its walls or surroundings.<br />
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平衡态热力学研究的是物质和能量在系统或物体中的转移,这些系统或物体在其周围的环境中,可以从一种热力学平衡状态转移到另一种状态。热力学平衡这个术语表示一种平衡状态,在这种状态下所有的宏观流动都是零; 对于最简单的系统或物体来说,它们的密集属性是均匀的,它们的压力垂直于它们的边界。在平衡状态下,系统宏观上截然不同的部分之间没有不平衡的势能或驱动力。平衡态热力学的一个中心目标是: 给定一个处于明确初始平衡状态的系统,给定其周围环境,给定其本构壁,计算在一个特定的热力学操作改变其周围或周围环境后,系统的最终平衡状态是什么。<br />
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[[Non-equilibrium thermodynamics]] is a branch of thermodynamics that deals with systems that are not in [[thermodynamic equilibrium]]. Most systems found in nature are not in thermodynamic equilibrium because they are not in stationary states, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are not in stationary states, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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非平衡态热力学是热力学的一个分支,主要研究非热力学平衡系统。自然界中发现的大多数系统都不在热力学平衡,因为它们不处于静止状态,并且不断不断地受到来自其他系统的物质和能量流动的影响。非平衡体系的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出目前已知的宏观热力学方法的范围。<br />
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--[[用户:厚朴|厚朴]]([[用户讨论:厚朴|讨论]]) 2020年7月20日 (一) 09:41 (CST)continuously and discontinuously的翻译是不是有些不恰当<br />
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==Laws of thermodynamics==<br />
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==Laws of thermodynamics==<br />
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热力学定律<br />
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{{Main|Laws of thermodynamics}}<br />
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Thermodynamics is principally based on a set of four laws which are universally valid when applied to systems that fall within the constraints implied by each. In the various theoretical descriptions of thermodynamics these laws may be expressed in seemingly differing forms, but the most prominent formulations are the following.<br />
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Thermodynamics is principally based on a set of four laws which are universally valid when applied to systems that fall within the constraints implied by each. In the various theoretical descriptions of thermodynamics these laws may be expressed in seemingly differing forms, but the most prominent formulations are the following.<br />
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热力学基本上是建立在一套四条定律的基础上的,这些定律在适用于每个定律所暗示的约束条件下的系统时是普遍有效的。在热力学的各种理论描述中,这些定律可能表现为看似不同的形式,但最突出的公式如下。<br />
--[[用户:厚朴|厚朴]]([[用户讨论:厚朴|讨论]]) 2020年7月20日 (一) 10:05 (CST) set翻译成一集 prominent翻译成著名?<br />
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===Zeroth Law===<br />
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===Zeroth Law===<br />
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第零定律<br />
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The [[zeroth law of thermodynamics]] states: ''If two systems are each in thermal equilibrium with a third, they are also in thermal equilibrium with each other.''<br />
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The zeroth law of thermodynamics states: If two systems are each in thermal equilibrium with a third, they are also in thermal equilibrium with each other.<br />
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美国热力学第零定律协会指出: 如果两个系统各有三分之一的热平衡,那么它们之间的热平衡也是一样的。<br />
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This statement implies that thermal equilibrium is an [[equivalence relation]] on the set of [[thermodynamic system]]s under consideration. Systems are said to be in equilibrium if the small, random exchanges between them (e.g. [[Brownian motion]]) do not lead to a net change in energy. This law is tacitly assumed in every measurement of temperature. Thus, if one seeks to decide whether two bodies are at the same [[temperature]], it is not necessary to bring them into contact and measure any changes of their observable properties in time.<ref>Moran, Michael J. and Howard N. Shapiro, 2008. ''Fundamentals of Engineering Thermodynamics''. 6th ed. Wiley and Sons: 16.</ref> The law provides an empirical definition of temperature, and justification for the construction of practical thermometers.<br />
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This statement implies that thermal equilibrium is an equivalence relation on the set of thermodynamic systems under consideration. Systems are said to be in equilibrium if the small, random exchanges between them (e.g. Brownian motion) do not lead to a net change in energy. This law is tacitly assumed in every measurement of temperature. Thus, if one seeks to decide whether two bodies are at the same temperature, it is not necessary to bring them into contact and measure any changes of their observable properties in time. The law provides an empirical definition of temperature, and justification for the construction of practical thermometers.<br />
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这种说法暗示了热平衡是热力学系统集合上的一个等价关系。如果系统之间的小的、随机的交换(例如:布朗运动)不会导致能量的净变化。这个定律在每次测量温度时都是默认的。因此,如果要确定两个物体是否处于同一温度,就没有必要使它们接触并及时测量它们可观测性质的任何变化。该定律提供了温度的经验定义,以及建造实用温度计的依据。<br />
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The zeroth law was not initially recognized as a separate law of thermodynamics, as its basis in thermodynamical equilibrium was implied in the other laws. The first, second, and third laws had been explicitly stated already, and found common acceptance in the physics community before the importance of the zeroth law for the definition of temperature was realized. As it was impractical to renumber the other laws, it was named the ''zeroth law''.<br />
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The zeroth law was not initially recognized as a separate law of thermodynamics, as its basis in thermodynamical equilibrium was implied in the other laws. The first, second, and third laws had been explicitly stated already, and found common acceptance in the physics community before the importance of the zeroth law for the definition of temperature was realized. As it was impractical to renumber the other laws, it was named the zeroth law.<br />
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第零定律最初并没有被认为是一个独立的热力学定律,因为它在热力学平衡中的基础在其他定律中也有暗示。第一定律、第二定律和第三定律在温度定义的第零定律的重要性被认识到之前已经被物理学界明确阐述,并且得到了普遍接受。由于对其他法律重新编号是不切实际的,因此将其命名为第零法律。<br />
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--[[用户:厚朴|厚朴]]([[用户讨论:厚朴|讨论]]) 2020年7月20日 (一) 10:05 (CST)法律 Law检查一遍<br />
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===First Law===<br />
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第一定律<br />
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The [[first law of thermodynamics]] states: ''In a process without transfer of matter, the change in [[internal energy]],'' {{math|Δ''U''}}'', of a [[thermodynamic system]] is equal to the energy gained as heat,'' {{math|''Q''}}'', less the thermodynamic work,'' {{math|''W''}}'', done by the system on its surroundings.''<ref>Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics, AIP Press, Woodbury NY, {{ISBN|0883187973}}, p. 79.</ref><ref group=nb>The sign convention (Q is heat supplied ''to'' the system as, W is work done ''by'' the system) is that of [[Rudolf Clausius]]. The opposite sign convention is customary in chemical thermodynamics.</ref><br />
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The first law of thermodynamics states: In a process without transfer of matter, the change in internal energy, , of a thermodynamic system is equal to the energy gained as heat, , less the thermodynamic work, , done by the system on its surroundings.<br />
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能量守恒定律指出: 在一个没有物质转移的过程中,一个热力学系统的内部能量的变化等于作为热量获得的能量,减去系统在其周围所做的热力学功。<br />
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:<math>\Delta U = Q - W</math>.<br />
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<math>\Delta U = Q - W</math>.<br />
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数学 Delta u q-w / 数学。<br />
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For processes that include transfer of matter, a further statement is needed: ''With due account of the respective fiducial reference states of the systems, when two systems, which may be of different chemical compositions, initially separated only by an impermeable wall, and otherwise isolated, are combined into a new system by the thermodynamic operation of removal of the wall, then''<br />
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For processes that include transfer of matter, a further statement is needed: With due account of the respective fiducial reference states of the systems, when two systems, which may be of different chemical compositions, initially separated only by an impermeable wall, and otherwise isolated, are combined into a new system by the thermodynamic operation of removal of the wall, then<br />
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对于包含物质转移的过程,需要进一步的陈述: 在适当考虑了系统各自的基准参考状态的情况下,当两个系统---- 它们可能是不同的化学成分,最初只是被不透水的墙隔开,或者是被隔离---- 通过移除热力学操作结合成一个新的系统时,那么<br />
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:<math>U_0 = U_1 + U_2</math>,<br />
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数学 u 0 u 1 + u 2 / math,<br />
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''where'' {{math|''U''<sub>0</sub>}} ''denotes the internal energy of the combined system, and'' {{math|''U''<sub>1</sub>}} ''and'' {{math|''U''<sub>2</sub>}} ''denote the internal energies of the respective separated systems.''<br />
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where denotes the internal energy of the combined system, and and denote the internal energies of the respective separated systems.<br />
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其中表示组合系统的内能,并表示各自分离系统的内能。<br />
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Adapted for thermodynamics, this law is an expression of the principle of [[conservation of energy]], which states that energy can be transformed (changed from one form to another), but cannot be created or destroyed.<ref>Callen, H.B. (1960/1985).''Thermodynamics and an Introduction to Thermostatistics'', second edition, John Wiley & Sons, Hoboken NY, {{ISBN|9780471862567}}, pp. 11–13.</ref><br />
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Adapted for thermodynamics, this law is an expression of the principle of conservation of energy, which states that energy can be transformed (changed from one form to another), but cannot be created or destroyed.<br />
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这一定律适用于热力学,是能量守恒定律的一种表述,它指出能量可以转换(从一种形式转变为另一种形式) ,但不能被创造或破坏。<br />
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Internal energy is a principal property of the [[thermodynamic state]], while heat and work are modes of energy transfer by which a process may change this state. A change of internal energy of a system may be achieved by any combination of heat added or removed and work performed on or by the system. As a [[State function|function of state]], the internal energy does not depend on the manner, or on the path through intermediate steps, by which the system arrived at its state.<br />
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Internal energy is a principal property of the thermodynamic state, while heat and work are modes of energy transfer by which a process may change this state. A change of internal energy of a system may be achieved by any combination of heat added or removed and work performed on or by the system. As a function of state, the internal energy does not depend on the manner, or on the path through intermediate steps, by which the system arrived at its state.<br />
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内能是热力学状态的主要特性,而热和功是能量传递的方式,通过这种方式,一个过程可以改变这种状态。系统内部能量的变化可以通过加热或除热以及在系统上或由系统所做的功的任何组合来实现。作为状态的函数,内能并不依赖于系统到达其状态的方式或中间步骤的路径。<br />
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===Second Law===<br />
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===Second Law===<br />
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第二定律<br />
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The [[second law of thermodynamics]] states: ''Heat cannot spontaneously flow from a colder location to a hotter location.''<ref name= "NKS note b" /><br />
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The second law of thermodynamics states: Heat cannot spontaneously flow from a colder location to a hotter location.<br />
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热力学第二定律指出: 热量不能自发地从较冷的地方流向较热的地方。<br />
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This law is an expression of the universal principle of decay observable in nature. The second law is an observation of the fact that over time, differences in temperature, pressure, and chemical potential tend to even out in a physical system that is isolated from the outside world. [[Entropy]] is a measure of how much this process has progressed. The entropy of an isolated system which is not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium. However, principles guiding systems that are far from equilibrium are still debatable. One of such principles is the [[entropy production|maximum entropy production]] principle.<ref>{{cite journal|last1=Onsager|first1=Lars|title=Reciprocal Relations in Irreversible Processes|journal=Phys. Rev.|date=1931|volume=37|issue=405|pages=405–426|doi=10.1103/physrev.37.405|bibcode=1931PhRv...37..405O|doi-access=free}}</ref><ref>{{cite book|last1=Ziegler|first1=H.|title=An Introduction to Thermomechanics|date=1983|location=North Holland}}</ref> It states that non-equilibrium systems behave such a way as to maximize its entropy production.<ref>{{cite journal|last1=Belkin|first1=Andrey|last2=Hubler|first2=A.|last3=Bezryadin|first3=A.|title=Self-Assembled Wiggling Nano-Structures and the Principle of Maximum Entropy Production|journal=Sci. Rep.|date=2015|doi=10.1038/srep08323|pmid=25662746|pmc=4321171|bibcode=2015NatSR...5E8323B|volume=5|page=8323}}</ref><br />
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This law is an expression of the universal principle of decay observable in nature. The second law is an observation of the fact that over time, differences in temperature, pressure, and chemical potential tend to even out in a physical system that is isolated from the outside world. Entropy is a measure of how much this process has progressed. The entropy of an isolated system which is not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium. However, principles guiding systems that are far from equilibrium are still debatable. One of such principles is the maximum entropy production principle. It states that non-equilibrium systems behave such a way as to maximize its entropy production.<br />
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这个定律是可以在自然界观察到的衰变的普遍原理的一种表述。第二定律是对这样一个事实的观察: 随着时间的推移,在与外界隔绝的物理系统中,温度、压力和化学势的差异趋于均衡。熵是对这个过程进展程度的度量。不处于平衡状态的孤立系统的熵会随着时间的推移而增加,在平衡状态时达到最大值。然而,远离平衡的原则指导体系仍然是有争议的。其中一个原则就是最大产生熵原则。它指出,非平衡系统的行为方式使其产生熵最大化。<br />
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In classical thermodynamics, the second law is a basic postulate applicable to any system involving heat energy transfer; in statistical thermodynamics, the second law is a consequence of the assumed randomness of molecular chaos. There are many versions of the second law, but they all have the same effect, which is to explain the phenomenon of [[irreversibility]] in nature.<br />
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In classical thermodynamics, the second law is a basic postulate applicable to any system involving heat energy transfer; in statistical thermodynamics, the second law is a consequence of the assumed randomness of molecular chaos. There are many versions of the second law, but they all have the same effect, which is to explain the phenomenon of irreversibility in nature.<br />
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在经典热力学中,第二定律是适用于任何涉及热能传递的系统的基本假设; 在统计热力学中,第二定律是假定的分子混沌随机性的结果。第二定律有许多版本,但它们都具有同样的效果,即解释自然界中的不可逆现象。<br />
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===Third Law===<br />
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===Third Law===<br />
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第三定律<br />
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The [[third law of thermodynamics]] states: ''As the temperature of a system approaches absolute zero, all processes cease and the entropy of the system approaches a minimum value.''<br />
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The third law of thermodynamics states: As the temperature of a system approaches absolute zero, all processes cease and the entropy of the system approaches a minimum value.<br />
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热力学第三定律指出: 当一个系统的温度接近绝对零度时,所有的过程停止,系统的熵接近最小值。<br />
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This law of thermodynamics is a statistical law of nature regarding entropy and the impossibility of reaching [[absolute zero]] of temperature. This law provides an absolute reference point for the determination of entropy. The entropy determined relative to this point is the absolute entropy. Alternate definitions include "the entropy of all systems and of all states of a system is smallest at absolute zero," or equivalently "it is impossible to reach the absolute zero of temperature by any finite number of processes".<br />
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This law of thermodynamics is a statistical law of nature regarding entropy and the impossibility of reaching absolute zero of temperature. This law provides an absolute reference point for the determination of entropy. The entropy determined relative to this point is the absolute entropy. Alternate definitions include "the entropy of all systems and of all states of a system is smallest at absolute zero," or equivalently "it is impossible to reach the absolute zero of temperature by any finite number of processes".<br />
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这个热力学定律是关于熵和不可能达到绝对零度的自然统计法则。这个定律为确定熵提供了一个绝对的参考点。相对于这个点确定的熵就是绝对熵。替代定义包括”系统的所有系统和系统的所有状态的熵在绝对零度时最小” ,或相当于”任何有限数目的过程都不可能达到绝对零度”。<br />
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Absolute zero, at which all activity would stop if it were possible to achieve, is −273.15&nbsp;°C (degrees Celsius), or −459.67&nbsp;°F (degrees Fahrenheit), or 0 K (kelvin), or 0° R (degrees [[Rankine scale|Rankine]]).<br />
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Absolute zero, at which all activity would stop if it were possible to achieve, is −273.15&nbsp;°C (degrees Celsius), or −459.67&nbsp;°F (degrees Fahrenheit), or 0 K (kelvin), or 0° R (degrees Rankine).<br />
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绝对零度是-273.15摄氏度(摄氏度) ,或-459.67华氏度(华氏度) ,或0 k (开尔文) ,或0 r (朗肯度)。<br />
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==System models==<br />
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==System models==<br />
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系统模型<br />
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[[File:system boundary.svg|200px|thumb|right|A diagram of a generic thermodynamic system]]<br />
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A diagram of a generic thermodynamic system<br />
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一个通用的热力学系统图表<br />
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An important concept in thermodynamics is the [[thermodynamic system]], which is a precisely defined region of the universe under study. Everything in the universe except the system is called the [[Environment (systems)|''surroundings'']]. A system is separated from the remainder of the universe by a [[Boundary (thermodynamic)|''boundary'']] which may be a physical boundary or notional, but which by convention defines a finite volume. Exchanges of [[Work (thermodynamics)|work]], [[heat]], or [[matter]] between the system and the surroundings take place across this boundary.<br />
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An important concept in thermodynamics is the thermodynamic system, which is a precisely defined region of the universe under study. Everything in the universe except the system is called the surroundings. A system is separated from the remainder of the universe by a boundary which may be a physical boundary or notional, but which by convention defines a finite volume. Exchanges of work, heat, or matter between the system and the surroundings take place across this boundary.<br />
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热力学中的一个重要概念是热力学系统,它是研究中的宇宙的一个精确定义的区域。除了这个系统之外,宇宙中的一切都被称为环境。一个系统通过一个边界从宇宙的其余部分中分离出来,这个边界可能是物理边界或者概念边界,但是按照惯例,它定义了一个有限的体积。系统和周围环境之间的功、热或物质的交换发生在这个边界上。<br />
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In practice, the boundary of a system is simply an imaginary dotted line drawn around a volume within which is going to be a change in the [[internal energy]] of that volume. Anything that passes across the boundary that effects a change in the internal energy of the system needs to be accounted for in the energy balance equation. The volume can be the region surrounding a single atom resonating energy, such as [[Max Planck]] defined in 1900; it can be a body of steam or air in a [[steam engine]], such as [[Nicolas Léonard Sadi Carnot|Sadi Carnot]] defined in 1824; it can be the body of a [[tropical cyclone]], such as [[Kerry Emanuel]] theorized in 1986 in the field of [[atmospheric thermodynamics]]; it could also be just one [[nuclide]] (i.e. a system of [[quark]]s) as hypothesized in [[quantum thermodynamics]], or the [[event horizon]] of a [[black hole thermodynamics|black hole]].<br />
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In practice, the boundary of a system is simply an imaginary dotted line drawn around a volume within which is going to be a change in the internal energy of that volume. Anything that passes across the boundary that effects a change in the internal energy of the system needs to be accounted for in the energy balance equation. The volume can be the region surrounding a single atom resonating energy, such as Max Planck defined in 1900; it can be a body of steam or air in a steam engine, such as Sadi Carnot defined in 1824; it can be the body of a tropical cyclone, such as Kerry Emanuel theorized in 1986 in the field of atmospheric thermodynamics; it could also be just one nuclide (i.e. a system of quarks) as hypothesized in quantum thermodynamics, or the event horizon of a black hole.<br />
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实际上,一个系统的边界只是一个虚构的虚线,它围绕着一个体积绘制,体积内部能量将发生变化。任何通过边界的影响系统内部能量的变化都需要在能量平衡方程中加以解释。体积可以是围绕单个原子共振能量的区域,如马克斯 · 普朗克在1900年定义的; 它可以是蒸汽机中的蒸汽体或空气体,如萨迪 · 卡诺在1824年定义的; 它可以是热带气旋的体,如 Kerry Emanuel 在1986年在大气热力学领域建立的理论; 它也可以只是一个核素(即:。量子热力学中假设的夸克系统,或黑洞的事件视界。<br />
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Boundaries are of four types: fixed, movable, real, and imaginary. For example, in an engine, a fixed boundary means the piston is locked at its position, within which a constant volume process might occur. If the piston is allowed to move that boundary is movable while the cylinder and cylinder head boundaries are fixed. For closed systems, boundaries are real while for open systems boundaries are often imaginary. In the case of a jet engine, a fixed imaginary boundary might be assumed at the intake of the engine, fixed boundaries along the surface of the case and a second fixed imaginary boundary across the exhaust nozzle.<br />
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Boundaries are of four types: fixed, movable, real, and imaginary. For example, in an engine, a fixed boundary means the piston is locked at its position, within which a constant volume process might occur. If the piston is allowed to move that boundary is movable while the cylinder and cylinder head boundaries are fixed. For closed systems, boundaries are real while for open systems boundaries are often imaginary. In the case of a jet engine, a fixed imaginary boundary might be assumed at the intake of the engine, fixed boundaries along the surface of the case and a second fixed imaginary boundary across the exhaust nozzle.<br />
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边界有四种类型: 固定的、可移动的、真实的和想象的。例如,在发动机中,一个固定的边界意味着活塞被锁定在它的位置,在那里可能发生一个定容过程。如果活塞允许移动,那么边界是可移动的,而气缸和气缸盖边界是固定的。对于封闭系统,边界是真实的,而对于开放系统,边界往往是虚构的。在喷气发动机的情况下,可以假定在发动机进气口处有一个固定的虚边界,沿着箱体表面有一个固定的边界,在排气喷嘴处有一个固定的虚边界。<br />
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Generally, thermodynamics distinguishes three classes of systems, defined in terms of what is allowed to cross their boundaries:<br />
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Generally, thermodynamics distinguishes three classes of systems, defined in terms of what is allowed to cross their boundaries:<br />
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一般来说,热力学区分了三类系统,根据允许什么跨越它们的边界来定义:<br />
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{{table of thermodynamic systems}}<br />
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As time passes in an isolated system, internal differences of pressures, densities, and temperatures tend to even out. A system in which all equalizing processes have gone to completion is said to be in a [[state (thermodynamic)|state]] of [[thermodynamic equilibrium]].<br />
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As time passes in an isolated system, internal differences of pressures, densities, and temperatures tend to even out. A system in which all equalizing processes have gone to completion is said to be in a state of thermodynamic equilibrium.<br />
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在一个孤立的系统中,随着时间的推移,压力、密度和温度的内部差异趋于平衡。一个所有均衡过程均已完成的系统被称为处于热力学平衡状态。<br />
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Once in thermodynamic equilibrium, a system's properties are, by definition, unchanging in time. Systems in equilibrium are much simpler and easier to understand than are systems which are not in equilibrium. Often, when analysing a dynamic thermodynamic process, the simplifying assumption is made that each intermediate state in the process is at equilibrium, producing thermodynamic processes which develop so slowly as to allow each intermediate step to be an equilibrium state and are said to be [[reversible process (thermodynamics)|reversible processes]].<br />
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Once in thermodynamic equilibrium, a system's properties are, by definition, unchanging in time. Systems in equilibrium are much simpler and easier to understand than are systems which are not in equilibrium. Often, when analysing a dynamic thermodynamic process, the simplifying assumption is made that each intermediate state in the process is at equilibrium, producing thermodynamic processes which develop so slowly as to allow each intermediate step to be an equilibrium state and are said to be reversible processes.<br />
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一旦进入热力学平衡,系统的属性,根据定义,在时间上是不变的。处于平衡状态的系统比不处于平衡状态的系统要简单得多,也更容易理解。通常,当分析一个动态热力学过程时,会做出这样的简化假设: 过程中的每一个居间态都处于平衡状态,产生的热力学过程发展得如此缓慢,以至于每一个中间步骤都是一个平衡状态,称之为可逆过程。<br />
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==States and processes==<br />
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==States and processes==<br />
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状态和过程<br />
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When a system is at equilibrium under a given set of conditions, it is said to be in a definite [[thermodynamic state]]. The state of the system can be described by a number of [[state function|state quantities]] that do not depend on the process by which the system arrived at its state. They are called [[intensive variable]]s or [[extensive variable]]s according to how they change when the size of the system changes. The properties of the system can be described by an [[equation of state]] which specifies the relationship between these variables. State may be thought of as the instantaneous quantitative description of a system with a set number of variables held constant.<br />
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When a system is at equilibrium under a given set of conditions, it is said to be in a definite thermodynamic state. The state of the system can be described by a number of state quantities that do not depend on the process by which the system arrived at its state. They are called intensive variables or extensive variables according to how they change when the size of the system changes. The properties of the system can be described by an equation of state which specifies the relationship between these variables. State may be thought of as the instantaneous quantitative description of a system with a set number of variables held constant.<br />
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当一个系统在一组给定的条件下处于平衡状态时,我们称之为处于一个确定的热力学状态。系统的状态可以用许多状态量来描述,这些状态量并不依赖于系统到达其状态的过程。它们被称为密集型变量或扩展型变量,这取决于它们在系统规模发生变化时的变化情况。系统的属性可以用一个状态方程来描述,它指定了这些变量之间的关系。状态可以被认为是一系列变量保持不变的系统的瞬时定量描述。<br />
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A [[thermodynamic process]] may be defined as the energetic evolution of a thermodynamic system proceeding from an initial state to a final state. It can be described by [[process function|process quantities]]. Typically, each thermodynamic process is distinguished from other processes in energetic character according to what parameters, such as temperature, pressure, or volume, etc., are held fixed; Furthermore, it is useful to group these processes into pairs, in which each variable held constant is one member of a [[conjugate variables (thermodynamics)|conjugate]] pair.<br />
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A thermodynamic process may be defined as the energetic evolution of a thermodynamic system proceeding from an initial state to a final state. It can be described by process quantities. Typically, each thermodynamic process is distinguished from other processes in energetic character according to what parameters, such as temperature, pressure, or volume, etc., are held fixed; Furthermore, it is useful to group these processes into pairs, in which each variable held constant is one member of a conjugate pair.<br />
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热力学过程可以被定义为热力学系统从初始状态到最终状态的能量演化。它可以用工艺量来描述。通常情况下,根据温度、压力、体积等参数的固定程度,每个热力学过程过程与能量特征中的其他过程是不同的; 此外,将这些过程分组成对也很有用,每个变量保持常数是一个共轭对的一个成员。<br />
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Several commonly studied thermodynamic processes are:<br />
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Several commonly studied thermodynamic processes are:<br />
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一些常见的研究热力学过程是:<br />
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* [[Adiabatic process]]: occurs without loss or gain of energy by [[heat]]<br />
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* [[Isenthalpic process]]: occurs at a constant [[enthalpy]]<br />
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* [[Isentropic process]]: a reversible adiabatic process, occurs at a constant [[entropy]]<br />
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* [[Isobaric process]]: occurs at constant [[pressure]]<br />
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* [[Isochoric process]]: occurs at constant [[Volume (thermodynamics)|volume]] (also called isometric/isovolumetric)<br />
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* [[Isothermal process]]: occurs at a constant [[temperature]]<br />
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* [[steady state|Steady state process]]: occurs without a change in the [[internal energy]]<br />
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== Instrumentation ==<br />
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== Instrumentation ==<br />
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仪器仪表<br />
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There are two types of [[thermodynamic instruments]], the '''meter''' and the '''reservoir'''. A thermodynamic meter is any device which measures any parameter of a [[thermodynamic system]]. In some cases, the thermodynamic parameter is actually defined in terms of an idealized measuring instrument. For example, the [[zeroth law of thermodynamics|zeroth law]] states that if two bodies are in thermal equilibrium with a third body, they are also in thermal equilibrium with each other. This principle, as noted by [[James Clerk Maxwell|James Maxwell]] in 1872, asserts that it is possible to measure temperature. An idealized [[thermometer]] is a sample of an ideal gas at constant pressure. From the [[ideal gas law]] ''pV=nRT'', the volume of such a sample can be used as an indicator of temperature; in this manner it defines temperature. Although pressure is defined mechanically, a pressure-measuring device, called a [[barometer]] may also be constructed from a sample of an ideal gas held at a constant temperature. A [[calorimeter]] is a device which is used to measure and define the internal energy of a system.<br />
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There are two types of thermodynamic instruments, the meter and the reservoir. A thermodynamic meter is any device which measures any parameter of a thermodynamic system. In some cases, the thermodynamic parameter is actually defined in terms of an idealized measuring instrument. For example, the zeroth law states that if two bodies are in thermal equilibrium with a third body, they are also in thermal equilibrium with each other. This principle, as noted by James Maxwell in 1872, asserts that it is possible to measure temperature. An idealized thermometer is a sample of an ideal gas at constant pressure. From the ideal gas law pV=nRT, the volume of such a sample can be used as an indicator of temperature; in this manner it defines temperature. Although pressure is defined mechanically, a pressure-measuring device, called a barometer may also be constructed from a sample of an ideal gas held at a constant temperature. A calorimeter is a device which is used to measure and define the internal energy of a system.<br />
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有两种类型的热力学设备,水表和水库。热力学仪表是测量热力学系统的任何参数的任何装置。在某些情况下,热力学参数实际上是用理想化的测量仪器来定义的。例如,第零定律指出,如果两个物体在热平衡中有第三个物体,那么它们也在热平衡中。正如詹姆斯 · 麦克斯韦尔在1872年指出的那样,这个原理断言测量温度是可能的。理想温度计是恒压下理想气体的样品。根据理想气体定律 pV nRT,这样一个样品的体积可以用作温度的指示器; 在这种方式下,它定义了温度。虽然压力是机械定义的,一个称为气压计的压力测量装置也可以由恒定温度下的理想气体样品构成。量热计是用来测量和定义系统内部能量的装置。<br />
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A thermodynamic reservoir is a system which is so large that its state parameters are not appreciably altered when it is brought into contact with the system of interest. When the reservoir is brought into contact with the system, the system is brought into equilibrium with the reservoir. For example, a pressure reservoir is a system at a particular pressure, which imposes that pressure upon the system to which it is mechanically connected. The Earth's atmosphere is often used as a pressure reservoir. If ocean water is used to cool a power plant, the ocean is often a temperature reservoir in the analysis of the power plant cycle.<br />
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A thermodynamic reservoir is a system which is so large that its state parameters are not appreciably altered when it is brought into contact with the system of interest. When the reservoir is brought into contact with the system, the system is brought into equilibrium with the reservoir. For example, a pressure reservoir is a system at a particular pressure, which imposes that pressure upon the system to which it is mechanically connected. The Earth's atmosphere is often used as a pressure reservoir. If ocean water is used to cool a power plant, the ocean is often a temperature reservoir in the analysis of the power plant cycle.<br />
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热力学储存器是这样一个系统,它的状态参数如此之大,当它与感兴趣的系统接触时,它的状态参数没有明显的改变。当油藏与系统接触时,系统与油藏达到平衡。例如,压力容器是一个处于特定压力下的系统,它对与之机械连接的系统施加压力。地球的大气层经常被用作压力储存器。如果用海水来冷却发电厂,在分析发电厂的循环过程中,海洋通常是一个温度储存库。<br />
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== Conjugate variables ==<br />
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== Conjugate variables ==<br />
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共轭变量<br />
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{{Main|Conjugate variables (thermodynamics)|l1=Conjugate variables}}<br />
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The central concept of thermodynamics is that of [[energy]], the ability to do [[Work (thermodynamics)|work]]. By the [[first law of thermodynamics|First Law]], the total energy of a system and its surroundings is conserved. Energy may be transferred into a system by heating, compression, or addition of matter, and extracted from a system by cooling, expansion, or extraction of matter. In [[mechanics]], for example, energy transfer equals the product of the force applied to a body and the resulting displacement.<br />
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The central concept of thermodynamics is that of energy, the ability to do work. By the First Law, the total energy of a system and its surroundings is conserved. Energy may be transferred into a system by heating, compression, or addition of matter, and extracted from a system by cooling, expansion, or extraction of matter. In mechanics, for example, energy transfer equals the product of the force applied to a body and the resulting displacement.<br />
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热力学的核心概念是能量,做功的能力。根据第一定律,系统及其周围环境的总能量是守恒的。能量可以通过加热、压缩或添加物质的方式转移到系统中,也可以通过冷却、膨胀或提取物质的方式从系统中提取。例如,在力学中,能量传递等于作用在物体上的力和由此产生的位移的乘积。<br />
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[[conjugate variables (thermodynamics)|Conjugate variables]] are pairs of thermodynamic concepts, with the first being akin to a "force" applied to some [[thermodynamic system]], the second being akin to the resulting "displacement," and the product of the two equalling the amount of energy transferred. The common conjugate variables are:<br />
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Conjugate variables are pairs of thermodynamic concepts, with the first being akin to a "force" applied to some thermodynamic system, the second being akin to the resulting "displacement," and the product of the two equalling the amount of energy transferred. The common conjugate variables are:<br />
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共轭变量是成对的热力学概念,第一个类似于施加在某些热力学系统上的“力” ,第二个类似于由此产生的“位移” ,两者的乘积等于所转移的能量。常见的共轭变量有:<br />
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* [[Pressure]]-[[Volume (thermodynamics)|volume]] (the [[Mechanics|mechanical]] parameters);<br />
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* [[Temperature]]-[[entropy]] (thermal parameters);<br />
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* [[Chemical potential]]-[[particle number]] (material parameters).<br />
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== Potentials ==<br />
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== Potentials ==<br />
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== Potentials ==<br />
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[[Thermodynamic potential]]s are different quantitative measures of the stored energy in a system. Potentials are used to measure the energy changes in systems as they evolve from an initial state to a final state. The potential used depends on the constraints of the system, such as constant temperature or pressure. For example, the Helmholtz and Gibbs energies are the energies available in a system to do useful work when the temperature and volume or the pressure and temperature are fixed, respectively.<br />
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Thermodynamic potentials are different quantitative measures of the stored energy in a system. Potentials are used to measure the energy changes in systems as they evolve from an initial state to a final state. The potential used depends on the constraints of the system, such as constant temperature or pressure. For example, the Helmholtz and Gibbs energies are the energies available in a system to do useful work when the temperature and volume or the pressure and temperature are fixed, respectively.<br />
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热力学势是体系中储存能量的不同定量度量。势能被用来测量系统从初始状态到最终状态的能量变化。所用的电位取决于系统的约束条件,如恒温或恒压。例如,亥姆霍兹能量和吉布斯能量是当温度和体积或压力和温度分别固定时,系统中可用于做有用功的能量。<br />
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The five most well known potentials are:<br />
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The five most well known potentials are:<br />
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五个最有名的潜力是:<br />
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{{table of thermodynamic potentials}}<br />
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where <math>T</math> is the [[thermodynamic temperature|temperature]], <math>S</math> the [[entropy]], <math>p</math> the [[pressure]], <math>V</math> the [[Volume (thermodynamics)|volume]], <math>\mu</math> the [[chemical potential]], <math>N</math> the number of particles in the system, and <math>i</math> is the count of particles types in the system.<br />
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where <math>T</math> is the temperature, <math>S</math> the entropy, <math>p</math> the pressure, <math>V</math> the volume, <math>\mu</math> the chemical potential, <math>N</math> the number of particles in the system, and <math>i</math> is the count of particles types in the system.<br />
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数学 t / math 是温度,数学 s / math 是熵,数学 p / math 是压力,数学 v / math 是体积,数学 mu / math 是化学势,数学 n / math 是系统中粒子的数量,数学 i / math 是系统中粒子类型的数量。<br />
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Thermodynamic potentials can be derived from the energy balance equation applied to a thermodynamic system. Other thermodynamic potentials can also be obtained through [[Legendre transformation]].<br />
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Thermodynamic potentials can be derived from the energy balance equation applied to a thermodynamic system. Other thermodynamic potentials can also be obtained through Legendre transformation.<br />
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热力学势可以从应用于热力学系统的能量平衡方程推导出来。其他热力学势也可以通过勒壤得转换得到。<br />
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== Applied fields ==<br />
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== Applied fields ==<br />
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应用领域<br />
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{ columns-list | colwidth 22em | <br />
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* [[Atmospheric thermodynamics]]<br />
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* [[Biological thermodynamics]]<br />
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* [[Black hole thermodynamics]]<br />
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* [[Chemical thermodynamics]]<br />
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* [[Classical thermodynamics]]<br />
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* [[Thermodynamic equilibrium|Equilibrium thermodynamics]]<br />
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* [[Industrial ecology]] (re: [[Exergy]])<br />
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* [[Maximum entropy thermodynamics]]<br />
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* [[Non-equilibrium thermodynamics]]<br />
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* [[Philosophy of thermal and statistical physics]]<br />
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* [[Psychrometrics]]<br />
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* [[Quantum thermodynamics]]<br />
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* [[Statistical thermodynamics]]<br />
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* [[Thermoeconomics]]<br />
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}}<br />
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}}<br />
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}}<br />
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== See also ==<br />
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== See also ==<br />
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参见<br />
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{{portal|Physics}}<br />
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* [[Thermodynamic process path]]<br />
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===Lists and timelines===<br />
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===Lists and timelines===<br />
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清单和时间线<br />
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* [[List of important publications in physics#Thermodynamics|List of important publications in thermodynamics]]<br />
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* [[List of textbooks in statistical mechanics|List of textbooks on thermodynamics and statistical mechanics]]<br />
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* [[List of thermal conductivities]]<br />
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* [[List of thermodynamic properties]]<br />
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* [[Table of thermodynamic equations]]<br />
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* [[Timeline of thermodynamics]]<br />
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== Notes ==<br />
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== Notes ==<br />
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注释<br />
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{{reflist|group=nb}}<br />
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==References==<br />
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==References==<br />
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参考资料<br />
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{{Reflist|35em}}<br />
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==Further reading==<br />
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==Further reading==<br />
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进一步阅读<br />
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* {{cite book|author1=Goldstein, Martin|author2=Inge F.|lastauthoramp=yes|title=The Refrigerator and the Universe|url=https://archive.org/details/refrigeratoruniv0000gold|url-access=registration|publisher=Harvard University Press|year=1993|isbn=978-0-674-75325-9|location=|pages=|oclc=32826343}} A nontechnical introduction, good on historical and interpretive matters.<br />
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* {{cite journal |last1=Kazakov |first1=Andrei |last2=Muzny |first2=Chris D. |last3=Chirico |first3=Robert D. |last4=Diky |first4=Vladimir V. |last5=Frenkel |first5=Michael |title=Web Thermo Tables – an On-Line Version of the TRC Thermodynamic Tables |journal=Journal of Research of the National Institute of Standards and Technology |volume=113 |issue=4 |year=2008 |pages=209–220 |issn=1044-677X |doi=10.6028/jres.113.016 |pmc=4651616 |pmid=27096122}}<br />
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* {{cite book|author=Gibbs J.W.|title=The Collected Works of J. Willard Gibbs Thermodynamics.|publisher=Longmans, Green and Co.|year=1928|isbn=|location=New York|pages=|oclc=}} Vol. 1, pp. 55–349.<br />
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* {{cite book|author=Guggenheim E.A.|title=Modern thermodynamics by the methods of Willard Gibbs|publisher=Methuen & co. ltd.|year=1933|isbn=|location=London|pages=|oclc=}}<br />
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* {{cite book|author=Denbigh K.|title=The Principles of Chemical Equilibrium: With Applications in Chemistry and Chemical Engineering.|publisher=Cambridge University Press|year=1981|isbn=|location=London|pages=|oclc=}}<br />
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* {{cite book|author=Stull, D.R., Westrum Jr., E.F. and Sinke, G.C.|title=The Chemical Thermodynamics of Organic Compounds.|publisher=John Wiley and Sons, Inc.|year=1969|isbn=|location=London|pages=|oclc=}}<br />
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* {{cite book|author=Bazarov I.P.|title=Thermodynamics: Textbook.|publisher=Lan publishing house|year=2010|isbn=978-5-8114-1003-3|location=St. Petersburg|page=384|oclc=}} 5th ed. (in Russian)<br />
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* {{cite book|author=Bawendi Moungi G., Alberty Robert A. and Silbey Robert J.|title=Physical Chemistry|publisher=J. Wiley & Sons, Incorporated|year=2004|isbn=|location=|pages=|oclc=}}<br />
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* {{cite book|author=Alberty Robert A.|title=Thermodynamics of Biochemical Reactions|publisher=Wiley-Interscience|year=2003|isbn=|location=|pages=|oclc=}}<br />
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* {{cite book|author=Alberty Robert A.|title=Biochemical Thermodynamics: Applications of Mathematica|journal=Methods of Biochemical Analysis|publisher=John Wiley & Sons, Inc.|year=2006|volume=48|isbn=978-0-471-75798-6|location=|pages=1–458|pmid=16878778|oclc=}}<br />
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The following titles are more technical:<br />
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The following titles are more technical:<br />
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下面的标题更具技术性:<br />
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* {{Cite book|title=Advanced Engineering Thermodynamics|last=Bejan|first=Adrian|publisher=Wiley|year=2016|isbn=978-1-119-05209-8|edition=4|location=|pages=}}<br />
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* {{cite book|author=Cengel, Yunus A., & Boles, Michael A.|title=Thermodynamics – an Engineering Approach|publisher=McGraw Hill|year=2002|isbn=978-0-07-238332-4|location=|pages=|oclc=45791449|url-access=registration|url=https://archive.org/details/thermodynamicsen00ceng_0}}<br />
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* {{cite book|author=Dunning-Davies, Jeremy|title=Concise Thermodynamics: Principles and Applications|publisher=Horwood Publishing|year=1997|isbn=978-1-8985-6315-0|location=|pages=|oclc=36025958}}<br />
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* {{cite book|author1=Kroemer, Herbert|author2=Kittel, Charles|lastauthoramp=yes|title=Thermal Physics|publisher=W.H. Freeman Company|year=1980|isbn=978-0-7167-1088-2|location=|pages=|oclc=32932988}}<br />
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== External links ==<br />
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== External links ==<br />
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外部链接<br />
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{{Wikibooks|Engineering Thermodynamics}}<br />
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{{wikiquote|Thermodynamics}}<br />
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* {{cite EB1911 |title=Thermodynamics |volume=26 |pages=808–814 |short=x |url=https://archive.org/details/encyclopaediabri26chisrich/page/808}}<br />
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* [http://tigger.uic.edu/~mansoori/Thermodynamic.Data.and.Property_html Thermodynamics Data & Property Calculation Websites]<br />
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* [http://tigger.uic.edu/~mansoori/Thermodynamics.Educational.Sites_html Thermodynamics Educational Websites]<br />
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* [http://scienceworld.wolfram.com/physics/topics/Thermodynamics.html Thermodynamics at ''ScienceWorld'']<br />
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* [http://www.wiley.com/legacy/college/boyer/0470003790/reviews/thermo/thermo_intro.htm Biochemistry Thermodynamics]<br />
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* [http://farside.ph.utexas.edu/teaching/sm1/lectures/lectures.html Thermodynamics and Statistical Mechanics]<br />
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* [https://web.archive.org/web/20090430200028/http://www.ent.ohiou.edu/~thermo/ Engineering Thermodynamics – A Graphical Approach]<br />
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* [http://farside.ph.utexas.edu/teaching/sm1/statmech.pdf Thermodynamics and Statistical Mechanics] by Richard Fitzpatrick<br />
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[[Category:Thermodynamics| ]]<br />
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[[Category:Chemical engineering]]<br />
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Category:Chemical engineering<br />
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类别: 化学工程<br />
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[[Category:Concepts in physics]]<br />
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Category:Concepts in physics<br />
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分类: 物理概念<br />
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[[Category:Subfields of physics]]<br />
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Category:Subfields of physics<br />
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分类: 物理学的子领域<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Thermodynamics]]. Its edit history can be viewed at [[热力学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E7%83%AD%E5%8A%9B%E5%AD%A6&diff=21959热力学2021-02-23T09:09:08Z<p>Jxzhou:</p>
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<div>此词条暂由jxzhou翻译,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{short description|Physics of heat, work, and temperature}}<br />
{{Use dmy dates|date=February 2016}}<br />
[[File:Carnot engine (hot body - working body - cold body).jpg|thumb|300px|right|Annotated color version of the original 1824 [[Carnot heat engine]] showing the hot body (boiler), working body (system, steam), and cold body (water), the letters labeled according to the stopping points in [[Carnot cycle]].]]<br />
{{Thermodynamics}}<br />
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'''Thermodynamics''' is a branch of [[physics]] that deals with [[heat]], [[Work (thermodynamics)|work]], and [[temperature]], and their relation to [[energy]], [[radiation]], and physical properties of [[matter]]. The behavior of these quantities is governed by the four [[laws of thermodynamics]] which convey a quantitative description using measurable macroscopic [[physical quantity|physical quantities]], but may be explained in terms of [[microscopic]] constituents by [[statistical mechanics]]. Thermodynamics applies to a wide variety of topics in [[science]] and [[engineering]], especially [[physical chemistry]], [[chemical engineering]] and [[mechanical engineering]], but also in other complex fields such as [[meteorology]].<br />
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热力学是物理学的一个分支,研究热、功和温度,以及它们与能量、辐射和物质物理性质的关系。这些量的行为遵循四个热力学定律,热力学定律用可测量的宏观物理量给出了一个定量描述,但是可以用统计力学以微观组成来解释。热力学适用于科学和工程中的各种各样的主题,尤其是物理化学、化学工程和机械工程,但也适用于气象学这样复杂的领域。<br />
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Historically, thermodynamics developed out of a desire to increase the [[thermodynamic efficiency|efficiency]] of early [[steam engine]]s, particularly through the work of French physicist [[Nicolas Léonard Sadi Carnot]] (1824) who believed that engine efficiency was the key that could help France win the [[Napoleonic Wars]].<ref>{{cite book | last = Clausius | first = Rudolf | title = On the Motive Power of Heat, and on the Laws which can be deduced from it for the Theory of Heat | publisher = Poggendorff's Annalen der Physik, LXXIX (Dover Reprint) | year = 1850 | isbn = 978-0-486-59065-3}}</ref> Scots-Irish physicist [[William Thomson, 1st Baron Kelvin|Lord Kelvin]] was the first to formulate a concise definition of thermodynamics in 1854<ref name=kelvin1854>{{cite book<br />
|title=Mathematical and Physical Papers<br />
|author= William Thomson, LL.D. D.C.L., F.R.S.<br />
|location=London, Cambridge<br />
|year=1882<br />
|volume=1<br />
|page=232<br />
|publisher=C.J. Clay, M.A. & Son, Cambridge University Press<br />
|url=https://books.google.com/books?id=nWMSAAAAIAAJ&q=On+an+Absolute+Thermometric+Scale+Founded+on+Carnot%E2%80%99s+Theory&pg=PA100<br />
}}</ref> which stated, "Thermo-dynamics is the subject of the relation of heat to forces acting between contiguous parts of bodies, and the relation of heat to electrical agency."<br />
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“热力学的主题是热量与物体相邻部分之间作用力的关系,以及热量与电能的关系。”<br />
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The initial application of thermodynamics to [[mechanical heat engine]]s was quickly extended to the study of chemical compounds and chemical reactions. [[Chemical thermodynamics]] studies the nature of the role of [[entropy]] in the process of [[chemical reaction]]s and has provided the bulk of expansion and knowledge of the field.<ref name="Gibbs 1876">{{cite book|author=Gibbs, Willard, J.|title=Transactions of the Connecticut Academy of Arts and Sciences|volume=III|pages=[https://archive.org/details/transactions03conn/page/108 108]–248, 343–524|year=1874–1878|url=https://archive.org/details/transactions03conn|publisher=New Haven}}</ref><ref name="Duhem 1886">Duhem, P.M.M. (1886). ''Le Potential Thermodynamique et ses Applications'', Hermann, Paris.</ref><ref name="Lewis Randall 1923">{{cite book | last1=Lewis | first1=Gilbert N. | last2=Randall | first2=Merle | title=Thermodynamics and the Free Energy of Chemical Substances | url=https://archive.org/details/thermodynamicsfr00gnle | publisher=McGraw-Hill Book Co. Inc. | year=1923}}</ref><ref name="Guggenheim 1933">Guggenheim, E.A. (1933). ''Modern Thermodynamics by the Methods of J.W. Gibbs'', Methuen, London.</ref><ref name="Guggenheim 1949/1967">Guggenheim, E.A. (1949/1967). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', 1st edition 1949, 5th edition 1967, North-Holland, Amsterdam.</ref><ref>{{cite book | author=Ilya Prigogine, I. & Defay, R., translated by D.H. Everett| title=Chemical Thermodynamics | year=1954 | publisher=Longmans, Green & Co., London. Includes classical non-equilibrium thermodynamics.}}<br />
</ref><ref name=Fermi>{{cite book<br />
|title=Thermodynamics<br />
|author=Enrico Fermi<br />
|url=https://books.google.com/books?id=VEZ1ljsT3IwC&q=thermodynamics<br />
|isbn=978-0486603612<br />
|publisher=Courier Dover Publications<br />
|year=1956<br />
|page=ix<br />
|oclc=230763036}}</ref><ref name="Perrot" >{{cite book | author=Perrot, Pierre | title=A to Z of Thermodynamics | publisher=Oxford University Press | year=1998 | isbn=978-0-19-856552-9 | oclc=123283342}}</ref><ref>{{cite book | author=Clark, John, O.E.| title=The Essential Dictionary of Science | publisher=Barnes & Noble Books | year=2004 | isbn=978-0-7607-4616-5 | oclc=58732844}}</ref> Other formulations of thermodynamics emerged. [[Statistical thermodynamics]], or statistical mechanics, concerns itself with [[statistics|statistical]] predictions of the collective motion of particles from their microscopic behavior. In 1909, [[Constantin Carathéodory]] presented a purely mathematical approach in an [[axiomatic]] formulation, a description often referred to as ''geometrical thermodynamics''.<br />
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热力学的其他公式出现了。统计热力学,或称统计力学热力学,从微观角度对粒子的集体运动进行统计预测。在1909年,康斯坦丁·卡拉西奥多里提出了一个纯粹的数学方法在一个公理化的公式,一个描述通常被称为几何热力学。<br />
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==Introduction==<br />
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引言<br />
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A description of any thermodynamic system employs the four [[laws of thermodynamics]] that form an axiomatic basis. The first law specifies that energy can be exchanged between physical systems as [[heat]] and [[Mechanical work|work]].<ref>{{cite book | author=Van Ness, H.C. | title=Understanding Thermodynamics | publisher=Dover Publications, Inc. | year=1983 | origyear=1969 | isbn=9780486632773 | oclc=8846081 | url-access=registration | url=https://archive.org/details/understandingthe00vann }}</ref> The second law defines the existence of a quantity called [[entropy]], that describes the direction, thermodynamically, that a system can evolve and quantifies the state of order of a system and that can be used to quantify the useful work that can be extracted from the system.<ref>{{cite book | author=Dugdale, J.S. | title=Entropy and its Physical Meaning | publisher=Taylor and Francis | year=1998 | isbn=978-0-7484-0569-5 | oclc=36457809}}</ref><br />
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A description of any thermodynamic system employs the four laws of thermodynamics that form an axiomatic basis. The first law specifies that energy can be exchanged between physical systems as heat and work. The second law defines the existence of a quantity called entropy, that describes the direction, thermodynamically, that a system can evolve and quantifies the state of order of a system and that can be used to quantify the useful work that can be extracted from the system.<br />
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任何热力学系统的描述都采用了构成公理基础的4个热力学定律。第一定律规定能量可以在物理系统之间以热和功的形式进行交换。第二定律定义了一个叫做熵的量的存在,这个量描述了一个系统可以进化和量化一个系统的有序状态的方向,可以用来量化可以从系统中提取的有用功。<br />
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In thermodynamics, interactions between large ensembles of objects are studied and categorized. Central to this are the concepts of the thermodynamic ''[[System (thermodynamics)|system]]'' and its ''[[Surroundings (thermodynamics)|surroundings]]''. A system is composed of particles, whose average motions define its properties, and those properties are in turn related to one another through [[Equation of state|equations of state]]. Properties can be combined to express [[internal energy]] and [[thermodynamic potential]]s, which are useful for determining conditions for [[Dynamic equilibrium|equilibrium]] and [[spontaneous process]]es.<br />
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In thermodynamics, interactions between large ensembles of objects are studied and categorized. Central to this are the concepts of the thermodynamic system and its surroundings. A system is composed of particles, whose average motions define its properties, and those properties are in turn related to one another through equations of state. Properties can be combined to express internal energy and thermodynamic potentials, which are useful for determining conditions for equilibrium and spontaneous processes.<br />
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在热力学中,研究和分类了物体大系综之间的相互作用。其核心是热力学系统及其周围环境的概念。一个系统是由粒子组成的,粒子的平均运动决定了它的性质,而这些性质又通过状态方程彼此相关。性质可以结合起来表示内能和热力学势,这对于确定平衡和自发过程的条件是有用的。<br />
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With these tools, thermodynamics can be used to describe how systems respond to changes in their environment. This can be applied to a wide variety of topics in [[science]] and [[engineering]], such as [[engine]]s, [[phase transition]]s, [[chemical reaction]]s, [[transport phenomena]], and even [[black hole]]s. The results of thermodynamics are essential for other fields of [[physics]] and for [[chemistry]], [[chemical engineering]], [[corrosion engineering]], [[aerospace engineering]], [[mechanical engineering]], [[cell biology]], [[biomedical engineering]], [[materials science]], and [[economics]], to name a few.<ref>{{Cite book | last1=Smith | first1=J.M. | last2=Van Ness | first2=H.C. | last3=Abbott | first3=M.M. | title=Introduction to Chemical Engineering Thermodynamics | journal=Journal of Chemical Education | volume=27 | issue=10 | page=584 | year=2005 | isbn=978-0-07-310445-4 | oclc=56491111| bibcode=1950JChEd..27..584S | doi=10.1021/ed027p584.3 }}</ref><ref>{{cite book | author=Haynie, Donald, T. | title=Biological Thermodynamics | publisher=Cambridge University Press | year=2001 | isbn=978-0-521-79549-4 | oclc=43993556}}</ref><br />
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With these tools, thermodynamics can be used to describe how systems respond to changes in their environment. This can be applied to a wide variety of topics in science and engineering, such as engines, phase transitions, chemical reactions, transport phenomena, and even black holes. The results of thermodynamics are essential for other fields of physics and for chemistry, chemical engineering, corrosion engineering, aerospace engineering, mechanical engineering, cell biology, biomedical engineering, materials science, and economics, to name a few.<br />
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有了这些工具,热力学可以用来描述系统如何响应环境中的变化。这可以应用于科学和工程的各种主题,如引擎,相变,化学反应,传输现象,甚至黑洞。热力学的结果对于物理学、化学、化学工程、腐蚀工程、航空航天工业奖、机械工程、细胞生物学、生物医学工程、材料科学和经济学等其他领域都是必不可少的。<br />
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This article is focused mainly on classical thermodynamics which primarily studies systems in [[thermodynamic equilibrium]]. [[Non-equilibrium thermodynamics]] is often treated as an extension of the classical treatment, but statistical mechanics has brought many advances to that field.<br />
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This article is focused mainly on classical thermodynamics which primarily studies systems in thermodynamic equilibrium. Non-equilibrium thermodynamics is often treated as an extension of the classical treatment, but statistical mechanics has brought many advances to that field.<br />
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这篇文章主要关注经典热力学,它主要研究热力学平衡中的系统。非平衡态热力学通常被视为古典治疗的延伸,但是统计力学已经在这个领域带来了许多进步。<br />
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[[File:Eight founding schools.png|400px|thumb|The [[thermodynamicist]]s representative of the original eight founding schools of thermodynamics. The schools with the most-lasting effect in founding the modern versions of thermodynamics are the Berlin school, particularly as established in [[Rudolf Clausius]]’s 1865 textbook ''The Mechanical Theory of Heat'', the Vienna school, with the [[statistical mechanics]] of [[Ludwig Boltzmann]], and the Gibbsian school at Yale University, American engineer [[Willard Gibbs]]' 1876 ''[[On the Equilibrium of Heterogeneous Substances]]'' launching [[chemical thermodynamics]].<ref name="autogenerated1">[http://www.eoht.info/page/Schools+of+thermodynamics Schools of thermodynamics] – EoHT.info.</ref>]]<br />
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The [[thermodynamicists representative of the original eight founding schools of thermodynamics. The schools with the most-lasting effect in founding the modern versions of thermodynamics are the Berlin school, particularly as established in Rudolf Clausius’s 1865 textbook The Mechanical Theory of Heat, the Vienna school, with the statistical mechanics of Ludwig Boltzmann, and the Gibbsian school at Yale University, American engineer Willard Gibbs' 1876 On the Equilibrium of Heterogeneous Substances launching chemical thermodynamics.]]<br />
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代表热力学最初八个学派的热力学学者。在建立现代版本的热力学方面影响最深远的学校是柏林学派,特别是由 Rudolf Clausius 在1865年的教科书《热力学的机械理论》中建立的维也纳学派,与统计力学路德维希·玻尔兹曼合作的维也纳学派,以及耶鲁大学的 Gibbsian 学派,美国工程师 Willard Gibbs 在1876年建立的关于多相物质平衡化学热力学<br />
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==History==<br />
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==History==<br />
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历史<br />
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The [[history of thermodynamics]] as a scientific discipline generally begins with [[Otto von Guericke]] who, in 1650, built and designed the world's first [[vacuum pump]] and demonstrated a [[vacuum]] using his [[Magdeburg hemispheres]]. Guericke was driven to make a vacuum in order to disprove [[Aristotle]]'s long-held supposition that 'nature abhors a vacuum'. Shortly after Guericke, the English physicist and chemist [[Robert Boyle]] had learned of Guericke's designs and, in 1656, in coordination with English scientist [[Robert Hooke]], built an air pump.<ref>{{cite book | author=Partington, J.R. | title=A Short History of Chemistry | url=https://archive.org/details/shorthistoryofch0000part_q6h4 | url-access=registration | publisher=Dover | year=1989 | isbn= | oclc=19353301| author-link=J. R. Partington }}</ref> Using this pump, Boyle and Hooke noticed a correlation between [[pressure]], [[temperature]], and [[Volume (thermodynamics)|volume]]. In time, [[Boyle's Law]] was formulated, which states that pressure and volume are [[inverse proportion|inversely proportional]]. Then, in 1679, based on these concepts, an associate of Boyle's named [[Denis Papin]] built a [[steam digester]], which was a closed vessel with a tightly fitting lid that confined steam until a high pressure was generated.<br />
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The history of thermodynamics as a scientific discipline generally begins with Otto von Guericke who, in 1650, built and designed the world's first vacuum pump and demonstrated a vacuum using his Magdeburg hemispheres. Guericke was driven to make a vacuum in order to disprove Aristotle's long-held supposition that 'nature abhors a vacuum'. Shortly after Guericke, the English physicist and chemist Robert Boyle had learned of Guericke's designs and, in 1656, in coordination with English scientist Robert Hooke, built an air pump. Using this pump, Boyle and Hooke noticed a correlation between pressure, temperature, and volume. In time, Boyle's Law was formulated, which states that pressure and volume are inversely proportional. Then, in 1679, based on these concepts, an associate of Boyle's named Denis Papin built a steam digester, which was a closed vessel with a tightly fitting lid that confined steam until a high pressure was generated.<br />
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热力学史作为一门科学学科通常始于1650年的奥托·冯·格里克,他建造并设计了世界上第一台真空泵,并用他的马德堡半球展示了真空。格里克被迫制造一个真空,以反驳亚里士多德长期以来的假设,即“自然憎恶真空”。在格里克之后不久,英国物理学家和化学家罗伯特 · 波义耳听说了格里克的设计,并在1656年与英国科学家罗伯特 · 胡克合作制造了一个空气泵。波义耳和胡克利用这台泵,注意到了压力、温度和体积之间的关系。随着时间的推移,波义耳定律被公式化了,它指出压强和体积成反比。然后,在1679年,基于这些概念,波义耳的一位名叫丹尼斯 · 帕平的合伙人建造了一个蒸汽消化器,这是一个封闭的容器,有一个紧密的盖子,将蒸汽封闭起来,直到产生高压。<br />
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Later designs implemented a steam release valve that kept the machine from exploding. By watching the valve rhythmically move up and down, Papin conceived of the idea of a [[piston]] and a cylinder engine. He did not, however, follow through with his design. Nevertheless, in 1697, based on Papin's designs, engineer [[Thomas Savery]] built the first engine, followed by [[Thomas Newcomen]] in 1712. Although these early engines were crude and inefficient, they attracted the attention of the leading scientists of the time.<br />
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Later designs implemented a steam release valve that kept the machine from exploding. By watching the valve rhythmically move up and down, Papin conceived of the idea of a piston and a cylinder engine. He did not, however, follow through with his design. Nevertheless, in 1697, based on Papin's designs, engineer Thomas Savery built the first engine, followed by Thomas Newcomen in 1712. Although these early engines were crude and inefficient, they attracted the attention of the leading scientists of the time.<br />
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后来的设计实现了一个蒸汽释放阀,以防止机器爆炸。通过观察阀门有节奏地上下运动,帕平构思了活塞和汽缸发动机的概念。然而,他并没有坚持他的设计。然而,在1697年,根据帕平的设计,工程师托马斯 · 萨维里制造了第一台发动机,随后在1712年托马斯 · 纽科门制造了第一台发动机。虽然这些早期的发动机粗糙和低效,他们吸引了当时的主要科学家的注意。<br />
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The fundamental concepts of [[heat capacity]] and [[latent heat]], which were necessary for the development of thermodynamics, were developed by Professor [[Joseph Black]] at the University of Glasgow, where [[James Watt]] was employed as an instrument maker. Black and Watt performed experiments together, but it was Watt who conceived the idea of the [[Watt steam engine#Separate condenser|external condenser]] which resulted in a large increase in [[steam engine]] efficiency.<ref>The Newcomen engine was improved from 1711 until Watt's work, making the efficiency comparison subject to qualification, but the increase from the 1865 version was on the order of 100%.</ref> Drawing on all the previous work led [[Nicolas Léonard Sadi Carnot|Sadi Carnot]], the "father of thermodynamics", to publish ''[[Reflections on the Motive Power of Fire]]'' (1824), a discourse on heat, power, energy and engine efficiency. The book outlined the basic energetic relations between the [[Carnot engine]], the [[Carnot cycle]], and '''motive power'''. It marked the start of thermodynamics as a modern science.<ref name="Perrot" /><br />
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The fundamental concepts of heat capacity and latent heat, which were necessary for the development of thermodynamics, were developed by Professor Joseph Black at the University of Glasgow, where James Watt was employed as an instrument maker. Black and Watt performed experiments together, but it was Watt who conceived the idea of the external condenser which resulted in a large increase in steam engine efficiency. Drawing on all the previous work led Sadi Carnot, the "father of thermodynamics", to publish Reflections on the Motive Power of Fire (1824), a discourse on heat, power, energy and engine efficiency. The book outlined the basic energetic relations between the Carnot engine, the Carnot cycle, and motive power. It marked the start of thermodynamics as a modern science.<br />
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热容量和潜热的基本概念是热力学发展所必需的,是由格拉斯哥大学的 Joseph Black 教授提出来的,James Watt 是那里的一个仪器制造商。布莱克和瓦特一起进行实验,但是瓦特提出了外部冷凝器的概念,从而大大提高了蒸汽机的效率。根据以前所有的工作,“热力学之父”萨迪 · 卡诺发表了《论火的动力(1824年) ,一篇关于热、动力、能源和发动机效率的论文。这本书概述了卡诺发动机、卡诺循环和动力之间的基本能量关系。它标志着热力学作为一门现代科学的开始。<br />
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The first thermodynamic textbook was written in 1859 by [[William John Macquorn Rankine|William Rankine]], originally trained as a physicist and a civil and mechanical engineering professor at the [[University of Glasgow]].<ref>{{cite book |author1=Cengel, Yunus A. |author2=Boles, Michael A. | title=Thermodynamics – an Engineering Approach | publisher=McGraw-Hill | year=2005 | isbn=978-0-07-310768-4}}</ref> The first and second laws of thermodynamics emerged simultaneously in the 1850s, primarily out of the works of [[William John Macquorn Rankine|William Rankine]], [[Rudolf Clausius]], and [[William Thomson, 1st Baron Kelvin|William Thomson]] (Lord Kelvin).<ref name = "NKS note b">''[[A New Kind of Science]]'' [https://www.wolframscience.com/nks/notes-9-3--history-of-thermodynamics/ Note (b) for Irreversibility and the Second Law of Thermodynamics]</ref><br />
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The first thermodynamic textbook was written in 1859 by William Rankine, originally trained as a physicist and a civil and mechanical engineering professor at the University of Glasgow. The first and second laws of thermodynamics emerged simultaneously in the 1850s, primarily out of the works of William Rankine, Rudolf Clausius, and William Thomson (Lord Kelvin).<br />
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第一本热力学教科书是 William Rankine 在1859年写的,他最初是格拉斯哥大学的物理学家和土木机械工程教授。第一个和第二个热力学定律同时出现在19世纪50年代,主要出自 William Rankine,Rudolf Clausius 和 William Thomson (Lord Kelvin)的作品。<br />
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The foundations of statistical thermodynamics were set out by physicists such as [[James Clerk Maxwell]], [[Ludwig Boltzmann]], [[Max Planck]], [[Rudolf Clausius]] and [[Josiah Willard Gibbs|J. Willard Gibbs]].<br />
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The foundations of statistical thermodynamics were set out by physicists such as James Clerk Maxwell, Ludwig Boltzmann, Max Planck, Rudolf Clausius and J. Willard Gibbs.<br />
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统计热力学的基础是由物理学家建立的,如詹姆斯·克拉克·麦克斯韦,路德维希·玻尔兹曼,马克斯 · 普朗克,Rudolf Clausius 和 j. Willard Gibbs。<br />
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During the years 1873–76 the American mathematical physicist [[Josiah Willard Gibbs]] published a series of three papers, the most famous being ''[[On the Equilibrium of Heterogeneous Substances]]'',<ref name="Gibbs 1876"/> in which he showed how [[thermodynamic processes]], including [[chemical reaction]]s, could be graphically analyzed, by studying the [[energy]], [[entropy]], [[Volume (thermodynamics)|volume]], [[temperature]] and [[pressure]] of the [[thermodynamic system]] in such a manner, one can determine if a process would occur spontaneously.<ref>{{cite book | author=Gibbs, Willard | title=The Scientific Papers of J. Willard Gibbs, Volume One: Thermodynamics | publisher=Ox Bow Press | year=1993 | isbn=978-0-918024-77-0 | oclc=27974820}}</ref> Also [[Pierre Duhem]] in the 19th century wrote about chemical thermodynamics.<ref name="Duhem 1886"/> During the early 20th century, chemists such as [[Gilbert N. Lewis]], [[Merle Randall]],<ref name="Lewis Randall 1923"/> and [[E. A. Guggenheim]]<ref name="Guggenheim 1933"/><ref name="Guggenheim 1949/1967"/> applied the mathematical methods of Gibbs to the analysis of chemical processes.<br />
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During the years 1873–76 the American mathematical physicist Josiah Willard Gibbs published a series of three papers, the most famous being On the Equilibrium of Heterogeneous Substances, Also Pierre Duhem in the 19th century wrote about chemical thermodynamics. During the early 20th century, chemists such as Gilbert N. Lewis, Merle Randall, and E. A. Guggenheim applied the mathematical methods of Gibbs to the analysis of chemical processes.<br />
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在1873年至1876年间,美国数学物理学家约西亚·威拉德·吉布斯发表了一系列的3篇论文,其中最著名的是关于多相物质平衡,也是 Pierre Duhem 在19世纪写的关于化学热力学的论文。在20世纪早期,化学家如吉尔伯特·牛顿·路易斯,Merle Randall 和 e. a. Guggenheim 将吉布斯的数学方法应用于化学过程的分析。<br />
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==Etymology==<br />
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==Etymology==<br />
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词源学<br />
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The etymology of ''thermodynamics'' has an intricate history.<ref name=eoht>{{cite web<br />
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The etymology of thermodynamics has an intricate history.<ref name=eoht>{{cite web<br />
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热力学的词源有一个错综复杂的历史<br />
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| 题目: 热力学(词源)<br />
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}}</ref> It was first spelled in a hyphenated form as an adjective (''thermo-dynamic'') and from 1854 to 1868 as the noun ''thermo-dynamics'' to represent the science of generalized heat engines.<ref name=eoht/><br />
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}}</ref> It was first spelled in a hyphenated form as an adjective (thermo-dynamic) and from 1854 to 1868 as the noun thermo-dynamics to represent the science of generalized heat engines.<br />
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它最初以连字符的形式作为形容词(热力学)拼写,从1854年到1868年作为名词热力学来代表广义热发动机的科学。<br />
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American [[Biophysics|biophysicist]] Donald Haynie claims that ''thermodynamics'' was coined in 1840 from the [[Greek language|Greek]] root [[wikt:θέρμη|θέρμη]] ''therme,'' meaning “heat”, and [[wikt:δύναμις|δύναμις]] ''dynamis,'' meaning “power”.<ref>{{cite book<br />
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American biophysicist Donald Haynie claims that thermodynamics was coined in 1840 from the Greek root θέρμη therme, meaning “heat”, and δύναμις dynamis, meaning “power”.<ref>{{cite book<br />
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美国生物物理学家唐纳德 · 海尼声称,热力学是在1840年从希腊词根 therme (意思是“热”)和 dynamis (意思是“力”)创造出来的。 文档{ cite book<br />
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生物热力学<br />
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Pierre Perrot claims that the term ''thermodynamics'' was coined by [[James Joule]] in 1858 to designate the science of relations between heat and power,<ref name="Perrot" /> however, Joule never used that term, but used instead the term ''perfect thermo-dynamic engine'' in reference to Thomson's 1849<ref name=kelvin1849/> phraseology.<ref name=eoht/><br />
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Pierre Perrot claims that the term thermodynamics was coined by James Joule in 1858 to designate the science of relations between heat and power, however, Joule never used that term, but used instead the term perfect thermo-dynamic engine in reference to Thomson's 1849 phraseology.<br />
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皮埃尔 · 佩罗声称,热力学这个术语是由詹姆斯 · 朱尔在1858年创造的,用来指代热量和能量之间关系的科学。然而,朱尔从来没有使用过这个术语,而是在汤姆森1849年的措辞中使用了完美热力学引擎这个术语。<br />
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By 1858, ''thermo-dynamics'', as a functional term, was used in [[William Thomson, 1st Baron Kelvin|William Thomson]]'s paper "An Account of Carnot's Theory of the Motive Power of Heat."<ref name=kelvin1849>Kelvin, William T. (1849) "An Account of Carnot's Theory of the Motive Power of Heat – with Numerical Results Deduced from Regnault's Experiments on Steam." ''Transactions of the Edinburg Royal Society, XVI. January 2.''[http://visualiseur.bnf.fr/Visualiseur?Destination=Gallica&O=NUMM-95118 Scanned Copy]</ref><br />
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By 1858, thermo-dynamics, as a functional term, was used in William Thomson's paper "An Account of Carnot's Theory of the Motive Power of Heat."<br />
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到1858年,热力学作为一个函数术语,被用于威廉 · 汤姆森的论文“卡诺的热动力理论的帐户。”<br />
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==Branches of thermodynamics==<br />
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==Branches of thermodynamics==<br />
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The study of thermodynamical systems has developed into several related branches, each using a different fundamental model as a theoretical or experimental basis, or applying the principles to varying types of systems.<br />
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The study of thermodynamical systems has developed into several related branches, each using a different fundamental model as a theoretical or experimental basis, or applying the principles to varying types of systems.<br />
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热力学系统的研究已经发展成为几个相关的分支,每个分支都使用不同的基本模型作为理论或实验基础,或者将这些原理应用于不同类型的系统。<br />
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===Classical thermodynamics===<br />
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===Classical thermodynamics===<br />
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经典热力学<br />
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Classical thermodynamics is the description of the states of thermodynamic systems at near-equilibrium, that uses macroscopic, measurable properties. It is used to model exchanges of energy, work and heat based on the [[laws of thermodynamics]]. The qualifier ''classical'' reflects the fact that it represents the first level of understanding of the subject as it developed in the 19th century and describes the changes of a system in terms of macroscopic empirical (large scale, and measurable) parameters. A microscopic interpretation of these concepts was later provided by the development of ''statistical mechanics''.<br />
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Classical thermodynamics is the description of the states of thermodynamic systems at near-equilibrium, that uses macroscopic, measurable properties. It is used to model exchanges of energy, work and heat based on the laws of thermodynamics. The qualifier classical reflects the fact that it represents the first level of understanding of the subject as it developed in the 19th century and describes the changes of a system in terms of macroscopic empirical (large scale, and measurable) parameters. A microscopic interpretation of these concepts was later provided by the development of statistical mechanics.<br />
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经典热力学是对近平衡态热力学系统状态的描述,它使用宏观的、可测量的性质。它被用来模拟能量、功和热量的交换,基于热力学定律。经典限定词反映了这样一个事实,即它代表了人们对这个学科在19世纪发展过程中的第一层次的理解,并且描述了一个系统在宏观经验(大尺度和可测量的)参数方面的变化。这些概念的微观解释后来由统计力学的发展提供。<br />
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===Statistical mechanics===<br />
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===Statistical mechanics===<br />
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统计力学<br />
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[[Statistical mechanics]], also called statistical thermodynamics, emerged with the development of atomic and molecular theories in the late 19th century and early 20th century, and supplemented classical thermodynamics with an interpretation of the microscopic interactions between individual particles or quantum-mechanical states. This field relates the microscopic properties of individual atoms and molecules to the macroscopic, bulk properties of materials that can be observed on the human scale, thereby explaining classical thermodynamics as a natural result of statistics, classical mechanics, and [[Quantum mechanics|quantum theory]] at the microscopic level.<ref name= "NKS note b" /><br />
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Statistical mechanics, also called statistical thermodynamics, emerged with the development of atomic and molecular theories in the late 19th century and early 20th century, and supplemented classical thermodynamics with an interpretation of the microscopic interactions between individual particles or quantum-mechanical states. This field relates the microscopic properties of individual atoms and molecules to the macroscopic, bulk properties of materials that can be observed on the human scale, thereby explaining classical thermodynamics as a natural result of statistics, classical mechanics, and quantum theory at the microscopic level.<br />
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统计力学,又称统计热力学,在19世纪末20世纪初随着原子和分子理论的发展而出现,对单个粒子或量子力学状态之间的微观相互作用的解释补充了经典热力学。这个领域将单个原子和分子的微观属性与可以在人类尺度上观察到的物质的宏观体积属性联系起来,从而在微观层次上解释了经典热力学作为统计学、经典力学、量子理论的自然结果。<br />
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===Chemical thermodynamics===<br />
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===Chemical thermodynamics===<br />
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化学热力学<br />
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[[Chemical thermodynamics]] is the study of the interrelation of [[energy]] with [[chemical reactions]] or with a physical change of [[thermodynamic state|state]] within the confines of the [[laws of thermodynamics]].<br />
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Chemical thermodynamics is the study of the interrelation of energy with chemical reactions or with a physical change of state within the confines of the laws of thermodynamics.<br />
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化学热力学是研究能量与化学反应或热力学定律范围内状态的物理变化之间的相互关系。<br />
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===Equilibrium thermodynamics===<br />
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===Equilibrium thermodynamics===<br />
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平衡热力学<br />
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[[Equilibrium thermodynamics]] is the study of transfers of matter and energy in systems or bodies that, by agencies in their surroundings, can be driven from one state of thermodynamic equilibrium to another. The term 'thermodynamic equilibrium' indicates a state of balance, in which all macroscopic flows are zero; in the case of the simplest systems or bodies, their intensive properties are homogeneous, and their pressures are perpendicular to their boundaries. In an equilibrium state there are no unbalanced potentials, or driving forces, between macroscopically distinct parts of the system. A central aim in equilibrium thermodynamics is: given a system in a well-defined initial equilibrium state, and given its surroundings, and given its constitutive walls, to calculate what will be the final equilibrium state of the system after a specified thermodynamic operation has changed its walls or surroundings.<br />
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Equilibrium thermodynamics is the study of transfers of matter and energy in systems or bodies that, by agencies in their surroundings, can be driven from one state of thermodynamic equilibrium to another. The term 'thermodynamic equilibrium' indicates a state of balance, in which all macroscopic flows are zero; in the case of the simplest systems or bodies, their intensive properties are homogeneous, and their pressures are perpendicular to their boundaries. In an equilibrium state there are no unbalanced potentials, or driving forces, between macroscopically distinct parts of the system. A central aim in equilibrium thermodynamics is: given a system in a well-defined initial equilibrium state, and given its surroundings, and given its constitutive walls, to calculate what will be the final equilibrium state of the system after a specified thermodynamic operation has changed its walls or surroundings.<br />
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平衡态热力学研究的是物质和能量在系统或物体中的转移,这些系统或物体在其周围的环境中,可以从一种热力学平衡状态转移到另一种状态。热力学平衡这个术语表示一种平衡状态,在这种状态下所有的宏观流动都是零; 对于最简单的系统或物体来说,它们的密集属性是均匀的,它们的压力垂直于它们的边界。在平衡状态下,系统宏观上截然不同的部分之间没有不平衡的势能或驱动力。平衡态热力学的一个中心目标是: 给定一个处于明确初始平衡状态的系统,给定其周围环境,给定其本构壁,计算在一个特定的热力学操作改变其周围或周围环境后,系统的最终平衡状态是什么。<br />
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[[Non-equilibrium thermodynamics]] is a branch of thermodynamics that deals with systems that are not in [[thermodynamic equilibrium]]. Most systems found in nature are not in thermodynamic equilibrium because they are not in stationary states, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are not in stationary states, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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非平衡态热力学是热力学的一个分支,主要研究非热力学平衡系统。自然界中发现的大多数系统都不在热力学平衡,因为它们不处于静止状态,并且不断不断地受到来自其他系统的物质和能量流动的影响。非平衡体系的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出目前已知的宏观热力学方法的范围。<br />
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--[[用户:厚朴|厚朴]]([[用户讨论:厚朴|讨论]]) 2020年7月20日 (一) 09:41 (CST)continuously and discontinuously的翻译是不是有些不恰当<br />
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==Laws of thermodynamics==<br />
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==Laws of thermodynamics==<br />
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热力学定律<br />
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{{Main|Laws of thermodynamics}}<br />
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Thermodynamics is principally based on a set of four laws which are universally valid when applied to systems that fall within the constraints implied by each. In the various theoretical descriptions of thermodynamics these laws may be expressed in seemingly differing forms, but the most prominent formulations are the following.<br />
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Thermodynamics is principally based on a set of four laws which are universally valid when applied to systems that fall within the constraints implied by each. In the various theoretical descriptions of thermodynamics these laws may be expressed in seemingly differing forms, but the most prominent formulations are the following.<br />
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热力学基本上是建立在一套四条定律的基础上的,这些定律在适用于每个定律所暗示的约束条件下的系统时是普遍有效的。在热力学的各种理论描述中,这些定律可能表现为看似不同的形式,但最突出的公式如下。<br />
--[[用户:厚朴|厚朴]]([[用户讨论:厚朴|讨论]]) 2020年7月20日 (一) 10:05 (CST) set翻译成一集 prominent翻译成著名?<br />
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===Zeroth Law===<br />
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===Zeroth Law===<br />
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第零定律<br />
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The [[zeroth law of thermodynamics]] states: ''If two systems are each in thermal equilibrium with a third, they are also in thermal equilibrium with each other.''<br />
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The zeroth law of thermodynamics states: If two systems are each in thermal equilibrium with a third, they are also in thermal equilibrium with each other.<br />
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美国热力学第零定律协会指出: 如果两个系统各有三分之一的热平衡,那么它们之间的热平衡也是一样的。<br />
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This statement implies that thermal equilibrium is an [[equivalence relation]] on the set of [[thermodynamic system]]s under consideration. Systems are said to be in equilibrium if the small, random exchanges between them (e.g. [[Brownian motion]]) do not lead to a net change in energy. This law is tacitly assumed in every measurement of temperature. Thus, if one seeks to decide whether two bodies are at the same [[temperature]], it is not necessary to bring them into contact and measure any changes of their observable properties in time.<ref>Moran, Michael J. and Howard N. Shapiro, 2008. ''Fundamentals of Engineering Thermodynamics''. 6th ed. Wiley and Sons: 16.</ref> The law provides an empirical definition of temperature, and justification for the construction of practical thermometers.<br />
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This statement implies that thermal equilibrium is an equivalence relation on the set of thermodynamic systems under consideration. Systems are said to be in equilibrium if the small, random exchanges between them (e.g. Brownian motion) do not lead to a net change in energy. This law is tacitly assumed in every measurement of temperature. Thus, if one seeks to decide whether two bodies are at the same temperature, it is not necessary to bring them into contact and measure any changes of their observable properties in time. The law provides an empirical definition of temperature, and justification for the construction of practical thermometers.<br />
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这种说法暗示了热平衡是热力学系统集合上的一个等价关系。如果系统之间的小的、随机的交换(例如:布朗运动)不会导致能量的净变化。这个定律在每次测量温度时都是默认的。因此,如果要确定两个物体是否处于同一温度,就没有必要使它们接触并及时测量它们可观测性质的任何变化。该定律提供了温度的经验定义,以及建造实用温度计的依据。<br />
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The zeroth law was not initially recognized as a separate law of thermodynamics, as its basis in thermodynamical equilibrium was implied in the other laws. The first, second, and third laws had been explicitly stated already, and found common acceptance in the physics community before the importance of the zeroth law for the definition of temperature was realized. As it was impractical to renumber the other laws, it was named the ''zeroth law''.<br />
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The zeroth law was not initially recognized as a separate law of thermodynamics, as its basis in thermodynamical equilibrium was implied in the other laws. The first, second, and third laws had been explicitly stated already, and found common acceptance in the physics community before the importance of the zeroth law for the definition of temperature was realized. As it was impractical to renumber the other laws, it was named the zeroth law.<br />
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第零定律最初并没有被认为是一个独立的热力学定律,因为它在热力学平衡中的基础在其他定律中也有暗示。第一定律、第二定律和第三定律在温度定义的第零定律的重要性被认识到之前已经被物理学界明确阐述,并且得到了普遍接受。由于对其他法律重新编号是不切实际的,因此将其命名为第零法律。<br />
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--[[用户:厚朴|厚朴]]([[用户讨论:厚朴|讨论]]) 2020年7月20日 (一) 10:05 (CST)法律 Law检查一遍<br />
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===First Law===<br />
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===First Law===<br />
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第一定律<br />
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The [[first law of thermodynamics]] states: ''In a process without transfer of matter, the change in [[internal energy]],'' {{math|Δ''U''}}'', of a [[thermodynamic system]] is equal to the energy gained as heat,'' {{math|''Q''}}'', less the thermodynamic work,'' {{math|''W''}}'', done by the system on its surroundings.''<ref>Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics, AIP Press, Woodbury NY, {{ISBN|0883187973}}, p. 79.</ref><ref group=nb>The sign convention (Q is heat supplied ''to'' the system as, W is work done ''by'' the system) is that of [[Rudolf Clausius]]. The opposite sign convention is customary in chemical thermodynamics.</ref><br />
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The first law of thermodynamics states: In a process without transfer of matter, the change in internal energy, , of a thermodynamic system is equal to the energy gained as heat, , less the thermodynamic work, , done by the system on its surroundings.<br />
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能量守恒定律指出: 在一个没有物质转移的过程中,一个热力学系统的内部能量的变化等于作为热量获得的能量,减去系统在其周围所做的热力学功。<br />
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:<math>\Delta U = Q - W</math>.<br />
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<math>\Delta U = Q - W</math>.<br />
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数学 Delta u q-w / 数学。<br />
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For processes that include transfer of matter, a further statement is needed: ''With due account of the respective fiducial reference states of the systems, when two systems, which may be of different chemical compositions, initially separated only by an impermeable wall, and otherwise isolated, are combined into a new system by the thermodynamic operation of removal of the wall, then''<br />
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For processes that include transfer of matter, a further statement is needed: With due account of the respective fiducial reference states of the systems, when two systems, which may be of different chemical compositions, initially separated only by an impermeable wall, and otherwise isolated, are combined into a new system by the thermodynamic operation of removal of the wall, then<br />
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对于包含物质转移的过程,需要进一步的陈述: 在适当考虑了系统各自的基准参考状态的情况下,当两个系统---- 它们可能是不同的化学成分,最初只是被不透水的墙隔开,或者是被隔离---- 通过移除热力学操作结合成一个新的系统时,那么<br />
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:<math>U_0 = U_1 + U_2</math>,<br />
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<math>U_0 = U_1 + U_2</math>,<br />
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数学 u 0 u 1 + u 2 / math,<br />
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''where'' {{math|''U''<sub>0</sub>}} ''denotes the internal energy of the combined system, and'' {{math|''U''<sub>1</sub>}} ''and'' {{math|''U''<sub>2</sub>}} ''denote the internal energies of the respective separated systems.''<br />
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where denotes the internal energy of the combined system, and and denote the internal energies of the respective separated systems.<br />
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其中表示组合系统的内能,并表示各自分离系统的内能。<br />
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Adapted for thermodynamics, this law is an expression of the principle of [[conservation of energy]], which states that energy can be transformed (changed from one form to another), but cannot be created or destroyed.<ref>Callen, H.B. (1960/1985).''Thermodynamics and an Introduction to Thermostatistics'', second edition, John Wiley & Sons, Hoboken NY, {{ISBN|9780471862567}}, pp. 11–13.</ref><br />
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Adapted for thermodynamics, this law is an expression of the principle of conservation of energy, which states that energy can be transformed (changed from one form to another), but cannot be created or destroyed.<br />
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这一定律适用于热力学,是能量守恒定律的一种表述,它指出能量可以转换(从一种形式转变为另一种形式) ,但不能被创造或破坏。<br />
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Internal energy is a principal property of the [[thermodynamic state]], while heat and work are modes of energy transfer by which a process may change this state. A change of internal energy of a system may be achieved by any combination of heat added or removed and work performed on or by the system. As a [[State function|function of state]], the internal energy does not depend on the manner, or on the path through intermediate steps, by which the system arrived at its state.<br />
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Internal energy is a principal property of the thermodynamic state, while heat and work are modes of energy transfer by which a process may change this state. A change of internal energy of a system may be achieved by any combination of heat added or removed and work performed on or by the system. As a function of state, the internal energy does not depend on the manner, or on the path through intermediate steps, by which the system arrived at its state.<br />
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内能是热力学状态的主要特性,而热和功是能量传递的方式,通过这种方式,一个过程可以改变这种状态。系统内部能量的变化可以通过加热或除热以及在系统上或由系统所做的功的任何组合来实现。作为状态的函数,内能并不依赖于系统到达其状态的方式或中间步骤的路径。<br />
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===Second Law===<br />
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===Second Law===<br />
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第二定律<br />
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The [[second law of thermodynamics]] states: ''Heat cannot spontaneously flow from a colder location to a hotter location.''<ref name= "NKS note b" /><br />
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The second law of thermodynamics states: Heat cannot spontaneously flow from a colder location to a hotter location.<br />
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热力学第二定律指出: 热量不能自发地从较冷的地方流向较热的地方。<br />
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This law is an expression of the universal principle of decay observable in nature. The second law is an observation of the fact that over time, differences in temperature, pressure, and chemical potential tend to even out in a physical system that is isolated from the outside world. [[Entropy]] is a measure of how much this process has progressed. The entropy of an isolated system which is not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium. However, principles guiding systems that are far from equilibrium are still debatable. One of such principles is the [[entropy production|maximum entropy production]] principle.<ref>{{cite journal|last1=Onsager|first1=Lars|title=Reciprocal Relations in Irreversible Processes|journal=Phys. Rev.|date=1931|volume=37|issue=405|pages=405–426|doi=10.1103/physrev.37.405|bibcode=1931PhRv...37..405O|doi-access=free}}</ref><ref>{{cite book|last1=Ziegler|first1=H.|title=An Introduction to Thermomechanics|date=1983|location=North Holland}}</ref> It states that non-equilibrium systems behave such a way as to maximize its entropy production.<ref>{{cite journal|last1=Belkin|first1=Andrey|last2=Hubler|first2=A.|last3=Bezryadin|first3=A.|title=Self-Assembled Wiggling Nano-Structures and the Principle of Maximum Entropy Production|journal=Sci. Rep.|date=2015|doi=10.1038/srep08323|pmid=25662746|pmc=4321171|bibcode=2015NatSR...5E8323B|volume=5|page=8323}}</ref><br />
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This law is an expression of the universal principle of decay observable in nature. The second law is an observation of the fact that over time, differences in temperature, pressure, and chemical potential tend to even out in a physical system that is isolated from the outside world. Entropy is a measure of how much this process has progressed. The entropy of an isolated system which is not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium. However, principles guiding systems that are far from equilibrium are still debatable. One of such principles is the maximum entropy production principle. It states that non-equilibrium systems behave such a way as to maximize its entropy production.<br />
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这个定律是可以在自然界观察到的衰变的普遍原理的一种表述。第二定律是对这样一个事实的观察: 随着时间的推移,在与外界隔绝的物理系统中,温度、压力和化学势的差异趋于均衡。熵是对这个过程进展程度的度量。不处于平衡状态的孤立系统的熵会随着时间的推移而增加,在平衡状态时达到最大值。然而,远离平衡的原则指导体系仍然是有争议的。其中一个原则就是最大产生熵原则。它指出,非平衡系统的行为方式使其产生熵最大化。<br />
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In classical thermodynamics, the second law is a basic postulate applicable to any system involving heat energy transfer; in statistical thermodynamics, the second law is a consequence of the assumed randomness of molecular chaos. There are many versions of the second law, but they all have the same effect, which is to explain the phenomenon of [[irreversibility]] in nature.<br />
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In classical thermodynamics, the second law is a basic postulate applicable to any system involving heat energy transfer; in statistical thermodynamics, the second law is a consequence of the assumed randomness of molecular chaos. There are many versions of the second law, but they all have the same effect, which is to explain the phenomenon of irreversibility in nature.<br />
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在经典热力学中,第二定律是适用于任何涉及热能传递的系统的基本假设; 在统计热力学中,第二定律是假定的分子混沌随机性的结果。第二定律有许多版本,但它们都具有同样的效果,即解释自然界中的不可逆现象。<br />
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===Third Law===<br />
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第三定律<br />
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The [[third law of thermodynamics]] states: ''As the temperature of a system approaches absolute zero, all processes cease and the entropy of the system approaches a minimum value.''<br />
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The third law of thermodynamics states: As the temperature of a system approaches absolute zero, all processes cease and the entropy of the system approaches a minimum value.<br />
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热力学第三定律指出: 当一个系统的温度接近绝对零度时,所有的过程停止,系统的熵接近最小值。<br />
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This law of thermodynamics is a statistical law of nature regarding entropy and the impossibility of reaching [[absolute zero]] of temperature. This law provides an absolute reference point for the determination of entropy. The entropy determined relative to this point is the absolute entropy. Alternate definitions include "the entropy of all systems and of all states of a system is smallest at absolute zero," or equivalently "it is impossible to reach the absolute zero of temperature by any finite number of processes".<br />
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This law of thermodynamics is a statistical law of nature regarding entropy and the impossibility of reaching absolute zero of temperature. This law provides an absolute reference point for the determination of entropy. The entropy determined relative to this point is the absolute entropy. Alternate definitions include "the entropy of all systems and of all states of a system is smallest at absolute zero," or equivalently "it is impossible to reach the absolute zero of temperature by any finite number of processes".<br />
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这个热力学定律是关于熵和不可能达到绝对零度的自然统计法则。这个定律为确定熵提供了一个绝对的参考点。相对于这个点确定的熵就是绝对熵。替代定义包括”系统的所有系统和系统的所有状态的熵在绝对零度时最小” ,或相当于”任何有限数目的过程都不可能达到绝对零度”。<br />
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Absolute zero, at which all activity would stop if it were possible to achieve, is −273.15&nbsp;°C (degrees Celsius), or −459.67&nbsp;°F (degrees Fahrenheit), or 0 K (kelvin), or 0° R (degrees [[Rankine scale|Rankine]]).<br />
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Absolute zero, at which all activity would stop if it were possible to achieve, is −273.15&nbsp;°C (degrees Celsius), or −459.67&nbsp;°F (degrees Fahrenheit), or 0 K (kelvin), or 0° R (degrees Rankine).<br />
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绝对零度是-273.15摄氏度(摄氏度) ,或-459.67华氏度(华氏度) ,或0 k (开尔文) ,或0 r (朗肯度)。<br />
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==System models==<br />
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==System models==<br />
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系统模型<br />
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[[File:system boundary.svg|200px|thumb|right|A diagram of a generic thermodynamic system]]<br />
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A diagram of a generic thermodynamic system<br />
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一个通用的热力学系统图表<br />
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An important concept in thermodynamics is the [[thermodynamic system]], which is a precisely defined region of the universe under study. Everything in the universe except the system is called the [[Environment (systems)|''surroundings'']]. A system is separated from the remainder of the universe by a [[Boundary (thermodynamic)|''boundary'']] which may be a physical boundary or notional, but which by convention defines a finite volume. Exchanges of [[Work (thermodynamics)|work]], [[heat]], or [[matter]] between the system and the surroundings take place across this boundary.<br />
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An important concept in thermodynamics is the thermodynamic system, which is a precisely defined region of the universe under study. Everything in the universe except the system is called the surroundings. A system is separated from the remainder of the universe by a boundary which may be a physical boundary or notional, but which by convention defines a finite volume. Exchanges of work, heat, or matter between the system and the surroundings take place across this boundary.<br />
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热力学中的一个重要概念是热力学系统,它是研究中的宇宙的一个精确定义的区域。除了这个系统之外,宇宙中的一切都被称为环境。一个系统通过一个边界从宇宙的其余部分中分离出来,这个边界可能是物理边界或者概念边界,但是按照惯例,它定义了一个有限的体积。系统和周围环境之间的功、热或物质的交换发生在这个边界上。<br />
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In practice, the boundary of a system is simply an imaginary dotted line drawn around a volume within which is going to be a change in the [[internal energy]] of that volume. Anything that passes across the boundary that effects a change in the internal energy of the system needs to be accounted for in the energy balance equation. The volume can be the region surrounding a single atom resonating energy, such as [[Max Planck]] defined in 1900; it can be a body of steam or air in a [[steam engine]], such as [[Nicolas Léonard Sadi Carnot|Sadi Carnot]] defined in 1824; it can be the body of a [[tropical cyclone]], such as [[Kerry Emanuel]] theorized in 1986 in the field of [[atmospheric thermodynamics]]; it could also be just one [[nuclide]] (i.e. a system of [[quark]]s) as hypothesized in [[quantum thermodynamics]], or the [[event horizon]] of a [[black hole thermodynamics|black hole]].<br />
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In practice, the boundary of a system is simply an imaginary dotted line drawn around a volume within which is going to be a change in the internal energy of that volume. Anything that passes across the boundary that effects a change in the internal energy of the system needs to be accounted for in the energy balance equation. The volume can be the region surrounding a single atom resonating energy, such as Max Planck defined in 1900; it can be a body of steam or air in a steam engine, such as Sadi Carnot defined in 1824; it can be the body of a tropical cyclone, such as Kerry Emanuel theorized in 1986 in the field of atmospheric thermodynamics; it could also be just one nuclide (i.e. a system of quarks) as hypothesized in quantum thermodynamics, or the event horizon of a black hole.<br />
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实际上,一个系统的边界只是一个虚构的虚线,它围绕着一个体积绘制,体积内部能量将发生变化。任何通过边界的影响系统内部能量的变化都需要在能量平衡方程中加以解释。体积可以是围绕单个原子共振能量的区域,如马克斯 · 普朗克在1900年定义的; 它可以是蒸汽机中的蒸汽体或空气体,如萨迪 · 卡诺在1824年定义的; 它可以是热带气旋的体,如 Kerry Emanuel 在1986年在大气热力学领域建立的理论; 它也可以只是一个核素(即:。量子热力学中假设的夸克系统,或黑洞的事件视界。<br />
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Boundaries are of four types: fixed, movable, real, and imaginary. For example, in an engine, a fixed boundary means the piston is locked at its position, within which a constant volume process might occur. If the piston is allowed to move that boundary is movable while the cylinder and cylinder head boundaries are fixed. For closed systems, boundaries are real while for open systems boundaries are often imaginary. In the case of a jet engine, a fixed imaginary boundary might be assumed at the intake of the engine, fixed boundaries along the surface of the case and a second fixed imaginary boundary across the exhaust nozzle.<br />
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Boundaries are of four types: fixed, movable, real, and imaginary. For example, in an engine, a fixed boundary means the piston is locked at its position, within which a constant volume process might occur. If the piston is allowed to move that boundary is movable while the cylinder and cylinder head boundaries are fixed. For closed systems, boundaries are real while for open systems boundaries are often imaginary. In the case of a jet engine, a fixed imaginary boundary might be assumed at the intake of the engine, fixed boundaries along the surface of the case and a second fixed imaginary boundary across the exhaust nozzle.<br />
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边界有四种类型: 固定的、可移动的、真实的和想象的。例如,在发动机中,一个固定的边界意味着活塞被锁定在它的位置,在那里可能发生一个定容过程。如果活塞允许移动,那么边界是可移动的,而气缸和气缸盖边界是固定的。对于封闭系统,边界是真实的,而对于开放系统,边界往往是虚构的。在喷气发动机的情况下,可以假定在发动机进气口处有一个固定的虚边界,沿着箱体表面有一个固定的边界,在排气喷嘴处有一个固定的虚边界。<br />
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Generally, thermodynamics distinguishes three classes of systems, defined in terms of what is allowed to cross their boundaries:<br />
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Generally, thermodynamics distinguishes three classes of systems, defined in terms of what is allowed to cross their boundaries:<br />
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一般来说,热力学区分了三类系统,根据允许什么跨越它们的边界来定义:<br />
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{{table of thermodynamic systems}}<br />
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As time passes in an isolated system, internal differences of pressures, densities, and temperatures tend to even out. A system in which all equalizing processes have gone to completion is said to be in a [[state (thermodynamic)|state]] of [[thermodynamic equilibrium]].<br />
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As time passes in an isolated system, internal differences of pressures, densities, and temperatures tend to even out. A system in which all equalizing processes have gone to completion is said to be in a state of thermodynamic equilibrium.<br />
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在一个孤立的系统中,随着时间的推移,压力、密度和温度的内部差异趋于平衡。一个所有均衡过程均已完成的系统被称为处于热力学平衡状态。<br />
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Once in thermodynamic equilibrium, a system's properties are, by definition, unchanging in time. Systems in equilibrium are much simpler and easier to understand than are systems which are not in equilibrium. Often, when analysing a dynamic thermodynamic process, the simplifying assumption is made that each intermediate state in the process is at equilibrium, producing thermodynamic processes which develop so slowly as to allow each intermediate step to be an equilibrium state and are said to be [[reversible process (thermodynamics)|reversible processes]].<br />
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Once in thermodynamic equilibrium, a system's properties are, by definition, unchanging in time. Systems in equilibrium are much simpler and easier to understand than are systems which are not in equilibrium. Often, when analysing a dynamic thermodynamic process, the simplifying assumption is made that each intermediate state in the process is at equilibrium, producing thermodynamic processes which develop so slowly as to allow each intermediate step to be an equilibrium state and are said to be reversible processes.<br />
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一旦进入热力学平衡,系统的属性,根据定义,在时间上是不变的。处于平衡状态的系统比不处于平衡状态的系统要简单得多,也更容易理解。通常,当分析一个动态热力学过程时,会做出这样的简化假设: 过程中的每一个居间态都处于平衡状态,产生的热力学过程发展得如此缓慢,以至于每一个中间步骤都是一个平衡状态,称之为可逆过程。<br />
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==States and processes==<br />
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==States and processes==<br />
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状态和过程<br />
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When a system is at equilibrium under a given set of conditions, it is said to be in a definite [[thermodynamic state]]. The state of the system can be described by a number of [[state function|state quantities]] that do not depend on the process by which the system arrived at its state. They are called [[intensive variable]]s or [[extensive variable]]s according to how they change when the size of the system changes. The properties of the system can be described by an [[equation of state]] which specifies the relationship between these variables. State may be thought of as the instantaneous quantitative description of a system with a set number of variables held constant.<br />
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When a system is at equilibrium under a given set of conditions, it is said to be in a definite thermodynamic state. The state of the system can be described by a number of state quantities that do not depend on the process by which the system arrived at its state. They are called intensive variables or extensive variables according to how they change when the size of the system changes. The properties of the system can be described by an equation of state which specifies the relationship between these variables. State may be thought of as the instantaneous quantitative description of a system with a set number of variables held constant.<br />
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当一个系统在一组给定的条件下处于平衡状态时,我们称之为处于一个确定的热力学状态。系统的状态可以用许多状态量来描述,这些状态量并不依赖于系统到达其状态的过程。它们被称为密集型变量或扩展型变量,这取决于它们在系统规模发生变化时的变化情况。系统的属性可以用一个状态方程来描述,它指定了这些变量之间的关系。状态可以被认为是一系列变量保持不变的系统的瞬时定量描述。<br />
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A [[thermodynamic process]] may be defined as the energetic evolution of a thermodynamic system proceeding from an initial state to a final state. It can be described by [[process function|process quantities]]. Typically, each thermodynamic process is distinguished from other processes in energetic character according to what parameters, such as temperature, pressure, or volume, etc., are held fixed; Furthermore, it is useful to group these processes into pairs, in which each variable held constant is one member of a [[conjugate variables (thermodynamics)|conjugate]] pair.<br />
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A thermodynamic process may be defined as the energetic evolution of a thermodynamic system proceeding from an initial state to a final state. It can be described by process quantities. Typically, each thermodynamic process is distinguished from other processes in energetic character according to what parameters, such as temperature, pressure, or volume, etc., are held fixed; Furthermore, it is useful to group these processes into pairs, in which each variable held constant is one member of a conjugate pair.<br />
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热力学过程可以被定义为热力学系统从初始状态到最终状态的能量演化。它可以用工艺量来描述。通常情况下,根据温度、压力、体积等参数的固定程度,每个热力学过程过程与能量特征中的其他过程是不同的; 此外,将这些过程分组成对也很有用,每个变量保持常数是一个共轭对的一个成员。<br />
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Several commonly studied thermodynamic processes are:<br />
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Several commonly studied thermodynamic processes are:<br />
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一些常见的研究热力学过程是:<br />
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* [[Adiabatic process]]: occurs without loss or gain of energy by [[heat]]<br />
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* [[Isenthalpic process]]: occurs at a constant [[enthalpy]]<br />
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* [[Isentropic process]]: a reversible adiabatic process, occurs at a constant [[entropy]]<br />
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* [[Isobaric process]]: occurs at constant [[pressure]]<br />
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* [[Isochoric process]]: occurs at constant [[Volume (thermodynamics)|volume]] (also called isometric/isovolumetric)<br />
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* [[Isothermal process]]: occurs at a constant [[temperature]]<br />
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* [[steady state|Steady state process]]: occurs without a change in the [[internal energy]]<br />
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== Instrumentation ==<br />
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== Instrumentation ==<br />
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仪器仪表<br />
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There are two types of [[thermodynamic instruments]], the '''meter''' and the '''reservoir'''. A thermodynamic meter is any device which measures any parameter of a [[thermodynamic system]]. In some cases, the thermodynamic parameter is actually defined in terms of an idealized measuring instrument. For example, the [[zeroth law of thermodynamics|zeroth law]] states that if two bodies are in thermal equilibrium with a third body, they are also in thermal equilibrium with each other. This principle, as noted by [[James Clerk Maxwell|James Maxwell]] in 1872, asserts that it is possible to measure temperature. An idealized [[thermometer]] is a sample of an ideal gas at constant pressure. From the [[ideal gas law]] ''pV=nRT'', the volume of such a sample can be used as an indicator of temperature; in this manner it defines temperature. Although pressure is defined mechanically, a pressure-measuring device, called a [[barometer]] may also be constructed from a sample of an ideal gas held at a constant temperature. A [[calorimeter]] is a device which is used to measure and define the internal energy of a system.<br />
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There are two types of thermodynamic instruments, the meter and the reservoir. A thermodynamic meter is any device which measures any parameter of a thermodynamic system. In some cases, the thermodynamic parameter is actually defined in terms of an idealized measuring instrument. For example, the zeroth law states that if two bodies are in thermal equilibrium with a third body, they are also in thermal equilibrium with each other. This principle, as noted by James Maxwell in 1872, asserts that it is possible to measure temperature. An idealized thermometer is a sample of an ideal gas at constant pressure. From the ideal gas law pV=nRT, the volume of such a sample can be used as an indicator of temperature; in this manner it defines temperature. Although pressure is defined mechanically, a pressure-measuring device, called a barometer may also be constructed from a sample of an ideal gas held at a constant temperature. A calorimeter is a device which is used to measure and define the internal energy of a system.<br />
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有两种类型的热力学设备,水表和水库。热力学仪表是测量热力学系统的任何参数的任何装置。在某些情况下,热力学参数实际上是用理想化的测量仪器来定义的。例如,第零定律指出,如果两个物体在热平衡中有第三个物体,那么它们也在热平衡中。正如詹姆斯 · 麦克斯韦尔在1872年指出的那样,这个原理断言测量温度是可能的。理想温度计是恒压下理想气体的样品。根据理想气体定律 pV nRT,这样一个样品的体积可以用作温度的指示器; 在这种方式下,它定义了温度。虽然压力是机械定义的,一个称为气压计的压力测量装置也可以由恒定温度下的理想气体样品构成。量热计是用来测量和定义系统内部能量的装置。<br />
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A thermodynamic reservoir is a system which is so large that its state parameters are not appreciably altered when it is brought into contact with the system of interest. When the reservoir is brought into contact with the system, the system is brought into equilibrium with the reservoir. For example, a pressure reservoir is a system at a particular pressure, which imposes that pressure upon the system to which it is mechanically connected. The Earth's atmosphere is often used as a pressure reservoir. If ocean water is used to cool a power plant, the ocean is often a temperature reservoir in the analysis of the power plant cycle.<br />
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A thermodynamic reservoir is a system which is so large that its state parameters are not appreciably altered when it is brought into contact with the system of interest. When the reservoir is brought into contact with the system, the system is brought into equilibrium with the reservoir. For example, a pressure reservoir is a system at a particular pressure, which imposes that pressure upon the system to which it is mechanically connected. The Earth's atmosphere is often used as a pressure reservoir. If ocean water is used to cool a power plant, the ocean is often a temperature reservoir in the analysis of the power plant cycle.<br />
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热力学储存器是这样一个系统,它的状态参数如此之大,当它与感兴趣的系统接触时,它的状态参数没有明显的改变。当油藏与系统接触时,系统与油藏达到平衡。例如,压力容器是一个处于特定压力下的系统,它对与之机械连接的系统施加压力。地球的大气层经常被用作压力储存器。如果用海水来冷却发电厂,在分析发电厂的循环过程中,海洋通常是一个温度储存库。<br />
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== Conjugate variables ==<br />
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== Conjugate variables ==<br />
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共轭变量<br />
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{{Main|Conjugate variables (thermodynamics)|l1=Conjugate variables}}<br />
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The central concept of thermodynamics is that of [[energy]], the ability to do [[Work (thermodynamics)|work]]. By the [[first law of thermodynamics|First Law]], the total energy of a system and its surroundings is conserved. Energy may be transferred into a system by heating, compression, or addition of matter, and extracted from a system by cooling, expansion, or extraction of matter. In [[mechanics]], for example, energy transfer equals the product of the force applied to a body and the resulting displacement.<br />
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The central concept of thermodynamics is that of energy, the ability to do work. By the First Law, the total energy of a system and its surroundings is conserved. Energy may be transferred into a system by heating, compression, or addition of matter, and extracted from a system by cooling, expansion, or extraction of matter. In mechanics, for example, energy transfer equals the product of the force applied to a body and the resulting displacement.<br />
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热力学的核心概念是能量,做功的能力。根据第一定律,系统及其周围环境的总能量是守恒的。能量可以通过加热、压缩或添加物质的方式转移到系统中,也可以通过冷却、膨胀或提取物质的方式从系统中提取。例如,在力学中,能量传递等于作用在物体上的力和由此产生的位移的乘积。<br />
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[[conjugate variables (thermodynamics)|Conjugate variables]] are pairs of thermodynamic concepts, with the first being akin to a "force" applied to some [[thermodynamic system]], the second being akin to the resulting "displacement," and the product of the two equalling the amount of energy transferred. The common conjugate variables are:<br />
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Conjugate variables are pairs of thermodynamic concepts, with the first being akin to a "force" applied to some thermodynamic system, the second being akin to the resulting "displacement," and the product of the two equalling the amount of energy transferred. The common conjugate variables are:<br />
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共轭变量是成对的热力学概念,第一个类似于施加在某些热力学系统上的“力” ,第二个类似于由此产生的“位移” ,两者的乘积等于所转移的能量。常见的共轭变量有:<br />
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* [[Pressure]]-[[Volume (thermodynamics)|volume]] (the [[Mechanics|mechanical]] parameters);<br />
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* [[Temperature]]-[[entropy]] (thermal parameters);<br />
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* [[Chemical potential]]-[[particle number]] (material parameters).<br />
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== Potentials ==<br />
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== Potentials ==<br />
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== Potentials ==<br />
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[[Thermodynamic potential]]s are different quantitative measures of the stored energy in a system. Potentials are used to measure the energy changes in systems as they evolve from an initial state to a final state. The potential used depends on the constraints of the system, such as constant temperature or pressure. For example, the Helmholtz and Gibbs energies are the energies available in a system to do useful work when the temperature and volume or the pressure and temperature are fixed, respectively.<br />
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Thermodynamic potentials are different quantitative measures of the stored energy in a system. Potentials are used to measure the energy changes in systems as they evolve from an initial state to a final state. The potential used depends on the constraints of the system, such as constant temperature or pressure. For example, the Helmholtz and Gibbs energies are the energies available in a system to do useful work when the temperature and volume or the pressure and temperature are fixed, respectively.<br />
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热力学势是体系中储存能量的不同定量度量。势能被用来测量系统从初始状态到最终状态的能量变化。所用的电位取决于系统的约束条件,如恒温或恒压。例如,亥姆霍兹能量和吉布斯能量是当温度和体积或压力和温度分别固定时,系统中可用于做有用功的能量。<br />
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The five most well known potentials are:<br />
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The five most well known potentials are:<br />
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五个最有名的潜力是:<br />
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{{table of thermodynamic potentials}}<br />
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where <math>T</math> is the [[thermodynamic temperature|temperature]], <math>S</math> the [[entropy]], <math>p</math> the [[pressure]], <math>V</math> the [[Volume (thermodynamics)|volume]], <math>\mu</math> the [[chemical potential]], <math>N</math> the number of particles in the system, and <math>i</math> is the count of particles types in the system.<br />
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where <math>T</math> is the temperature, <math>S</math> the entropy, <math>p</math> the pressure, <math>V</math> the volume, <math>\mu</math> the chemical potential, <math>N</math> the number of particles in the system, and <math>i</math> is the count of particles types in the system.<br />
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数学 t / math 是温度,数学 s / math 是熵,数学 p / math 是压力,数学 v / math 是体积,数学 mu / math 是化学势,数学 n / math 是系统中粒子的数量,数学 i / math 是系统中粒子类型的数量。<br />
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Thermodynamic potentials can be derived from the energy balance equation applied to a thermodynamic system. Other thermodynamic potentials can also be obtained through [[Legendre transformation]].<br />
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Thermodynamic potentials can be derived from the energy balance equation applied to a thermodynamic system. Other thermodynamic potentials can also be obtained through Legendre transformation.<br />
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热力学势可以从应用于热力学系统的能量平衡方程推导出来。其他热力学势也可以通过勒壤得转换得到。<br />
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== Applied fields ==<br />
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== Applied fields ==<br />
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应用领域<br />
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{{columns-list|colwidth=22em|<br />
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{{columns-list|colwidth=22em|<br />
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{ columns-list | colwidth 22em | <br />
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* [[Atmospheric thermodynamics]]<br />
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* [[Biological thermodynamics]]<br />
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* [[Black hole thermodynamics]]<br />
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* [[Chemical thermodynamics]]<br />
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* [[Classical thermodynamics]]<br />
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* [[Thermodynamic equilibrium|Equilibrium thermodynamics]]<br />
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* [[Industrial ecology]] (re: [[Exergy]])<br />
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* [[Maximum entropy thermodynamics]]<br />
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* [[Non-equilibrium thermodynamics]]<br />
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* [[Philosophy of thermal and statistical physics]]<br />
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* [[Psychrometrics]]<br />
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* [[Quantum thermodynamics]]<br />
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* [[Statistical thermodynamics]]<br />
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* [[Thermoeconomics]]<br />
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}}<br />
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}}<br />
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}}<br />
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== See also ==<br />
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== See also ==<br />
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参见<br />
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{{portal|Physics}}<br />
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* [[Thermodynamic process path]]<br />
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===Lists and timelines===<br />
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===Lists and timelines===<br />
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清单和时间线<br />
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* [[List of important publications in physics#Thermodynamics|List of important publications in thermodynamics]]<br />
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* [[List of textbooks in statistical mechanics|List of textbooks on thermodynamics and statistical mechanics]]<br />
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* [[List of thermal conductivities]]<br />
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* [[List of thermodynamic properties]]<br />
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* [[Table of thermodynamic equations]]<br />
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* [[Timeline of thermodynamics]]<br />
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== Notes ==<br />
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== Notes ==<br />
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注释<br />
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{{reflist|group=nb}}<br />
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==References==<br />
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==References==<br />
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参考资料<br />
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{{Reflist|35em}}<br />
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==Further reading==<br />
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==Further reading==<br />
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进一步阅读<br />
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* {{cite book|author1=Goldstein, Martin|author2=Inge F.|lastauthoramp=yes|title=The Refrigerator and the Universe|url=https://archive.org/details/refrigeratoruniv0000gold|url-access=registration|publisher=Harvard University Press|year=1993|isbn=978-0-674-75325-9|location=|pages=|oclc=32826343}} A nontechnical introduction, good on historical and interpretive matters.<br />
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* {{cite journal |last1=Kazakov |first1=Andrei |last2=Muzny |first2=Chris D. |last3=Chirico |first3=Robert D. |last4=Diky |first4=Vladimir V. |last5=Frenkel |first5=Michael |title=Web Thermo Tables – an On-Line Version of the TRC Thermodynamic Tables |journal=Journal of Research of the National Institute of Standards and Technology |volume=113 |issue=4 |year=2008 |pages=209–220 |issn=1044-677X |doi=10.6028/jres.113.016 |pmc=4651616 |pmid=27096122}}<br />
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* {{cite book|author=Gibbs J.W.|title=The Collected Works of J. Willard Gibbs Thermodynamics.|publisher=Longmans, Green and Co.|year=1928|isbn=|location=New York|pages=|oclc=}} Vol. 1, pp. 55–349.<br />
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* {{cite book|author=Guggenheim E.A.|title=Modern thermodynamics by the methods of Willard Gibbs|publisher=Methuen & co. ltd.|year=1933|isbn=|location=London|pages=|oclc=}}<br />
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* {{cite book|author=Denbigh K.|title=The Principles of Chemical Equilibrium: With Applications in Chemistry and Chemical Engineering.|publisher=Cambridge University Press|year=1981|isbn=|location=London|pages=|oclc=}}<br />
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* {{cite book|author=Stull, D.R., Westrum Jr., E.F. and Sinke, G.C.|title=The Chemical Thermodynamics of Organic Compounds.|publisher=John Wiley and Sons, Inc.|year=1969|isbn=|location=London|pages=|oclc=}}<br />
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* {{cite book|author=Bazarov I.P.|title=Thermodynamics: Textbook.|publisher=Lan publishing house|year=2010|isbn=978-5-8114-1003-3|location=St. Petersburg|page=384|oclc=}} 5th ed. (in Russian)<br />
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* {{cite book|author=Bawendi Moungi G., Alberty Robert A. and Silbey Robert J.|title=Physical Chemistry|publisher=J. Wiley & Sons, Incorporated|year=2004|isbn=|location=|pages=|oclc=}}<br />
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* {{cite book|author=Alberty Robert A.|title=Thermodynamics of Biochemical Reactions|publisher=Wiley-Interscience|year=2003|isbn=|location=|pages=|oclc=}}<br />
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* {{cite book|author=Alberty Robert A.|title=Biochemical Thermodynamics: Applications of Mathematica|journal=Methods of Biochemical Analysis|publisher=John Wiley & Sons, Inc.|year=2006|volume=48|isbn=978-0-471-75798-6|location=|pages=1–458|pmid=16878778|oclc=}}<br />
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The following titles are more technical:<br />
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The following titles are more technical:<br />
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下面的标题更具技术性:<br />
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* {{Cite book|title=Advanced Engineering Thermodynamics|last=Bejan|first=Adrian|publisher=Wiley|year=2016|isbn=978-1-119-05209-8|edition=4|location=|pages=}}<br />
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* {{cite book|author=Cengel, Yunus A., & Boles, Michael A.|title=Thermodynamics – an Engineering Approach|publisher=McGraw Hill|year=2002|isbn=978-0-07-238332-4|location=|pages=|oclc=45791449|url-access=registration|url=https://archive.org/details/thermodynamicsen00ceng_0}}<br />
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* {{cite book|author=Dunning-Davies, Jeremy|title=Concise Thermodynamics: Principles and Applications|publisher=Horwood Publishing|year=1997|isbn=978-1-8985-6315-0|location=|pages=|oclc=36025958}}<br />
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* {{cite book|author1=Kroemer, Herbert|author2=Kittel, Charles|lastauthoramp=yes|title=Thermal Physics|publisher=W.H. Freeman Company|year=1980|isbn=978-0-7167-1088-2|location=|pages=|oclc=32932988}}<br />
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== External links ==<br />
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== External links ==<br />
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外部链接<br />
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{{Wikibooks|Engineering Thermodynamics}}<br />
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{{wikiquote|Thermodynamics}}<br />
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* {{cite EB1911 |title=Thermodynamics |volume=26 |pages=808–814 |short=x |url=https://archive.org/details/encyclopaediabri26chisrich/page/808}}<br />
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* [http://tigger.uic.edu/~mansoori/Thermodynamic.Data.and.Property_html Thermodynamics Data & Property Calculation Websites]<br />
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* [http://tigger.uic.edu/~mansoori/Thermodynamics.Educational.Sites_html Thermodynamics Educational Websites]<br />
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* [http://scienceworld.wolfram.com/physics/topics/Thermodynamics.html Thermodynamics at ''ScienceWorld'']<br />
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* [http://www.wiley.com/legacy/college/boyer/0470003790/reviews/thermo/thermo_intro.htm Biochemistry Thermodynamics]<br />
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* [http://farside.ph.utexas.edu/teaching/sm1/lectures/lectures.html Thermodynamics and Statistical Mechanics]<br />
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* [https://web.archive.org/web/20090430200028/http://www.ent.ohiou.edu/~thermo/ Engineering Thermodynamics – A Graphical Approach]<br />
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* [http://farside.ph.utexas.edu/teaching/sm1/statmech.pdf Thermodynamics and Statistical Mechanics] by Richard Fitzpatrick<br />
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[[Category:Thermodynamics| ]]<br />
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[[Category:Chemical engineering]]<br />
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Category:Chemical engineering<br />
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类别: 化学工程<br />
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[[Category:Concepts in physics]]<br />
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Category:Concepts in physics<br />
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分类: 物理概念<br />
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Category:Subfields of physics<br />
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分类: 物理学的子领域<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Thermodynamics]]. Its edit history can be viewed at [[热力学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E7%83%AD%E5%8A%9B%E5%AD%A6&diff=21957热力学2021-02-23T07:10:02Z<p>Jxzhou:</p>
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<div>此词条暂由jxzhou翻译,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{short description|Physics of heat, work, and temperature}}<br />
{{Use dmy dates|date=February 2016}}<br />
[[File:Carnot engine (hot body - working body - cold body).jpg|thumb|300px|right|Annotated color version of the original 1824 [[Carnot heat engine]] showing the hot body (boiler), working body (system, steam), and cold body (water), the letters labeled according to the stopping points in [[Carnot cycle]].]]<br />
{{Thermodynamics}}<br />
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'''Thermodynamics''' is a branch of [[physics]] that deals with [[heat]], [[Work (thermodynamics)|work]], and [[temperature]], and their relation to [[energy]], [[radiation]], and physical properties of [[matter]]. The behavior of these quantities is governed by the four [[laws of thermodynamics]] which convey a quantitative description using measurable macroscopic [[physical quantity|physical quantities]], but may be explained in terms of [[microscopic]] constituents by [[statistical mechanics]]. Thermodynamics applies to a wide variety of topics in [[science]] and [[engineering]], especially [[physical chemistry]], [[chemical engineering]] and [[mechanical engineering]], but also in other complex fields such as [[meteorology]].<br />
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热力学是物理学的一个分支,研究热、功和温度,以及它们与能量、辐射和物质物理性质的关系。这些量的行为遵循四个热力学定律,它们用可测量的宏观物理量传递了一个定量描述,但是可以用微观成分来解释统计力学。热力学适用于科学和工程中的各种各样的课题,尤其是物理化学、化学工程和机械工程,但也适用于气象学这样复杂的领域。<br />
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Historically, thermodynamics developed out of a desire to increase the [[thermodynamic efficiency|efficiency]] of early [[steam engine]]s, particularly through the work of French physicist [[Nicolas Léonard Sadi Carnot]] (1824) who believed that engine efficiency was the key that could help France win the [[Napoleonic Wars]].<ref>{{cite book | last = Clausius | first = Rudolf | title = On the Motive Power of Heat, and on the Laws which can be deduced from it for the Theory of Heat | publisher = Poggendorff's Annalen der Physik, LXXIX (Dover Reprint) | year = 1850 | isbn = 978-0-486-59065-3}}</ref> Scots-Irish physicist [[William Thomson, 1st Baron Kelvin|Lord Kelvin]] was the first to formulate a concise definition of thermodynamics in 1854<ref name=kelvin1854>{{cite book<br />
|title=Mathematical and Physical Papers<br />
|author= William Thomson, LL.D. D.C.L., F.R.S.<br />
|location=London, Cambridge<br />
|year=1882<br />
|volume=1<br />
|page=232<br />
|publisher=C.J. Clay, M.A. & Son, Cambridge University Press<br />
|url=https://books.google.com/books?id=nWMSAAAAIAAJ&q=On+an+Absolute+Thermometric+Scale+Founded+on+Carnot%E2%80%99s+Theory&pg=PA100<br />
}}</ref> which stated, "Thermo-dynamics is the subject of the relation of heat to forces acting between contiguous parts of bodies, and the relation of heat to electrical agency."<br />
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“热力学的主题是热量与物体相邻部分之间作用力的关系,以及热量与电能的关系。”<br />
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The initial application of thermodynamics to [[mechanical heat engine]]s was quickly extended to the study of chemical compounds and chemical reactions. [[Chemical thermodynamics]] studies the nature of the role of [[entropy]] in the process of [[chemical reaction]]s and has provided the bulk of expansion and knowledge of the field.<ref name="Gibbs 1876">{{cite book|author=Gibbs, Willard, J.|title=Transactions of the Connecticut Academy of Arts and Sciences|volume=III|pages=[https://archive.org/details/transactions03conn/page/108 108]–248, 343–524|year=1874–1878|url=https://archive.org/details/transactions03conn|publisher=New Haven}}</ref><ref name="Duhem 1886">Duhem, P.M.M. (1886). ''Le Potential Thermodynamique et ses Applications'', Hermann, Paris.</ref><ref name="Lewis Randall 1923">{{cite book | last1=Lewis | first1=Gilbert N. | last2=Randall | first2=Merle | title=Thermodynamics and the Free Energy of Chemical Substances | url=https://archive.org/details/thermodynamicsfr00gnle | publisher=McGraw-Hill Book Co. Inc. | year=1923}}</ref><ref name="Guggenheim 1933">Guggenheim, E.A. (1933). ''Modern Thermodynamics by the Methods of J.W. Gibbs'', Methuen, London.</ref><ref name="Guggenheim 1949/1967">Guggenheim, E.A. (1949/1967). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', 1st edition 1949, 5th edition 1967, North-Holland, Amsterdam.</ref><ref>{{cite book | author=Ilya Prigogine, I. & Defay, R., translated by D.H. Everett| title=Chemical Thermodynamics | year=1954 | publisher=Longmans, Green & Co., London. Includes classical non-equilibrium thermodynamics.}}<br />
</ref><ref name=Fermi>{{cite book<br />
|title=Thermodynamics<br />
|author=Enrico Fermi<br />
|url=https://books.google.com/books?id=VEZ1ljsT3IwC&q=thermodynamics<br />
|isbn=978-0486603612<br />
|publisher=Courier Dover Publications<br />
|year=1956<br />
|page=ix<br />
|oclc=230763036}}</ref><ref name="Perrot" >{{cite book | author=Perrot, Pierre | title=A to Z of Thermodynamics | publisher=Oxford University Press | year=1998 | isbn=978-0-19-856552-9 | oclc=123283342}}</ref><ref>{{cite book | author=Clark, John, O.E.| title=The Essential Dictionary of Science | publisher=Barnes & Noble Books | year=2004 | isbn=978-0-7607-4616-5 | oclc=58732844}}</ref> Other formulations of thermodynamics emerged. [[Statistical thermodynamics]], or statistical mechanics, concerns itself with [[statistics|statistical]] predictions of the collective motion of particles from their microscopic behavior. In 1909, [[Constantin Carathéodory]] presented a purely mathematical approach in an [[axiomatic]] formulation, a description often referred to as ''geometrical thermodynamics''.<br />
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热力学的其他公式出现了。统计热力学,或称统计力学热力学,从微观角度对粒子的集体运动进行统计预测。在1909年,康斯坦丁·卡拉西奥多里提出了一个纯粹的数学方法在一个公理化的公式,一个描述通常被称为几何热力学。<br />
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==Introduction==<br />
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引言<br />
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A description of any thermodynamic system employs the four [[laws of thermodynamics]] that form an axiomatic basis. The first law specifies that energy can be exchanged between physical systems as [[heat]] and [[Mechanical work|work]].<ref>{{cite book | author=Van Ness, H.C. | title=Understanding Thermodynamics | publisher=Dover Publications, Inc. | year=1983 | origyear=1969 | isbn=9780486632773 | oclc=8846081 | url-access=registration | url=https://archive.org/details/understandingthe00vann }}</ref> The second law defines the existence of a quantity called [[entropy]], that describes the direction, thermodynamically, that a system can evolve and quantifies the state of order of a system and that can be used to quantify the useful work that can be extracted from the system.<ref>{{cite book | author=Dugdale, J.S. | title=Entropy and its Physical Meaning | publisher=Taylor and Francis | year=1998 | isbn=978-0-7484-0569-5 | oclc=36457809}}</ref><br />
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A description of any thermodynamic system employs the four laws of thermodynamics that form an axiomatic basis. The first law specifies that energy can be exchanged between physical systems as heat and work. The second law defines the existence of a quantity called entropy, that describes the direction, thermodynamically, that a system can evolve and quantifies the state of order of a system and that can be used to quantify the useful work that can be extracted from the system.<br />
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任何热力学系统的描述都采用了构成公理基础的4个热力学定律。第一定律规定能量可以在物理系统之间以热和功的形式进行交换。第二定律定义了一个叫做熵的量的存在,这个量描述了一个系统可以进化和量化一个系统的有序状态的方向,可以用来量化可以从系统中提取的有用功。<br />
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In thermodynamics, interactions between large ensembles of objects are studied and categorized. Central to this are the concepts of the thermodynamic ''[[System (thermodynamics)|system]]'' and its ''[[Surroundings (thermodynamics)|surroundings]]''. A system is composed of particles, whose average motions define its properties, and those properties are in turn related to one another through [[Equation of state|equations of state]]. Properties can be combined to express [[internal energy]] and [[thermodynamic potential]]s, which are useful for determining conditions for [[Dynamic equilibrium|equilibrium]] and [[spontaneous process]]es.<br />
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In thermodynamics, interactions between large ensembles of objects are studied and categorized. Central to this are the concepts of the thermodynamic system and its surroundings. A system is composed of particles, whose average motions define its properties, and those properties are in turn related to one another through equations of state. Properties can be combined to express internal energy and thermodynamic potentials, which are useful for determining conditions for equilibrium and spontaneous processes.<br />
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在热力学中,研究和分类了物体大系综之间的相互作用。其核心是热力学系统及其周围环境的概念。一个系统是由粒子组成的,粒子的平均运动决定了它的性质,而这些性质又通过状态方程彼此相关。性质可以结合起来表示内能和热力学势,这对于确定平衡和自发过程的条件是有用的。<br />
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With these tools, thermodynamics can be used to describe how systems respond to changes in their environment. This can be applied to a wide variety of topics in [[science]] and [[engineering]], such as [[engine]]s, [[phase transition]]s, [[chemical reaction]]s, [[transport phenomena]], and even [[black hole]]s. The results of thermodynamics are essential for other fields of [[physics]] and for [[chemistry]], [[chemical engineering]], [[corrosion engineering]], [[aerospace engineering]], [[mechanical engineering]], [[cell biology]], [[biomedical engineering]], [[materials science]], and [[economics]], to name a few.<ref>{{Cite book | last1=Smith | first1=J.M. | last2=Van Ness | first2=H.C. | last3=Abbott | first3=M.M. | title=Introduction to Chemical Engineering Thermodynamics | journal=Journal of Chemical Education | volume=27 | issue=10 | page=584 | year=2005 | isbn=978-0-07-310445-4 | oclc=56491111| bibcode=1950JChEd..27..584S | doi=10.1021/ed027p584.3 }}</ref><ref>{{cite book | author=Haynie, Donald, T. | title=Biological Thermodynamics | publisher=Cambridge University Press | year=2001 | isbn=978-0-521-79549-4 | oclc=43993556}}</ref><br />
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With these tools, thermodynamics can be used to describe how systems respond to changes in their environment. This can be applied to a wide variety of topics in science and engineering, such as engines, phase transitions, chemical reactions, transport phenomena, and even black holes. The results of thermodynamics are essential for other fields of physics and for chemistry, chemical engineering, corrosion engineering, aerospace engineering, mechanical engineering, cell biology, biomedical engineering, materials science, and economics, to name a few.<br />
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有了这些工具,热力学可以用来描述系统如何响应环境中的变化。这可以应用于科学和工程的各种主题,如引擎,相变,化学反应,传输现象,甚至黑洞。热力学的结果对于物理学、化学、化学工程、腐蚀工程、航空航天工业奖、机械工程、细胞生物学、生物医学工程、材料科学和经济学等其他领域都是必不可少的。<br />
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This article is focused mainly on classical thermodynamics which primarily studies systems in [[thermodynamic equilibrium]]. [[Non-equilibrium thermodynamics]] is often treated as an extension of the classical treatment, but statistical mechanics has brought many advances to that field.<br />
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This article is focused mainly on classical thermodynamics which primarily studies systems in thermodynamic equilibrium. Non-equilibrium thermodynamics is often treated as an extension of the classical treatment, but statistical mechanics has brought many advances to that field.<br />
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这篇文章主要关注经典热力学,它主要研究热力学平衡中的系统。非平衡态热力学通常被视为古典治疗的延伸,但是统计力学已经在这个领域带来了许多进步。<br />
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[[File:Eight founding schools.png|400px|thumb|The [[thermodynamicist]]s representative of the original eight founding schools of thermodynamics. The schools with the most-lasting effect in founding the modern versions of thermodynamics are the Berlin school, particularly as established in [[Rudolf Clausius]]’s 1865 textbook ''The Mechanical Theory of Heat'', the Vienna school, with the [[statistical mechanics]] of [[Ludwig Boltzmann]], and the Gibbsian school at Yale University, American engineer [[Willard Gibbs]]' 1876 ''[[On the Equilibrium of Heterogeneous Substances]]'' launching [[chemical thermodynamics]].<ref name="autogenerated1">[http://www.eoht.info/page/Schools+of+thermodynamics Schools of thermodynamics] – EoHT.info.</ref>]]<br />
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The [[thermodynamicists representative of the original eight founding schools of thermodynamics. The schools with the most-lasting effect in founding the modern versions of thermodynamics are the Berlin school, particularly as established in Rudolf Clausius’s 1865 textbook The Mechanical Theory of Heat, the Vienna school, with the statistical mechanics of Ludwig Boltzmann, and the Gibbsian school at Yale University, American engineer Willard Gibbs' 1876 On the Equilibrium of Heterogeneous Substances launching chemical thermodynamics.]]<br />
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代表热力学最初八个学派的热力学学者。在建立现代版本的热力学方面影响最深远的学校是柏林学派,特别是由 Rudolf Clausius 在1865年的教科书《热力学的机械理论》中建立的维也纳学派,与统计力学路德维希·玻尔兹曼合作的维也纳学派,以及耶鲁大学的 Gibbsian 学派,美国工程师 Willard Gibbs 在1876年建立的关于多相物质平衡化学热力学<br />
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==History==<br />
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==History==<br />
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历史<br />
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The [[history of thermodynamics]] as a scientific discipline generally begins with [[Otto von Guericke]] who, in 1650, built and designed the world's first [[vacuum pump]] and demonstrated a [[vacuum]] using his [[Magdeburg hemispheres]]. Guericke was driven to make a vacuum in order to disprove [[Aristotle]]'s long-held supposition that 'nature abhors a vacuum'. Shortly after Guericke, the English physicist and chemist [[Robert Boyle]] had learned of Guericke's designs and, in 1656, in coordination with English scientist [[Robert Hooke]], built an air pump.<ref>{{cite book | author=Partington, J.R. | title=A Short History of Chemistry | url=https://archive.org/details/shorthistoryofch0000part_q6h4 | url-access=registration | publisher=Dover | year=1989 | isbn= | oclc=19353301| author-link=J. R. Partington }}</ref> Using this pump, Boyle and Hooke noticed a correlation between [[pressure]], [[temperature]], and [[Volume (thermodynamics)|volume]]. In time, [[Boyle's Law]] was formulated, which states that pressure and volume are [[inverse proportion|inversely proportional]]. Then, in 1679, based on these concepts, an associate of Boyle's named [[Denis Papin]] built a [[steam digester]], which was a closed vessel with a tightly fitting lid that confined steam until a high pressure was generated.<br />
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The history of thermodynamics as a scientific discipline generally begins with Otto von Guericke who, in 1650, built and designed the world's first vacuum pump and demonstrated a vacuum using his Magdeburg hemispheres. Guericke was driven to make a vacuum in order to disprove Aristotle's long-held supposition that 'nature abhors a vacuum'. Shortly after Guericke, the English physicist and chemist Robert Boyle had learned of Guericke's designs and, in 1656, in coordination with English scientist Robert Hooke, built an air pump. Using this pump, Boyle and Hooke noticed a correlation between pressure, temperature, and volume. In time, Boyle's Law was formulated, which states that pressure and volume are inversely proportional. Then, in 1679, based on these concepts, an associate of Boyle's named Denis Papin built a steam digester, which was a closed vessel with a tightly fitting lid that confined steam until a high pressure was generated.<br />
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热力学史作为一门科学学科通常始于1650年的奥托·冯·格里克,他建造并设计了世界上第一台真空泵,并用他的马德堡半球展示了真空。格里克被迫制造一个真空,以反驳亚里士多德长期以来的假设,即“自然憎恶真空”。在格里克之后不久,英国物理学家和化学家罗伯特 · 波义耳听说了格里克的设计,并在1656年与英国科学家罗伯特 · 胡克合作制造了一个空气泵。波义耳和胡克利用这台泵,注意到了压力、温度和体积之间的关系。随着时间的推移,波义耳定律被公式化了,它指出压强和体积成反比。然后,在1679年,基于这些概念,波义耳的一位名叫丹尼斯 · 帕平的合伙人建造了一个蒸汽消化器,这是一个封闭的容器,有一个紧密的盖子,将蒸汽封闭起来,直到产生高压。<br />
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Later designs implemented a steam release valve that kept the machine from exploding. By watching the valve rhythmically move up and down, Papin conceived of the idea of a [[piston]] and a cylinder engine. He did not, however, follow through with his design. Nevertheless, in 1697, based on Papin's designs, engineer [[Thomas Savery]] built the first engine, followed by [[Thomas Newcomen]] in 1712. Although these early engines were crude and inefficient, they attracted the attention of the leading scientists of the time.<br />
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Later designs implemented a steam release valve that kept the machine from exploding. By watching the valve rhythmically move up and down, Papin conceived of the idea of a piston and a cylinder engine. He did not, however, follow through with his design. Nevertheless, in 1697, based on Papin's designs, engineer Thomas Savery built the first engine, followed by Thomas Newcomen in 1712. Although these early engines were crude and inefficient, they attracted the attention of the leading scientists of the time.<br />
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后来的设计实现了一个蒸汽释放阀,以防止机器爆炸。通过观察阀门有节奏地上下运动,帕平构思了活塞和汽缸发动机的概念。然而,他并没有坚持他的设计。然而,在1697年,根据帕平的设计,工程师托马斯 · 萨维里制造了第一台发动机,随后在1712年托马斯 · 纽科门制造了第一台发动机。虽然这些早期的发动机粗糙和低效,他们吸引了当时的主要科学家的注意。<br />
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The fundamental concepts of [[heat capacity]] and [[latent heat]], which were necessary for the development of thermodynamics, were developed by Professor [[Joseph Black]] at the University of Glasgow, where [[James Watt]] was employed as an instrument maker. Black and Watt performed experiments together, but it was Watt who conceived the idea of the [[Watt steam engine#Separate condenser|external condenser]] which resulted in a large increase in [[steam engine]] efficiency.<ref>The Newcomen engine was improved from 1711 until Watt's work, making the efficiency comparison subject to qualification, but the increase from the 1865 version was on the order of 100%.</ref> Drawing on all the previous work led [[Nicolas Léonard Sadi Carnot|Sadi Carnot]], the "father of thermodynamics", to publish ''[[Reflections on the Motive Power of Fire]]'' (1824), a discourse on heat, power, energy and engine efficiency. The book outlined the basic energetic relations between the [[Carnot engine]], the [[Carnot cycle]], and '''motive power'''. It marked the start of thermodynamics as a modern science.<ref name="Perrot" /><br />
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The fundamental concepts of heat capacity and latent heat, which were necessary for the development of thermodynamics, were developed by Professor Joseph Black at the University of Glasgow, where James Watt was employed as an instrument maker. Black and Watt performed experiments together, but it was Watt who conceived the idea of the external condenser which resulted in a large increase in steam engine efficiency. Drawing on all the previous work led Sadi Carnot, the "father of thermodynamics", to publish Reflections on the Motive Power of Fire (1824), a discourse on heat, power, energy and engine efficiency. The book outlined the basic energetic relations between the Carnot engine, the Carnot cycle, and motive power. It marked the start of thermodynamics as a modern science.<br />
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热容量和潜热的基本概念是热力学发展所必需的,是由格拉斯哥大学的 Joseph Black 教授提出来的,James Watt 是那里的一个仪器制造商。布莱克和瓦特一起进行实验,但是瓦特提出了外部冷凝器的概念,从而大大提高了蒸汽机的效率。根据以前所有的工作,“热力学之父”萨迪 · 卡诺发表了《论火的动力(1824年) ,一篇关于热、动力、能源和发动机效率的论文。这本书概述了卡诺发动机、卡诺循环和动力之间的基本能量关系。它标志着热力学作为一门现代科学的开始。<br />
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The first thermodynamic textbook was written in 1859 by [[William John Macquorn Rankine|William Rankine]], originally trained as a physicist and a civil and mechanical engineering professor at the [[University of Glasgow]].<ref>{{cite book |author1=Cengel, Yunus A. |author2=Boles, Michael A. | title=Thermodynamics – an Engineering Approach | publisher=McGraw-Hill | year=2005 | isbn=978-0-07-310768-4}}</ref> The first and second laws of thermodynamics emerged simultaneously in the 1850s, primarily out of the works of [[William John Macquorn Rankine|William Rankine]], [[Rudolf Clausius]], and [[William Thomson, 1st Baron Kelvin|William Thomson]] (Lord Kelvin).<ref name = "NKS note b">''[[A New Kind of Science]]'' [https://www.wolframscience.com/nks/notes-9-3--history-of-thermodynamics/ Note (b) for Irreversibility and the Second Law of Thermodynamics]</ref><br />
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The first thermodynamic textbook was written in 1859 by William Rankine, originally trained as a physicist and a civil and mechanical engineering professor at the University of Glasgow. The first and second laws of thermodynamics emerged simultaneously in the 1850s, primarily out of the works of William Rankine, Rudolf Clausius, and William Thomson (Lord Kelvin).<br />
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第一本热力学教科书是 William Rankine 在1859年写的,他最初是格拉斯哥大学的物理学家和土木机械工程教授。第一个和第二个热力学定律同时出现在19世纪50年代,主要出自 William Rankine,Rudolf Clausius 和 William Thomson (Lord Kelvin)的作品。<br />
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The foundations of statistical thermodynamics were set out by physicists such as [[James Clerk Maxwell]], [[Ludwig Boltzmann]], [[Max Planck]], [[Rudolf Clausius]] and [[Josiah Willard Gibbs|J. Willard Gibbs]].<br />
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The foundations of statistical thermodynamics were set out by physicists such as James Clerk Maxwell, Ludwig Boltzmann, Max Planck, Rudolf Clausius and J. Willard Gibbs.<br />
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统计热力学的基础是由物理学家建立的,如詹姆斯·克拉克·麦克斯韦,路德维希·玻尔兹曼,马克斯 · 普朗克,Rudolf Clausius 和 j. Willard Gibbs。<br />
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During the years 1873–76 the American mathematical physicist [[Josiah Willard Gibbs]] published a series of three papers, the most famous being ''[[On the Equilibrium of Heterogeneous Substances]]'',<ref name="Gibbs 1876"/> in which he showed how [[thermodynamic processes]], including [[chemical reaction]]s, could be graphically analyzed, by studying the [[energy]], [[entropy]], [[Volume (thermodynamics)|volume]], [[temperature]] and [[pressure]] of the [[thermodynamic system]] in such a manner, one can determine if a process would occur spontaneously.<ref>{{cite book | author=Gibbs, Willard | title=The Scientific Papers of J. Willard Gibbs, Volume One: Thermodynamics | publisher=Ox Bow Press | year=1993 | isbn=978-0-918024-77-0 | oclc=27974820}}</ref> Also [[Pierre Duhem]] in the 19th century wrote about chemical thermodynamics.<ref name="Duhem 1886"/> During the early 20th century, chemists such as [[Gilbert N. Lewis]], [[Merle Randall]],<ref name="Lewis Randall 1923"/> and [[E. A. Guggenheim]]<ref name="Guggenheim 1933"/><ref name="Guggenheim 1949/1967"/> applied the mathematical methods of Gibbs to the analysis of chemical processes.<br />
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During the years 1873–76 the American mathematical physicist Josiah Willard Gibbs published a series of three papers, the most famous being On the Equilibrium of Heterogeneous Substances, Also Pierre Duhem in the 19th century wrote about chemical thermodynamics. During the early 20th century, chemists such as Gilbert N. Lewis, Merle Randall, and E. A. Guggenheim applied the mathematical methods of Gibbs to the analysis of chemical processes.<br />
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在1873年至1876年间,美国数学物理学家约西亚·威拉德·吉布斯发表了一系列的3篇论文,其中最著名的是关于多相物质平衡,也是 Pierre Duhem 在19世纪写的关于化学热力学的论文。在20世纪早期,化学家如吉尔伯特·牛顿·路易斯,Merle Randall 和 e. a. Guggenheim 将吉布斯的数学方法应用于化学过程的分析。<br />
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==Etymology==<br />
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==Etymology==<br />
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词源学<br />
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这个术语的历史是丰富的,需要更多的补充<br />
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The etymology of ''thermodynamics'' has an intricate history.<ref name=eoht>{{cite web<br />
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The etymology of thermodynamics has an intricate history.<ref name=eoht>{{cite web<br />
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热力学的词源有一个错综复杂的历史<br />
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|url=http://www.eoht.info/page/Thermo-dynamics<br />
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|title=Thermodynamics (etymology)<br />
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| 题目: 热力学(词源)<br />
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出版商 EoHT.info<br />
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}}</ref> It was first spelled in a hyphenated form as an adjective (''thermo-dynamic'') and from 1854 to 1868 as the noun ''thermo-dynamics'' to represent the science of generalized heat engines.<ref name=eoht/><br />
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}}</ref> It was first spelled in a hyphenated form as an adjective (thermo-dynamic) and from 1854 to 1868 as the noun thermo-dynamics to represent the science of generalized heat engines.<br />
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它最初以连字符的形式作为形容词(热力学)拼写,从1854年到1868年作为名词热力学来代表广义热发动机的科学。<br />
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American [[Biophysics|biophysicist]] Donald Haynie claims that ''thermodynamics'' was coined in 1840 from the [[Greek language|Greek]] root [[wikt:θέρμη|θέρμη]] ''therme,'' meaning “heat”, and [[wikt:δύναμις|δύναμις]] ''dynamis,'' meaning “power”.<ref>{{cite book<br />
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American biophysicist Donald Haynie claims that thermodynamics was coined in 1840 from the Greek root θέρμη therme, meaning “heat”, and δύναμις dynamis, meaning “power”.<ref>{{cite book<br />
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美国生物物理学家唐纳德 · 海尼声称,热力学是在1840年从希腊词根 therme (意思是“热”)和 dynamis (意思是“力”)创造出来的。 文档{ cite book<br />
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生物热力学<br />
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作者唐纳德 · t · 海尼<br />
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剑桥大学出版社<br />
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Pierre Perrot claims that the term ''thermodynamics'' was coined by [[James Joule]] in 1858 to designate the science of relations between heat and power,<ref name="Perrot" /> however, Joule never used that term, but used instead the term ''perfect thermo-dynamic engine'' in reference to Thomson's 1849<ref name=kelvin1849/> phraseology.<ref name=eoht/><br />
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Pierre Perrot claims that the term thermodynamics was coined by James Joule in 1858 to designate the science of relations between heat and power, however, Joule never used that term, but used instead the term perfect thermo-dynamic engine in reference to Thomson's 1849 phraseology.<br />
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皮埃尔 · 佩罗声称,热力学这个术语是由詹姆斯 · 朱尔在1858年创造的,用来指代热量和能量之间关系的科学。然而,朱尔从来没有使用过这个术语,而是在汤姆森1849年的措辞中使用了完美热力学引擎这个术语。<br />
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By 1858, ''thermo-dynamics'', as a functional term, was used in [[William Thomson, 1st Baron Kelvin|William Thomson]]'s paper "An Account of Carnot's Theory of the Motive Power of Heat."<ref name=kelvin1849>Kelvin, William T. (1849) "An Account of Carnot's Theory of the Motive Power of Heat – with Numerical Results Deduced from Regnault's Experiments on Steam." ''Transactions of the Edinburg Royal Society, XVI. January 2.''[http://visualiseur.bnf.fr/Visualiseur?Destination=Gallica&O=NUMM-95118 Scanned Copy]</ref><br />
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By 1858, thermo-dynamics, as a functional term, was used in William Thomson's paper "An Account of Carnot's Theory of the Motive Power of Heat."<br />
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到1858年,热力学作为一个函数术语,被用于威廉 · 汤姆森的论文“卡诺的热动力理论的帐户。”<br />
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==Branches of thermodynamics==<br />
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==Branches of thermodynamics==<br />
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The study of thermodynamical systems has developed into several related branches, each using a different fundamental model as a theoretical or experimental basis, or applying the principles to varying types of systems.<br />
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The study of thermodynamical systems has developed into several related branches, each using a different fundamental model as a theoretical or experimental basis, or applying the principles to varying types of systems.<br />
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热力学系统的研究已经发展成为几个相关的分支,每个分支都使用不同的基本模型作为理论或实验基础,或者将这些原理应用于不同类型的系统。<br />
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===Classical thermodynamics===<br />
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===Classical thermodynamics===<br />
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Classical thermodynamics is the description of the states of thermodynamic systems at near-equilibrium, that uses macroscopic, measurable properties. It is used to model exchanges of energy, work and heat based on the [[laws of thermodynamics]]. The qualifier ''classical'' reflects the fact that it represents the first level of understanding of the subject as it developed in the 19th century and describes the changes of a system in terms of macroscopic empirical (large scale, and measurable) parameters. A microscopic interpretation of these concepts was later provided by the development of ''statistical mechanics''.<br />
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Classical thermodynamics is the description of the states of thermodynamic systems at near-equilibrium, that uses macroscopic, measurable properties. It is used to model exchanges of energy, work and heat based on the laws of thermodynamics. The qualifier classical reflects the fact that it represents the first level of understanding of the subject as it developed in the 19th century and describes the changes of a system in terms of macroscopic empirical (large scale, and measurable) parameters. A microscopic interpretation of these concepts was later provided by the development of statistical mechanics.<br />
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经典热力学是对近平衡态热力学系统状态的描述,它使用宏观的、可测量的性质。它被用来模拟能量、功和热量的交换,基于热力学定律。经典限定词反映了这样一个事实,即它代表了人们对这个学科在19世纪发展过程中的第一层次的理解,并且描述了一个系统在宏观经验(大尺度和可测量的)参数方面的变化。这些概念的微观解释后来由统计力学的发展提供。<br />
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===Statistical mechanics===<br />
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===Statistical mechanics===<br />
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[[Statistical mechanics]], also called statistical thermodynamics, emerged with the development of atomic and molecular theories in the late 19th century and early 20th century, and supplemented classical thermodynamics with an interpretation of the microscopic interactions between individual particles or quantum-mechanical states. This field relates the microscopic properties of individual atoms and molecules to the macroscopic, bulk properties of materials that can be observed on the human scale, thereby explaining classical thermodynamics as a natural result of statistics, classical mechanics, and [[Quantum mechanics|quantum theory]] at the microscopic level.<ref name= "NKS note b" /><br />
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Statistical mechanics, also called statistical thermodynamics, emerged with the development of atomic and molecular theories in the late 19th century and early 20th century, and supplemented classical thermodynamics with an interpretation of the microscopic interactions between individual particles or quantum-mechanical states. This field relates the microscopic properties of individual atoms and molecules to the macroscopic, bulk properties of materials that can be observed on the human scale, thereby explaining classical thermodynamics as a natural result of statistics, classical mechanics, and quantum theory at the microscopic level.<br />
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统计力学,又称统计热力学,在19世纪末20世纪初随着原子和分子理论的发展而出现,对单个粒子或量子力学状态之间的微观相互作用的解释补充了经典热力学。这个领域将单个原子和分子的微观属性与可以在人类尺度上观察到的物质的宏观体积属性联系起来,从而在微观层次上解释了经典热力学作为统计学、经典力学、量子理论的自然结果。<br />
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===Chemical thermodynamics===<br />
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[[Chemical thermodynamics]] is the study of the interrelation of [[energy]] with [[chemical reactions]] or with a physical change of [[thermodynamic state|state]] within the confines of the [[laws of thermodynamics]].<br />
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Chemical thermodynamics is the study of the interrelation of energy with chemical reactions or with a physical change of state within the confines of the laws of thermodynamics.<br />
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化学热力学是研究能量与化学反应或热力学定律范围内状态的物理变化之间的相互关系。<br />
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===Equilibrium thermodynamics===<br />
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===Equilibrium thermodynamics===<br />
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平衡热力学<br />
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[[Equilibrium thermodynamics]] is the study of transfers of matter and energy in systems or bodies that, by agencies in their surroundings, can be driven from one state of thermodynamic equilibrium to another. The term 'thermodynamic equilibrium' indicates a state of balance, in which all macroscopic flows are zero; in the case of the simplest systems or bodies, their intensive properties are homogeneous, and their pressures are perpendicular to their boundaries. In an equilibrium state there are no unbalanced potentials, or driving forces, between macroscopically distinct parts of the system. A central aim in equilibrium thermodynamics is: given a system in a well-defined initial equilibrium state, and given its surroundings, and given its constitutive walls, to calculate what will be the final equilibrium state of the system after a specified thermodynamic operation has changed its walls or surroundings.<br />
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Equilibrium thermodynamics is the study of transfers of matter and energy in systems or bodies that, by agencies in their surroundings, can be driven from one state of thermodynamic equilibrium to another. The term 'thermodynamic equilibrium' indicates a state of balance, in which all macroscopic flows are zero; in the case of the simplest systems or bodies, their intensive properties are homogeneous, and their pressures are perpendicular to their boundaries. In an equilibrium state there are no unbalanced potentials, or driving forces, between macroscopically distinct parts of the system. A central aim in equilibrium thermodynamics is: given a system in a well-defined initial equilibrium state, and given its surroundings, and given its constitutive walls, to calculate what will be the final equilibrium state of the system after a specified thermodynamic operation has changed its walls or surroundings.<br />
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平衡态热力学研究的是物质和能量在系统或物体中的转移,这些系统或物体在其周围的环境中,可以从一种热力学平衡状态转移到另一种状态。热力学平衡这个术语表示一种平衡状态,在这种状态下所有的宏观流动都是零; 对于最简单的系统或物体来说,它们的密集属性是均匀的,它们的压力垂直于它们的边界。在平衡状态下,系统宏观上截然不同的部分之间没有不平衡的势能或驱动力。平衡态热力学的一个中心目标是: 给定一个处于明确初始平衡状态的系统,给定其周围环境,给定其本构壁,计算在一个特定的热力学操作改变其周围或周围环境后,系统的最终平衡状态是什么。<br />
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[[Non-equilibrium thermodynamics]] is a branch of thermodynamics that deals with systems that are not in [[thermodynamic equilibrium]]. Most systems found in nature are not in thermodynamic equilibrium because they are not in stationary states, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are not in stationary states, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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非平衡态热力学是热力学的一个分支,主要研究非热力学平衡系统。自然界中发现的大多数系统都不在热力学平衡,因为它们不处于静止状态,并且不断不断地受到来自其他系统的物质和能量流动的影响。非平衡体系的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出目前已知的宏观热力学方法的范围。<br />
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--[[用户:厚朴|厚朴]]([[用户讨论:厚朴|讨论]]) 2020年7月20日 (一) 09:41 (CST)continuously and discontinuously的翻译是不是有些不恰当<br />
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==Laws of thermodynamics==<br />
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==Laws of thermodynamics==<br />
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热力学定律<br />
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{{Main|Laws of thermodynamics}}<br />
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Thermodynamics is principally based on a set of four laws which are universally valid when applied to systems that fall within the constraints implied by each. In the various theoretical descriptions of thermodynamics these laws may be expressed in seemingly differing forms, but the most prominent formulations are the following.<br />
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Thermodynamics is principally based on a set of four laws which are universally valid when applied to systems that fall within the constraints implied by each. In the various theoretical descriptions of thermodynamics these laws may be expressed in seemingly differing forms, but the most prominent formulations are the following.<br />
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热力学基本上是建立在一套四条定律的基础上的,这些定律在适用于每个定律所暗示的约束条件下的系统时是普遍有效的。在热力学的各种理论描述中,这些定律可能表现为看似不同的形式,但最突出的公式如下。<br />
--[[用户:厚朴|厚朴]]([[用户讨论:厚朴|讨论]]) 2020年7月20日 (一) 10:05 (CST) set翻译成一集 prominent翻译成著名?<br />
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===Zeroth Law===<br />
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===Zeroth Law===<br />
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第零定律<br />
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The [[zeroth law of thermodynamics]] states: ''If two systems are each in thermal equilibrium with a third, they are also in thermal equilibrium with each other.''<br />
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The zeroth law of thermodynamics states: If two systems are each in thermal equilibrium with a third, they are also in thermal equilibrium with each other.<br />
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美国热力学第零定律协会指出: 如果两个系统各有三分之一的热平衡,那么它们之间的热平衡也是一样的。<br />
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This statement implies that thermal equilibrium is an [[equivalence relation]] on the set of [[thermodynamic system]]s under consideration. Systems are said to be in equilibrium if the small, random exchanges between them (e.g. [[Brownian motion]]) do not lead to a net change in energy. This law is tacitly assumed in every measurement of temperature. Thus, if one seeks to decide whether two bodies are at the same [[temperature]], it is not necessary to bring them into contact and measure any changes of their observable properties in time.<ref>Moran, Michael J. and Howard N. Shapiro, 2008. ''Fundamentals of Engineering Thermodynamics''. 6th ed. Wiley and Sons: 16.</ref> The law provides an empirical definition of temperature, and justification for the construction of practical thermometers.<br />
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This statement implies that thermal equilibrium is an equivalence relation on the set of thermodynamic systems under consideration. Systems are said to be in equilibrium if the small, random exchanges between them (e.g. Brownian motion) do not lead to a net change in energy. This law is tacitly assumed in every measurement of temperature. Thus, if one seeks to decide whether two bodies are at the same temperature, it is not necessary to bring them into contact and measure any changes of their observable properties in time. The law provides an empirical definition of temperature, and justification for the construction of practical thermometers.<br />
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这种说法暗示了热平衡是热力学系统集合上的一个等价关系。如果系统之间的小的、随机的交换(例如:布朗运动)不会导致能量的净变化。这个定律在每次测量温度时都是默认的。因此,如果要确定两个物体是否处于同一温度,就没有必要使它们接触并及时测量它们可观测性质的任何变化。该定律提供了温度的经验定义,以及建造实用温度计的依据。<br />
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The zeroth law was not initially recognized as a separate law of thermodynamics, as its basis in thermodynamical equilibrium was implied in the other laws. The first, second, and third laws had been explicitly stated already, and found common acceptance in the physics community before the importance of the zeroth law for the definition of temperature was realized. As it was impractical to renumber the other laws, it was named the ''zeroth law''.<br />
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The zeroth law was not initially recognized as a separate law of thermodynamics, as its basis in thermodynamical equilibrium was implied in the other laws. The first, second, and third laws had been explicitly stated already, and found common acceptance in the physics community before the importance of the zeroth law for the definition of temperature was realized. As it was impractical to renumber the other laws, it was named the zeroth law.<br />
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第零定律最初并没有被认为是一个独立的热力学定律,因为它在热力学平衡中的基础在其他定律中也有暗示。第一定律、第二定律和第三定律在温度定义的第零定律的重要性被认识到之前已经被物理学界明确阐述,并且得到了普遍接受。由于对其他法律重新编号是不切实际的,因此将其命名为第零法律。<br />
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--[[用户:厚朴|厚朴]]([[用户讨论:厚朴|讨论]]) 2020年7月20日 (一) 10:05 (CST)法律 Law检查一遍<br />
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===First Law===<br />
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===First Law===<br />
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第一定律<br />
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The [[first law of thermodynamics]] states: ''In a process without transfer of matter, the change in [[internal energy]],'' {{math|Δ''U''}}'', of a [[thermodynamic system]] is equal to the energy gained as heat,'' {{math|''Q''}}'', less the thermodynamic work,'' {{math|''W''}}'', done by the system on its surroundings.''<ref>Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics, AIP Press, Woodbury NY, {{ISBN|0883187973}}, p. 79.</ref><ref group=nb>The sign convention (Q is heat supplied ''to'' the system as, W is work done ''by'' the system) is that of [[Rudolf Clausius]]. The opposite sign convention is customary in chemical thermodynamics.</ref><br />
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The first law of thermodynamics states: In a process without transfer of matter, the change in internal energy, , of a thermodynamic system is equal to the energy gained as heat, , less the thermodynamic work, , done by the system on its surroundings.<br />
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能量守恒定律指出: 在一个没有物质转移的过程中,一个热力学系统的内部能量的变化等于作为热量获得的能量,减去系统在其周围所做的热力学功。<br />
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:<math>\Delta U = Q - W</math>.<br />
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<math>\Delta U = Q - W</math>.<br />
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数学 Delta u q-w / 数学。<br />
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For processes that include transfer of matter, a further statement is needed: ''With due account of the respective fiducial reference states of the systems, when two systems, which may be of different chemical compositions, initially separated only by an impermeable wall, and otherwise isolated, are combined into a new system by the thermodynamic operation of removal of the wall, then''<br />
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For processes that include transfer of matter, a further statement is needed: With due account of the respective fiducial reference states of the systems, when two systems, which may be of different chemical compositions, initially separated only by an impermeable wall, and otherwise isolated, are combined into a new system by the thermodynamic operation of removal of the wall, then<br />
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对于包含物质转移的过程,需要进一步的陈述: 在适当考虑了系统各自的基准参考状态的情况下,当两个系统---- 它们可能是不同的化学成分,最初只是被不透水的墙隔开,或者是被隔离---- 通过移除热力学操作结合成一个新的系统时,那么<br />
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:<math>U_0 = U_1 + U_2</math>,<br />
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<math>U_0 = U_1 + U_2</math>,<br />
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数学 u 0 u 1 + u 2 / math,<br />
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''where'' {{math|''U''<sub>0</sub>}} ''denotes the internal energy of the combined system, and'' {{math|''U''<sub>1</sub>}} ''and'' {{math|''U''<sub>2</sub>}} ''denote the internal energies of the respective separated systems.''<br />
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where denotes the internal energy of the combined system, and and denote the internal energies of the respective separated systems.<br />
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其中表示组合系统的内能,并表示各自分离系统的内能。<br />
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Adapted for thermodynamics, this law is an expression of the principle of [[conservation of energy]], which states that energy can be transformed (changed from one form to another), but cannot be created or destroyed.<ref>Callen, H.B. (1960/1985).''Thermodynamics and an Introduction to Thermostatistics'', second edition, John Wiley & Sons, Hoboken NY, {{ISBN|9780471862567}}, pp. 11–13.</ref><br />
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Adapted for thermodynamics, this law is an expression of the principle of conservation of energy, which states that energy can be transformed (changed from one form to another), but cannot be created or destroyed.<br />
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这一定律适用于热力学,是能量守恒定律的一种表述,它指出能量可以转换(从一种形式转变为另一种形式) ,但不能被创造或破坏。<br />
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Internal energy is a principal property of the [[thermodynamic state]], while heat and work are modes of energy transfer by which a process may change this state. A change of internal energy of a system may be achieved by any combination of heat added or removed and work performed on or by the system. As a [[State function|function of state]], the internal energy does not depend on the manner, or on the path through intermediate steps, by which the system arrived at its state.<br />
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Internal energy is a principal property of the thermodynamic state, while heat and work are modes of energy transfer by which a process may change this state. A change of internal energy of a system may be achieved by any combination of heat added or removed and work performed on or by the system. As a function of state, the internal energy does not depend on the manner, or on the path through intermediate steps, by which the system arrived at its state.<br />
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内能是热力学状态的主要特性,而热和功是能量传递的方式,通过这种方式,一个过程可以改变这种状态。系统内部能量的变化可以通过加热或除热以及在系统上或由系统所做的功的任何组合来实现。作为状态的函数,内能并不依赖于系统到达其状态的方式或中间步骤的路径。<br />
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===Second Law===<br />
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===Second Law===<br />
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第二定律<br />
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The [[second law of thermodynamics]] states: ''Heat cannot spontaneously flow from a colder location to a hotter location.''<ref name= "NKS note b" /><br />
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The second law of thermodynamics states: Heat cannot spontaneously flow from a colder location to a hotter location.<br />
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热力学第二定律指出: 热量不能自发地从较冷的地方流向较热的地方。<br />
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This law is an expression of the universal principle of decay observable in nature. The second law is an observation of the fact that over time, differences in temperature, pressure, and chemical potential tend to even out in a physical system that is isolated from the outside world. [[Entropy]] is a measure of how much this process has progressed. The entropy of an isolated system which is not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium. However, principles guiding systems that are far from equilibrium are still debatable. One of such principles is the [[entropy production|maximum entropy production]] principle.<ref>{{cite journal|last1=Onsager|first1=Lars|title=Reciprocal Relations in Irreversible Processes|journal=Phys. Rev.|date=1931|volume=37|issue=405|pages=405–426|doi=10.1103/physrev.37.405|bibcode=1931PhRv...37..405O|doi-access=free}}</ref><ref>{{cite book|last1=Ziegler|first1=H.|title=An Introduction to Thermomechanics|date=1983|location=North Holland}}</ref> It states that non-equilibrium systems behave such a way as to maximize its entropy production.<ref>{{cite journal|last1=Belkin|first1=Andrey|last2=Hubler|first2=A.|last3=Bezryadin|first3=A.|title=Self-Assembled Wiggling Nano-Structures and the Principle of Maximum Entropy Production|journal=Sci. Rep.|date=2015|doi=10.1038/srep08323|pmid=25662746|pmc=4321171|bibcode=2015NatSR...5E8323B|volume=5|page=8323}}</ref><br />
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This law is an expression of the universal principle of decay observable in nature. The second law is an observation of the fact that over time, differences in temperature, pressure, and chemical potential tend to even out in a physical system that is isolated from the outside world. Entropy is a measure of how much this process has progressed. The entropy of an isolated system which is not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium. However, principles guiding systems that are far from equilibrium are still debatable. One of such principles is the maximum entropy production principle. It states that non-equilibrium systems behave such a way as to maximize its entropy production.<br />
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这个定律是可以在自然界观察到的衰变的普遍原理的一种表述。第二定律是对这样一个事实的观察: 随着时间的推移,在与外界隔绝的物理系统中,温度、压力和化学势的差异趋于均衡。熵是对这个过程进展程度的度量。不处于平衡状态的孤立系统的熵会随着时间的推移而增加,在平衡状态时达到最大值。然而,远离平衡的原则指导体系仍然是有争议的。其中一个原则就是最大产生熵原则。它指出,非平衡系统的行为方式使其产生熵最大化。<br />
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In classical thermodynamics, the second law is a basic postulate applicable to any system involving heat energy transfer; in statistical thermodynamics, the second law is a consequence of the assumed randomness of molecular chaos. There are many versions of the second law, but they all have the same effect, which is to explain the phenomenon of [[irreversibility]] in nature.<br />
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In classical thermodynamics, the second law is a basic postulate applicable to any system involving heat energy transfer; in statistical thermodynamics, the second law is a consequence of the assumed randomness of molecular chaos. There are many versions of the second law, but they all have the same effect, which is to explain the phenomenon of irreversibility in nature.<br />
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在经典热力学中,第二定律是适用于任何涉及热能传递的系统的基本假设; 在统计热力学中,第二定律是假定的分子混沌随机性的结果。第二定律有许多版本,但它们都具有同样的效果,即解释自然界中的不可逆现象。<br />
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===Third Law===<br />
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===Third Law===<br />
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第三定律<br />
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The [[third law of thermodynamics]] states: ''As the temperature of a system approaches absolute zero, all processes cease and the entropy of the system approaches a minimum value.''<br />
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The third law of thermodynamics states: As the temperature of a system approaches absolute zero, all processes cease and the entropy of the system approaches a minimum value.<br />
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热力学第三定律指出: 当一个系统的温度接近绝对零度时,所有的过程停止,系统的熵接近最小值。<br />
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This law of thermodynamics is a statistical law of nature regarding entropy and the impossibility of reaching [[absolute zero]] of temperature. This law provides an absolute reference point for the determination of entropy. The entropy determined relative to this point is the absolute entropy. Alternate definitions include "the entropy of all systems and of all states of a system is smallest at absolute zero," or equivalently "it is impossible to reach the absolute zero of temperature by any finite number of processes".<br />
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This law of thermodynamics is a statistical law of nature regarding entropy and the impossibility of reaching absolute zero of temperature. This law provides an absolute reference point for the determination of entropy. The entropy determined relative to this point is the absolute entropy. Alternate definitions include "the entropy of all systems and of all states of a system is smallest at absolute zero," or equivalently "it is impossible to reach the absolute zero of temperature by any finite number of processes".<br />
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这个热力学定律是关于熵和不可能达到绝对零度的自然统计法则。这个定律为确定熵提供了一个绝对的参考点。相对于这个点确定的熵就是绝对熵。替代定义包括”系统的所有系统和系统的所有状态的熵在绝对零度时最小” ,或相当于”任何有限数目的过程都不可能达到绝对零度”。<br />
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Absolute zero, at which all activity would stop if it were possible to achieve, is −273.15&nbsp;°C (degrees Celsius), or −459.67&nbsp;°F (degrees Fahrenheit), or 0 K (kelvin), or 0° R (degrees [[Rankine scale|Rankine]]).<br />
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Absolute zero, at which all activity would stop if it were possible to achieve, is −273.15&nbsp;°C (degrees Celsius), or −459.67&nbsp;°F (degrees Fahrenheit), or 0 K (kelvin), or 0° R (degrees Rankine).<br />
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绝对零度是-273.15摄氏度(摄氏度) ,或-459.67华氏度(华氏度) ,或0 k (开尔文) ,或0 r (朗肯度)。<br />
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==System models==<br />
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系统模型<br />
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[[File:system boundary.svg|200px|thumb|right|A diagram of a generic thermodynamic system]]<br />
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A diagram of a generic thermodynamic system<br />
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一个通用的热力学系统图表<br />
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An important concept in thermodynamics is the [[thermodynamic system]], which is a precisely defined region of the universe under study. Everything in the universe except the system is called the [[Environment (systems)|''surroundings'']]. A system is separated from the remainder of the universe by a [[Boundary (thermodynamic)|''boundary'']] which may be a physical boundary or notional, but which by convention defines a finite volume. Exchanges of [[Work (thermodynamics)|work]], [[heat]], or [[matter]] between the system and the surroundings take place across this boundary.<br />
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An important concept in thermodynamics is the thermodynamic system, which is a precisely defined region of the universe under study. Everything in the universe except the system is called the surroundings. A system is separated from the remainder of the universe by a boundary which may be a physical boundary or notional, but which by convention defines a finite volume. Exchanges of work, heat, or matter between the system and the surroundings take place across this boundary.<br />
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热力学中的一个重要概念是热力学系统,它是研究中的宇宙的一个精确定义的区域。除了这个系统之外,宇宙中的一切都被称为环境。一个系统通过一个边界从宇宙的其余部分中分离出来,这个边界可能是物理边界或者概念边界,但是按照惯例,它定义了一个有限的体积。系统和周围环境之间的功、热或物质的交换发生在这个边界上。<br />
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In practice, the boundary of a system is simply an imaginary dotted line drawn around a volume within which is going to be a change in the [[internal energy]] of that volume. Anything that passes across the boundary that effects a change in the internal energy of the system needs to be accounted for in the energy balance equation. The volume can be the region surrounding a single atom resonating energy, such as [[Max Planck]] defined in 1900; it can be a body of steam or air in a [[steam engine]], such as [[Nicolas Léonard Sadi Carnot|Sadi Carnot]] defined in 1824; it can be the body of a [[tropical cyclone]], such as [[Kerry Emanuel]] theorized in 1986 in the field of [[atmospheric thermodynamics]]; it could also be just one [[nuclide]] (i.e. a system of [[quark]]s) as hypothesized in [[quantum thermodynamics]], or the [[event horizon]] of a [[black hole thermodynamics|black hole]].<br />
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In practice, the boundary of a system is simply an imaginary dotted line drawn around a volume within which is going to be a change in the internal energy of that volume. Anything that passes across the boundary that effects a change in the internal energy of the system needs to be accounted for in the energy balance equation. The volume can be the region surrounding a single atom resonating energy, such as Max Planck defined in 1900; it can be a body of steam or air in a steam engine, such as Sadi Carnot defined in 1824; it can be the body of a tropical cyclone, such as Kerry Emanuel theorized in 1986 in the field of atmospheric thermodynamics; it could also be just one nuclide (i.e. a system of quarks) as hypothesized in quantum thermodynamics, or the event horizon of a black hole.<br />
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实际上,一个系统的边界只是一个虚构的虚线,它围绕着一个体积绘制,体积内部能量将发生变化。任何通过边界的影响系统内部能量的变化都需要在能量平衡方程中加以解释。体积可以是围绕单个原子共振能量的区域,如马克斯 · 普朗克在1900年定义的; 它可以是蒸汽机中的蒸汽体或空气体,如萨迪 · 卡诺在1824年定义的; 它可以是热带气旋的体,如 Kerry Emanuel 在1986年在大气热力学领域建立的理论; 它也可以只是一个核素(即:。量子热力学中假设的夸克系统,或黑洞的事件视界。<br />
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Boundaries are of four types: fixed, movable, real, and imaginary. For example, in an engine, a fixed boundary means the piston is locked at its position, within which a constant volume process might occur. If the piston is allowed to move that boundary is movable while the cylinder and cylinder head boundaries are fixed. For closed systems, boundaries are real while for open systems boundaries are often imaginary. In the case of a jet engine, a fixed imaginary boundary might be assumed at the intake of the engine, fixed boundaries along the surface of the case and a second fixed imaginary boundary across the exhaust nozzle.<br />
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Boundaries are of four types: fixed, movable, real, and imaginary. For example, in an engine, a fixed boundary means the piston is locked at its position, within which a constant volume process might occur. If the piston is allowed to move that boundary is movable while the cylinder and cylinder head boundaries are fixed. For closed systems, boundaries are real while for open systems boundaries are often imaginary. In the case of a jet engine, a fixed imaginary boundary might be assumed at the intake of the engine, fixed boundaries along the surface of the case and a second fixed imaginary boundary across the exhaust nozzle.<br />
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边界有四种类型: 固定的、可移动的、真实的和想象的。例如,在发动机中,一个固定的边界意味着活塞被锁定在它的位置,在那里可能发生一个定容过程。如果活塞允许移动,那么边界是可移动的,而气缸和气缸盖边界是固定的。对于封闭系统,边界是真实的,而对于开放系统,边界往往是虚构的。在喷气发动机的情况下,可以假定在发动机进气口处有一个固定的虚边界,沿着箱体表面有一个固定的边界,在排气喷嘴处有一个固定的虚边界。<br />
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Generally, thermodynamics distinguishes three classes of systems, defined in terms of what is allowed to cross their boundaries:<br />
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Generally, thermodynamics distinguishes three classes of systems, defined in terms of what is allowed to cross their boundaries:<br />
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一般来说,热力学区分了三类系统,根据允许什么跨越它们的边界来定义:<br />
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{{table of thermodynamic systems}}<br />
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As time passes in an isolated system, internal differences of pressures, densities, and temperatures tend to even out. A system in which all equalizing processes have gone to completion is said to be in a [[state (thermodynamic)|state]] of [[thermodynamic equilibrium]].<br />
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As time passes in an isolated system, internal differences of pressures, densities, and temperatures tend to even out. A system in which all equalizing processes have gone to completion is said to be in a state of thermodynamic equilibrium.<br />
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在一个孤立的系统中,随着时间的推移,压力、密度和温度的内部差异趋于平衡。一个所有均衡过程均已完成的系统被称为处于热力学平衡状态。<br />
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Once in thermodynamic equilibrium, a system's properties are, by definition, unchanging in time. Systems in equilibrium are much simpler and easier to understand than are systems which are not in equilibrium. Often, when analysing a dynamic thermodynamic process, the simplifying assumption is made that each intermediate state in the process is at equilibrium, producing thermodynamic processes which develop so slowly as to allow each intermediate step to be an equilibrium state and are said to be [[reversible process (thermodynamics)|reversible processes]].<br />
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Once in thermodynamic equilibrium, a system's properties are, by definition, unchanging in time. Systems in equilibrium are much simpler and easier to understand than are systems which are not in equilibrium. Often, when analysing a dynamic thermodynamic process, the simplifying assumption is made that each intermediate state in the process is at equilibrium, producing thermodynamic processes which develop so slowly as to allow each intermediate step to be an equilibrium state and are said to be reversible processes.<br />
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一旦进入热力学平衡,系统的属性,根据定义,在时间上是不变的。处于平衡状态的系统比不处于平衡状态的系统要简单得多,也更容易理解。通常,当分析一个动态热力学过程时,会做出这样的简化假设: 过程中的每一个居间态都处于平衡状态,产生的热力学过程发展得如此缓慢,以至于每一个中间步骤都是一个平衡状态,称之为可逆过程。<br />
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==States and processes==<br />
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==States and processes==<br />
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状态和过程<br />
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When a system is at equilibrium under a given set of conditions, it is said to be in a definite [[thermodynamic state]]. The state of the system can be described by a number of [[state function|state quantities]] that do not depend on the process by which the system arrived at its state. They are called [[intensive variable]]s or [[extensive variable]]s according to how they change when the size of the system changes. The properties of the system can be described by an [[equation of state]] which specifies the relationship between these variables. State may be thought of as the instantaneous quantitative description of a system with a set number of variables held constant.<br />
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When a system is at equilibrium under a given set of conditions, it is said to be in a definite thermodynamic state. The state of the system can be described by a number of state quantities that do not depend on the process by which the system arrived at its state. They are called intensive variables or extensive variables according to how they change when the size of the system changes. The properties of the system can be described by an equation of state which specifies the relationship between these variables. State may be thought of as the instantaneous quantitative description of a system with a set number of variables held constant.<br />
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当一个系统在一组给定的条件下处于平衡状态时,我们称之为处于一个确定的热力学状态。系统的状态可以用许多状态量来描述,这些状态量并不依赖于系统到达其状态的过程。它们被称为密集型变量或扩展型变量,这取决于它们在系统规模发生变化时的变化情况。系统的属性可以用一个状态方程来描述,它指定了这些变量之间的关系。状态可以被认为是一系列变量保持不变的系统的瞬时定量描述。<br />
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A [[thermodynamic process]] may be defined as the energetic evolution of a thermodynamic system proceeding from an initial state to a final state. It can be described by [[process function|process quantities]]. Typically, each thermodynamic process is distinguished from other processes in energetic character according to what parameters, such as temperature, pressure, or volume, etc., are held fixed; Furthermore, it is useful to group these processes into pairs, in which each variable held constant is one member of a [[conjugate variables (thermodynamics)|conjugate]] pair.<br />
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A thermodynamic process may be defined as the energetic evolution of a thermodynamic system proceeding from an initial state to a final state. It can be described by process quantities. Typically, each thermodynamic process is distinguished from other processes in energetic character according to what parameters, such as temperature, pressure, or volume, etc., are held fixed; Furthermore, it is useful to group these processes into pairs, in which each variable held constant is one member of a conjugate pair.<br />
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热力学过程可以被定义为热力学系统从初始状态到最终状态的能量演化。它可以用工艺量来描述。通常情况下,根据温度、压力、体积等参数的固定程度,每个热力学过程过程与能量特征中的其他过程是不同的; 此外,将这些过程分组成对也很有用,每个变量保持常数是一个共轭对的一个成员。<br />
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Several commonly studied thermodynamic processes are:<br />
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Several commonly studied thermodynamic processes are:<br />
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一些常见的研究热力学过程是:<br />
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* [[Adiabatic process]]: occurs without loss or gain of energy by [[heat]]<br />
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* [[Isenthalpic process]]: occurs at a constant [[enthalpy]]<br />
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* [[Isentropic process]]: a reversible adiabatic process, occurs at a constant [[entropy]]<br />
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* [[Isobaric process]]: occurs at constant [[pressure]]<br />
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* [[Isochoric process]]: occurs at constant [[Volume (thermodynamics)|volume]] (also called isometric/isovolumetric)<br />
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* [[Isothermal process]]: occurs at a constant [[temperature]]<br />
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* [[steady state|Steady state process]]: occurs without a change in the [[internal energy]]<br />
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== Instrumentation ==<br />
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== Instrumentation ==<br />
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仪器仪表<br />
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There are two types of [[thermodynamic instruments]], the '''meter''' and the '''reservoir'''. A thermodynamic meter is any device which measures any parameter of a [[thermodynamic system]]. In some cases, the thermodynamic parameter is actually defined in terms of an idealized measuring instrument. For example, the [[zeroth law of thermodynamics|zeroth law]] states that if two bodies are in thermal equilibrium with a third body, they are also in thermal equilibrium with each other. This principle, as noted by [[James Clerk Maxwell|James Maxwell]] in 1872, asserts that it is possible to measure temperature. An idealized [[thermometer]] is a sample of an ideal gas at constant pressure. From the [[ideal gas law]] ''pV=nRT'', the volume of such a sample can be used as an indicator of temperature; in this manner it defines temperature. Although pressure is defined mechanically, a pressure-measuring device, called a [[barometer]] may also be constructed from a sample of an ideal gas held at a constant temperature. A [[calorimeter]] is a device which is used to measure and define the internal energy of a system.<br />
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There are two types of thermodynamic instruments, the meter and the reservoir. A thermodynamic meter is any device which measures any parameter of a thermodynamic system. In some cases, the thermodynamic parameter is actually defined in terms of an idealized measuring instrument. For example, the zeroth law states that if two bodies are in thermal equilibrium with a third body, they are also in thermal equilibrium with each other. This principle, as noted by James Maxwell in 1872, asserts that it is possible to measure temperature. An idealized thermometer is a sample of an ideal gas at constant pressure. From the ideal gas law pV=nRT, the volume of such a sample can be used as an indicator of temperature; in this manner it defines temperature. Although pressure is defined mechanically, a pressure-measuring device, called a barometer may also be constructed from a sample of an ideal gas held at a constant temperature. A calorimeter is a device which is used to measure and define the internal energy of a system.<br />
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有两种类型的热力学设备,水表和水库。热力学仪表是测量热力学系统的任何参数的任何装置。在某些情况下,热力学参数实际上是用理想化的测量仪器来定义的。例如,第零定律指出,如果两个物体在热平衡中有第三个物体,那么它们也在热平衡中。正如詹姆斯 · 麦克斯韦尔在1872年指出的那样,这个原理断言测量温度是可能的。理想温度计是恒压下理想气体的样品。根据理想气体定律 pV nRT,这样一个样品的体积可以用作温度的指示器; 在这种方式下,它定义了温度。虽然压力是机械定义的,一个称为气压计的压力测量装置也可以由恒定温度下的理想气体样品构成。量热计是用来测量和定义系统内部能量的装置。<br />
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A thermodynamic reservoir is a system which is so large that its state parameters are not appreciably altered when it is brought into contact with the system of interest. When the reservoir is brought into contact with the system, the system is brought into equilibrium with the reservoir. For example, a pressure reservoir is a system at a particular pressure, which imposes that pressure upon the system to which it is mechanically connected. The Earth's atmosphere is often used as a pressure reservoir. If ocean water is used to cool a power plant, the ocean is often a temperature reservoir in the analysis of the power plant cycle.<br />
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A thermodynamic reservoir is a system which is so large that its state parameters are not appreciably altered when it is brought into contact with the system of interest. When the reservoir is brought into contact with the system, the system is brought into equilibrium with the reservoir. For example, a pressure reservoir is a system at a particular pressure, which imposes that pressure upon the system to which it is mechanically connected. The Earth's atmosphere is often used as a pressure reservoir. If ocean water is used to cool a power plant, the ocean is often a temperature reservoir in the analysis of the power plant cycle.<br />
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热力学储存器是这样一个系统,它的状态参数如此之大,当它与感兴趣的系统接触时,它的状态参数没有明显的改变。当油藏与系统接触时,系统与油藏达到平衡。例如,压力容器是一个处于特定压力下的系统,它对与之机械连接的系统施加压力。地球的大气层经常被用作压力储存器。如果用海水来冷却发电厂,在分析发电厂的循环过程中,海洋通常是一个温度储存库。<br />
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== Conjugate variables ==<br />
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== Conjugate variables ==<br />
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共轭变量<br />
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{{Main|Conjugate variables (thermodynamics)|l1=Conjugate variables}}<br />
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The central concept of thermodynamics is that of [[energy]], the ability to do [[Work (thermodynamics)|work]]. By the [[first law of thermodynamics|First Law]], the total energy of a system and its surroundings is conserved. Energy may be transferred into a system by heating, compression, or addition of matter, and extracted from a system by cooling, expansion, or extraction of matter. In [[mechanics]], for example, energy transfer equals the product of the force applied to a body and the resulting displacement.<br />
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The central concept of thermodynamics is that of energy, the ability to do work. By the First Law, the total energy of a system and its surroundings is conserved. Energy may be transferred into a system by heating, compression, or addition of matter, and extracted from a system by cooling, expansion, or extraction of matter. In mechanics, for example, energy transfer equals the product of the force applied to a body and the resulting displacement.<br />
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热力学的核心概念是能量,做功的能力。根据第一定律,系统及其周围环境的总能量是守恒的。能量可以通过加热、压缩或添加物质的方式转移到系统中,也可以通过冷却、膨胀或提取物质的方式从系统中提取。例如,在力学中,能量传递等于作用在物体上的力和由此产生的位移的乘积。<br />
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[[conjugate variables (thermodynamics)|Conjugate variables]] are pairs of thermodynamic concepts, with the first being akin to a "force" applied to some [[thermodynamic system]], the second being akin to the resulting "displacement," and the product of the two equalling the amount of energy transferred. The common conjugate variables are:<br />
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Conjugate variables are pairs of thermodynamic concepts, with the first being akin to a "force" applied to some thermodynamic system, the second being akin to the resulting "displacement," and the product of the two equalling the amount of energy transferred. The common conjugate variables are:<br />
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共轭变量是成对的热力学概念,第一个类似于施加在某些热力学系统上的“力” ,第二个类似于由此产生的“位移” ,两者的乘积等于所转移的能量。常见的共轭变量有:<br />
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* [[Pressure]]-[[Volume (thermodynamics)|volume]] (the [[Mechanics|mechanical]] parameters);<br />
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* [[Temperature]]-[[entropy]] (thermal parameters);<br />
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* [[Chemical potential]]-[[particle number]] (material parameters).<br />
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== Potentials ==<br />
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== Potentials ==<br />
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== Potentials ==<br />
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[[Thermodynamic potential]]s are different quantitative measures of the stored energy in a system. Potentials are used to measure the energy changes in systems as they evolve from an initial state to a final state. The potential used depends on the constraints of the system, such as constant temperature or pressure. For example, the Helmholtz and Gibbs energies are the energies available in a system to do useful work when the temperature and volume or the pressure and temperature are fixed, respectively.<br />
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Thermodynamic potentials are different quantitative measures of the stored energy in a system. Potentials are used to measure the energy changes in systems as they evolve from an initial state to a final state. The potential used depends on the constraints of the system, such as constant temperature or pressure. For example, the Helmholtz and Gibbs energies are the energies available in a system to do useful work when the temperature and volume or the pressure and temperature are fixed, respectively.<br />
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热力学势是体系中储存能量的不同定量度量。势能被用来测量系统从初始状态到最终状态的能量变化。所用的电位取决于系统的约束条件,如恒温或恒压。例如,亥姆霍兹能量和吉布斯能量是当温度和体积或压力和温度分别固定时,系统中可用于做有用功的能量。<br />
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The five most well known potentials are:<br />
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The five most well known potentials are:<br />
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五个最有名的潜力是:<br />
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{{table of thermodynamic potentials}}<br />
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where <math>T</math> is the [[thermodynamic temperature|temperature]], <math>S</math> the [[entropy]], <math>p</math> the [[pressure]], <math>V</math> the [[Volume (thermodynamics)|volume]], <math>\mu</math> the [[chemical potential]], <math>N</math> the number of particles in the system, and <math>i</math> is the count of particles types in the system.<br />
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where <math>T</math> is the temperature, <math>S</math> the entropy, <math>p</math> the pressure, <math>V</math> the volume, <math>\mu</math> the chemical potential, <math>N</math> the number of particles in the system, and <math>i</math> is the count of particles types in the system.<br />
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数学 t / math 是温度,数学 s / math 是熵,数学 p / math 是压力,数学 v / math 是体积,数学 mu / math 是化学势,数学 n / math 是系统中粒子的数量,数学 i / math 是系统中粒子类型的数量。<br />
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Thermodynamic potentials can be derived from the energy balance equation applied to a thermodynamic system. Other thermodynamic potentials can also be obtained through [[Legendre transformation]].<br />
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Thermodynamic potentials can be derived from the energy balance equation applied to a thermodynamic system. Other thermodynamic potentials can also be obtained through Legendre transformation.<br />
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热力学势可以从应用于热力学系统的能量平衡方程推导出来。其他热力学势也可以通过勒壤得转换得到。<br />
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== Applied fields ==<br />
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== Applied fields ==<br />
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应用领域<br />
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{{columns-list|colwidth=22em|<br />
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{{columns-list|colwidth=22em|<br />
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{ columns-list | colwidth 22em | <br />
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* [[Atmospheric thermodynamics]]<br />
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* [[Biological thermodynamics]]<br />
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* [[Black hole thermodynamics]]<br />
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* [[Chemical thermodynamics]]<br />
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* [[Classical thermodynamics]]<br />
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* [[Thermodynamic equilibrium|Equilibrium thermodynamics]]<br />
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* [[Industrial ecology]] (re: [[Exergy]])<br />
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* [[Maximum entropy thermodynamics]]<br />
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* [[Non-equilibrium thermodynamics]]<br />
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* [[Philosophy of thermal and statistical physics]]<br />
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* [[Psychrometrics]]<br />
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* [[Quantum thermodynamics]]<br />
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* [[Statistical thermodynamics]]<br />
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* [[Thermoeconomics]]<br />
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}}<br />
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}}<br />
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}}<br />
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== See also ==<br />
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== See also ==<br />
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参见<br />
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{{portal|Physics}}<br />
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* [[Thermodynamic process path]]<br />
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===Lists and timelines===<br />
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===Lists and timelines===<br />
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清单和时间线<br />
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* [[List of important publications in physics#Thermodynamics|List of important publications in thermodynamics]]<br />
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* [[List of textbooks in statistical mechanics|List of textbooks on thermodynamics and statistical mechanics]]<br />
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* [[List of thermal conductivities]]<br />
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* [[List of thermodynamic properties]]<br />
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* [[Table of thermodynamic equations]]<br />
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* [[Timeline of thermodynamics]]<br />
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== Notes ==<br />
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== Notes ==<br />
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注释<br />
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{{reflist|group=nb}}<br />
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==References==<br />
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==References==<br />
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参考资料<br />
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{{Reflist|35em}}<br />
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==Further reading==<br />
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==Further reading==<br />
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进一步阅读<br />
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* {{cite book|author1=Goldstein, Martin|author2=Inge F.|lastauthoramp=yes|title=The Refrigerator and the Universe|url=https://archive.org/details/refrigeratoruniv0000gold|url-access=registration|publisher=Harvard University Press|year=1993|isbn=978-0-674-75325-9|location=|pages=|oclc=32826343}} A nontechnical introduction, good on historical and interpretive matters.<br />
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* {{cite journal |last1=Kazakov |first1=Andrei |last2=Muzny |first2=Chris D. |last3=Chirico |first3=Robert D. |last4=Diky |first4=Vladimir V. |last5=Frenkel |first5=Michael |title=Web Thermo Tables – an On-Line Version of the TRC Thermodynamic Tables |journal=Journal of Research of the National Institute of Standards and Technology |volume=113 |issue=4 |year=2008 |pages=209–220 |issn=1044-677X |doi=10.6028/jres.113.016 |pmc=4651616 |pmid=27096122}}<br />
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* {{cite book|author=Gibbs J.W.|title=The Collected Works of J. Willard Gibbs Thermodynamics.|publisher=Longmans, Green and Co.|year=1928|isbn=|location=New York|pages=|oclc=}} Vol. 1, pp. 55–349.<br />
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* {{cite book|author=Guggenheim E.A.|title=Modern thermodynamics by the methods of Willard Gibbs|publisher=Methuen & co. ltd.|year=1933|isbn=|location=London|pages=|oclc=}}<br />
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* {{cite book|author=Denbigh K.|title=The Principles of Chemical Equilibrium: With Applications in Chemistry and Chemical Engineering.|publisher=Cambridge University Press|year=1981|isbn=|location=London|pages=|oclc=}}<br />
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* {{cite book|author=Stull, D.R., Westrum Jr., E.F. and Sinke, G.C.|title=The Chemical Thermodynamics of Organic Compounds.|publisher=John Wiley and Sons, Inc.|year=1969|isbn=|location=London|pages=|oclc=}}<br />
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* {{cite book|author=Bazarov I.P.|title=Thermodynamics: Textbook.|publisher=Lan publishing house|year=2010|isbn=978-5-8114-1003-3|location=St. Petersburg|page=384|oclc=}} 5th ed. (in Russian)<br />
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* {{cite book|author=Bawendi Moungi G., Alberty Robert A. and Silbey Robert J.|title=Physical Chemistry|publisher=J. Wiley & Sons, Incorporated|year=2004|isbn=|location=|pages=|oclc=}}<br />
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* {{cite book|author=Alberty Robert A.|title=Thermodynamics of Biochemical Reactions|publisher=Wiley-Interscience|year=2003|isbn=|location=|pages=|oclc=}}<br />
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* {{cite book|author=Alberty Robert A.|title=Biochemical Thermodynamics: Applications of Mathematica|journal=Methods of Biochemical Analysis|publisher=John Wiley & Sons, Inc.|year=2006|volume=48|isbn=978-0-471-75798-6|location=|pages=1–458|pmid=16878778|oclc=}}<br />
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The following titles are more technical:<br />
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The following titles are more technical:<br />
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下面的标题更具技术性:<br />
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* {{Cite book|title=Advanced Engineering Thermodynamics|last=Bejan|first=Adrian|publisher=Wiley|year=2016|isbn=978-1-119-05209-8|edition=4|location=|pages=}}<br />
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* {{cite book|author=Cengel, Yunus A., & Boles, Michael A.|title=Thermodynamics – an Engineering Approach|publisher=McGraw Hill|year=2002|isbn=978-0-07-238332-4|location=|pages=|oclc=45791449|url-access=registration|url=https://archive.org/details/thermodynamicsen00ceng_0}}<br />
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* {{cite book|author=Dunning-Davies, Jeremy|title=Concise Thermodynamics: Principles and Applications|publisher=Horwood Publishing|year=1997|isbn=978-1-8985-6315-0|location=|pages=|oclc=36025958}}<br />
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* {{cite book|author1=Kroemer, Herbert|author2=Kittel, Charles|lastauthoramp=yes|title=Thermal Physics|publisher=W.H. Freeman Company|year=1980|isbn=978-0-7167-1088-2|location=|pages=|oclc=32932988}}<br />
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== External links ==<br />
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== External links ==<br />
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外部链接<br />
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{{Wikibooks|Engineering Thermodynamics}}<br />
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{{wikiquote|Thermodynamics}}<br />
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* {{cite EB1911 |title=Thermodynamics |volume=26 |pages=808–814 |short=x |url=https://archive.org/details/encyclopaediabri26chisrich/page/808}}<br />
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* [http://tigger.uic.edu/~mansoori/Thermodynamic.Data.and.Property_html Thermodynamics Data & Property Calculation Websites]<br />
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* [http://tigger.uic.edu/~mansoori/Thermodynamics.Educational.Sites_html Thermodynamics Educational Websites]<br />
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* [http://scienceworld.wolfram.com/physics/topics/Thermodynamics.html Thermodynamics at ''ScienceWorld'']<br />
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* [http://www.wiley.com/legacy/college/boyer/0470003790/reviews/thermo/thermo_intro.htm Biochemistry Thermodynamics]<br />
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* [http://farside.ph.utexas.edu/teaching/sm1/lectures/lectures.html Thermodynamics and Statistical Mechanics]<br />
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* [https://web.archive.org/web/20090430200028/http://www.ent.ohiou.edu/~thermo/ Engineering Thermodynamics – A Graphical Approach]<br />
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* [http://farside.ph.utexas.edu/teaching/sm1/statmech.pdf Thermodynamics and Statistical Mechanics] by Richard Fitzpatrick<br />
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<small>This page was moved from [[wikipedia:en:Thermodynamics]]. Its edit history can be viewed at [[热力学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E8%87%AA%E7%BB%84%E7%BB%87%E4%B8%B4%E7%95%8C%E6%80%A7&diff=21924自组织临界性2021-02-21T11:42:48Z<p>Jxzhou:</p>
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<div>此词条暂由水流心不竞初译,未经审校,带来阅读不便,请见谅。<br />
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In [[physics]], '''self-organized criticality''' ('''SOC''') is a property of [[dynamical system]]s that have a [[critical phenomena|critical point]] as an [[attractor]]. Their macroscopic behavior thus displays the spatial or temporal [[scale invariance|scale-invariance]] characteristic of the [[critical point (physics)|critical point]] of a [[phase transition]], but without the need to tune control parameters to a precise value, because the system, effectively, tunes itself as it evolves towards criticality.<br />
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In physics, self-organized criticality (SOC) is a property of dynamical systems that have a critical point as an attractor. Their macroscopic behavior thus displays the spatial or temporal scale-invariance characteristic of the critical point of a phase transition, but without the need to tune control parameters to a precise value, because the system, effectively, tunes itself as it evolves towards criticality.<br />
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在物理学中,'''<font color="#ff8000"> 自组织临界性Self-organized criticality (SOC)</font>'''是动力系统的一种特性,动力系统有一个临界点作为'''<font color="#ff8000"> 吸引子Attractor</font>'''。它们在相变临界点的宏观行为因此显示了空间或时间尺度不变特性,但不需要把控制参数调整到一个精确的值,因为系统有效地自我调整趋向于临界状态。<br />
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The concept was put forward by [[Per Bak]], [[Chao Tang]] and [[Kurt Wiesenfeld]] ("BTW") in a paper<ref name=Bak1987><br />
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The concept was put forward by Per Bak, Chao Tang and Kurt Wiesenfeld ("BTW") in a paper<ref name=Bak1987><br />
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这个概念是由 Per Bak,Chao Tang 和 Kurt Wiesenfeld (“ BTW”)在一篇名为 bak1987的论文中提出的<br />
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{{cite journal<br />
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{{cite journal<br />
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{引用期刊<br />
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| author = [[Per Bak|Bak, P.]], [[Chao Tang|Tang, C.]] and [[Kurt Wiesenfeld|Wiesenfeld, K.]]<br />
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| author = Bak, P., Tang, C. and Wiesenfeld, K.<br />
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作者 Bak,p. ,Tang,c. and Wiesenfeld,k。<br />
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| year = 1987<br />
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| year = 1987<br />
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1987年<br />
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| title = Self-organized criticality: an explanation of 1/''f'' noise<br />
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| title = Self-organized criticality: an explanation of 1/f noise<br />
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自组织临界性: 1 / f 噪音的解释<br />
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| journal = [[Physical Review Letters]]<br />
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| journal = Physical Review Letters<br />
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物理评论快报<br />
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| volume = 59<br />
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| volume = 59<br />
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第59卷<br />
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| issue = 4<br />
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| issue = 4<br />
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第四期<br />
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| pages = 381&ndash;384<br />
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| pages = 381&ndash;384<br />
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381-- 384<br />
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| doi = 10.1103/PhysRevLett.59.381<br />
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| doi = 10.1103/PhysRevLett.59.381<br />
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10.1103 / physrvlett. 59.381<br />
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| pmid = 10035754<br />
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| pmid = 10035754<br />
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10035754<br />
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| bibcode=1987PhRvL..59..381B<br />
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| bibcode=1987PhRvL..59..381B<br />
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| bibcode 1987PhRvL. . 59. . 381 b<br />
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}}<br />
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}}<br />
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}}<br />
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Papercore summary: [https://archive.is/20130704122906/http://papercore.org/Bak1987 http://papercore.org/Bak1987].</ref> <br />
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Papercore summary: [https://archive.is/20130704122906/http://papercore.org/Bak1987 http://papercore.org/Bak1987].</ref> <br />
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论文摘要: [ https://archive.is/20130704122906/http://Papercore.org/bak1987 http://Papercore.org/bak1987] / 参考<br />
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published in 1987 in ''[[Physical Review Letters]]'', and is considered to be one of the mechanisms by which [[complexity]]<ref name=Bak1995><br />
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published in 1987 in Physical Review Letters, and is considered to be one of the mechanisms by which complexity<ref name=Bak1995><br />
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1987年发表在《物理评论快报》上,被认为是复杂性在自然界出现的机制之一<br />
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{{cite journal<br />
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{{cite journal<br />
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{引用期刊<br />
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| author = [[Per Bak|Bak, P.]], and [[Maya Paczuski|Paczuski, M.]]<br />
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| author = Bak, P., and Paczuski, M.<br />
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作者 Bak,p,and Paczuski,m。<br />
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| year = 1995<br />
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| year = 1995<br />
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1995年<br />
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| title = Complexity, contingency, and criticality<br />
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| title = Complexity, contingency, and criticality<br />
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| 标题复杂性、偶然性和临界性<br />
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| journal =Proc Natl Acad Sci U S A <br />
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| journal =Proc Natl Acad Sci U S A <br />
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美国科学促进协会<br />
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| volume = 92<br />
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| volume = 92<br />
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第92卷<br />
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| pages = 6689&ndash;6696<br />
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| pages = 6689&ndash;6696<br />
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6689-- 6696<br />
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| pmid = 11607561<br />
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| pmid = 11607561<br />
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11607561<br />
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| doi = 10.1073/pnas.92.15.6689<br />
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| doi = 10.1073/pnas.92.15.6689<br />
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10.1073 / pnas. 92.15.6689<br />
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| issue = 15<br />
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| issue = 15<br />
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第15期<br />
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| pmc = 41396<br />
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| pmc = 41396<br />
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41396<br />
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|bibcode = 1995PNAS...92.6689B }}</ref> arises in nature. Its concepts have been applied across fields as diverse as [[geophysics]],<ref name=SmalleyTurcotteSolla85><br />
<br />
|bibcode = 1995PNAS...92.6689B }}</ref> arises in nature. Its concepts have been applied across fields as diverse as geophysics,<ref name=SmalleyTurcotteSolla85><br />
<br />
| bibcode 1995PNAS... 92.6689 b } / ref 它的概念已经被应用于各个领域,比如地球物理学,参考名称 smalleyturcottesolla85<br />
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{{cite journal<br />
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{{cite journal<br />
<br />
{引用期刊<br />
<br />
|author1=Smalley, R. F., Jr. |author2=Turcotte, D. L. |author3=Solla, S. A. | year = 1985<br />
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|author1=Smalley, R. F., Jr. |author2=Turcotte, D. L. |author3=Solla, S. A. | year = 1985<br />
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1 Smalley,r. f. ,jr. | author2 Turcotte,d. l. | author3 Solla,s. a.1985年<br />
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| title = A renormalization group approach to the stick-slip behavior of faults<br />
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| title = A renormalization group approach to the stick-slip behavior of faults<br />
<br />
| 题目: 断层粘滑行为的重整化群方法<br />
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| journal = Journal of Geophysical Research<br />
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| journal = Journal of Geophysical Research<br />
<br />
地球物理研究期刊<br />
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| bibcode = 1985JGR....90.1894S<br />
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| bibcode = 1985JGR....90.1894S<br />
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1985JGR... 90.1894 s<br />
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| doi = 10.1029/JB090iB02p01894<br />
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| doi = 10.1029/JB090iB02p01894<br />
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| doi 10.1029 / JB090iB02p01894<br />
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| volume = 90<br />
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| volume = 90<br />
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第90卷<br />
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| issue = B2<br />
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| issue = B2<br />
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| 第二期<br />
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| pages = 1894<br />
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| pages = 1894<br />
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1894页<br />
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|url=https://semanticscholar.org/paper/6776d17957204c198e278bda98c935ab1cf8f22b }}</ref> [[physical cosmology]], [[evolutionary biology]] and [[ecology]], [[bio-inspired computing]] and [[optimization (mathematics)]], [[economics]], [[quantum gravity]], [[sociology]], [[solar physics]], [[plasma physics]], [[neurobiology]]<ref name=LinkenkaerHansen2001><br />
<br />
|url=https://semanticscholar.org/paper/6776d17957204c198e278bda98c935ab1cf8f22b }}</ref> physical cosmology, evolutionary biology and ecology, bio-inspired computing and optimization (mathematics), economics, quantum gravity, sociology, solar physics, plasma physics, neurobiology<ref name=LinkenkaerHansen2001><br />
<br />
[ https://semanticscholar.org/paper/6776d17957204c198e278bda98c935ab1cf8f22b ] / ref 物理宇宙学,进化生物学和生态学,生物启发计算和优化(数学) ,经济学,量子引力,社会学,太阳物理学,等离子物理学,神经生物学参考名称 linkenkaerhansen2001<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
|author1=K. Linkenkaer-Hansen |author2=V. V. Nikouline |author3=J. M. Palva |author4=R. J. Ilmoniemi. |last-author-amp=yes | year = 2001<br />
<br />
|author1=K. Linkenkaer-Hansen |author2=V. V. Nikouline |author3=J. M. Palva |author4=R. J. Ilmoniemi. |last-author-amp=yes | year = 2001<br />
<br />
1 k.Linkenkaer-hansen | author2 v.3 j.4 r.作者: j. Ilmoniemi。最后一个作者2001年<br />
<br />
| title = Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations<br />
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| title = Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations<br />
<br />
人类大脑振荡中的长程时间相关性和标度行为<br />
<br />
| journal = J. Neurosci.<br />
<br />
| journal = J. Neurosci.<br />
<br />
作者: j. Neurosci。<br />
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| volume = 21<br />
<br />
| volume = 21<br />
<br />
第21卷<br />
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| pages = 1370&ndash;1377<br />
<br />
| pages = 1370&ndash;1377<br />
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1370-- 1377<br />
<br />
| pmid = 11160408<br />
<br />
| pmid = 11160408<br />
<br />
11160408<br />
<br />
| issue = 4<br />
<br />
| issue = 4<br />
<br />
第四期<br />
<br />
|doi=10.1523/JNEUROSCI.21-04-01370.2001 |pmc=6762238 }}</ref><ref name=Beggs2003><br />
<br />
|doi=10.1523/JNEUROSCI.21-04-01370.2001 |pmc=6762238 }}</ref><ref name=Beggs2003><br />
<br />
| doi 10.1523 / jneurosci. 21-04-01370.2001 | pmc 6762238} / ref name begs2003<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
|author1=J. M. Beggs |author2=D. Plenz<br />
<br />
|author1=J. M. Beggs |author2=D. Plenz<br />
<br />
1 j.2 d.Plenz<br />
<br />
|lastauthoramp=yes | year = 2006<br />
<br />
|lastauthoramp=yes | year = 2006<br />
<br />
2006年<br />
<br />
| title = Neuronal Avalanches in Neocortical Circuits<br />
<br />
| title = Neuronal Avalanches in Neocortical Circuits<br />
<br />
新皮层神经回路中的神经雪崩<br />
<br />
| journal = J. Neurosci.<br />
<br />
| journal = J. Neurosci.<br />
<br />
作者: j. Neurosci。<br />
<br />
| volume = 23<br />
<br />
| volume = 23<br />
<br />
第23卷<br />
<br />
|issue=35<br />
<br />
|issue=35<br />
<br />
第35期<br />
<br />
|pages=11167–77<br />
<br />
|pages=11167–77<br />
<br />
第11167-77页<br />
<br />
|doi=10.1523/JNEUROSCI.23-35-11167.2003<br />
<br />
|doi=10.1523/JNEUROSCI.23-35-11167.2003<br />
<br />
10.1523 / jneurosci. 23-35-11167.2003<br />
<br />
|pmid=14657176<br />
<br />
|pmid=14657176<br />
<br />
14657176<br />
<br />
|pmc=6741045<br />
<br />
|pmc=6741045<br />
<br />
6741045<br />
<br />
}}</ref><ref name=Chialvo2004><br />
<br />
}}</ref><ref name=Chialvo2004><br />
<br />
} / ref ref name chialvo2004<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author =Chialvo, D. R.<br />
<br />
| author =Chialvo, D. R.<br />
<br />
作者 Chialvo,d. r。<br />
<br />
| year = 2004<br />
<br />
| year = 2004<br />
<br />
2004年<br />
<br />
| title = Critical brain networks<br />
<br />
| title = Critical brain networks<br />
<br />
关键的大脑网络<br />
<br />
| journal = Physica A<br />
<br />
| journal = Physica A<br />
<br />
物理学杂志 a<br />
<br />
| volume = 340<br />
<br />
| volume = 340<br />
<br />
第340卷<br />
<br />
| issue =4<br />
<br />
| issue =4<br />
<br />
第四期<br />
<br />
| pages = 756&ndash;765<br />
<br />
| pages = 756&ndash;765<br />
<br />
756-- 765<br />
<br />
| doi = 10.1016/j.physa.2004.05.064<br />
<br />
| doi = 10.1016/j.physa.2004.05.064<br />
<br />
10.1016 / j.physa. 2004.05.064<br />
<br />
|arxiv = cond-mat/0402538 |bibcode = 2004PhyA..340..756R | author-link = Dante R. Chialvo<br />
<br />
|arxiv = cond-mat/0402538 |bibcode = 2004PhyA..340..756R | author-link = Dante R. Chialvo<br />
<br />
| arxiv cond-mat / 0402538 | bibcode 2004PhyA. . 340. . 756 r | author-link Dante r. Chialvo<br />
<br />
}}</ref> and others.<br />
<br />
}}</ref> and others.<br />
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} / ref and others.<br />
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SOC is typically observed in slowly driven [[non-equilibrium thermodynamics|non-equilibrium]] systems with many [[degrees of freedom (physics and chemistry)|degrees of freedom]] and strongly [[nonlinearity|nonlinear]] dynamics. Many individual examples have been identified since BTW's original paper, but to date there is no known set of general characteristics that ''guarantee'' a system will display SOC.<br />
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SOC is typically observed in slowly driven non-equilibrium systems with many degrees of freedom and strongly nonlinear dynamics. Many individual examples have been identified since BTW's original paper, but to date there is no known set of general characteristics that guarantee a system will display SOC.<br />
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'''<font color="#ff8000"> SOC</font>'''通常在多自由度、强非线性动力学的缓慢驱动非平衡系统中被观察到。自从 BTW 的原始论文以来,已经确定了许多单独的例子,但是到目前为止还没有一组已知的一般特征来保证一个系统将显示 '''<font color="#ff8000"> SOC</font>'''。<br />
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== Overview 概览==<br />
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Self-organized criticality is one of a number of important discoveries made in [[statistical physics]] and related fields over the latter half of the 20th century, discoveries which relate particularly to the study of [[complexity]] in nature. For example, the study of [[cellular automata]], from the early discoveries of [[Stanislaw Ulam]] and [[John von Neumann]] through to [[John Horton Conway|John Conway]]'s [[Conway's Game of Life|Game of Life]] and the extensive work of [[Stephen Wolfram]], made it clear that complexity could be generated as an [[emergence|emergent]] feature of extended systems with simple local interactions. Over a similar period of time, [[Benoît Mandelbrot]]'s large body of work on [[fractals]] showed that much complexity in nature could be described by certain ubiquitous mathematical laws, while the extensive study of [[phase transition]]s carried out in the 1960s and 1970s showed how [[scale invariance|scale invariant]] phenomena such as [[fractals]] and [[power law]]s emerged at the [[critical point (physics)|critical point]] between phases.<br />
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Self-organized criticality is one of a number of important discoveries made in statistical physics and related fields over the latter half of the 20th century, discoveries which relate particularly to the study of complexity in nature. For example, the study of cellular automata, from the early discoveries of Stanislaw Ulam and John von Neumann through to John Conway's Game of Life and the extensive work of Stephen Wolfram, made it clear that complexity could be generated as an emergent feature of extended systems with simple local interactions. Over a similar period of time, Benoît Mandelbrot's large body of work on fractals showed that much complexity in nature could be described by certain ubiquitous mathematical laws, while the extensive study of phase transitions carried out in the 1960s and 1970s showed how scale invariant phenomena such as fractals and power laws emerged at the critical point between phases.<br />
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'''<font color="#ff8000"> 自组织临界性Self-organized criticality(SOC)</font>'''是20世纪下半叶统计物理学及相关领域的众多重要发现之一,这些发现尤其与研究自然界的复杂性有关。例如,元胞自动机的研究---- 从 Stanislaw Ulam 和约翰·冯·诺伊曼的早期发现到 John Conway 的生命游戏和 Stephen Wolfram 的大量工作---- 清楚地表明,复杂性可以作为具有简单局部相互作用的扩展系统的一个涌现特征而产生。在相似的时间段内,beno t Mandelbrot 关于分形的大量工作表明,自然界的许多复杂性可以用某些无处不在的数学定律来描述,而在20世纪60年代和70年代对相变的广泛研究表明,诸如分形和幂律等尺度不变现象是如何出现在相变的临界点上的。<br />
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The term ''self-organized criticality'' was firstly introduced by [[Per Bak|Bak]], [[Chao Tang|Tang]] and [[Kurt Wiesenfeld|Wiesenfeld]]'s 1987 paper, which clearly linked together those factors: a simple [[cellular automaton]] was shown to produce several characteristic features observed in natural complexity ([[fractal]] geometry, [[pink noise|pink (1/f) noise]] and [[power law]]s) in a way that could be linked to [[critical point (physics)|critical-point phenomena]]. Crucially, however, the paper emphasized that the complexity observed emerged in a robust manner that did not depend on finely tuned details of the system: variable parameters in the model could be changed widely without affecting the emergence of critical behavior: hence, ''[[self-organized]]'' criticality. Thus, the key result of BTW's paper was its discovery of a mechanism by which the emergence of complexity from simple local interactions could be ''spontaneous''&mdash;and therefore plausible as a source of natural complexity&mdash;rather than something that was only possible in artificial situations in which control parameters are tuned to precise critical values. The publication of this research sparked considerable interest from both theoreticians and experimentalists, producing some of the most cited papers in the scientific literature.<br />
<br />
The term self-organized criticality was firstly introduced by Bak, Tang and Wiesenfeld's 1987 paper, which clearly linked together those factors: a simple cellular automaton was shown to produce several characteristic features observed in natural complexity (fractal geometry, pink (1/f) noise and power laws) in a way that could be linked to critical-point phenomena. Crucially, however, the paper emphasized that the complexity observed emerged in a robust manner that did not depend on finely tuned details of the system: variable parameters in the model could be changed widely without affecting the emergence of critical behavior: hence, self-organized criticality. Thus, the key result of BTW's paper was its discovery of a mechanism by which the emergence of complexity from simple local interactions could be spontaneous&mdash;and therefore plausible as a source of natural complexity&mdash;rather than something that was only possible in artificial situations in which control parameters are tuned to precise critical values. The publication of this research sparked considerable interest from both theoreticians and experimentalists, producing some of the most cited papers in the scientific literature.<br />
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'''<font color="#ff8000"> 自组织临界性Self-organized criticality(SOC)</font>'''这个术语最早由 Bak,Tang 和 Wiesenfeld 在1987年的论文中提出,这篇论文将这些因素清楚地联系在一起: 一个简单的细胞自动机被证明可以产生在自然复杂性中观察到的几个特征(分形几何、粉红噪声和幂律) ,这种方式可以与临界点现象联系起来。然而,关键的是,这篇论文强调,观察到的复杂性是以一种强有力的方式出现的,并不依赖于系统精细调整的细节: 模型中的可变参数可以被广泛改变,而不会影响临界行为的涌现: 因此,具有自组织临界性。因此,BTW 论文的关键结果是发现了一种机制,通过这种机制,从简单的局部相互作用中产生的复杂性可能是自发的---- 因此是合理的自然复杂性的来源---- 而不是只有在控制参数调整到精确的临界值的人工情况下才可能出现的东西。这项研究的发表引起了理论家和实验家的极大兴趣,产生了一些在科学文献中被引用最多的论文。<br />
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Due to BTW's metaphorical visualization of their model as a "[[Bak–Tang–Wiesenfeld sandpile|sandpile]]" on which new sand grains were being slowly sprinkled to cause "avalanches", much of the initial experimental work tended to focus on examining real avalanches in [[granular matter]], the most famous and extensive such study probably being the Oslo ricepile experiment{{Citation needed|date=March 2018}}. Other experiments include those carried out on magnetic-domain patterns, the [[Barkhausen effect]] and vortices in [[superconductors]]. <br />
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Due to BTW's metaphorical visualization of their model as a "sandpile" on which new sand grains were being slowly sprinkled to cause "avalanches", much of the initial experimental work tended to focus on examining real avalanches in granular matter, the most famous and extensive such study probably being the Oslo ricepile experiment. Other experiments include those carried out on magnetic-domain patterns, the Barkhausen effect and vortices in superconductors. <br />
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由于 BTW 将他们的模型比喻为一个“沙堆” ,在沙堆上缓慢地喷洒新的沙粒以引起“雪崩” ,所以最初的实验工作主要集中在研究颗粒物质中的真实雪崩,其中最著名和最广泛的研究可能是奥斯陆地震实验。其他实验还包括在磁畴图案、超导体中的巴克豪森效应和涡旋上进行的实验。<br />
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<br />
<br />
<br />
<br />
Early theoretical work included the development of a variety of alternative SOC-generating dynamics distinct from the BTW model, attempts to prove model properties analytically (including calculating the [[critical exponent]]s<ref name=Tang1988a><br />
<br />
Early theoretical work included the development of a variety of alternative SOC-generating dynamics distinct from the BTW model, attempts to prove model properties analytically (including calculating the critical exponents<ref name=Tang1988a><br />
<br />
早期的理论工作包括开发各种不同于 BTW 模型的 soc 生成动力学,试图解析证明模型的性质(包括计算临界指数,参见 tang1988a<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[Chao Tang|Tang, C.]] and [[Per Bak|Bak, P.]]<br />
<br />
| author = Tang, C. and Bak, P.<br />
<br />
作者 Tang,c. and Bak,p。<br />
<br />
| year = 1988<br />
<br />
| year = 1988<br />
<br />
1988年<br />
<br />
| title = Critical exponents and scaling relations for self-organized critical phenomena<br />
<br />
| title = Critical exponents and scaling relations for self-organized critical phenomena<br />
<br />
自组织临界现象的临界指数和标度关系<br />
<br />
| journal = [[Physical Review Letters]]<br />
<br />
| journal = Physical Review Letters<br />
<br />
物理评论快报<br />
<br />
| volume = 60<br />
<br />
| volume = 60<br />
<br />
第60卷<br />
<br />
| issue = 23<br />
<br />
| issue = 23<br />
<br />
第23期<br />
<br />
| pages = 2347&ndash;2350<br />
<br />
| pages = 2347&ndash;2350<br />
<br />
2347-- 2350<br />
<br />
| doi = 10.1103/PhysRevLett.60.2347<br />
<br />
| doi = 10.1103/PhysRevLett.60.2347<br />
<br />
10.1103 / physrvlett. 60.2347<br />
<br />
| bibcode= 1988PhRvL..60.2347T<br />
<br />
| bibcode= 1988PhRvL..60.2347T<br />
<br />
1988 / phrvl. 60.2347 t<br />
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| pmid=10038328<br />
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| pmid=10038328<br />
<br />
10038328<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
</ref><ref name=Tang1988b><br />
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</ref><ref name=Tang1988b><br />
<br />
/ ref / name tang1988b<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[Chao Tang|Tang, C.]] and [[Per Bak|Bak, P.]]<br />
<br />
| author = Tang, C. and Bak, P.<br />
<br />
作者 Tang,c. and Bak,p。<br />
<br />
| year = 1988<br />
<br />
| year = 1988<br />
<br />
1988年<br />
<br />
| title = Mean field theory of self-organized critical phenomena<br />
<br />
| title = Mean field theory of self-organized critical phenomena<br />
<br />
自组织临界现象的平均场理论<br />
<br />
| journal = [[Journal of Statistical Physics]]<br />
<br />
| journal = Journal of Statistical Physics<br />
<br />
统计物理学杂志<br />
<br />
| volume = 51<br />
<br />
| volume = 51<br />
<br />
第51卷<br />
<br />
| issue = 5–6<br />
<br />
| issue = 5–6<br />
<br />
第5-6期<br />
<br />
| pages = 797&ndash;802<br />
<br />
| pages = 797&ndash;802<br />
<br />
797802页<br />
<br />
| doi = 10.1007/BF01014884<br />
<br />
| doi = 10.1007/BF01014884<br />
<br />
10.1007 / BF01014884<br />
<br />
| bibcode= 1988JSP....51..797T<br />
<br />
| bibcode= 1988JSP....51..797T<br />
<br />
1988JSP... 51. . 797 t<br />
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| url = https://zenodo.org/record/1232502<br />
<br />
| url = https://zenodo.org/record/1232502<br />
<br />
Https://zenodo.org/record/1232502<br />
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| type = Submitted manuscript<br />
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| type = Submitted manuscript<br />
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| 打印提交的手稿<br />
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}}<br />
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}}<br />
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}}<br />
<br />
</ref>), and examination of the conditions necessary for SOC to emerge. One of the important issues for the latter investigation was whether [[conservation of energy]] was required in the local dynamical exchanges of models: the answer in general is no, but with (minor) reservations, as some exchange dynamics (such as those of BTW) do require local conservation at least on average. In the long term, key theoretical issues yet to be resolved include the calculation of the possible [[universality class]]es of SOC behavior and the question of whether it is possible to derive a general rule for determining if an arbitrary [[algorithm]] displays SOC.<br />
<br />
</ref>), and examination of the conditions necessary for SOC to emerge. One of the important issues for the latter investigation was whether conservation of energy was required in the local dynamical exchanges of models: the answer in general is no, but with (minor) reservations, as some exchange dynamics (such as those of BTW) do require local conservation at least on average. In the long term, key theoretical issues yet to be resolved include the calculation of the possible universality classes of SOC behavior and the question of whether it is possible to derive a general rule for determining if an arbitrary algorithm displays SOC.<br />
<br />
/ ref) ,以及研究出现 '''<font color="#ff8000"> SOC</font>'''的必要条件。后一项研究的一个重要问题是,在局部动态交换模型时是否需要能量守恒: 一般的答案是否定的,但有一些保留意见,因为一些交换动力学(如 BTW 的动态)确实需要局部至少平均的能量守恒。从长远来看,有待解决的关键理论问题包括 '''<font color="#ff8000"> SOC</font>''' 行为可能的普适性类的计算,以及是否有可能推导出一个确定任意算法是否显示 '''<font color="#ff8000"> SOC</font>''' 的一般规则的问题。<br />
<br />
<br />
<br />
<br />
<br />
Alongside these largely lab-based approaches, many other investigations have centered around large-scale natural or social systems that are known (or suspected) to display [[scale invariance|scale-invariant]] behavior. Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: [[earthquakes]] (which, long before SOC was discovered, were known as a source of scale-invariant behavior such as the [[Gutenberg–Richter law]] describing the statistical distribution of earthquake size, and the [[Aftershock|Omori law]] describing the frequency of aftershocks<ref name=TurcotteSmalleySolla85><br />
<br />
Alongside these largely lab-based approaches, many other investigations have centered around large-scale natural or social systems that are known (or suspected) to display scale-invariant behavior. Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: earthquakes (which, long before SOC was discovered, were known as a source of scale-invariant behavior such as the Gutenberg–Richter law describing the statistical distribution of earthquake size, and the Omori law describing the frequency of aftershocks<ref name=TurcotteSmalleySolla85><br />
<br />
除了这些大部分基于实验室的方法,许多其他的研究都集中在大规模的自然或社会系统上,这些系统已经知道(或怀疑)表现出尺度不变的行为。虽然这些方法并不总是受到研究对象专家的欢迎(至少最初是这样) ,但 '''<font color="#ff8000"> SOC</font>''' 已经成为解释一些自然现象的强有力的候选者,包括: 地震(早在 '''<font color="#ff8000"> SOC</font>''' 被发现之前,地震就被认为是尺度不变行为的来源,例如描述地震大小统计分布的古腾堡-里克特定律,以及描述余震频率的描述余震的 Omori 定律,命名为 turcottesmalleysolla85<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
|author1=Turcotte, D. L. |author2=Smalley, R. F., Jr. |author3=Solla, S. A. | year = 1985<br />
<br />
|author1=Turcotte, D. L. |author2=Smalley, R. F., Jr. |author3=Solla, S. A. | year = 1985<br />
<br />
1 Turcotte,D.l. | author2 Smalley,r. f. ,jr. | author3 Solla,s. a.1985年<br />
<br />
| title = Collapse of loaded fractal trees<br />
<br />
| title = Collapse of loaded fractal trees<br />
<br />
负载分形树的崩溃<br />
<br />
| journal = Nature <br />
<br />
| journal = Nature <br />
<br />
自然》杂志<br />
<br />
| doi= 10.1038/313671a0<br />
<br />
| doi= 10.1038/313671a0<br />
<br />
10.1038 / 313671a0<br />
<br />
| volume = 313<br />
<br />
| volume = 313<br />
<br />
第313卷<br />
<br />
| issue = 6004<br />
<br />
| issue = 6004<br />
<br />
第6004期<br />
<br />
| pages = 671–672|bibcode = 1985Natur.313..671T <br />
<br />
| pages = 671–672|bibcode = 1985Natur.313..671T <br />
<br />
| 第671-672页 | bibcode 1985 / natur. 313. . 671 t<br />
<br />
}}</ref><ref name=SmalleyTurcotteSolla85 />); [[solar flares]]; fluctuations in economic systems such as [[financial markets]] (references to SOC are common in [[econophysics]]); [[landscape formation]]; [[forest fires]]; [[landslides]]; [[epidemics]]; neuronal avalanches in the cortex;<ref name="Beggs2003" /><ref name=Poil2012><br />
<br />
}}</ref>); solar flares; fluctuations in economic systems such as financial markets (references to SOC are common in econophysics); landscape formation; forest fires; landslides; epidemics; neuronal avalanches in the cortex;<ref name=Poil2012><br />
<br />
太阳耀斑; 经济系统的波动,比如金融市场(经济物理学中经常提到 SOC) ; 景观形成; 森林火灾; 滑坡; 流行病; 大脑皮层的神经雪崩; 参考名为 poil2012<br />
<br />
{{cite journal<br />
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{{cite journal<br />
<br />
{引用期刊<br />
<br />
| pmid = 22815496<br />
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| pmid = 22815496<br />
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22815496<br />
<br />
|date=Jul 2012<br />
<br />
|date=Jul 2012<br />
<br />
2012年7月<br />
<br />
|author1=Poil, SS |author2=Hardstone, R |author3=Mansvelder, HD |author4=Linkenkaer-Hansen, K | title = Critical-state dynamics of avalanches and oscillations jointly emerge from balanced excitation/inhibition in neuronal networks<br />
<br />
|author1=Poil, SS |author2=Hardstone, R |author3=Mansvelder, HD |author4=Linkenkaer-Hansen, K | title = Critical-state dynamics of avalanches and oscillations jointly emerge from balanced excitation/inhibition in neuronal networks<br />
<br />
1 Poil,SS | author2 Hardstone,r | author3 mansveder,HD | author4 Linkenkaer-Hansen,k | title 雪崩和振荡的临界状态动力学联合出现在神经元网络的平衡兴奋 / 抑制中<br />
<br />
| volume = 32<br />
<br />
| volume = 32<br />
<br />
第32卷<br />
<br />
| issue = 29<br />
<br />
| issue = 29<br />
<br />
第29期<br />
<br />
| pages = 9817–23 <br />
<br />
| pages = 9817–23 <br />
<br />
第9817-23页<br />
<br />
| doi = 10.1523/JNEUROSCI.5990-11.2012<br />
<br />
| doi = 10.1523/JNEUROSCI.5990-11.2012<br />
<br />
| doi 10.1523 / jneurosci. 5990-11.2012<br />
<br />
| journal = Journal of Neuroscience<br />
<br />
| journal = Journal of Neuroscience<br />
<br />
神经科学杂志<br />
<br />
| pmc=3553543<br />
<br />
| pmc=3553543<br />
<br />
3553543<br />
<br />
}}</ref> 1/f noise in the amplitude of electrophysiological signals;<ref name=LinkenkaerHansen2001 /> and [[biological evolution]] (where SOC has been invoked, for example, as the dynamical mechanism behind the theory of "[[punctuated equilibrium|punctuated equilibria]]" put forward by [[Niles Eldredge]] and [[Stephen Jay Gould]]). These "applied" investigations of SOC have included both modelling (either developing new models or adapting existing ones to the specifics of a given natural system) and extensive data analysis to determine the existence and/or characteristics of natural scaling laws.<br />
<br />
}}</ref> 1/f noise in the amplitude of electrophysiological signals; and biological evolution (where SOC has been invoked, for example, as the dynamical mechanism behind the theory of "punctuated equilibria" put forward by Niles Eldredge and Stephen Jay Gould). These "applied" investigations of SOC have included both modelling (either developing new models or adapting existing ones to the specifics of a given natural system) and extensive data analysis to determine the existence and/or characteristics of natural scaling laws.<br />
<br />
{} / ref 电生理信号振幅的1 / f 噪声,以及生物进化(其中 SOC 已被调用,例如,作为背后的动力机制的理论“间断平衡”由 Niles Eldredge 和史蒂芬·古尔德提出)。对SOC的这些”应用”研究既包括建模(开发新模型或使现有模型适应特定自然系统的具体情况) ,也包括广泛的数据分析,以确定是否存在和 / 或具有自然幂率的特点。<br />
<br />
<br />
<br />
<br />
<br />
In addition, SOC has been applied to computational algorithms. Recently, it has been found that the avalanches from an SOC process, like the BTW model, make effective patterns in a random search for optimal solutions on graphs.<ref name=Hoffmann2018><br />
<br />
In addition, SOC has been applied to computational algorithms. Recently, it has been found that the avalanches from an SOC process, like the BTW model, make effective patterns in a random search for optimal solutions on graphs.<ref name=Hoffmann2018><br />
<br />
此外,SOC 已经应用于计算算法。最近,人们发现来自 SOC 过程的雪崩,如 BTW 模型,在图的最优解的随机搜索中形成有效的模式。 参考名称 hoffmann2018<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[H. Hoffmann|Hoffmann, H.]] and [[D. W. Payton|Payton, D. W.]]<br />
<br />
| author = Hoffmann, H. and Payton, D. W.<br />
<br />
作者: 霍夫曼 h. 和佩顿 d. w。<br />
<br />
| year = 2018<br />
<br />
| year = 2018<br />
<br />
2018年<br />
<br />
| title = Optimization by Self-Organized Criticality<br />
<br />
| title = Optimization by Self-Organized Criticality<br />
<br />
最佳化作者: 自组织临界性<br />
<br />
| journal = [[Scientific Reports]]<br />
<br />
| journal = Scientific Reports<br />
<br />
科学报告<br />
<br />
| volume = 8<br />
<br />
| volume = 8<br />
<br />
第八卷<br />
<br />
| issue = 1<br />
<br />
| issue = 1<br />
<br />
第一期<br />
<br />
| pages = 2358<br />
<br />
| pages = 2358<br />
<br />
2358页<br />
<br />
| doi=10.1038/s41598-018-20275-7<br />
<br />
| doi=10.1038/s41598-018-20275-7<br />
<br />
10.1038 / s41598-018-20275-7<br />
<br />
| pmid = 29402956<br />
<br />
| pmid = 29402956<br />
<br />
29402956<br />
<br />
| pmc = 5799203<br />
<br />
| pmc = 5799203<br />
<br />
5799203<br />
<br />
| bibcode = 2018NatSR...8.2358H<br />
<br />
| bibcode = 2018NatSR...8.2358H<br />
<br />
| bibcode 2018NatSR... 8.2358 h<br />
<br />
}}</ref> <br />
<br />
}}</ref> <br />
<br />
{} / ref<br />
<br />
An example of such an optimization problem is [[graph coloring]]. The SOC process apparently helps the optimization from getting stuck in a [[local optimum]] without the use of any [[Simulated_annealing|annealing]] scheme, as suggested by previous work on [[extremal optimization]].<br />
<br />
An example of such an optimization problem is graph coloring. The SOC process apparently helps the optimization from getting stuck in a local optimum without the use of any annealing scheme, as suggested by previous work on extremal optimization.<br />
<br />
图着色就是这种最佳化问题的一个例子。'''<font color="#ff8000"> SOC</font>''' 过程显然有助于避免优化陷入局部最优,而无需使用任何以前的极值优化工作所建议的退火方案。<br />
<br />
<br />
<br />
<br />
The recent excitement generated by [[scale-free networks]] has raised some interesting new questions for SOC-related research: a number of different SOC models have been shown to generate such networks as an emergent phenomenon, as opposed to the simpler models proposed by network researchers where the network tends to be assumed to exist independently of any physical space or dynamics. While many single phenomena have been shown to exhibit scale-free properties over narrow ranges, a phenomenon offering by far a larger amount of data is solvent-accessible surface areas in globular proteins.<ref name=Moret2007><br />
<br />
The recent excitement generated by scale-free networks has raised some interesting new questions for SOC-related research: a number of different SOC models have been shown to generate such networks as an emergent phenomenon, as opposed to the simpler models proposed by network researchers where the network tends to be assumed to exist independently of any physical space or dynamics. While many single phenomena have been shown to exhibit scale-free properties over narrow ranges, a phenomenon offering by far a larger amount of data is solvent-accessible surface areas in globular proteins.<ref name=Moret2007><br />
<br />
'''<font color="#ff8000"> 无标度网络Scale-free networks</font>'''最近引起的兴奋为 '''<font color="#ff8000"> SOC</font>'''相关研究提出了一些有趣的新问题: 许多不同的 '''<font color="#ff8000"> SOC</font>'''模型已经被证明是作为一种涌现现象产生这样的网络,而不是网络研究人员提出的更简单的模型,其中网络往往被假定独立于任何物理空间或动力学存在。虽然许多单一现象已被证明在狭窄的范围内表现出无标度特性,但是到目前为止提供了大量数据的现象是球状蛋白质中溶剂可及的表面区域。 参考名称 moret2007<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[M. A. Moret|Moret, M. A.]] and [[G. Zebende|Zebende, G.]]<br />
<br />
| author = Moret, M. A. and Zebende, G.<br />
<br />
作者: Moret,M.a. and Zebende,g。<br />
<br />
| year = 2007<br />
<br />
| year = 2007<br />
<br />
2007年<br />
<br />
| title = Amino acid hydrophobicity and accessible surface area<br />
<br />
| title = Amino acid hydrophobicity and accessible surface area<br />
<br />
氨基酸疏水性和可达表面积<br />
<br />
| journal = [[Phys. Rev. E]]<br />
<br />
| journal = Phys. Rev. E<br />
<br />
体育杂志。牧师。E<br />
<br />
| volume = 75<br />
<br />
| volume = 75<br />
<br />
第75卷<br />
<br />
| issue = 1<br />
<br />
| issue = 1<br />
<br />
第一期<br />
<br />
| pages = 011920<br />
<br />
| pages = 011920<br />
<br />
011920页<br />
<br />
| doi=10.1103/PhysRevE.75.011920<br />
<br />
| doi=10.1103/PhysRevE.75.011920<br />
<br />
10.1103 / physarve. 75.011920<br />
<br />
| pmid = 17358197<br />
<br />
| pmid = 17358197<br />
<br />
17358197<br />
<br />
| bibcode = 2007PhRvE..75a1920M<br />
<br />
| bibcode = 2007PhRvE..75a1920M<br />
<br />
2007 / phrve. . 75 / a1920M<br />
<br />
}}</ref><br />
<br />
}}</ref><br />
<br />
{} / ref<br />
<br />
These studies quantify the differential geometry of proteins, and resolve many evolutionary puzzles regarding the biological emergence of complexity.<ref name=Phillips2014><br />
<br />
These studies quantify the differential geometry of proteins, and resolve many evolutionary puzzles regarding the biological emergence of complexity.<ref name=Phillips2014><br />
<br />
这些研究量化了蛋白质的微分几何,并解决了许多关于生物复杂性出现的进化之谜<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = Phillips, J. C.<br />
<br />
| author = Phillips, J. C.<br />
<br />
作者: 菲利普斯。<br />
<br />
| year = 2014<br />
<br />
| year = 2014<br />
<br />
2014年<br />
<br />
| title = Fractals and self-organized criticality in proteins<br />
<br />
| title = Fractals and self-organized criticality in proteins<br />
<br />
标题蛋白质中的分形和自组织临界性<br />
<br />
| journal = Physica A<br />
<br />
| journal = Physica A<br />
<br />
物理学杂志 a<br />
<br />
| volume = 415<br />
<br />
| volume = 415<br />
<br />
第415卷<br />
<br />
| pages = 440–448 <br />
<br />
| pages = 440–448 <br />
<br />
第440-448页<br />
<br />
| doi=10.1016/j.physa.2014.08.034<br />
<br />
| doi=10.1016/j.physa.2014.08.034<br />
<br />
| doi 10.1016 / j.physa. 2014.08.034<br />
<br />
| bibcode = 2014PhyA..415..440P<br />
<br />
| bibcode = 2014PhyA..415..440P<br />
<br />
| bibcode 2014PhyA. . 415. . 440 p<br />
<br />
| author-link = J. C. Phillips<br />
<br />
| author-link = J. C. Phillips<br />
<br />
作者链接 J.c. 菲利普斯<br />
<br />
}}</ref><br />
<br />
}}</ref><br />
<br />
{} / ref<br />
<br />
<br />
<br />
<br />
<br />
Despite the considerable interest and research output generated from the SOC hypothesis, there remains no general agreement with regards to its mechanisms in abstract mathematical form. Bak Tang and Wiesenfeld based their hypothesis on the behavior of their sandpile model.<ref name=Bak1987/> However,<br />
<br />
Despite the considerable interest and research output generated from the SOC hypothesis, there remains no general agreement with regards to its mechanisms in abstract mathematical form. Bak Tang and Wiesenfeld based their hypothesis on the behavior of their sandpile model. However,<br />
<br />
尽管 SOC 假说引起了相当大的兴趣和研究成果,但是关于其抽象数学形式的机制仍然没有普遍的一致性。Bak Tang 和 Wiesenfeld 基于他们的沙堆模型的行为建立了他们的假设。然而,<br />
<br />
it has been argued that this model would actually generate 1/f<sup>2</sup> noise rather than 1/f noise.<ref name=Jensen1989><br />
<br />
it has been argued that this model would actually generate 1/f<sup>2</sup> noise rather than 1/f noise.<ref name=Jensen1989><br />
<br />
有人认为,这种模型实际上会产生1 / f sup 2 / sup 噪声而不是1 / f 噪声<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[H. J. Jensen|Jensen, H. J.]], [[K. Christensen|Christensen, K.]] and [[H. C. Fogedby|Fogedby, H. C.]]<br />
<br />
| author = Jensen, H. J., Christensen, K. and Fogedby, H. C.<br />
<br />
作者 Jensen,h. j. ,Christensen,k. and fogeby,h. c。<br />
<br />
| year = 1989<br />
<br />
| year = 1989<br />
<br />
1989年<br />
<br />
| title = 1/f noise, distribution of lifetimes, and a pile of sand<br />
<br />
| title = 1/f noise, distribution of lifetimes, and a pile of sand<br />
<br />
标题1 / f 噪音,寿命分布,和一堆沙子<br />
<br />
| journal = [[Phys. Rev. B]]<br />
<br />
| journal = Phys. Rev. B<br />
<br />
体育杂志。牧师。B<br />
<br />
| volume = 40<br />
<br />
| volume = 40<br />
<br />
第40卷<br />
<br />
| issue = 10<br />
<br />
| issue = 10<br />
<br />
第10期<br />
<br />
| pages = 7425–7427<br />
<br />
| pages = 7425–7427<br />
<br />
第7425-7427页<br />
<br />
| doi=10.1103/physrevb.40.7425<br />
<br />
| doi=10.1103/physrevb.40.7425<br />
<br />
10.1103 / physirevb. 40.7425<br />
<br />
| pmid = 9991162<br />
<br />
| pmid = 9991162<br />
<br />
9991162<br />
<br />
|bibcode = 1989PhRvB..40.7425J }}<br />
<br />
|bibcode = 1989PhRvB..40.7425J }}<br />
<br />
1989 / phrvb. 40.7425 j }<br />
<br />
</ref><br />
<br />
</ref><br />
<br />
/ 参考<br />
<br />
This claim was based on untested scaling assumptions, and a more rigorous analysis showed that sandpile models <br />
<br />
This claim was based on untested scaling assumptions, and a more rigorous analysis showed that sandpile models <br />
<br />
这种说法是基于未经测试的比例假设,更严格的分析表明沙堆模型<br />
<br />
generally produce 1/f<sup>a</sup> spectra, with a<2. <ref name=Laurson2005><br />
<br />
generally produce 1/f<sup>a</sup> spectra, with a<2. <ref name=Laurson2005><br />
<br />
一般产生1 / f sup a / sup 光谱,其中 a < 2。参考名称 laurson2005<br />
<br />
{{cite journal |author1=Laurson, Lasse |author2=Alava, Mikko J. |author3=Zapperi, Stefano |title=Letter: Power spectra of self-organized critical sand piles |journal=Journal of Statistical Mechanics: Theory and Experiment |volume=0511 |id=L001 |date=15 September 2005 }}</ref><br />
<br />
</ref><br />
<br />
/ 参考<br />
<br />
Other simulation models were proposed later that could produce true 1/f noise,<ref name=Maslov1999><br />
<br />
Other simulation models were proposed later that could produce true 1/f noise,<ref name=Maslov1999><br />
<br />
其他模拟模型后来被提出,可以产生真正的1 / f 噪声,参考名称 maslov1999<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[S. Maslov|Maslov, S.]], [[C. Tang|Tang, C.]] and [[Y. –C. Zhang|Zhang, Y. - C.]]<br />
<br />
| author = Maslov, S., Tang, C. and Zhang, Y. - C.<br />
<br />
作者 Maslov,s. ,Tang,c. and Zhang,y。- c.<br />
<br />
| year = 1999<br />
<br />
| year = 1999<br />
<br />
1999年<br />
<br />
| title = 1/f noise in Bak-Tang-Wiesenfeld models on narrow stripes<br />
<br />
| title = 1/f noise in Bak-Tang-Wiesenfeld models on narrow stripes<br />
<br />
| 标题1 / f Bak-Tang-Wiesenfeld 窄条纹模型的噪音<br />
<br />
| journal = [[Phys. Rev. Lett.]]<br />
<br />
| journal = Phys. Rev. Lett.<br />
<br />
体育杂志。牧师。莱特。<br />
<br />
| volume = 83<br />
<br />
| volume = 83<br />
<br />
第83卷<br />
<br />
| issue = 12<br />
<br />
| issue = 12<br />
<br />
第12期<br />
<br />
| pages = 2449–2452<br />
<br />
| pages = 2449–2452<br />
<br />
2449-2452页<br />
<br />
| doi=10.1103/physrevlett.83.2449<br />
<br />
| doi=10.1103/physrevlett.83.2449<br />
<br />
10.1103 / physrvlett. 83.2449<br />
<br />
|arxiv = cond-mat/9902074 |bibcode = 1999PhRvL..83.2449M }}<br />
<br />
|arxiv = cond-mat/9902074 |bibcode = 1999PhRvL..83.2449M }}<br />
<br />
| arxiv cond-mat / 9902074 | bibcode 1999PhRvL. . 83.2449 m }<br />
<br />
</ref> and experimental sandpile models were observed to yield 1/f noise.<ref name=Frette1996><br />
<br />
</ref> and experimental sandpile models were observed to yield 1/f noise.<ref name=Frette1996><br />
<br />
/ ref 和实验沙堆模型被观察到产生1 / f 噪音。参考名称 frette1996<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[V.Frette|Frette, V.]], [[K. Christiansen|Christinasen, K.]], [[A. Malthe-Sørenssen|Malthe-Sørenssen, A.]], [[J. Feder|Feder, J]], [[T. Jøssang|Jøssang, T]] and [[P. Meakin|Meaken, P]]<br />
<br />
| author = Frette, V., Christinasen, K., Malthe-Sørenssen, A., Feder, J, Jøssang, T and Meaken, P<br />
<br />
| author = Frette, V., Christinasen, K., Malthe-Sørenssen, A., Feder, J, Jøssang, T and Meaken, P<br />
<br />
| year = 1996<br />
<br />
| year = 1996<br />
<br />
1996年<br />
<br />
| title = Avalanche dynamics in a pile of rice<br />
<br />
| title = Avalanche dynamics in a pile of rice<br />
<br />
| 题目: 大米堆中的雪崩动力学<br />
<br />
| journal = [[Nature (journal)|Nature]]<br />
<br />
| journal = Nature<br />
<br />
自然》杂志<br />
<br />
| volume = 379<br />
<br />
| volume = 379<br />
<br />
第379卷<br />
<br />
| issue = 6560<br />
<br />
| issue = 6560<br />
<br />
第6560期<br />
<br />
| pages = 49–52<br />
<br />
| pages = 49–52<br />
<br />
第49-52页<br />
<br />
| doi =10.1038/379049a0 <br />
<br />
| doi =10.1038/379049a0 <br />
<br />
10.1038 / 379049a0<br />
<br />
| bibcode= 1996Natur.379...49F}}<br />
<br />
| bibcode= 1996Natur.379...49F}}<br />
<br />
1996 / natur. 379... 49F }<br />
<br />
</ref> In addition to the nonconservative theoretical model mentioned above, other theoretical models for SOC have been based upon [[information theory]]<ref name=Dewar2003><br />
<br />
</ref> In addition to the nonconservative theoretical model mentioned above, other theoretical models for SOC have been based upon information theory<ref name=Dewar2003><br />
<br />
除了上面提到的非保守理论模型之外,其他关于 SOC 的理论模型都是基于信息论,例如 dewar2003<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = Dewar, R.<br />
<br />
| author = Dewar, R.<br />
<br />
作者杜瓦,r。<br />
<br />
| year = 2003<br />
<br />
| year = 2003<br />
<br />
2003年<br />
<br />
| title = Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states<br />
<br />
| title = Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states<br />
<br />
非平衡态中涨落定理、最大产生熵和自组织临界性的信息论解释<br />
<br />
| journal =J. Phys. A: Math. Gen. <br />
<br />
| journal =J. Phys. A: Math. Gen. <br />
<br />
| j 杂志。女名女子名。答: 数学。将军。<br />
<br />
| volume = 36<br />
<br />
| volume = 36<br />
<br />
第36卷<br />
<br />
| pages =631&ndash;641<br />
<br />
| pages =631&ndash;641<br />
<br />
631-- 641<br />
<br />
| pmid = <br />
<br />
| pmid = <br />
<br />
我不会让你失望的<br />
<br />
| doi = 10.1088/0305-4470/36/3/303<br />
<br />
| doi = 10.1088/0305-4470/36/3/303<br />
<br />
10.1088 / 0305-4470 / 36 / 3 / 303<br />
<br />
| issue = 3<br />
<br />
| issue = 3<br />
<br />
第三期<br />
<br />
| pmc = <br />
<br />
| pmc = <br />
<br />
我会的,我会的,我会的<br />
<br />
|bibcode = 2003JPhA...36..631D|arxiv = cond-mat/0005382 | author-link = R Dewar<br />
<br />
|bibcode = 2003JPhA...36..631D|arxiv = cond-mat/0005382 | author-link = R Dewar<br />
<br />
| bibcode 2003JPhA... 36. . 631 d | arxiv cond-mat / 0005382 | author-link r Dewar<br />
<br />
}}</ref>, <br />
<br />
}}</ref>, <br />
<br />
} / ref,<br />
<br />
[[mean field theory]]<ref name=Vespignani1998><br />
<br />
mean field theory<ref name=Vespignani1998><br />
<br />
平均场理论参考名称 vespignani1998<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[Alessandro Vespignani|Vespignani, A.]], and [[Stefano Zapperi|Zapperi, S.]]<br />
<br />
| author = Vespignani, A., and Zapperi, S.<br />
<br />
作者 Vespignani,a,和 Zapperi,s。<br />
<br />
| year = 1998<br />
<br />
| year = 1998<br />
<br />
1998年<br />
<br />
| title = How self-organized criticality works: a unified mean-field picture<br />
<br />
| title = How self-organized criticality works: a unified mean-field picture<br />
<br />
标题自组织临界性如何工作: 一个统一的平均场图片<br />
<br />
| journal =Phys. Rev. E <br />
<br />
| journal =Phys. Rev. E <br />
<br />
体育杂志。牧师。E<br />
<br />
| volume = 57<br />
<br />
| volume = 57<br />
<br />
第57卷<br />
<br />
| pages =6345–6362<br />
<br />
| pages =6345–6362<br />
<br />
6345-6362页<br />
<br />
| pmid = <br />
<br />
| pmid = <br />
<br />
我不会让你失望的<br />
<br />
| doi = 10.1103/physreve.57.6345<br />
<br />
| doi = 10.1103/physreve.57.6345<br />
<br />
10.1103 / physorve. 57.6345<br />
<br />
| issue = 6<br />
<br />
| issue = 6<br />
<br />
第六期<br />
<br />
| pmc = <br />
<br />
| pmc = <br />
<br />
我会的,我会的,我会的<br />
<br />
| bibcode = 1998PhRvE..57.6345V<br />
<br />
| bibcode = 1998PhRvE..57.6345V<br />
<br />
| bibcode 1998PhRvE. . 57.6345 v<br />
<br />
| arxiv = cond-mat/9709192<br />
<br />
| arxiv = cond-mat/9709192<br />
<br />
| arxiv = cond-mat/9709192<br />
<br />
| hdl = 2047/d20002173<br />
<br />
| hdl = 2047/d20002173<br />
<br />
2047 / d20002173<br />
<br />
}}</ref>,<br />
<br />
}}</ref>,<br />
<br />
} / ref,<br />
<br />
the [[convergence of random variables]]<ref name=Kendal2015><br />
<br />
the convergence of random variables<ref name=Kendal2015><br />
<br />
随机变量的收敛裁判名称 kendal 2015<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = Kendal, WS<br />
<br />
| author = Kendal, WS<br />
<br />
作者 Kendal,WS<br />
<br />
| year = 2015<br />
<br />
| year = 2015<br />
<br />
2015年<br />
<br />
| title = Self-organized criticality attributed to a central limit-like convergence effect<br />
<br />
| title = Self-organized criticality attributed to a central limit-like convergence effect<br />
<br />
| 标题自组织临界性归因于类似中心极限的聚合效应<br />
<br />
| journal =Physica A <br />
<br />
| journal =Physica A <br />
<br />
物理学杂志 a<br />
<br />
| volume = 421<br />
<br />
| volume = 421<br />
<br />
第421卷<br />
<br />
| pages =141&ndash;150<br />
<br />
| pages =141&ndash;150<br />
<br />
141-- 150页<br />
<br />
| pmid = <br />
<br />
| pmid = <br />
<br />
我不会让你失望的<br />
<br />
| doi = 10.1016/j.physa.2014.11.035<br />
<br />
| doi = 10.1016/j.physa.2014.11.035<br />
<br />
| doi 10.1016 / j.physa. 2014.11.035<br />
<br />
| issue = <br />
<br />
| issue = <br />
<br />
发行<br />
<br />
| pmc = <br />
<br />
| pmc = <br />
<br />
我会的,我会的,我会的<br />
<br />
|bibcode =2015PhyA..421..141K | author-link = Wayne Kendal<br />
<br />
|bibcode =2015PhyA..421..141K | author-link = Wayne Kendal<br />
<br />
| bibcode 2015PhyA. . 421. . 141 k | 作者链接 Wayne Kendal<br />
<br />
}}</ref>,<br />
<br />
}}</ref>,<br />
<br />
} / ref,<br />
<br />
and cluster formation.<ref name=Hoffmann2018b><br />
<br />
and cluster formation.<ref name=Hoffmann2018b><br />
<br />
和簇的形成。参考名称 hoffmann2018b<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = Hoffmann, H.<br />
<br />
| author = Hoffmann, H.<br />
<br />
作者: 霍夫曼。<br />
<br />
| year = 2018<br />
<br />
| year = 2018<br />
<br />
2018年<br />
<br />
| title = Impact of Network Topology on Self-Organized Criticality<br />
<br />
| title = Impact of Network Topology on Self-Organized Criticality<br />
<br />
网络拓扑对自组织临界性的影响<br />
<br />
| journal = Phys. Rev. E <br />
<br />
| journal = Phys. Rev. E <br />
<br />
体育杂志。牧师。E<br />
<br />
| volume = 97<br />
<br />
| volume = 97<br />
<br />
第97卷<br />
<br />
| pages =022313<br />
<br />
| pages =022313<br />
<br />
022313页<br />
<br />
| pmid = 29548239<br />
<br />
| pmid = 29548239<br />
<br />
29548239<br />
<br />
| doi = 10.1103/PhysRevE.97.022313<br />
<br />
| doi = 10.1103/PhysRevE.97.022313<br />
<br />
10.1103 / physarve. 97.022313<br />
<br />
| issue = 2<br />
<br />
| issue = 2<br />
<br />
第二期<br />
<br />
| pmc = <br />
<br />
| pmc = <br />
<br />
我会的,我会的,我会的<br />
<br />
| bibcode =2018PhRvE..97b2313H <br />
<br />
| bibcode =2018PhRvE..97b2313H <br />
<br />
2018 / phrve. . 97 / b2313H<br />
<br />
| author-link = Heiko Hoffmann<br />
<br />
| author-link = Heiko Hoffmann<br />
<br />
作者: 海科 · 霍夫曼<br />
<br />
| doi-access = free<br />
<br />
| doi-access = free<br />
<br />
免费访问<br />
<br />
}}</ref> A continuous model of self-organised criticality is proposed by using [[tropical geometry]].<ref>{{Cite journal|last=Kalinin|first=N.|last2=Guzmán-Sáenz|first2=A.|last3=Prieto|first3=Y.|last4=Shkolnikov|first4=M.|last5=Kalinina|first5=V.|last6=Lupercio|first6=E.|date=2018-08-15|title=Self-organized criticality and pattern emergence through the lens of tropical geometry|journal=Proceedings of the National Academy of Sciences|volume=115|issue=35|language=en|pages=E8135–E8142|doi=10.1073/pnas.1805847115|issn=0027-8424|pmid=30111541|pmc=6126730|arxiv=1806.09153}}</ref><br />
<br />
}}</ref> A continuous model of self-organised criticality is proposed by using tropical geometry.<br />
<br />
{} / ref 一个'''<font color="#ff8000"> 自组织临界Self-organised criticality</font>'''的连续模型是通过使用热带几何来提出的。<br />
<br />
== Examples of self-organized critical dynamics自组织临界动力学的例子 ==<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
In chronological order of development:<br />
<br />
In chronological order of development:<br />
<br />
按发展时间顺序排列:<br />
<br />
<br />
<br />
<br />
<br />
* Stick-slip model of fault failure<ref name="TurcotteSmalleySolla85" /><ref name="SmalleyTurcotteSolla85" /><br />
<br />
*断层破坏的粘滑模型<ref name="TurcotteSmalleySolla85" /><ref name="SmalleyTurcotteSolla85" /><br />
<br />
*[[Abelian sandpile model|Bak–Tang–Wiesenfeld sandpile]]<br />
<br />
*[[阿贝尔沙堆模型| Bak–Tang–Wiesenfeld沙堆]]<br />
<br />
* [[Forest-fire model]]<br />
<br />
*[[森林火灾模型]]<br />
<br />
* [[Olami–Feder–Christensen model]]<br />
<br />
* [[奥拉米·费德·克里斯滕森模型]]<br />
<br />
* [[Bak–Sneppen model]]<br />
<br />
*[[背景模型]]<br />
<br />
== See also 参见==<br />
<br />
<br />
<br />
* [[Pink noise|1/f noise]]<br />
<br />
*[[粉红噪音| 1/f噪音]]<br />
<br />
* [[Complex system]]s<br />
<br />
* [[复杂系统]]s<br />
<br />
* [[Critical brain hypothesis]]<br />
<br />
*[[【关键大脑假说】]]<br />
<br />
* [[Critical exponents]]<br />
<br />
*[[临界指数]]<br />
<br />
* [[Detrended fluctuation analysis]], a method to detect power-law scaling in time series.<br />
<br />
*[[Detrended涨落分析]],一种检测中幂律标度的方法<br />
<br />
* [[Dual-phase evolution]], another process that contributes to self-organization in complex systems.<br />
<br />
* [[双相演化]],另一个有助于自我组织的过程<br />
<br />
* [[Fractal]]s<br />
<br />
* [[分形]]s;<br />
<br />
* [[Ilya Prigogine]], a systems scientist who helped formalize dissipative system behavior in general terms.<br />
<br />
*[[伊利亚·普里高津]],一位帮助将耗散系统形式化的系统科学家<br />
<br />
* [[Power law]]s<br />
<br />
*[[幂律]]s<br />
<br />
* [[Red Queen hypothesis]]<br />
<br />
*[[红皇后假说]]<br />
<br />
* [[Scale invariance]]<br />
<br />
* [[标度不变性]]<br />
<br />
* [[Self-organization]]<br />
<br />
* [[自组织]]<br />
<br />
* [[Self-organized criticality control]]<br />
<br />
*[[自组织临界控制]]<br />
<br />
==References参考资料==<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<references/><br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
== Further reading延伸阅读 ==<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = Adami, C.<br />
<br />
| author = Adami, C.<br />
<br />
作者: 阿达米。<br />
<br />
| year = 1995<br />
<br />
| year = 1995<br />
<br />
1995年<br />
<br />
| title = Self-organized criticality in living systems<br />
<br />
| title = Self-organized criticality in living systems<br />
<br />
| 生命系统中的自组织临界性<br />
<br />
| journal = [[Physics Letters A]]<br />
<br />
| journal = Physics Letters A<br />
<br />
物理学快报<br />
<br />
| volume = 203<br />
<br />
| volume = 203<br />
<br />
第203卷<br />
<br />
| issue = 1<br />
<br />
| issue = 1<br />
<br />
第一期<br />
<br />
| pages = 29&ndash;32<br />
<br />
| pages = 29&ndash;32<br />
<br />
29-- 32页<br />
<br />
| doi = 10.1016/0375-9601(95)00372-A<br />
<br />
| doi = 10.1016/0375-9601(95)00372-A<br />
<br />
| doi 10.1016 / 0375-9601(95)00372-A<br />
<br />
|bibcode = 1995PhLA..203...29A | arxiv = adap-org/9401001<br />
<br />
|bibcode = 1995PhLA..203...29A | arxiv = adap-org/9401001<br />
<br />
|bibcode = 1995PhLA..203...29A | arxiv = adap-org/9401001<br />
<br />
| citeseerx = 10.1.1.456.9543<br />
<br />
| citeseerx = 10.1.1.456.9543<br />
<br />
10.1.1.456.9543<br />
<br />
| author-link = Adami, C<br />
<br />
| author-link = Adami, C<br />
<br />
| 作者链接阿达米,c<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite book<br />
<br />
<br />
<br />
| author = Bak, P.<br />
<br />
| author = Bak, P.<br />
<br />
作者 Bak,p。<br />
<br />
| year = 1996<br />
<br />
| year = 1996<br />
<br />
1996年<br />
<br />
| title = How Nature Works: The Science of Self-Organized Criticality<br />
<br />
| title = How Nature Works: The Science of Self-Organized Criticality<br />
<br />
自然如何运作: 自组织临界性的科学<br />
<br />
| publisher = Copernicus<br />
<br />
| publisher = Copernicus<br />
<br />
出版商哥白尼<br />
<br />
| location = New York<br />
<br />
| location = New York<br />
<br />
| 地点: 纽约<br />
<br />
| isbn = 978-0-387-94791-4<br />
<br />
| isbn = 978-0-387-94791-4<br />
<br />
[国际标准图书编号978-0-387-94791-4]<br />
<br />
| author-link = Per Bak<br />
<br />
| author-link = Per Bak<br />
<br />
| 作者链接 Per Bak<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = [[Per Bak|Bak, P.]] and [[Maya Paczuski|Paczuski, M.]]<br />
<br />
| author = Bak, P. and Paczuski, M.<br />
<br />
作者 Bak,p. and Paczuski,m。<br />
<br />
| year = 1995<br />
<br />
| year = 1995<br />
<br />
1995年<br />
<br />
| title = Complexity, contingency, and criticality<br />
<br />
| title = Complexity, contingency, and criticality<br />
<br />
| 标题复杂性、偶然性和临界性<br />
<br />
| journal = [[Proceedings of the National Academy of Sciences|Proceedings of the National Academy of Sciences of the USA]]<br />
<br />
| journal = Proceedings of the National Academy of Sciences of the USA<br />
<br />
美国美国国家科学院院刊杂志<br />
<br />
| volume = 92<br />
<br />
| volume = 92<br />
<br />
第92卷<br />
<br />
| pages = 6689&ndash;6696<br />
<br />
| pages = 6689&ndash;6696<br />
<br />
6689-- 6696<br />
<br />
| url = http://pnas.org/cgi/content/abstract/92/15/6689<br />
<br />
| url = http://pnas.org/cgi/content/abstract/92/15/6689<br />
<br />
Http://pnas.org/cgi/content/abstract/92/15/6689<br />
<br />
| doi = 10.1073/pnas.92.15.6689<br />
<br />
| doi = 10.1073/pnas.92.15.6689<br />
<br />
10.1073 / pnas. 92.15.6689<br />
<br />
| pmid = 11607561<br />
<br />
| pmid = 11607561<br />
<br />
11607561<br />
<br />
| issue = 15<br />
<br />
| issue = 15<br />
<br />
第15期<br />
<br />
| pmc = 41396<br />
<br />
| pmc = 41396<br />
<br />
41396<br />
<br />
|bibcode = 1995PNAS...92.6689B }}<br />
<br />
|bibcode = 1995PNAS...92.6689B }}<br />
<br />
92.6689 b }<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = [[Per Bak|Bak, P.]] and [[Kim Sneppen|Sneppen, K.]]<br />
<br />
| author = Bak, P. and Sneppen, K.<br />
<br />
作者 Bak,p. and Sneppen,k。<br />
<br />
| year = 1993<br />
<br />
| year = 1993<br />
<br />
1993年<br />
<br />
| title = Punctuated equilibrium and criticality in a simple model of evolution <br />
<br />
| title = Punctuated equilibrium and criticality in a simple model of evolution <br />
<br />
| 简单演化模型中的间断平衡和临界性<br />
<br />
| journal = [[Physical Review Letters]]<br />
<br />
| journal = Physical Review Letters<br />
<br />
物理评论快报<br />
<br />
| volume = 71<br />
<br />
| volume = 71<br />
<br />
第71卷<br />
<br />
| issue = 24<br />
<br />
| issue = 24<br />
<br />
第24期<br />
<br />
| pages = 4083&ndash;4086<br />
<br />
| pages = 4083&ndash;4086<br />
<br />
4083-- 4086<br />
<br />
| doi = 10.1103/PhysRevLett.71.4083<br />
<br />
| doi = 10.1103/PhysRevLett.71.4083<br />
<br />
10.1103 / physrvlett. 71.4083<br />
<br />
| pmid=10055149<br />
<br />
| pmid=10055149<br />
<br />
10055149<br />
<br />
| bibcode=1993PhRvL..71.4083B}}<br />
<br />
| bibcode=1993PhRvL..71.4083B}}<br />
<br />
1993 phrvl. . 71.4083 b }<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = [[Per Bak|Bak, P.]], [[Chao Tang|Tang, C.]] and [[Kurt Wiesenfeld|Wiesenfeld, K.]]<br />
<br />
| author = Bak, P., Tang, C. and Wiesenfeld, K.<br />
<br />
作者 Bak,p. ,Tang,c. and Wiesenfeld,k。<br />
<br />
| year = 1987<br />
<br />
| year = 1987<br />
<br />
1987年<br />
<br />
| title = Self-organized criticality: an explanation of <math>1/f</math> noise<br />
<br />
| title = Self-organized criticality: an explanation of <math>1/f</math> noise<br />
<br />
| 题目自组织临界性: 数学噪音的解释<br />
<br />
| journal = [[Physical Review Letters]]<br />
<br />
| journal = Physical Review Letters<br />
<br />
物理评论快报<br />
<br />
| volume = 59<br />
<br />
| volume = 59<br />
<br />
第59卷<br />
<br />
| issue = 4<br />
<br />
| issue = 4<br />
<br />
第四期<br />
<br />
| pages = 381&ndash;384<br />
<br />
| pages = 381&ndash;384<br />
<br />
381-- 384<br />
<br />
| doi = 10.1103/PhysRevLett.59.381<br />
<br />
| doi = 10.1103/PhysRevLett.59.381<br />
<br />
10.1103 / physrvlett. 59.381<br />
<br />
| pmid = 10035754<br />
<br />
| pmid = 10035754<br />
<br />
10035754<br />
<br />
| bibcode=1987PhRvL..59..381B}}<br />
<br />
| bibcode=1987PhRvL..59..381B}}<br />
<br />
1987 / phrvl. . 59. . 381 b }<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = [[Per Bak|Bak, P.]], [[Chao Tang|Tang, C.]] and [[Kurt Wiesenfeld|Wiesenfeld, K.]]<br />
<br />
| author = Bak, P., Tang, C. and Wiesenfeld, K.<br />
<br />
作者 Bak,p. ,Tang,c. and Wiesenfeld,k。<br />
<br />
| year = 1988<br />
<br />
| year = 1988<br />
<br />
1988年<br />
<br />
| title = Self-organized criticality<br />
<br />
| title = Self-organized criticality<br />
<br />
标题自组织临界性<br />
<br />
| journal = [[Physical Review A]]<br />
<br />
| journal = Physical Review A<br />
<br />
物理评论 a 期刊<br />
<br />
| volume = 38<br />
<br />
| volume = 38<br />
<br />
第38卷<br />
<br />
| issue = 1<br />
<br />
| issue = 1<br />
<br />
第一期<br />
<br />
| pages = 364&ndash;374<br />
<br />
| pages = 364&ndash;374<br />
<br />
364-- 374<br />
<br />
| doi = 10.1103/PhysRevA.38.364<br />
<br />
| doi = 10.1103/PhysRevA.38.364<br />
<br />
10.1103 / PhysRevA. 38.364<br />
<br />
| pmid = 9900174<br />
<br />
| pmid = 9900174<br />
<br />
9900174<br />
<br />
|bibcode = 1988PhRvA..38..364B }} [https://archive.is/20130415140421/http://www.papercore.org/PerBak1987 Papercore summary].<br />
<br />
|bibcode = 1988PhRvA..38..364B }} [https://archive.is/20130415140421/http://www.papercore.org/PerBak1987 Papercore summary].<br />
<br />
| bibcode 1988PhRvA. . 38. . 364 b }[ https://archive.is/20130415140421/http://www.Papercore.org/perbak1987文件核心摘要]。<br />
<br />
<br />
<br />
<br />
<br />
* {{cite book<br />
<br />
<br />
<br />
| author = Buchanan, M.<br />
<br />
| author = Buchanan, M.<br />
<br />
作者: 布坎南。<br />
<br />
| year = 2000<br />
<br />
| year = 2000<br />
<br />
2000年<br />
<br />
| title = Ubiquity<br />
<br />
| title = Ubiquity<br />
<br />
标题: Ubiquity<br />
<br />
| publisher = Weidenfeld &amp; Nicolson<br />
<br />
| publisher = Weidenfeld &amp; Nicolson<br />
<br />
| publisher = Weidenfeld &amp; Nicolson<br />
<br />
| location = London<br />
<br />
| location = London<br />
<br />
地点: 伦敦<br />
<br />
| isbn = 978-0-7538-1297-6<br />
<br />
| isbn = 978-0-7538-1297-6<br />
<br />
[国际标准图书编号978-0-7538-1297-6]<br />
<br />
| author-link = Mark Buchanan<br />
<br />
| author-link = Mark Buchanan<br />
<br />
马克 · 布坎南<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite book<br />
<br />
<br />
<br />
| author = Jensen, H. J.<br />
<br />
| author = Jensen, H. J.<br />
<br />
作者 Jensen,h. j。<br />
<br />
| year = 1998<br />
<br />
| year = 1998<br />
<br />
1998年<br />
<br />
| title = Self-Organized Criticality<br />
<br />
| title = Self-Organized Criticality<br />
<br />
标题自组织临界性<br />
<br />
| publisher = [[Cambridge University Press]]<br />
<br />
| publisher = Cambridge University Press<br />
<br />
出版商剑桥大学出版社<br />
<br />
| location = Cambridge<br />
<br />
| location = Cambridge<br />
<br />
| 地点: 剑桥<br />
<br />
| isbn = 978-0-521-48371-1<br />
<br />
| isbn = 978-0-521-48371-1<br />
<br />
[国际标准图书编号978-0-521-48371-1]<br />
<br />
| author-link = Henrik Jeldtoft Jensen<br />
<br />
| author-link = Henrik Jeldtoft Jensen<br />
<br />
作者: 亨里克 · 耶尔德托夫特 · 詹森<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = Katz, J. I.<br />
<br />
| author = Katz, J. I.<br />
<br />
作者 Katz,j. i。<br />
<br />
| year = 1986<br />
<br />
| year = 1986<br />
<br />
1986年<br />
<br />
| title = A model of propagating brittle failure in heterogeneous media<br />
<br />
| title = A model of propagating brittle failure in heterogeneous media<br />
<br />
在非均匀介质中传播脆性破坏的模型<br />
<br />
| journal = Journal of Geophysical Research<br />
<br />
| journal = Journal of Geophysical Research<br />
<br />
地球物理研究期刊<br />
<br />
| bibcode = 1986JGR....9110412K<br />
<br />
| bibcode = 1986JGR....9110412K<br />
<br />
| bibcode 1986JGR... 9110412K<br />
<br />
| doi = 10.1029/JB091iB10p10412<br />
<br />
| doi = 10.1029/JB091iB10p10412<br />
<br />
| doi 10.1029 / JB091iB10p10412<br />
<br />
| volume = 91<br />
<br />
| volume = 91<br />
<br />
第91卷<br />
<br />
| issue = B10<br />
<br />
| issue = B10<br />
<br />
第10期<br />
<br />
| pages = 10412<br />
<br />
| pages = 10412<br />
<br />
10412页<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = Kron, T./Grund, T.<br />
<br />
| author = Kron, T./Grund, T.<br />
<br />
作者: Kron t. / Grund t。<br />
<br />
| year = 2009<br />
<br />
| year = 2009<br />
<br />
2009年<br />
<br />
| title = Society as a Selforganized Critical System<br />
<br />
| title = Society as a Selforganized Critical System<br />
<br />
作为一个自组织的批判系统的社会<br />
<br />
| journal = Cybernetics and Human Knowing<br />
<br />
| journal = Cybernetics and Human Knowing<br />
<br />
控制论与人类认知<br />
<br />
| volume = 16<br />
<br />
| volume = 16<br />
<br />
第16卷<br />
<br />
| pages = 65–82<br />
<br />
| pages = 65–82<br />
<br />
第65-82页<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{Cite book<br />
<br />
<br />
<br />
| author = Paczuski, M.<br />
<br />
| author = Paczuski, M.<br />
<br />
作者: 帕祖斯基。<br />
<br />
| year = 2005<br />
<br />
| year = 2005<br />
<br />
2005年<br />
<br />
| title = Networks as renormalized models for emergent behavior in physical systems<br />
<br />
| title = Networks as renormalized models for emergent behavior in physical systems<br />
<br />
作为物理系统中突发行为的重整化模型的网络<br />
<br />
| journal = Complexity<br />
<br />
| journal = Complexity<br />
<br />
杂志复杂性<br />
<br />
| pages = 363–374<br />
<br />
| pages = 363–374<br />
<br />
第363-374页<br />
<br />
| arxiv = physics/0502028<br />
<br />
| arxiv = physics/0502028<br />
<br />
| arxiv physics / 0502028<br />
<br />
|bibcode = 2005cmn..conf..363P |doi = 10.1142/9789812701558_0042<br />
<br />
|bibcode = 2005cmn..conf..363P |doi = 10.1142/9789812701558_0042<br />
<br />
2005 / cmn. conf. 363 p | doi 10.1142 / 97898127015580042<br />
<br />
| series = The Science and Culture Series – Physics<br />
<br />
| series = The Science and Culture Series – Physics<br />
<br />
| 科学与文化系列-物理学<br />
<br />
| isbn = 978-981-256-525-9 | citeseerx = 10.1.1.261.9886<br />
<br />
| isbn = 978-981-256-525-9 | citeseerx = 10.1.1.261.9886<br />
<br />
| isbn 978-981-256-525-9 | citeserx 10.1.1.261.9886<br />
<br />
| author-link = Maya Paczuski<br />
<br />
| author-link = Maya Paczuski<br />
<br />
| 作者链接 Maya Paczuski<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite book<br />
<br />
<br />
<br />
| author = Turcotte, D. L.<br />
<br />
| author = Turcotte, D. L.<br />
<br />
作者: Turcotte,D.l。<br />
<br />
| year = 1997<br />
<br />
| year = 1997<br />
<br />
1997年<br />
<br />
| title = Fractals and Chaos in Geology and Geophysics<br />
<br />
| title = Fractals and Chaos in Geology and Geophysics<br />
<br />
地质学与地球物理学中的分形与混沌<br />
<br />
| publisher = [[Cambridge University Press]]<br />
<br />
| publisher = Cambridge University Press<br />
<br />
出版商剑桥大学出版社<br />
<br />
| location = Cambridge<br />
<br />
| location = Cambridge<br />
<br />
| 地点: 剑桥<br />
<br />
| isbn = 978-0-521-56733-6<br />
<br />
| isbn = 978-0-521-56733-6<br />
<br />
[国际标准图书馆编号978-0-521-56733-6]<br />
<br />
| author-link = Donald L. Turcotte<br />
<br />
| author-link = Donald L. Turcotte<br />
<br />
作者: Donald l. Turcotte<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = Turcotte, D. L.<br />
<br />
| author = Turcotte, D. L.<br />
<br />
作者: Turcotte,D.l。<br />
<br />
| year = 1999<br />
<br />
| year = 1999<br />
<br />
1999年<br />
<br />
| title = Self-organized criticality<br />
<br />
| title = Self-organized criticality<br />
<br />
标题自组织临界性<br />
<br />
| journal = [[Reports on Progress in Physics]]<br />
<br />
| journal = Reports on Progress in Physics<br />
<br />
物理学进展报告<br />
<br />
| volume = 62<br />
<br />
| volume = 62<br />
<br />
第62卷<br />
<br />
| issue = 10<br />
<br />
| issue = 10<br />
<br />
第10期<br />
<br />
| pages = 1377&ndash;1429<br />
<br />
| pages = 1377&ndash;1429<br />
<br />
13771429页<br />
<br />
| doi = 10.1088/0034-4885/62/10/201<br />
<br />
| doi = 10.1088/0034-4885/62/10/201<br />
<br />
10.1088 / 0034-4885 / 62 / 10 / 201<br />
<br />
|bibcode = 1999RPPh...62.1377T | author-link = Donald L. Turcotte<br />
<br />
|bibcode = 1999RPPh...62.1377T | author-link = Donald L. Turcotte<br />
<br />
| bibcode 1999RPPh... 62.1377 t | 作者链接 Donald l. Turcotte<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = Md. Nurujjaman/A. N. Sekar Iyengar<br />
<br />
| author = Md. Nurujjaman/A. N. Sekar Iyengar<br />
<br />
作者马里兰大学。Nurujjaman / a.N. Sekar Iyengar<br />
<br />
| year = 2007<br />
<br />
| year = 2007<br />
<br />
2007年<br />
<br />
| title = Realization of {SOC} behavior in a dc glow discharge plasma<br />
<br />
| title = Realization of {SOC} behavior in a dc glow discharge plasma<br />
<br />
直流辉光放电等离子体{ SOC }行为的实现<br />
<br />
| journal = [[Physics Letters A]]<br />
<br />
| journal = Physics Letters A<br />
<br />
物理学快报<br />
<br />
| volume = 360<br />
<br />
| volume = 360<br />
<br />
第360卷<br />
<br />
| issue = 6<br />
<br />
| issue = 6<br />
<br />
第六期<br />
<br />
| pages = 717&ndash;721<br />
<br />
| pages = 717&ndash;721<br />
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|arxiv = physics/0611069 |bibcode = 2007PhLA..360..717N |doi = 10.1016/j.physleta.2006.09.005 | author-link = Md. Nurujjaman/A. N. Sekar Iyengar<br />
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|arxiv = physics/0611069 |bibcode = 2007PhLA..360..717N |doi = 10.1016/j.physleta.2006.09.005 | author-link = Md. Nurujjaman/A. N. Sekar Iyengar<br />
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| arxiv physics / 0611069 | bibcode 2007 phla. . 360. . 717 n | doi 10.1016 / j.physleta. 2006.09.005 | author-link md.Nurujjaman / a.N. Sekar Iyengar<br />
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*[http://xstructure.inr.ac.ru/x-bin/theme2.py?arxiv=cond-mat&level=1&index1=20771 Self-organized criticality on arxiv.org]<br />
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[[Category:Critical phenomena]]<br />
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Category:Critical phenomena<br />
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范畴: 关键现象<br />
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[[Category:Applied and interdisciplinary physics]]<br />
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Category:Applied and interdisciplinary physics<br />
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类别: 应用和跨学科物理学<br />
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[[Category:Chaos theory]]<br />
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Category:Chaos theory<br />
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范畴: 混沌理论<br />
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[[Category:Self-organization]]<br />
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Category:Self-organization<br />
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类别: 自我组织<br />
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<small>This page was moved from [[wikipedia:en:Self-organized criticality]]. Its edit history can be viewed at [[自组织临界性/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E8%87%AA%E7%BB%84%E7%BB%87%E4%B8%B4%E7%95%8C%E6%80%A7&diff=21923自组织临界性2021-02-21T11:30:35Z<p>Jxzhou:/* Overview 概览 */</p>
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<div>此词条暂由水流心不竞初译,未经审校,带来阅读不便,请见谅。<br />
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In [[physics]], '''self-organized criticality''' ('''SOC''') is a property of [[dynamical system]]s that have a [[critical phenomena|critical point]] as an [[attractor]]. Their macroscopic behavior thus displays the spatial or temporal [[scale invariance|scale-invariance]] characteristic of the [[critical point (physics)|critical point]] of a [[phase transition]], but without the need to tune control parameters to a precise value, because the system, effectively, tunes itself as it evolves towards criticality.<br />
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In physics, self-organized criticality (SOC) is a property of dynamical systems that have a critical point as an attractor. Their macroscopic behavior thus displays the spatial or temporal scale-invariance characteristic of the critical point of a phase transition, but without the need to tune control parameters to a precise value, because the system, effectively, tunes itself as it evolves towards criticality.<br />
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在物理学中,'''<font color="#ff8000"> 自组织临界性Self-organized criticality (SOC)</font>'''是动力系统的一种特性,动力系统有一个临界点作为'''<font color="#ff8000"> 吸引子Attractor</font>'''。它们的宏观行为因此显示了相变临界点的空间或时间尺度不变特性,但不需要把控制参数调整到一个精确的值,因为系统在趋向于临界状态时有效地自我调整。<br />
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The concept was put forward by [[Per Bak]], [[Chao Tang]] and [[Kurt Wiesenfeld]] ("BTW") in a paper<ref name=Bak1987><br />
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The concept was put forward by Per Bak, Chao Tang and Kurt Wiesenfeld ("BTW") in a paper<ref name=Bak1987><br />
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这个概念是由 Per Bak,Chao Tang 和 Kurt Wiesenfeld (“ BTW”)在一篇名为 bak1987的论文中提出的<br />
<br />
{{cite journal<br />
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{{cite journal<br />
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{引用期刊<br />
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| author = [[Per Bak|Bak, P.]], [[Chao Tang|Tang, C.]] and [[Kurt Wiesenfeld|Wiesenfeld, K.]]<br />
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| author = Bak, P., Tang, C. and Wiesenfeld, K.<br />
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作者 Bak,p. ,Tang,c. and Wiesenfeld,k。<br />
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| year = 1987<br />
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| year = 1987<br />
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1987年<br />
<br />
| title = Self-organized criticality: an explanation of 1/''f'' noise<br />
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| title = Self-organized criticality: an explanation of 1/f noise<br />
<br />
自组织临界性: 1 / f 噪音的解释<br />
<br />
| journal = [[Physical Review Letters]]<br />
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| journal = Physical Review Letters<br />
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物理评论快报<br />
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| volume = 59<br />
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| volume = 59<br />
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第59卷<br />
<br />
| issue = 4<br />
<br />
| issue = 4<br />
<br />
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<br />
| pages = 381&ndash;384<br />
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| pages = 381&ndash;384<br />
<br />
381-- 384<br />
<br />
| doi = 10.1103/PhysRevLett.59.381<br />
<br />
| doi = 10.1103/PhysRevLett.59.381<br />
<br />
10.1103 / physrvlett. 59.381<br />
<br />
| pmid = 10035754<br />
<br />
| pmid = 10035754<br />
<br />
10035754<br />
<br />
| bibcode=1987PhRvL..59..381B<br />
<br />
| bibcode=1987PhRvL..59..381B<br />
<br />
| bibcode 1987PhRvL. . 59. . 381 b<br />
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}}<br />
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}}<br />
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}}<br />
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Papercore summary: [https://archive.is/20130704122906/http://papercore.org/Bak1987 http://papercore.org/Bak1987].</ref> <br />
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Papercore summary: [https://archive.is/20130704122906/http://papercore.org/Bak1987 http://papercore.org/Bak1987].</ref> <br />
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论文摘要: [ https://archive.is/20130704122906/http://Papercore.org/bak1987 http://Papercore.org/bak1987] / 参考<br />
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published in 1987 in ''[[Physical Review Letters]]'', and is considered to be one of the mechanisms by which [[complexity]]<ref name=Bak1995><br />
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published in 1987 in Physical Review Letters, and is considered to be one of the mechanisms by which complexity<ref name=Bak1995><br />
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1987年发表在《物理评论快报》上,被认为是复杂性的机制之一<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[Per Bak|Bak, P.]], and [[Maya Paczuski|Paczuski, M.]]<br />
<br />
| author = Bak, P., and Paczuski, M.<br />
<br />
作者 Bak,p,and Paczuski,m。<br />
<br />
| year = 1995<br />
<br />
| year = 1995<br />
<br />
1995年<br />
<br />
| title = Complexity, contingency, and criticality<br />
<br />
| title = Complexity, contingency, and criticality<br />
<br />
| 标题复杂性、偶然性和临界性<br />
<br />
| journal =Proc Natl Acad Sci U S A <br />
<br />
| journal =Proc Natl Acad Sci U S A <br />
<br />
美国科学促进协会<br />
<br />
| volume = 92<br />
<br />
| volume = 92<br />
<br />
第92卷<br />
<br />
| pages = 6689&ndash;6696<br />
<br />
| pages = 6689&ndash;6696<br />
<br />
6689-- 6696<br />
<br />
| pmid = 11607561<br />
<br />
| pmid = 11607561<br />
<br />
11607561<br />
<br />
| doi = 10.1073/pnas.92.15.6689<br />
<br />
| doi = 10.1073/pnas.92.15.6689<br />
<br />
10.1073 / pnas. 92.15.6689<br />
<br />
| issue = 15<br />
<br />
| issue = 15<br />
<br />
第15期<br />
<br />
| pmc = 41396<br />
<br />
| pmc = 41396<br />
<br />
41396<br />
<br />
|bibcode = 1995PNAS...92.6689B }}</ref> arises in nature. Its concepts have been applied across fields as diverse as [[geophysics]],<ref name=SmalleyTurcotteSolla85><br />
<br />
|bibcode = 1995PNAS...92.6689B }}</ref> arises in nature. Its concepts have been applied across fields as diverse as geophysics,<ref name=SmalleyTurcotteSolla85><br />
<br />
| bibcode 1995PNAS... 92.6689 b } / ref 在自然界中出现。它的概念已经被应用于各个领域,比如地球物理学,参考名称 smalleyturcottesolla85<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
|author1=Smalley, R. F., Jr. |author2=Turcotte, D. L. |author3=Solla, S. A. | year = 1985<br />
<br />
|author1=Smalley, R. F., Jr. |author2=Turcotte, D. L. |author3=Solla, S. A. | year = 1985<br />
<br />
1 Smalley,r. f. ,jr. | author2 Turcotte,d. l. | author3 Solla,s. a.1985年<br />
<br />
| title = A renormalization group approach to the stick-slip behavior of faults<br />
<br />
| title = A renormalization group approach to the stick-slip behavior of faults<br />
<br />
| 题目: 断层粘滑行为的重整化群方法<br />
<br />
| journal = Journal of Geophysical Research<br />
<br />
| journal = Journal of Geophysical Research<br />
<br />
地球物理研究期刊<br />
<br />
| bibcode = 1985JGR....90.1894S<br />
<br />
| bibcode = 1985JGR....90.1894S<br />
<br />
1985JGR... 90.1894 s<br />
<br />
| doi = 10.1029/JB090iB02p01894<br />
<br />
| doi = 10.1029/JB090iB02p01894<br />
<br />
| doi 10.1029 / JB090iB02p01894<br />
<br />
| volume = 90<br />
<br />
| volume = 90<br />
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| 第二期<br />
<br />
| pages = 1894<br />
<br />
| pages = 1894<br />
<br />
1894页<br />
<br />
|url=https://semanticscholar.org/paper/6776d17957204c198e278bda98c935ab1cf8f22b }}</ref> [[physical cosmology]], [[evolutionary biology]] and [[ecology]], [[bio-inspired computing]] and [[optimization (mathematics)]], [[economics]], [[quantum gravity]], [[sociology]], [[solar physics]], [[plasma physics]], [[neurobiology]]<ref name=LinkenkaerHansen2001><br />
<br />
|url=https://semanticscholar.org/paper/6776d17957204c198e278bda98c935ab1cf8f22b }}</ref> physical cosmology, evolutionary biology and ecology, bio-inspired computing and optimization (mathematics), economics, quantum gravity, sociology, solar physics, plasma physics, neurobiology<ref name=LinkenkaerHansen2001><br />
<br />
[ https://semanticscholar.org/paper/6776d17957204c198e278bda98c935ab1cf8f22b ] / ref 物理宇宙学,进化生物学和生态学,生物启发计算和优化(数学) ,经济学,量子引力,社会学,太阳物理学,等离子物理学,神经生物学参考名称 linkenkaerhansen2001<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
|author1=K. Linkenkaer-Hansen |author2=V. V. Nikouline |author3=J. M. Palva |author4=R. J. Ilmoniemi. |last-author-amp=yes | year = 2001<br />
<br />
|author1=K. Linkenkaer-Hansen |author2=V. V. Nikouline |author3=J. M. Palva |author4=R. J. Ilmoniemi. |last-author-amp=yes | year = 2001<br />
<br />
1 k.Linkenkaer-hansen | author2 v.3 j.4 r.作者: j. Ilmoniemi。最后一个作者2001年<br />
<br />
| title = Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations<br />
<br />
| title = Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations<br />
<br />
人类大脑振荡中的长程时间相关性和标度行为<br />
<br />
| journal = J. Neurosci.<br />
<br />
| journal = J. Neurosci.<br />
<br />
作者: j. Neurosci。<br />
<br />
| volume = 21<br />
<br />
| volume = 21<br />
<br />
第21卷<br />
<br />
| pages = 1370&ndash;1377<br />
<br />
| pages = 1370&ndash;1377<br />
<br />
1370-- 1377<br />
<br />
| pmid = 11160408<br />
<br />
| pmid = 11160408<br />
<br />
11160408<br />
<br />
| issue = 4<br />
<br />
| issue = 4<br />
<br />
第四期<br />
<br />
|doi=10.1523/JNEUROSCI.21-04-01370.2001 |pmc=6762238 }}</ref><ref name=Beggs2003><br />
<br />
|doi=10.1523/JNEUROSCI.21-04-01370.2001 |pmc=6762238 }}</ref><ref name=Beggs2003><br />
<br />
| doi 10.1523 / jneurosci. 21-04-01370.2001 | pmc 6762238} / ref name begs2003<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
|author1=J. M. Beggs |author2=D. Plenz<br />
<br />
|author1=J. M. Beggs |author2=D. Plenz<br />
<br />
1 j.2 d.Plenz<br />
<br />
|lastauthoramp=yes | year = 2006<br />
<br />
|lastauthoramp=yes | year = 2006<br />
<br />
2006年<br />
<br />
| title = Neuronal Avalanches in Neocortical Circuits<br />
<br />
| title = Neuronal Avalanches in Neocortical Circuits<br />
<br />
新皮层神经回路中的神经雪崩<br />
<br />
| journal = J. Neurosci.<br />
<br />
| journal = J. Neurosci.<br />
<br />
作者: j. Neurosci。<br />
<br />
| volume = 23<br />
<br />
| volume = 23<br />
<br />
第23卷<br />
<br />
|issue=35<br />
<br />
|issue=35<br />
<br />
第35期<br />
<br />
|pages=11167–77<br />
<br />
|pages=11167–77<br />
<br />
第11167-77页<br />
<br />
|doi=10.1523/JNEUROSCI.23-35-11167.2003<br />
<br />
|doi=10.1523/JNEUROSCI.23-35-11167.2003<br />
<br />
10.1523 / jneurosci. 23-35-11167.2003<br />
<br />
|pmid=14657176<br />
<br />
|pmid=14657176<br />
<br />
14657176<br />
<br />
|pmc=6741045<br />
<br />
|pmc=6741045<br />
<br />
6741045<br />
<br />
}}</ref><ref name=Chialvo2004><br />
<br />
}}</ref><ref name=Chialvo2004><br />
<br />
} / ref ref name chialvo2004<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author =Chialvo, D. R.<br />
<br />
| author =Chialvo, D. R.<br />
<br />
作者 Chialvo,d. r。<br />
<br />
| year = 2004<br />
<br />
| year = 2004<br />
<br />
2004年<br />
<br />
| title = Critical brain networks<br />
<br />
| title = Critical brain networks<br />
<br />
关键的大脑网络<br />
<br />
| journal = Physica A<br />
<br />
| journal = Physica A<br />
<br />
物理学杂志 a<br />
<br />
| volume = 340<br />
<br />
| volume = 340<br />
<br />
第340卷<br />
<br />
| issue =4<br />
<br />
| issue =4<br />
<br />
第四期<br />
<br />
| pages = 756&ndash;765<br />
<br />
| pages = 756&ndash;765<br />
<br />
756-- 765<br />
<br />
| doi = 10.1016/j.physa.2004.05.064<br />
<br />
| doi = 10.1016/j.physa.2004.05.064<br />
<br />
10.1016 / j.physa. 2004.05.064<br />
<br />
|arxiv = cond-mat/0402538 |bibcode = 2004PhyA..340..756R | author-link = Dante R. Chialvo<br />
<br />
|arxiv = cond-mat/0402538 |bibcode = 2004PhyA..340..756R | author-link = Dante R. Chialvo<br />
<br />
| arxiv cond-mat / 0402538 | bibcode 2004PhyA. . 340. . 756 r | author-link Dante r. Chialvo<br />
<br />
}}</ref> and others.<br />
<br />
}}</ref> and others.<br />
<br />
} / ref and others.<br />
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SOC is typically observed in slowly driven [[non-equilibrium thermodynamics|non-equilibrium]] systems with many [[degrees of freedom (physics and chemistry)|degrees of freedom]] and strongly [[nonlinearity|nonlinear]] dynamics. Many individual examples have been identified since BTW's original paper, but to date there is no known set of general characteristics that ''guarantee'' a system will display SOC.<br />
<br />
SOC is typically observed in slowly driven non-equilibrium systems with many degrees of freedom and strongly nonlinear dynamics. Many individual examples have been identified since BTW's original paper, but to date there is no known set of general characteristics that guarantee a system will display SOC.<br />
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'''<font color="#ff8000"> SOC</font>'''是典型的多自由度、强非线性动力学的缓慢驱动非平衡系统。自从 BTW 的原始论文以来,已经确定了许多单独的例子,但是到目前为止还没有一组已知的一般特征来保证一个系统将显示 '''<font color="#ff8000"> SOC</font>'''。<br />
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== Overview 概览==<br />
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Self-organized criticality is one of a number of important discoveries made in [[statistical physics]] and related fields over the latter half of the 20th century, discoveries which relate particularly to the study of [[complexity]] in nature. For example, the study of [[cellular automata]], from the early discoveries of [[Stanislaw Ulam]] and [[John von Neumann]] through to [[John Horton Conway|John Conway]]'s [[Conway's Game of Life|Game of Life]] and the extensive work of [[Stephen Wolfram]], made it clear that complexity could be generated as an [[emergence|emergent]] feature of extended systems with simple local interactions. Over a similar period of time, [[Benoît Mandelbrot]]'s large body of work on [[fractals]] showed that much complexity in nature could be described by certain ubiquitous mathematical laws, while the extensive study of [[phase transition]]s carried out in the 1960s and 1970s showed how [[scale invariance|scale invariant]] phenomena such as [[fractals]] and [[power law]]s emerged at the [[critical point (physics)|critical point]] between phases.<br />
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Self-organized criticality is one of a number of important discoveries made in statistical physics and related fields over the latter half of the 20th century, discoveries which relate particularly to the study of complexity in nature. For example, the study of cellular automata, from the early discoveries of Stanislaw Ulam and John von Neumann through to John Conway's Game of Life and the extensive work of Stephen Wolfram, made it clear that complexity could be generated as an emergent feature of extended systems with simple local interactions. Over a similar period of time, Benoît Mandelbrot's large body of work on fractals showed that much complexity in nature could be described by certain ubiquitous mathematical laws, while the extensive study of phase transitions carried out in the 1960s and 1970s showed how scale invariant phenomena such as fractals and power laws emerged at the critical point between phases.<br />
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'''<font color="#ff8000"> 自组织临界性Self-organized criticality(SOC)</font>'''是20世纪下半叶统计物理学及相关领域的众多重要发现之一,这些发现尤其与研究自然界的复杂性有关。例如,元胞自动机的研究---- 从 Stanislaw Ulam 和约翰·冯·诺伊曼的早期发现到 John Conway 的生命游戏和 Stephen Wolfram 的大量工作---- 清楚地表明,复杂性可以作为具有简单局部相互作用的扩展系统的一个涌现特征而产生。在相似的时间段内,beno t Mandelbrot 关于分形的大量工作表明,自然界的许多复杂性可以用某些无处不在的数学定律来描述,而在20世纪60年代和70年代对相变的广泛研究表明,诸如分形和幂律等尺度不变现象是如何出现在相变的临界点上的。<br />
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The term ''self-organized criticality'' was firstly introduced by [[Per Bak|Bak]], [[Chao Tang|Tang]] and [[Kurt Wiesenfeld|Wiesenfeld]]'s 1987 paper, which clearly linked together those factors: a simple [[cellular automaton]] was shown to produce several characteristic features observed in natural complexity ([[fractal]] geometry, [[pink noise|pink (1/f) noise]] and [[power law]]s) in a way that could be linked to [[critical point (physics)|critical-point phenomena]]. Crucially, however, the paper emphasized that the complexity observed emerged in a robust manner that did not depend on finely tuned details of the system: variable parameters in the model could be changed widely without affecting the emergence of critical behavior: hence, ''[[self-organized]]'' criticality. Thus, the key result of BTW's paper was its discovery of a mechanism by which the emergence of complexity from simple local interactions could be ''spontaneous''&mdash;and therefore plausible as a source of natural complexity&mdash;rather than something that was only possible in artificial situations in which control parameters are tuned to precise critical values. The publication of this research sparked considerable interest from both theoreticians and experimentalists, producing some of the most cited papers in the scientific literature.<br />
<br />
The term self-organized criticality was firstly introduced by Bak, Tang and Wiesenfeld's 1987 paper, which clearly linked together those factors: a simple cellular automaton was shown to produce several characteristic features observed in natural complexity (fractal geometry, pink (1/f) noise and power laws) in a way that could be linked to critical-point phenomena. Crucially, however, the paper emphasized that the complexity observed emerged in a robust manner that did not depend on finely tuned details of the system: variable parameters in the model could be changed widely without affecting the emergence of critical behavior: hence, self-organized criticality. Thus, the key result of BTW's paper was its discovery of a mechanism by which the emergence of complexity from simple local interactions could be spontaneous&mdash;and therefore plausible as a source of natural complexity&mdash;rather than something that was only possible in artificial situations in which control parameters are tuned to precise critical values. The publication of this research sparked considerable interest from both theoreticians and experimentalists, producing some of the most cited papers in the scientific literature.<br />
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'''<font color="#ff8000"> 自组织临界性Self-organized criticality(SOC)</font>'''这个术语最早由 Bak,Tang 和 Wiesenfeld 在1987年的论文中提出,这篇论文将这些因素清楚地联系在一起: 一个简单的细胞自动机被证明可以产生在自然复杂性中观察到的几个特征(分形几何、粉红噪声和幂律) ,这种方式可以与临界点现象联系起来。然而,关键的是,这篇论文强调,观察到的复杂性是以一种强有力的方式出现的,并不依赖于系统精细调整的细节: 模型中的可变参数可以被广泛改变,而不会影响临界行为的涌现: 因此,具有自组织临界性。因此,BTW 论文的关键结果是发现了一种机制,通过这种机制,从简单的局部相互作用中产生的复杂性可能是自发的---- 因此是合理的自然复杂性的来源---- 而不是只有在控制参数调整到精确的临界值的人工情况下才可能出现的东西。这项研究的发表引起了理论家和实验家的极大兴趣,产生了一些在科学文献中被引用最多的论文。<br />
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Due to BTW's metaphorical visualization of their model as a "[[Bak–Tang–Wiesenfeld sandpile|sandpile]]" on which new sand grains were being slowly sprinkled to cause "avalanches", much of the initial experimental work tended to focus on examining real avalanches in [[granular matter]], the most famous and extensive such study probably being the Oslo ricepile experiment{{Citation needed|date=March 2018}}. Other experiments include those carried out on magnetic-domain patterns, the [[Barkhausen effect]] and vortices in [[superconductors]]. <br />
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Due to BTW's metaphorical visualization of their model as a "sandpile" on which new sand grains were being slowly sprinkled to cause "avalanches", much of the initial experimental work tended to focus on examining real avalanches in granular matter, the most famous and extensive such study probably being the Oslo ricepile experiment. Other experiments include those carried out on magnetic-domain patterns, the Barkhausen effect and vortices in superconductors. <br />
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由于 BTW 将他们的模型比喻为一个“沙堆” ,在沙堆上缓慢地喷洒新的沙粒以引起“雪崩” ,所以最初的实验工作主要集中在研究颗粒物质中的真实雪崩,其中最著名和最广泛的研究可能是奥斯陆地震实验。其他实验还包括在磁畴图案、超导体中的巴克豪森效应和涡旋上进行的实验。<br />
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Early theoretical work included the development of a variety of alternative SOC-generating dynamics distinct from the BTW model, attempts to prove model properties analytically (including calculating the [[critical exponent]]s<ref name=Tang1988a><br />
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Early theoretical work included the development of a variety of alternative SOC-generating dynamics distinct from the BTW model, attempts to prove model properties analytically (including calculating the critical exponents<ref name=Tang1988a><br />
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早期的理论工作包括开发各种不同于 BTW 模型的 soc 生成动力学,试图解析证明模型的性质(包括计算临界指数,参见 tang1988a<br />
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{{cite journal<br />
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{{cite journal<br />
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{引用期刊<br />
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| author = [[Chao Tang|Tang, C.]] and [[Per Bak|Bak, P.]]<br />
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| author = Tang, C. and Bak, P.<br />
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作者 Tang,c. and Bak,p。<br />
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| year = 1988<br />
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| year = 1988<br />
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1988年<br />
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| title = Critical exponents and scaling relations for self-organized critical phenomena<br />
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| title = Critical exponents and scaling relations for self-organized critical phenomena<br />
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自组织临界现象的临界指数和标度关系<br />
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| journal = [[Physical Review Letters]]<br />
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| journal = Physical Review Letters<br />
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物理评论快报<br />
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| doi = 10.1103/PhysRevLett.60.2347<br />
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| doi = 10.1103/PhysRevLett.60.2347<br />
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10.1103 / physrvlett. 60.2347<br />
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| bibcode= 1988PhRvL..60.2347T<br />
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| bibcode= 1988PhRvL..60.2347T<br />
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1988 / phrvl. 60.2347 t<br />
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/ ref / name tang1988b<br />
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{{cite journal<br />
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{{cite journal<br />
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{引用期刊<br />
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| author = [[Chao Tang|Tang, C.]] and [[Per Bak|Bak, P.]]<br />
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| author = Tang, C. and Bak, P.<br />
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作者 Tang,c. and Bak,p。<br />
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| year = 1988<br />
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| year = 1988<br />
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1988年<br />
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| title = Mean field theory of self-organized critical phenomena<br />
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| title = Mean field theory of self-organized critical phenomena<br />
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自组织临界现象的平均场理论<br />
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| journal = [[Journal of Statistical Physics]]<br />
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| journal = Journal of Statistical Physics<br />
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统计物理学杂志<br />
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| bibcode= 1988JSP....51..797T<br />
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1988JSP... 51. . 797 t<br />
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| url = https://zenodo.org/record/1232502<br />
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</ref>), and examination of the conditions necessary for SOC to emerge. One of the important issues for the latter investigation was whether [[conservation of energy]] was required in the local dynamical exchanges of models: the answer in general is no, but with (minor) reservations, as some exchange dynamics (such as those of BTW) do require local conservation at least on average. In the long term, key theoretical issues yet to be resolved include the calculation of the possible [[universality class]]es of SOC behavior and the question of whether it is possible to derive a general rule for determining if an arbitrary [[algorithm]] displays SOC.<br />
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</ref>), and examination of the conditions necessary for SOC to emerge. One of the important issues for the latter investigation was whether conservation of energy was required in the local dynamical exchanges of models: the answer in general is no, but with (minor) reservations, as some exchange dynamics (such as those of BTW) do require local conservation at least on average. In the long term, key theoretical issues yet to be resolved include the calculation of the possible universality classes of SOC behavior and the question of whether it is possible to derive a general rule for determining if an arbitrary algorithm displays SOC.<br />
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/ ref) ,以及研究出现 '''<font color="#ff8000"> SOC</font>'''的必要条件。后一项研究的一个重要问题是,在局部动态交换模型时是否需要能量守恒: 一般的答案是否定的,但有一些保留意见,因为一些交换动力学(如 BTW 的动态)确实需要局部至少平均的能量守恒。从长远来看,有待解决的关键理论问题包括 '''<font color="#ff8000"> SOC</font>''' 行为可能的普适性类的计算,以及是否有可能推导出一个确定任意算法是否显示 '''<font color="#ff8000"> SOC</font>''' 的一般规则的问题。<br />
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Alongside these largely lab-based approaches, many other investigations have centered around large-scale natural or social systems that are known (or suspected) to display [[scale invariance|scale-invariant]] behavior. Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: [[earthquakes]] (which, long before SOC was discovered, were known as a source of scale-invariant behavior such as the [[Gutenberg–Richter law]] describing the statistical distribution of earthquake size, and the [[Aftershock|Omori law]] describing the frequency of aftershocks<ref name=TurcotteSmalleySolla85><br />
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Alongside these largely lab-based approaches, many other investigations have centered around large-scale natural or social systems that are known (or suspected) to display scale-invariant behavior. Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: earthquakes (which, long before SOC was discovered, were known as a source of scale-invariant behavior such as the Gutenberg–Richter law describing the statistical distribution of earthquake size, and the Omori law describing the frequency of aftershocks<ref name=TurcotteSmalleySolla85><br />
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除了这些大部分基于实验室的方法,许多其他的研究都集中在大规模的自然或社会系统上,这些系统已经知道(或怀疑)表现出尺度不变的行为。虽然这些方法并不总是受到研究对象专家的欢迎(至少最初是这样) ,但 '''<font color="#ff8000"> SOC</font>''' 已经成为解释一些自然现象的强有力的候选者,包括: 地震(早在 '''<font color="#ff8000"> SOC</font>''' 被发现之前,地震就被认为是尺度不变行为的来源,例如描述地震大小统计分布的古腾堡-里克特定律,以及描述余震频率的描述余震的 Omori 定律,命名为 turcottesmalleysolla85<br />
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{引用期刊<br />
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|author1=Turcotte, D. L. |author2=Smalley, R. F., Jr. |author3=Solla, S. A. | year = 1985<br />
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|author1=Turcotte, D. L. |author2=Smalley, R. F., Jr. |author3=Solla, S. A. | year = 1985<br />
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1 Turcotte,D.l. | author2 Smalley,r. f. ,jr. | author3 Solla,s. a.1985年<br />
<br />
| title = Collapse of loaded fractal trees<br />
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| title = Collapse of loaded fractal trees<br />
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负载分形树的崩溃<br />
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| journal = Nature <br />
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| journal = Nature <br />
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自然》杂志<br />
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| doi= 10.1038/313671a0<br />
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| doi= 10.1038/313671a0<br />
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10.1038 / 313671a0<br />
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| volume = 313<br />
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| volume = 313<br />
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第313卷<br />
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| issue = 6004<br />
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第6004期<br />
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| pages = 671–672|bibcode = 1985Natur.313..671T <br />
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| 第671-672页 | bibcode 1985 / natur. 313. . 671 t<br />
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}}</ref><ref name=SmalleyTurcotteSolla85 />); [[solar flares]]; fluctuations in economic systems such as [[financial markets]] (references to SOC are common in [[econophysics]]); [[landscape formation]]; [[forest fires]]; [[landslides]]; [[epidemics]]; neuronal avalanches in the cortex;<ref name="Beggs2003" /><ref name=Poil2012><br />
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}}</ref>); solar flares; fluctuations in economic systems such as financial markets (references to SOC are common in econophysics); landscape formation; forest fires; landslides; epidemics; neuronal avalanches in the cortex;<ref name=Poil2012><br />
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太阳耀斑; 经济系统的波动,比如金融市场(经济物理学中经常提到 SOC) ; 景观形成; 森林火灾; 滑坡; 流行病; 大脑皮层的神经雪崩; 参考名为 poil2012<br />
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{引用期刊<br />
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|date=Jul 2012<br />
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2012年7月<br />
<br />
|author1=Poil, SS |author2=Hardstone, R |author3=Mansvelder, HD |author4=Linkenkaer-Hansen, K | title = Critical-state dynamics of avalanches and oscillations jointly emerge from balanced excitation/inhibition in neuronal networks<br />
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|author1=Poil, SS |author2=Hardstone, R |author3=Mansvelder, HD |author4=Linkenkaer-Hansen, K | title = Critical-state dynamics of avalanches and oscillations jointly emerge from balanced excitation/inhibition in neuronal networks<br />
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1 Poil,SS | author2 Hardstone,r | author3 mansveder,HD | author4 Linkenkaer-Hansen,k | title 雪崩和振荡的临界状态动力学联合出现在神经元网络的平衡兴奋 / 抑制中<br />
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| volume = 32<br />
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| doi = 10.1523/JNEUROSCI.5990-11.2012<br />
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| doi = 10.1523/JNEUROSCI.5990-11.2012<br />
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| doi 10.1523 / jneurosci. 5990-11.2012<br />
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| journal = Journal of Neuroscience<br />
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| journal = Journal of Neuroscience<br />
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神经科学杂志<br />
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| pmc=3553543<br />
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3553543<br />
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}}</ref> 1/f noise in the amplitude of electrophysiological signals;<ref name=LinkenkaerHansen2001 /> and [[biological evolution]] (where SOC has been invoked, for example, as the dynamical mechanism behind the theory of "[[punctuated equilibrium|punctuated equilibria]]" put forward by [[Niles Eldredge]] and [[Stephen Jay Gould]]). These "applied" investigations of SOC have included both modelling (either developing new models or adapting existing ones to the specifics of a given natural system) and extensive data analysis to determine the existence and/or characteristics of natural scaling laws.<br />
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}}</ref> 1/f noise in the amplitude of electrophysiological signals; and biological evolution (where SOC has been invoked, for example, as the dynamical mechanism behind the theory of "punctuated equilibria" put forward by Niles Eldredge and Stephen Jay Gould). These "applied" investigations of SOC have included both modelling (either developing new models or adapting existing ones to the specifics of a given natural system) and extensive data analysis to determine the existence and/or characteristics of natural scaling laws.<br />
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{} / ref 电生理信号振幅的1 / f 噪声,以及生物进化(其中 SOC 已被调用,例如,作为背后的动力机制的理论“间断平衡”由 Niles Eldredge 和史蒂芬·古尔德提出)。对SOC的这些”应用”研究既包括建模(开发新模型或使现有模型适应特定自然系统的具体情况) ,也包括广泛的数据分析,以确定是否存在和 / 或具有自然幂率的特点。<br />
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In addition, SOC has been applied to computational algorithms. Recently, it has been found that the avalanches from an SOC process, like the BTW model, make effective patterns in a random search for optimal solutions on graphs.<ref name=Hoffmann2018><br />
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In addition, SOC has been applied to computational algorithms. Recently, it has been found that the avalanches from an SOC process, like the BTW model, make effective patterns in a random search for optimal solutions on graphs.<ref name=Hoffmann2018><br />
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此外,SOC 已经应用于计算算法。最近,人们发现来自 SOC 过程的雪崩,如 BTW 模型,在图的最优解的随机搜索中形成有效的模式。 参考名称 hoffmann2018<br />
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{引用期刊<br />
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| author = [[H. Hoffmann|Hoffmann, H.]] and [[D. W. Payton|Payton, D. W.]]<br />
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| author = Hoffmann, H. and Payton, D. W.<br />
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作者: 霍夫曼 h. 和佩顿 d. w。<br />
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| year = 2018<br />
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| year = 2018<br />
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<br />
| title = Optimization by Self-Organized Criticality<br />
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| title = Optimization by Self-Organized Criticality<br />
<br />
最佳化作者: 自组织临界性<br />
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| journal = [[Scientific Reports]]<br />
<br />
| journal = Scientific Reports<br />
<br />
科学报告<br />
<br />
| volume = 8<br />
<br />
| volume = 8<br />
<br />
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| issue = 1<br />
<br />
| issue = 1<br />
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<br />
| pages = 2358<br />
<br />
| pages = 2358<br />
<br />
2358页<br />
<br />
| doi=10.1038/s41598-018-20275-7<br />
<br />
| doi=10.1038/s41598-018-20275-7<br />
<br />
10.1038 / s41598-018-20275-7<br />
<br />
| pmid = 29402956<br />
<br />
| pmid = 29402956<br />
<br />
29402956<br />
<br />
| pmc = 5799203<br />
<br />
| pmc = 5799203<br />
<br />
5799203<br />
<br />
| bibcode = 2018NatSR...8.2358H<br />
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| bibcode = 2018NatSR...8.2358H<br />
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| bibcode 2018NatSR... 8.2358 h<br />
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}}</ref> <br />
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}}</ref> <br />
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{} / ref<br />
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An example of such an optimization problem is [[graph coloring]]. The SOC process apparently helps the optimization from getting stuck in a [[local optimum]] without the use of any [[Simulated_annealing|annealing]] scheme, as suggested by previous work on [[extremal optimization]].<br />
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An example of such an optimization problem is graph coloring. The SOC process apparently helps the optimization from getting stuck in a local optimum without the use of any annealing scheme, as suggested by previous work on extremal optimization.<br />
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图着色就是这种最佳化问题的一个例子。'''<font color="#ff8000"> SOC</font>''' 过程显然有助于避免优化陷入局部最优,而无需使用任何以前的极值优化工作所建议的退火方案。<br />
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The recent excitement generated by [[scale-free networks]] has raised some interesting new questions for SOC-related research: a number of different SOC models have been shown to generate such networks as an emergent phenomenon, as opposed to the simpler models proposed by network researchers where the network tends to be assumed to exist independently of any physical space or dynamics. While many single phenomena have been shown to exhibit scale-free properties over narrow ranges, a phenomenon offering by far a larger amount of data is solvent-accessible surface areas in globular proteins.<ref name=Moret2007><br />
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The recent excitement generated by scale-free networks has raised some interesting new questions for SOC-related research: a number of different SOC models have been shown to generate such networks as an emergent phenomenon, as opposed to the simpler models proposed by network researchers where the network tends to be assumed to exist independently of any physical space or dynamics. While many single phenomena have been shown to exhibit scale-free properties over narrow ranges, a phenomenon offering by far a larger amount of data is solvent-accessible surface areas in globular proteins.<ref name=Moret2007><br />
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'''<font color="#ff8000"> 无标度网络Scale-free networks</font>'''最近引起的兴奋为 '''<font color="#ff8000"> SOC</font>'''相关研究提出了一些有趣的新问题: 许多不同的 '''<font color="#ff8000"> SOC</font>'''模型已经被证明是作为一种涌现现象产生这样的网络,而不是网络研究人员提出的更简单的模型,其中网络往往被假定独立于任何物理空间或动力学存在。虽然许多单一现象已被证明在狭窄的范围内表现出无标度特性,但是到目前为止提供了大量数据的现象是球状蛋白质中溶剂可及的表面区域。 参考名称 moret2007<br />
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{引用期刊<br />
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| author = [[M. A. Moret|Moret, M. A.]] and [[G. Zebende|Zebende, G.]]<br />
<br />
| author = Moret, M. A. and Zebende, G.<br />
<br />
作者: Moret,M.a. and Zebende,g。<br />
<br />
| year = 2007<br />
<br />
| year = 2007<br />
<br />
2007年<br />
<br />
| title = Amino acid hydrophobicity and accessible surface area<br />
<br />
| title = Amino acid hydrophobicity and accessible surface area<br />
<br />
氨基酸疏水性和可达表面积<br />
<br />
| journal = [[Phys. Rev. E]]<br />
<br />
| journal = Phys. Rev. E<br />
<br />
体育杂志。牧师。E<br />
<br />
| volume = 75<br />
<br />
| volume = 75<br />
<br />
第75卷<br />
<br />
| issue = 1<br />
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| pages = 011920<br />
<br />
| pages = 011920<br />
<br />
011920页<br />
<br />
| doi=10.1103/PhysRevE.75.011920<br />
<br />
| doi=10.1103/PhysRevE.75.011920<br />
<br />
10.1103 / physarve. 75.011920<br />
<br />
| pmid = 17358197<br />
<br />
| pmid = 17358197<br />
<br />
17358197<br />
<br />
| bibcode = 2007PhRvE..75a1920M<br />
<br />
| bibcode = 2007PhRvE..75a1920M<br />
<br />
2007 / phrve. . 75 / a1920M<br />
<br />
}}</ref><br />
<br />
}}</ref><br />
<br />
{} / ref<br />
<br />
These studies quantify the differential geometry of proteins, and resolve many evolutionary puzzles regarding the biological emergence of complexity.<ref name=Phillips2014><br />
<br />
These studies quantify the differential geometry of proteins, and resolve many evolutionary puzzles regarding the biological emergence of complexity.<ref name=Phillips2014><br />
<br />
这些研究量化了蛋白质的微分几何,并解决了许多关于生物复杂性出现的进化之谜<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = Phillips, J. C.<br />
<br />
| author = Phillips, J. C.<br />
<br />
作者: 菲利普斯。<br />
<br />
| year = 2014<br />
<br />
| year = 2014<br />
<br />
2014年<br />
<br />
| title = Fractals and self-organized criticality in proteins<br />
<br />
| title = Fractals and self-organized criticality in proteins<br />
<br />
标题蛋白质中的分形和自组织临界性<br />
<br />
| journal = Physica A<br />
<br />
| journal = Physica A<br />
<br />
物理学杂志 a<br />
<br />
| volume = 415<br />
<br />
| volume = 415<br />
<br />
第415卷<br />
<br />
| pages = 440–448 <br />
<br />
| pages = 440–448 <br />
<br />
第440-448页<br />
<br />
| doi=10.1016/j.physa.2014.08.034<br />
<br />
| doi=10.1016/j.physa.2014.08.034<br />
<br />
| doi 10.1016 / j.physa. 2014.08.034<br />
<br />
| bibcode = 2014PhyA..415..440P<br />
<br />
| bibcode = 2014PhyA..415..440P<br />
<br />
| bibcode 2014PhyA. . 415. . 440 p<br />
<br />
| author-link = J. C. Phillips<br />
<br />
| author-link = J. C. Phillips<br />
<br />
作者链接 J.c. 菲利普斯<br />
<br />
}}</ref><br />
<br />
}}</ref><br />
<br />
{} / ref<br />
<br />
<br />
<br />
<br />
<br />
Despite the considerable interest and research output generated from the SOC hypothesis, there remains no general agreement with regards to its mechanisms in abstract mathematical form. Bak Tang and Wiesenfeld based their hypothesis on the behavior of their sandpile model.<ref name=Bak1987/> However,<br />
<br />
Despite the considerable interest and research output generated from the SOC hypothesis, there remains no general agreement with regards to its mechanisms in abstract mathematical form. Bak Tang and Wiesenfeld based their hypothesis on the behavior of their sandpile model. However,<br />
<br />
尽管 SOC 假说引起了相当大的兴趣和研究成果,但是关于其抽象数学形式的机制仍然没有普遍的一致性。Bak Tang 和 Wiesenfeld 基于他们的沙堆模型的行为建立了他们的假设。然而,<br />
<br />
it has been argued that this model would actually generate 1/f<sup>2</sup> noise rather than 1/f noise.<ref name=Jensen1989><br />
<br />
it has been argued that this model would actually generate 1/f<sup>2</sup> noise rather than 1/f noise.<ref name=Jensen1989><br />
<br />
有人认为,这种模型实际上会产生1 / f sup 2 / sup 噪声而不是1 / f 噪声<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[H. J. Jensen|Jensen, H. J.]], [[K. Christensen|Christensen, K.]] and [[H. C. Fogedby|Fogedby, H. C.]]<br />
<br />
| author = Jensen, H. J., Christensen, K. and Fogedby, H. C.<br />
<br />
作者 Jensen,h. j. ,Christensen,k. and fogeby,h. c。<br />
<br />
| year = 1989<br />
<br />
| year = 1989<br />
<br />
1989年<br />
<br />
| title = 1/f noise, distribution of lifetimes, and a pile of sand<br />
<br />
| title = 1/f noise, distribution of lifetimes, and a pile of sand<br />
<br />
标题1 / f 噪音,寿命分布,和一堆沙子<br />
<br />
| journal = [[Phys. Rev. B]]<br />
<br />
| journal = Phys. Rev. B<br />
<br />
体育杂志。牧师。B<br />
<br />
| volume = 40<br />
<br />
| volume = 40<br />
<br />
第40卷<br />
<br />
| issue = 10<br />
<br />
| issue = 10<br />
<br />
第10期<br />
<br />
| pages = 7425–7427<br />
<br />
| pages = 7425–7427<br />
<br />
第7425-7427页<br />
<br />
| doi=10.1103/physrevb.40.7425<br />
<br />
| doi=10.1103/physrevb.40.7425<br />
<br />
10.1103 / physirevb. 40.7425<br />
<br />
| pmid = 9991162<br />
<br />
| pmid = 9991162<br />
<br />
9991162<br />
<br />
|bibcode = 1989PhRvB..40.7425J }}<br />
<br />
|bibcode = 1989PhRvB..40.7425J }}<br />
<br />
1989 / phrvb. 40.7425 j }<br />
<br />
</ref><br />
<br />
</ref><br />
<br />
/ 参考<br />
<br />
This claim was based on untested scaling assumptions, and a more rigorous analysis showed that sandpile models <br />
<br />
This claim was based on untested scaling assumptions, and a more rigorous analysis showed that sandpile models <br />
<br />
这种说法是基于未经测试的比例假设,更严格的分析表明沙堆模型<br />
<br />
generally produce 1/f<sup>a</sup> spectra, with a<2. <ref name=Laurson2005><br />
<br />
generally produce 1/f<sup>a</sup> spectra, with a<2. <ref name=Laurson2005><br />
<br />
一般产生1 / f sup a / sup 光谱,其中 a < 2。参考名称 laurson2005<br />
<br />
{{cite journal |author1=Laurson, Lasse |author2=Alava, Mikko J. |author3=Zapperi, Stefano |title=Letter: Power spectra of self-organized critical sand piles |journal=Journal of Statistical Mechanics: Theory and Experiment |volume=0511 |id=L001 |date=15 September 2005 }}</ref><br />
<br />
</ref><br />
<br />
/ 参考<br />
<br />
Other simulation models were proposed later that could produce true 1/f noise,<ref name=Maslov1999><br />
<br />
Other simulation models were proposed later that could produce true 1/f noise,<ref name=Maslov1999><br />
<br />
其他模拟模型后来被提出,可以产生真正的1 / f 噪声,参考名称 maslov1999<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[S. Maslov|Maslov, S.]], [[C. Tang|Tang, C.]] and [[Y. –C. Zhang|Zhang, Y. - C.]]<br />
<br />
| author = Maslov, S., Tang, C. and Zhang, Y. - C.<br />
<br />
作者 Maslov,s. ,Tang,c. and Zhang,y。- c.<br />
<br />
| year = 1999<br />
<br />
| year = 1999<br />
<br />
1999年<br />
<br />
| title = 1/f noise in Bak-Tang-Wiesenfeld models on narrow stripes<br />
<br />
| title = 1/f noise in Bak-Tang-Wiesenfeld models on narrow stripes<br />
<br />
| 标题1 / f Bak-Tang-Wiesenfeld 窄条纹模型的噪音<br />
<br />
| journal = [[Phys. Rev. Lett.]]<br />
<br />
| journal = Phys. Rev. Lett.<br />
<br />
体育杂志。牧师。莱特。<br />
<br />
| volume = 83<br />
<br />
| volume = 83<br />
<br />
第83卷<br />
<br />
| issue = 12<br />
<br />
| issue = 12<br />
<br />
第12期<br />
<br />
| pages = 2449–2452<br />
<br />
| pages = 2449–2452<br />
<br />
2449-2452页<br />
<br />
| doi=10.1103/physrevlett.83.2449<br />
<br />
| doi=10.1103/physrevlett.83.2449<br />
<br />
10.1103 / physrvlett. 83.2449<br />
<br />
|arxiv = cond-mat/9902074 |bibcode = 1999PhRvL..83.2449M }}<br />
<br />
|arxiv = cond-mat/9902074 |bibcode = 1999PhRvL..83.2449M }}<br />
<br />
| arxiv cond-mat / 9902074 | bibcode 1999PhRvL. . 83.2449 m }<br />
<br />
</ref> and experimental sandpile models were observed to yield 1/f noise.<ref name=Frette1996><br />
<br />
</ref> and experimental sandpile models were observed to yield 1/f noise.<ref name=Frette1996><br />
<br />
/ ref 和实验沙堆模型被观察到产生1 / f 噪音。参考名称 frette1996<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[V.Frette|Frette, V.]], [[K. Christiansen|Christinasen, K.]], [[A. Malthe-Sørenssen|Malthe-Sørenssen, A.]], [[J. Feder|Feder, J]], [[T. Jøssang|Jøssang, T]] and [[P. Meakin|Meaken, P]]<br />
<br />
| author = Frette, V., Christinasen, K., Malthe-Sørenssen, A., Feder, J, Jøssang, T and Meaken, P<br />
<br />
| author = Frette, V., Christinasen, K., Malthe-Sørenssen, A., Feder, J, Jøssang, T and Meaken, P<br />
<br />
| year = 1996<br />
<br />
| year = 1996<br />
<br />
1996年<br />
<br />
| title = Avalanche dynamics in a pile of rice<br />
<br />
| title = Avalanche dynamics in a pile of rice<br />
<br />
| 题目: 大米堆中的雪崩动力学<br />
<br />
| journal = [[Nature (journal)|Nature]]<br />
<br />
| journal = Nature<br />
<br />
自然》杂志<br />
<br />
| volume = 379<br />
<br />
| volume = 379<br />
<br />
第379卷<br />
<br />
| issue = 6560<br />
<br />
| issue = 6560<br />
<br />
第6560期<br />
<br />
| pages = 49–52<br />
<br />
| pages = 49–52<br />
<br />
第49-52页<br />
<br />
| doi =10.1038/379049a0 <br />
<br />
| doi =10.1038/379049a0 <br />
<br />
10.1038 / 379049a0<br />
<br />
| bibcode= 1996Natur.379...49F}}<br />
<br />
| bibcode= 1996Natur.379...49F}}<br />
<br />
1996 / natur. 379... 49F }<br />
<br />
</ref> In addition to the nonconservative theoretical model mentioned above, other theoretical models for SOC have been based upon [[information theory]]<ref name=Dewar2003><br />
<br />
</ref> In addition to the nonconservative theoretical model mentioned above, other theoretical models for SOC have been based upon information theory<ref name=Dewar2003><br />
<br />
除了上面提到的非保守理论模型之外,其他关于 SOC 的理论模型都是基于信息论,例如 dewar2003<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = Dewar, R.<br />
<br />
| author = Dewar, R.<br />
<br />
作者杜瓦,r。<br />
<br />
| year = 2003<br />
<br />
| year = 2003<br />
<br />
2003年<br />
<br />
| title = Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states<br />
<br />
| title = Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states<br />
<br />
非平衡态中涨落定理、最大产生熵和自组织临界性的信息论解释<br />
<br />
| journal =J. Phys. A: Math. Gen. <br />
<br />
| journal =J. Phys. A: Math. Gen. <br />
<br />
| j 杂志。女名女子名。答: 数学。将军。<br />
<br />
| volume = 36<br />
<br />
| volume = 36<br />
<br />
第36卷<br />
<br />
| pages =631&ndash;641<br />
<br />
| pages =631&ndash;641<br />
<br />
631-- 641<br />
<br />
| pmid = <br />
<br />
| pmid = <br />
<br />
我不会让你失望的<br />
<br />
| doi = 10.1088/0305-4470/36/3/303<br />
<br />
| doi = 10.1088/0305-4470/36/3/303<br />
<br />
10.1088 / 0305-4470 / 36 / 3 / 303<br />
<br />
| issue = 3<br />
<br />
| issue = 3<br />
<br />
第三期<br />
<br />
| pmc = <br />
<br />
| pmc = <br />
<br />
我会的,我会的,我会的<br />
<br />
|bibcode = 2003JPhA...36..631D|arxiv = cond-mat/0005382 | author-link = R Dewar<br />
<br />
|bibcode = 2003JPhA...36..631D|arxiv = cond-mat/0005382 | author-link = R Dewar<br />
<br />
| bibcode 2003JPhA... 36. . 631 d | arxiv cond-mat / 0005382 | author-link r Dewar<br />
<br />
}}</ref>, <br />
<br />
}}</ref>, <br />
<br />
} / ref,<br />
<br />
[[mean field theory]]<ref name=Vespignani1998><br />
<br />
mean field theory<ref name=Vespignani1998><br />
<br />
平均场理论参考名称 vespignani1998<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[Alessandro Vespignani|Vespignani, A.]], and [[Stefano Zapperi|Zapperi, S.]]<br />
<br />
| author = Vespignani, A., and Zapperi, S.<br />
<br />
作者 Vespignani,a,和 Zapperi,s。<br />
<br />
| year = 1998<br />
<br />
| year = 1998<br />
<br />
1998年<br />
<br />
| title = How self-organized criticality works: a unified mean-field picture<br />
<br />
| title = How self-organized criticality works: a unified mean-field picture<br />
<br />
标题自组织临界性如何工作: 一个统一的平均场图片<br />
<br />
| journal =Phys. Rev. E <br />
<br />
| journal =Phys. Rev. E <br />
<br />
体育杂志。牧师。E<br />
<br />
| volume = 57<br />
<br />
| volume = 57<br />
<br />
第57卷<br />
<br />
| pages =6345–6362<br />
<br />
| pages =6345–6362<br />
<br />
6345-6362页<br />
<br />
| pmid = <br />
<br />
| pmid = <br />
<br />
我不会让你失望的<br />
<br />
| doi = 10.1103/physreve.57.6345<br />
<br />
| doi = 10.1103/physreve.57.6345<br />
<br />
10.1103 / physorve. 57.6345<br />
<br />
| issue = 6<br />
<br />
| issue = 6<br />
<br />
第六期<br />
<br />
| pmc = <br />
<br />
| pmc = <br />
<br />
我会的,我会的,我会的<br />
<br />
| bibcode = 1998PhRvE..57.6345V<br />
<br />
| bibcode = 1998PhRvE..57.6345V<br />
<br />
| bibcode 1998PhRvE. . 57.6345 v<br />
<br />
| arxiv = cond-mat/9709192<br />
<br />
| arxiv = cond-mat/9709192<br />
<br />
| arxiv = cond-mat/9709192<br />
<br />
| hdl = 2047/d20002173<br />
<br />
| hdl = 2047/d20002173<br />
<br />
2047 / d20002173<br />
<br />
}}</ref>,<br />
<br />
}}</ref>,<br />
<br />
} / ref,<br />
<br />
the [[convergence of random variables]]<ref name=Kendal2015><br />
<br />
the convergence of random variables<ref name=Kendal2015><br />
<br />
随机变量的收敛裁判名称 kendal 2015<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = Kendal, WS<br />
<br />
| author = Kendal, WS<br />
<br />
作者 Kendal,WS<br />
<br />
| year = 2015<br />
<br />
| year = 2015<br />
<br />
2015年<br />
<br />
| title = Self-organized criticality attributed to a central limit-like convergence effect<br />
<br />
| title = Self-organized criticality attributed to a central limit-like convergence effect<br />
<br />
| 标题自组织临界性归因于类似中心极限的聚合效应<br />
<br />
| journal =Physica A <br />
<br />
| journal =Physica A <br />
<br />
物理学杂志 a<br />
<br />
| volume = 421<br />
<br />
| volume = 421<br />
<br />
第421卷<br />
<br />
| pages =141&ndash;150<br />
<br />
| pages =141&ndash;150<br />
<br />
141-- 150页<br />
<br />
| pmid = <br />
<br />
| pmid = <br />
<br />
我不会让你失望的<br />
<br />
| doi = 10.1016/j.physa.2014.11.035<br />
<br />
| doi = 10.1016/j.physa.2014.11.035<br />
<br />
| doi 10.1016 / j.physa. 2014.11.035<br />
<br />
| issue = <br />
<br />
| issue = <br />
<br />
发行<br />
<br />
| pmc = <br />
<br />
| pmc = <br />
<br />
我会的,我会的,我会的<br />
<br />
|bibcode =2015PhyA..421..141K | author-link = Wayne Kendal<br />
<br />
|bibcode =2015PhyA..421..141K | author-link = Wayne Kendal<br />
<br />
| bibcode 2015PhyA. . 421. . 141 k | 作者链接 Wayne Kendal<br />
<br />
}}</ref>,<br />
<br />
}}</ref>,<br />
<br />
} / ref,<br />
<br />
and cluster formation.<ref name=Hoffmann2018b><br />
<br />
and cluster formation.<ref name=Hoffmann2018b><br />
<br />
和簇的形成。参考名称 hoffmann2018b<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = Hoffmann, H.<br />
<br />
| author = Hoffmann, H.<br />
<br />
作者: 霍夫曼。<br />
<br />
| year = 2018<br />
<br />
| year = 2018<br />
<br />
2018年<br />
<br />
| title = Impact of Network Topology on Self-Organized Criticality<br />
<br />
| title = Impact of Network Topology on Self-Organized Criticality<br />
<br />
网络拓扑对自组织临界性的影响<br />
<br />
| journal = Phys. Rev. E <br />
<br />
| journal = Phys. Rev. E <br />
<br />
体育杂志。牧师。E<br />
<br />
| volume = 97<br />
<br />
| volume = 97<br />
<br />
第97卷<br />
<br />
| pages =022313<br />
<br />
| pages =022313<br />
<br />
022313页<br />
<br />
| pmid = 29548239<br />
<br />
| pmid = 29548239<br />
<br />
29548239<br />
<br />
| doi = 10.1103/PhysRevE.97.022313<br />
<br />
| doi = 10.1103/PhysRevE.97.022313<br />
<br />
10.1103 / physarve. 97.022313<br />
<br />
| issue = 2<br />
<br />
| issue = 2<br />
<br />
第二期<br />
<br />
| pmc = <br />
<br />
| pmc = <br />
<br />
我会的,我会的,我会的<br />
<br />
| bibcode =2018PhRvE..97b2313H <br />
<br />
| bibcode =2018PhRvE..97b2313H <br />
<br />
2018 / phrve. . 97 / b2313H<br />
<br />
| author-link = Heiko Hoffmann<br />
<br />
| author-link = Heiko Hoffmann<br />
<br />
作者: 海科 · 霍夫曼<br />
<br />
| doi-access = free<br />
<br />
| doi-access = free<br />
<br />
免费访问<br />
<br />
}}</ref> A continuous model of self-organised criticality is proposed by using [[tropical geometry]].<ref>{{Cite journal|last=Kalinin|first=N.|last2=Guzmán-Sáenz|first2=A.|last3=Prieto|first3=Y.|last4=Shkolnikov|first4=M.|last5=Kalinina|first5=V.|last6=Lupercio|first6=E.|date=2018-08-15|title=Self-organized criticality and pattern emergence through the lens of tropical geometry|journal=Proceedings of the National Academy of Sciences|volume=115|issue=35|language=en|pages=E8135–E8142|doi=10.1073/pnas.1805847115|issn=0027-8424|pmid=30111541|pmc=6126730|arxiv=1806.09153}}</ref><br />
<br />
}}</ref> A continuous model of self-organised criticality is proposed by using tropical geometry.<br />
<br />
{} / ref 一个'''<font color="#ff8000"> 自组织临界Self-organised criticality</font>'''的连续模型是通过使用热带几何来提出的。<br />
<br />
== Examples of self-organized critical dynamics自组织临界动力学的例子 ==<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
In chronological order of development:<br />
<br />
In chronological order of development:<br />
<br />
按发展时间顺序排列:<br />
<br />
<br />
<br />
<br />
<br />
* Stick-slip model of fault failure<ref name="TurcotteSmalleySolla85" /><ref name="SmalleyTurcotteSolla85" /><br />
<br />
*断层破坏的粘滑模型<ref name="TurcotteSmalleySolla85" /><ref name="SmalleyTurcotteSolla85" /><br />
<br />
*[[Abelian sandpile model|Bak–Tang–Wiesenfeld sandpile]]<br />
<br />
*[[阿贝尔沙堆模型| Bak–Tang–Wiesenfeld沙堆]]<br />
<br />
* [[Forest-fire model]]<br />
<br />
*[[森林火灾模型]]<br />
<br />
* [[Olami–Feder–Christensen model]]<br />
<br />
* [[奥拉米·费德·克里斯滕森模型]]<br />
<br />
* [[Bak–Sneppen model]]<br />
<br />
*[[背景模型]]<br />
<br />
== See also 参见==<br />
<br />
<br />
<br />
* [[Pink noise|1/f noise]]<br />
<br />
*[[粉红噪音| 1/f噪音]]<br />
<br />
* [[Complex system]]s<br />
<br />
* [[复杂系统]]s<br />
<br />
* [[Critical brain hypothesis]]<br />
<br />
*[[【关键大脑假说】]]<br />
<br />
* [[Critical exponents]]<br />
<br />
*[[临界指数]]<br />
<br />
* [[Detrended fluctuation analysis]], a method to detect power-law scaling in time series.<br />
<br />
*[[Detrended涨落分析]],一种检测中幂律标度的方法<br />
<br />
* [[Dual-phase evolution]], another process that contributes to self-organization in complex systems.<br />
<br />
* [[双相演化]],另一个有助于自我组织的过程<br />
<br />
* [[Fractal]]s<br />
<br />
* [[分形]]s;<br />
<br />
* [[Ilya Prigogine]], a systems scientist who helped formalize dissipative system behavior in general terms.<br />
<br />
*[[伊利亚·普里高津]],一位帮助将耗散系统形式化的系统科学家<br />
<br />
* [[Power law]]s<br />
<br />
*[[幂律]]s<br />
<br />
* [[Red Queen hypothesis]]<br />
<br />
*[[红皇后假说]]<br />
<br />
* [[Scale invariance]]<br />
<br />
* [[标度不变性]]<br />
<br />
* [[Self-organization]]<br />
<br />
* [[自组织]]<br />
<br />
* [[Self-organized criticality control]]<br />
<br />
*[[自组织临界控制]]<br />
<br />
==References参考资料==<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<references/><br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
== Further reading延伸阅读 ==<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = Adami, C.<br />
<br />
| author = Adami, C.<br />
<br />
作者: 阿达米。<br />
<br />
| year = 1995<br />
<br />
| year = 1995<br />
<br />
1995年<br />
<br />
| title = Self-organized criticality in living systems<br />
<br />
| title = Self-organized criticality in living systems<br />
<br />
| 生命系统中的自组织临界性<br />
<br />
| journal = [[Physics Letters A]]<br />
<br />
| journal = Physics Letters A<br />
<br />
物理学快报<br />
<br />
| volume = 203<br />
<br />
| volume = 203<br />
<br />
第203卷<br />
<br />
| issue = 1<br />
<br />
| issue = 1<br />
<br />
第一期<br />
<br />
| pages = 29&ndash;32<br />
<br />
| pages = 29&ndash;32<br />
<br />
29-- 32页<br />
<br />
| doi = 10.1016/0375-9601(95)00372-A<br />
<br />
| doi = 10.1016/0375-9601(95)00372-A<br />
<br />
| doi 10.1016 / 0375-9601(95)00372-A<br />
<br />
|bibcode = 1995PhLA..203...29A | arxiv = adap-org/9401001<br />
<br />
|bibcode = 1995PhLA..203...29A | arxiv = adap-org/9401001<br />
<br />
|bibcode = 1995PhLA..203...29A | arxiv = adap-org/9401001<br />
<br />
| citeseerx = 10.1.1.456.9543<br />
<br />
| citeseerx = 10.1.1.456.9543<br />
<br />
10.1.1.456.9543<br />
<br />
| author-link = Adami, C<br />
<br />
| author-link = Adami, C<br />
<br />
| 作者链接阿达米,c<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite book<br />
<br />
<br />
<br />
| author = Bak, P.<br />
<br />
| author = Bak, P.<br />
<br />
作者 Bak,p。<br />
<br />
| year = 1996<br />
<br />
| year = 1996<br />
<br />
1996年<br />
<br />
| title = How Nature Works: The Science of Self-Organized Criticality<br />
<br />
| title = How Nature Works: The Science of Self-Organized Criticality<br />
<br />
自然如何运作: 自组织临界性的科学<br />
<br />
| publisher = Copernicus<br />
<br />
| publisher = Copernicus<br />
<br />
出版商哥白尼<br />
<br />
| location = New York<br />
<br />
| location = New York<br />
<br />
| 地点: 纽约<br />
<br />
| isbn = 978-0-387-94791-4<br />
<br />
| isbn = 978-0-387-94791-4<br />
<br />
[国际标准图书编号978-0-387-94791-4]<br />
<br />
| author-link = Per Bak<br />
<br />
| author-link = Per Bak<br />
<br />
| 作者链接 Per Bak<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = [[Per Bak|Bak, P.]] and [[Maya Paczuski|Paczuski, M.]]<br />
<br />
| author = Bak, P. and Paczuski, M.<br />
<br />
作者 Bak,p. and Paczuski,m。<br />
<br />
| year = 1995<br />
<br />
| year = 1995<br />
<br />
1995年<br />
<br />
| title = Complexity, contingency, and criticality<br />
<br />
| title = Complexity, contingency, and criticality<br />
<br />
| 标题复杂性、偶然性和临界性<br />
<br />
| journal = [[Proceedings of the National Academy of Sciences|Proceedings of the National Academy of Sciences of the USA]]<br />
<br />
| journal = Proceedings of the National Academy of Sciences of the USA<br />
<br />
美国美国国家科学院院刊杂志<br />
<br />
| volume = 92<br />
<br />
| volume = 92<br />
<br />
第92卷<br />
<br />
| pages = 6689&ndash;6696<br />
<br />
| pages = 6689&ndash;6696<br />
<br />
6689-- 6696<br />
<br />
| url = http://pnas.org/cgi/content/abstract/92/15/6689<br />
<br />
| url = http://pnas.org/cgi/content/abstract/92/15/6689<br />
<br />
Http://pnas.org/cgi/content/abstract/92/15/6689<br />
<br />
| doi = 10.1073/pnas.92.15.6689<br />
<br />
| doi = 10.1073/pnas.92.15.6689<br />
<br />
10.1073 / pnas. 92.15.6689<br />
<br />
| pmid = 11607561<br />
<br />
| pmid = 11607561<br />
<br />
11607561<br />
<br />
| issue = 15<br />
<br />
| issue = 15<br />
<br />
第15期<br />
<br />
| pmc = 41396<br />
<br />
| pmc = 41396<br />
<br />
41396<br />
<br />
|bibcode = 1995PNAS...92.6689B }}<br />
<br />
|bibcode = 1995PNAS...92.6689B }}<br />
<br />
92.6689 b }<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = [[Per Bak|Bak, P.]] and [[Kim Sneppen|Sneppen, K.]]<br />
<br />
| author = Bak, P. and Sneppen, K.<br />
<br />
作者 Bak,p. and Sneppen,k。<br />
<br />
| year = 1993<br />
<br />
| year = 1993<br />
<br />
1993年<br />
<br />
| title = Punctuated equilibrium and criticality in a simple model of evolution <br />
<br />
| title = Punctuated equilibrium and criticality in a simple model of evolution <br />
<br />
| 简单演化模型中的间断平衡和临界性<br />
<br />
| journal = [[Physical Review Letters]]<br />
<br />
| journal = Physical Review Letters<br />
<br />
物理评论快报<br />
<br />
| volume = 71<br />
<br />
| volume = 71<br />
<br />
第71卷<br />
<br />
| issue = 24<br />
<br />
| issue = 24<br />
<br />
第24期<br />
<br />
| pages = 4083&ndash;4086<br />
<br />
| pages = 4083&ndash;4086<br />
<br />
4083-- 4086<br />
<br />
| doi = 10.1103/PhysRevLett.71.4083<br />
<br />
| doi = 10.1103/PhysRevLett.71.4083<br />
<br />
10.1103 / physrvlett. 71.4083<br />
<br />
| pmid=10055149<br />
<br />
| pmid=10055149<br />
<br />
10055149<br />
<br />
| bibcode=1993PhRvL..71.4083B}}<br />
<br />
| bibcode=1993PhRvL..71.4083B}}<br />
<br />
1993 phrvl. . 71.4083 b }<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = [[Per Bak|Bak, P.]], [[Chao Tang|Tang, C.]] and [[Kurt Wiesenfeld|Wiesenfeld, K.]]<br />
<br />
| author = Bak, P., Tang, C. and Wiesenfeld, K.<br />
<br />
作者 Bak,p. ,Tang,c. and Wiesenfeld,k。<br />
<br />
| year = 1987<br />
<br />
| year = 1987<br />
<br />
1987年<br />
<br />
| title = Self-organized criticality: an explanation of <math>1/f</math> noise<br />
<br />
| title = Self-organized criticality: an explanation of <math>1/f</math> noise<br />
<br />
| 题目自组织临界性: 数学噪音的解释<br />
<br />
| journal = [[Physical Review Letters]]<br />
<br />
| journal = Physical Review Letters<br />
<br />
物理评论快报<br />
<br />
| volume = 59<br />
<br />
| volume = 59<br />
<br />
第59卷<br />
<br />
| issue = 4<br />
<br />
| issue = 4<br />
<br />
第四期<br />
<br />
| pages = 381&ndash;384<br />
<br />
| pages = 381&ndash;384<br />
<br />
381-- 384<br />
<br />
| doi = 10.1103/PhysRevLett.59.381<br />
<br />
| doi = 10.1103/PhysRevLett.59.381<br />
<br />
10.1103 / physrvlett. 59.381<br />
<br />
| pmid = 10035754<br />
<br />
| pmid = 10035754<br />
<br />
10035754<br />
<br />
| bibcode=1987PhRvL..59..381B}}<br />
<br />
| bibcode=1987PhRvL..59..381B}}<br />
<br />
1987 / phrvl. . 59. . 381 b }<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = [[Per Bak|Bak, P.]], [[Chao Tang|Tang, C.]] and [[Kurt Wiesenfeld|Wiesenfeld, K.]]<br />
<br />
| author = Bak, P., Tang, C. and Wiesenfeld, K.<br />
<br />
作者 Bak,p. ,Tang,c. and Wiesenfeld,k。<br />
<br />
| year = 1988<br />
<br />
| year = 1988<br />
<br />
1988年<br />
<br />
| title = Self-organized criticality<br />
<br />
| title = Self-organized criticality<br />
<br />
标题自组织临界性<br />
<br />
| journal = [[Physical Review A]]<br />
<br />
| journal = Physical Review A<br />
<br />
物理评论 a 期刊<br />
<br />
| volume = 38<br />
<br />
| volume = 38<br />
<br />
第38卷<br />
<br />
| issue = 1<br />
<br />
| issue = 1<br />
<br />
第一期<br />
<br />
| pages = 364&ndash;374<br />
<br />
| pages = 364&ndash;374<br />
<br />
364-- 374<br />
<br />
| doi = 10.1103/PhysRevA.38.364<br />
<br />
| doi = 10.1103/PhysRevA.38.364<br />
<br />
10.1103 / PhysRevA. 38.364<br />
<br />
| pmid = 9900174<br />
<br />
| pmid = 9900174<br />
<br />
9900174<br />
<br />
|bibcode = 1988PhRvA..38..364B }} [https://archive.is/20130415140421/http://www.papercore.org/PerBak1987 Papercore summary].<br />
<br />
|bibcode = 1988PhRvA..38..364B }} [https://archive.is/20130415140421/http://www.papercore.org/PerBak1987 Papercore summary].<br />
<br />
| bibcode 1988PhRvA. . 38. . 364 b }[ https://archive.is/20130415140421/http://www.Papercore.org/perbak1987文件核心摘要]。<br />
<br />
<br />
<br />
<br />
<br />
* {{cite book<br />
<br />
<br />
<br />
| author = Buchanan, M.<br />
<br />
| author = Buchanan, M.<br />
<br />
作者: 布坎南。<br />
<br />
| year = 2000<br />
<br />
| year = 2000<br />
<br />
2000年<br />
<br />
| title = Ubiquity<br />
<br />
| title = Ubiquity<br />
<br />
标题: Ubiquity<br />
<br />
| publisher = Weidenfeld &amp; Nicolson<br />
<br />
| publisher = Weidenfeld &amp; Nicolson<br />
<br />
| publisher = Weidenfeld &amp; Nicolson<br />
<br />
| location = London<br />
<br />
| location = London<br />
<br />
地点: 伦敦<br />
<br />
| isbn = 978-0-7538-1297-6<br />
<br />
| isbn = 978-0-7538-1297-6<br />
<br />
[国际标准图书编号978-0-7538-1297-6]<br />
<br />
| author-link = Mark Buchanan<br />
<br />
| author-link = Mark Buchanan<br />
<br />
马克 · 布坎南<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite book<br />
<br />
<br />
<br />
| author = Jensen, H. J.<br />
<br />
| author = Jensen, H. J.<br />
<br />
作者 Jensen,h. j。<br />
<br />
| year = 1998<br />
<br />
| year = 1998<br />
<br />
1998年<br />
<br />
| title = Self-Organized Criticality<br />
<br />
| title = Self-Organized Criticality<br />
<br />
标题自组织临界性<br />
<br />
| publisher = [[Cambridge University Press]]<br />
<br />
| publisher = Cambridge University Press<br />
<br />
出版商剑桥大学出版社<br />
<br />
| location = Cambridge<br />
<br />
| location = Cambridge<br />
<br />
| 地点: 剑桥<br />
<br />
| isbn = 978-0-521-48371-1<br />
<br />
| isbn = 978-0-521-48371-1<br />
<br />
[国际标准图书编号978-0-521-48371-1]<br />
<br />
| author-link = Henrik Jeldtoft Jensen<br />
<br />
| author-link = Henrik Jeldtoft Jensen<br />
<br />
作者: 亨里克 · 耶尔德托夫特 · 詹森<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = Katz, J. I.<br />
<br />
| author = Katz, J. I.<br />
<br />
作者 Katz,j. i。<br />
<br />
| year = 1986<br />
<br />
| year = 1986<br />
<br />
1986年<br />
<br />
| title = A model of propagating brittle failure in heterogeneous media<br />
<br />
| title = A model of propagating brittle failure in heterogeneous media<br />
<br />
在非均匀介质中传播脆性破坏的模型<br />
<br />
| journal = Journal of Geophysical Research<br />
<br />
| journal = Journal of Geophysical Research<br />
<br />
地球物理研究期刊<br />
<br />
| bibcode = 1986JGR....9110412K<br />
<br />
| bibcode = 1986JGR....9110412K<br />
<br />
| bibcode 1986JGR... 9110412K<br />
<br />
| doi = 10.1029/JB091iB10p10412<br />
<br />
| doi = 10.1029/JB091iB10p10412<br />
<br />
| doi 10.1029 / JB091iB10p10412<br />
<br />
| volume = 91<br />
<br />
| volume = 91<br />
<br />
第91卷<br />
<br />
| issue = B10<br />
<br />
| issue = B10<br />
<br />
第10期<br />
<br />
| pages = 10412<br />
<br />
| pages = 10412<br />
<br />
10412页<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = Kron, T./Grund, T.<br />
<br />
| author = Kron, T./Grund, T.<br />
<br />
作者: Kron t. / Grund t。<br />
<br />
| year = 2009<br />
<br />
| year = 2009<br />
<br />
2009年<br />
<br />
| title = Society as a Selforganized Critical System<br />
<br />
| title = Society as a Selforganized Critical System<br />
<br />
作为一个自组织的批判系统的社会<br />
<br />
| journal = Cybernetics and Human Knowing<br />
<br />
| journal = Cybernetics and Human Knowing<br />
<br />
控制论与人类认知<br />
<br />
| volume = 16<br />
<br />
| volume = 16<br />
<br />
第16卷<br />
<br />
| pages = 65–82<br />
<br />
| pages = 65–82<br />
<br />
第65-82页<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{Cite book<br />
<br />
<br />
<br />
| author = Paczuski, M.<br />
<br />
| author = Paczuski, M.<br />
<br />
作者: 帕祖斯基。<br />
<br />
| year = 2005<br />
<br />
| year = 2005<br />
<br />
2005年<br />
<br />
| title = Networks as renormalized models for emergent behavior in physical systems<br />
<br />
| title = Networks as renormalized models for emergent behavior in physical systems<br />
<br />
作为物理系统中突发行为的重整化模型的网络<br />
<br />
| journal = Complexity<br />
<br />
| journal = Complexity<br />
<br />
杂志复杂性<br />
<br />
| pages = 363–374<br />
<br />
| pages = 363–374<br />
<br />
第363-374页<br />
<br />
| arxiv = physics/0502028<br />
<br />
| arxiv = physics/0502028<br />
<br />
| arxiv physics / 0502028<br />
<br />
|bibcode = 2005cmn..conf..363P |doi = 10.1142/9789812701558_0042<br />
<br />
|bibcode = 2005cmn..conf..363P |doi = 10.1142/9789812701558_0042<br />
<br />
2005 / cmn. conf. 363 p | doi 10.1142 / 97898127015580042<br />
<br />
| series = The Science and Culture Series – Physics<br />
<br />
| series = The Science and Culture Series – Physics<br />
<br />
| 科学与文化系列-物理学<br />
<br />
| isbn = 978-981-256-525-9 | citeseerx = 10.1.1.261.9886<br />
<br />
| isbn = 978-981-256-525-9 | citeseerx = 10.1.1.261.9886<br />
<br />
| isbn 978-981-256-525-9 | citeserx 10.1.1.261.9886<br />
<br />
| author-link = Maya Paczuski<br />
<br />
| author-link = Maya Paczuski<br />
<br />
| 作者链接 Maya Paczuski<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite book<br />
<br />
<br />
<br />
| author = Turcotte, D. L.<br />
<br />
| author = Turcotte, D. L.<br />
<br />
作者: Turcotte,D.l。<br />
<br />
| year = 1997<br />
<br />
| year = 1997<br />
<br />
1997年<br />
<br />
| title = Fractals and Chaos in Geology and Geophysics<br />
<br />
| title = Fractals and Chaos in Geology and Geophysics<br />
<br />
地质学与地球物理学中的分形与混沌<br />
<br />
| publisher = [[Cambridge University Press]]<br />
<br />
| publisher = Cambridge University Press<br />
<br />
出版商剑桥大学出版社<br />
<br />
| location = Cambridge<br />
<br />
| location = Cambridge<br />
<br />
| 地点: 剑桥<br />
<br />
| isbn = 978-0-521-56733-6<br />
<br />
| isbn = 978-0-521-56733-6<br />
<br />
[国际标准图书馆编号978-0-521-56733-6]<br />
<br />
| author-link = Donald L. Turcotte<br />
<br />
| author-link = Donald L. Turcotte<br />
<br />
作者: Donald l. Turcotte<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = Turcotte, D. L.<br />
<br />
| author = Turcotte, D. L.<br />
<br />
作者: Turcotte,D.l。<br />
<br />
| year = 1999<br />
<br />
| year = 1999<br />
<br />
1999年<br />
<br />
| title = Self-organized criticality<br />
<br />
| title = Self-organized criticality<br />
<br />
标题自组织临界性<br />
<br />
| journal = [[Reports on Progress in Physics]]<br />
<br />
| journal = Reports on Progress in Physics<br />
<br />
物理学进展报告<br />
<br />
| volume = 62<br />
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| volume = 62<br />
<br />
第62卷<br />
<br />
| issue = 10<br />
<br />
| issue = 10<br />
<br />
第10期<br />
<br />
| pages = 1377&ndash;1429<br />
<br />
| pages = 1377&ndash;1429<br />
<br />
13771429页<br />
<br />
| doi = 10.1088/0034-4885/62/10/201<br />
<br />
| doi = 10.1088/0034-4885/62/10/201<br />
<br />
10.1088 / 0034-4885 / 62 / 10 / 201<br />
<br />
|bibcode = 1999RPPh...62.1377T | author-link = Donald L. Turcotte<br />
<br />
|bibcode = 1999RPPh...62.1377T | author-link = Donald L. Turcotte<br />
<br />
| bibcode 1999RPPh... 62.1377 t | 作者链接 Donald l. Turcotte<br />
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}}<br />
<br />
}}<br />
<br />
}}<br />
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* {{cite journal<br />
<br />
<br />
<br />
| author = Md. Nurujjaman/A. N. Sekar Iyengar<br />
<br />
| author = Md. Nurujjaman/A. N. Sekar Iyengar<br />
<br />
作者马里兰大学。Nurujjaman / a.N. Sekar Iyengar<br />
<br />
| year = 2007<br />
<br />
| year = 2007<br />
<br />
2007年<br />
<br />
| title = Realization of {SOC} behavior in a dc glow discharge plasma<br />
<br />
| title = Realization of {SOC} behavior in a dc glow discharge plasma<br />
<br />
直流辉光放电等离子体{ SOC }行为的实现<br />
<br />
| journal = [[Physics Letters A]]<br />
<br />
| journal = Physics Letters A<br />
<br />
物理学快报<br />
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| volume = 360<br />
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| volume = 360<br />
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第360卷<br />
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| issue = 6<br />
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| issue = 6<br />
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第六期<br />
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| pages = 717&ndash;721<br />
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| pages = 717&ndash;721<br />
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717-- 721页<br />
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|arxiv = physics/0611069 |bibcode = 2007PhLA..360..717N |doi = 10.1016/j.physleta.2006.09.005 | author-link = Md. Nurujjaman/A. N. Sekar Iyengar<br />
<br />
|arxiv = physics/0611069 |bibcode = 2007PhLA..360..717N |doi = 10.1016/j.physleta.2006.09.005 | author-link = Md. Nurujjaman/A. N. Sekar Iyengar<br />
<br />
| arxiv physics / 0611069 | bibcode 2007 phla. . 360. . 717 n | doi 10.1016 / j.physleta. 2006.09.005 | author-link md.Nurujjaman / a.N. Sekar Iyengar<br />
<br />
}}<br />
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}}<br />
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}}<br />
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*[http://xstructure.inr.ac.ru/x-bin/theme2.py?arxiv=cond-mat&level=1&index1=20771 Self-organized criticality on arxiv.org]<br />
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[[Category:Critical phenomena]]<br />
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Category:Critical phenomena<br />
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范畴: 关键现象<br />
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[[Category:Applied and interdisciplinary physics]]<br />
<br />
Category:Applied and interdisciplinary physics<br />
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类别: 应用和跨学科物理学<br />
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[[Category:Chaos theory]]<br />
<br />
Category:Chaos theory<br />
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范畴: 混沌理论<br />
<br />
[[Category:Self-organization]]<br />
<br />
Category:Self-organization<br />
<br />
类别: 自我组织<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Self-organized criticality]]. Its edit history can be viewed at [[自组织临界性/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E8%87%AA%E7%BB%84%E7%BB%87%E4%B8%B4%E7%95%8C%E6%80%A7&diff=21922自组织临界性2021-02-21T11:21:27Z<p>Jxzhou:/* Overview 概览 */</p>
<hr />
<div>此词条暂由水流心不竞初译,未经审校,带来阅读不便,请见谅。<br />
<br />
In [[physics]], '''self-organized criticality''' ('''SOC''') is a property of [[dynamical system]]s that have a [[critical phenomena|critical point]] as an [[attractor]]. Their macroscopic behavior thus displays the spatial or temporal [[scale invariance|scale-invariance]] characteristic of the [[critical point (physics)|critical point]] of a [[phase transition]], but without the need to tune control parameters to a precise value, because the system, effectively, tunes itself as it evolves towards criticality.<br />
<br />
In physics, self-organized criticality (SOC) is a property of dynamical systems that have a critical point as an attractor. Their macroscopic behavior thus displays the spatial or temporal scale-invariance characteristic of the critical point of a phase transition, but without the need to tune control parameters to a precise value, because the system, effectively, tunes itself as it evolves towards criticality.<br />
<br />
在物理学中,'''<font color="#ff8000"> 自组织临界性Self-organized criticality (SOC)</font>'''是动力系统的一种特性,动力系统有一个临界点作为'''<font color="#ff8000"> 吸引子Attractor</font>'''。它们的宏观行为因此显示了相变临界点的空间或时间尺度不变特性,但不需要把控制参数调整到一个精确的值,因为系统在趋向于临界状态时有效地自我调整。<br />
<br />
<br />
<br />
<br />
<br />
The concept was put forward by [[Per Bak]], [[Chao Tang]] and [[Kurt Wiesenfeld]] ("BTW") in a paper<ref name=Bak1987><br />
<br />
The concept was put forward by Per Bak, Chao Tang and Kurt Wiesenfeld ("BTW") in a paper<ref name=Bak1987><br />
<br />
这个概念是由 Per Bak,Chao Tang 和 Kurt Wiesenfeld (“ BTW”)在一篇名为 bak1987的论文中提出的<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[Per Bak|Bak, P.]], [[Chao Tang|Tang, C.]] and [[Kurt Wiesenfeld|Wiesenfeld, K.]]<br />
<br />
| author = Bak, P., Tang, C. and Wiesenfeld, K.<br />
<br />
作者 Bak,p. ,Tang,c. and Wiesenfeld,k。<br />
<br />
| year = 1987<br />
<br />
| year = 1987<br />
<br />
1987年<br />
<br />
| title = Self-organized criticality: an explanation of 1/''f'' noise<br />
<br />
| title = Self-organized criticality: an explanation of 1/f noise<br />
<br />
自组织临界性: 1 / f 噪音的解释<br />
<br />
| journal = [[Physical Review Letters]]<br />
<br />
| journal = Physical Review Letters<br />
<br />
物理评论快报<br />
<br />
| volume = 59<br />
<br />
| volume = 59<br />
<br />
第59卷<br />
<br />
| issue = 4<br />
<br />
| issue = 4<br />
<br />
第四期<br />
<br />
| pages = 381&ndash;384<br />
<br />
| pages = 381&ndash;384<br />
<br />
381-- 384<br />
<br />
| doi = 10.1103/PhysRevLett.59.381<br />
<br />
| doi = 10.1103/PhysRevLett.59.381<br />
<br />
10.1103 / physrvlett. 59.381<br />
<br />
| pmid = 10035754<br />
<br />
| pmid = 10035754<br />
<br />
10035754<br />
<br />
| bibcode=1987PhRvL..59..381B<br />
<br />
| bibcode=1987PhRvL..59..381B<br />
<br />
| bibcode 1987PhRvL. . 59. . 381 b<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
Papercore summary: [https://archive.is/20130704122906/http://papercore.org/Bak1987 http://papercore.org/Bak1987].</ref> <br />
<br />
Papercore summary: [https://archive.is/20130704122906/http://papercore.org/Bak1987 http://papercore.org/Bak1987].</ref> <br />
<br />
论文摘要: [ https://archive.is/20130704122906/http://Papercore.org/bak1987 http://Papercore.org/bak1987] / 参考<br />
<br />
published in 1987 in ''[[Physical Review Letters]]'', and is considered to be one of the mechanisms by which [[complexity]]<ref name=Bak1995><br />
<br />
published in 1987 in Physical Review Letters, and is considered to be one of the mechanisms by which complexity<ref name=Bak1995><br />
<br />
1987年发表在《物理评论快报》上,被认为是复杂性的机制之一<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[Per Bak|Bak, P.]], and [[Maya Paczuski|Paczuski, M.]]<br />
<br />
| author = Bak, P., and Paczuski, M.<br />
<br />
作者 Bak,p,and Paczuski,m。<br />
<br />
| year = 1995<br />
<br />
| year = 1995<br />
<br />
1995年<br />
<br />
| title = Complexity, contingency, and criticality<br />
<br />
| title = Complexity, contingency, and criticality<br />
<br />
| 标题复杂性、偶然性和临界性<br />
<br />
| journal =Proc Natl Acad Sci U S A <br />
<br />
| journal =Proc Natl Acad Sci U S A <br />
<br />
美国科学促进协会<br />
<br />
| volume = 92<br />
<br />
| volume = 92<br />
<br />
第92卷<br />
<br />
| pages = 6689&ndash;6696<br />
<br />
| pages = 6689&ndash;6696<br />
<br />
6689-- 6696<br />
<br />
| pmid = 11607561<br />
<br />
| pmid = 11607561<br />
<br />
11607561<br />
<br />
| doi = 10.1073/pnas.92.15.6689<br />
<br />
| doi = 10.1073/pnas.92.15.6689<br />
<br />
10.1073 / pnas. 92.15.6689<br />
<br />
| issue = 15<br />
<br />
| issue = 15<br />
<br />
第15期<br />
<br />
| pmc = 41396<br />
<br />
| pmc = 41396<br />
<br />
41396<br />
<br />
|bibcode = 1995PNAS...92.6689B }}</ref> arises in nature. Its concepts have been applied across fields as diverse as [[geophysics]],<ref name=SmalleyTurcotteSolla85><br />
<br />
|bibcode = 1995PNAS...92.6689B }}</ref> arises in nature. Its concepts have been applied across fields as diverse as geophysics,<ref name=SmalleyTurcotteSolla85><br />
<br />
| bibcode 1995PNAS... 92.6689 b } / ref 在自然界中出现。它的概念已经被应用于各个领域,比如地球物理学,参考名称 smalleyturcottesolla85<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
|author1=Smalley, R. F., Jr. |author2=Turcotte, D. L. |author3=Solla, S. A. | year = 1985<br />
<br />
|author1=Smalley, R. F., Jr. |author2=Turcotte, D. L. |author3=Solla, S. A. | year = 1985<br />
<br />
1 Smalley,r. f. ,jr. | author2 Turcotte,d. l. | author3 Solla,s. a.1985年<br />
<br />
| title = A renormalization group approach to the stick-slip behavior of faults<br />
<br />
| title = A renormalization group approach to the stick-slip behavior of faults<br />
<br />
| 题目: 断层粘滑行为的重整化群方法<br />
<br />
| journal = Journal of Geophysical Research<br />
<br />
| journal = Journal of Geophysical Research<br />
<br />
地球物理研究期刊<br />
<br />
| bibcode = 1985JGR....90.1894S<br />
<br />
| bibcode = 1985JGR....90.1894S<br />
<br />
1985JGR... 90.1894 s<br />
<br />
| doi = 10.1029/JB090iB02p01894<br />
<br />
| doi = 10.1029/JB090iB02p01894<br />
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| doi 10.1029 / JB090iB02p01894<br />
<br />
| volume = 90<br />
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| volume = 90<br />
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第90卷<br />
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| issue = B2<br />
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| issue = B2<br />
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| 第二期<br />
<br />
| pages = 1894<br />
<br />
| pages = 1894<br />
<br />
1894页<br />
<br />
|url=https://semanticscholar.org/paper/6776d17957204c198e278bda98c935ab1cf8f22b }}</ref> [[physical cosmology]], [[evolutionary biology]] and [[ecology]], [[bio-inspired computing]] and [[optimization (mathematics)]], [[economics]], [[quantum gravity]], [[sociology]], [[solar physics]], [[plasma physics]], [[neurobiology]]<ref name=LinkenkaerHansen2001><br />
<br />
|url=https://semanticscholar.org/paper/6776d17957204c198e278bda98c935ab1cf8f22b }}</ref> physical cosmology, evolutionary biology and ecology, bio-inspired computing and optimization (mathematics), economics, quantum gravity, sociology, solar physics, plasma physics, neurobiology<ref name=LinkenkaerHansen2001><br />
<br />
[ https://semanticscholar.org/paper/6776d17957204c198e278bda98c935ab1cf8f22b ] / ref 物理宇宙学,进化生物学和生态学,生物启发计算和优化(数学) ,经济学,量子引力,社会学,太阳物理学,等离子物理学,神经生物学参考名称 linkenkaerhansen2001<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
|author1=K. Linkenkaer-Hansen |author2=V. V. Nikouline |author3=J. M. Palva |author4=R. J. Ilmoniemi. |last-author-amp=yes | year = 2001<br />
<br />
|author1=K. Linkenkaer-Hansen |author2=V. V. Nikouline |author3=J. M. Palva |author4=R. J. Ilmoniemi. |last-author-amp=yes | year = 2001<br />
<br />
1 k.Linkenkaer-hansen | author2 v.3 j.4 r.作者: j. Ilmoniemi。最后一个作者2001年<br />
<br />
| title = Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations<br />
<br />
| title = Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations<br />
<br />
人类大脑振荡中的长程时间相关性和标度行为<br />
<br />
| journal = J. Neurosci.<br />
<br />
| journal = J. Neurosci.<br />
<br />
作者: j. Neurosci。<br />
<br />
| volume = 21<br />
<br />
| volume = 21<br />
<br />
第21卷<br />
<br />
| pages = 1370&ndash;1377<br />
<br />
| pages = 1370&ndash;1377<br />
<br />
1370-- 1377<br />
<br />
| pmid = 11160408<br />
<br />
| pmid = 11160408<br />
<br />
11160408<br />
<br />
| issue = 4<br />
<br />
| issue = 4<br />
<br />
第四期<br />
<br />
|doi=10.1523/JNEUROSCI.21-04-01370.2001 |pmc=6762238 }}</ref><ref name=Beggs2003><br />
<br />
|doi=10.1523/JNEUROSCI.21-04-01370.2001 |pmc=6762238 }}</ref><ref name=Beggs2003><br />
<br />
| doi 10.1523 / jneurosci. 21-04-01370.2001 | pmc 6762238} / ref name begs2003<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
|author1=J. M. Beggs |author2=D. Plenz<br />
<br />
|author1=J. M. Beggs |author2=D. Plenz<br />
<br />
1 j.2 d.Plenz<br />
<br />
|lastauthoramp=yes | year = 2006<br />
<br />
|lastauthoramp=yes | year = 2006<br />
<br />
2006年<br />
<br />
| title = Neuronal Avalanches in Neocortical Circuits<br />
<br />
| title = Neuronal Avalanches in Neocortical Circuits<br />
<br />
新皮层神经回路中的神经雪崩<br />
<br />
| journal = J. Neurosci.<br />
<br />
| journal = J. Neurosci.<br />
<br />
作者: j. Neurosci。<br />
<br />
| volume = 23<br />
<br />
| volume = 23<br />
<br />
第23卷<br />
<br />
|issue=35<br />
<br />
|issue=35<br />
<br />
第35期<br />
<br />
|pages=11167–77<br />
<br />
|pages=11167–77<br />
<br />
第11167-77页<br />
<br />
|doi=10.1523/JNEUROSCI.23-35-11167.2003<br />
<br />
|doi=10.1523/JNEUROSCI.23-35-11167.2003<br />
<br />
10.1523 / jneurosci. 23-35-11167.2003<br />
<br />
|pmid=14657176<br />
<br />
|pmid=14657176<br />
<br />
14657176<br />
<br />
|pmc=6741045<br />
<br />
|pmc=6741045<br />
<br />
6741045<br />
<br />
}}</ref><ref name=Chialvo2004><br />
<br />
}}</ref><ref name=Chialvo2004><br />
<br />
} / ref ref name chialvo2004<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author =Chialvo, D. R.<br />
<br />
| author =Chialvo, D. R.<br />
<br />
作者 Chialvo,d. r。<br />
<br />
| year = 2004<br />
<br />
| year = 2004<br />
<br />
2004年<br />
<br />
| title = Critical brain networks<br />
<br />
| title = Critical brain networks<br />
<br />
关键的大脑网络<br />
<br />
| journal = Physica A<br />
<br />
| journal = Physica A<br />
<br />
物理学杂志 a<br />
<br />
| volume = 340<br />
<br />
| volume = 340<br />
<br />
第340卷<br />
<br />
| issue =4<br />
<br />
| issue =4<br />
<br />
第四期<br />
<br />
| pages = 756&ndash;765<br />
<br />
| pages = 756&ndash;765<br />
<br />
756-- 765<br />
<br />
| doi = 10.1016/j.physa.2004.05.064<br />
<br />
| doi = 10.1016/j.physa.2004.05.064<br />
<br />
10.1016 / j.physa. 2004.05.064<br />
<br />
|arxiv = cond-mat/0402538 |bibcode = 2004PhyA..340..756R | author-link = Dante R. Chialvo<br />
<br />
|arxiv = cond-mat/0402538 |bibcode = 2004PhyA..340..756R | author-link = Dante R. Chialvo<br />
<br />
| arxiv cond-mat / 0402538 | bibcode 2004PhyA. . 340. . 756 r | author-link Dante r. Chialvo<br />
<br />
}}</ref> and others.<br />
<br />
}}</ref> and others.<br />
<br />
} / ref and others.<br />
<br />
<br />
<br />
<br />
<br />
SOC is typically observed in slowly driven [[non-equilibrium thermodynamics|non-equilibrium]] systems with many [[degrees of freedom (physics and chemistry)|degrees of freedom]] and strongly [[nonlinearity|nonlinear]] dynamics. Many individual examples have been identified since BTW's original paper, but to date there is no known set of general characteristics that ''guarantee'' a system will display SOC.<br />
<br />
SOC is typically observed in slowly driven non-equilibrium systems with many degrees of freedom and strongly nonlinear dynamics. Many individual examples have been identified since BTW's original paper, but to date there is no known set of general characteristics that guarantee a system will display SOC.<br />
<br />
'''<font color="#ff8000"> SOC</font>'''是典型的多自由度、强非线性动力学的缓慢驱动非平衡系统。自从 BTW 的原始论文以来,已经确定了许多单独的例子,但是到目前为止还没有一组已知的一般特征来保证一个系统将显示 '''<font color="#ff8000"> SOC</font>'''。<br />
<br />
<br />
<br />
<br />
<br />
== Overview 概览==<br />
<br />
<br />
<br />
<br />
<br />
<br />
Self-organized criticality is one of a number of important discoveries made in [[statistical physics]] and related fields over the latter half of the 20th century, discoveries which relate particularly to the study of [[complexity]] in nature. For example, the study of [[cellular automata]], from the early discoveries of [[Stanislaw Ulam]] and [[John von Neumann]] through to [[John Horton Conway|John Conway]]'s [[Conway's Game of Life|Game of Life]] and the extensive work of [[Stephen Wolfram]], made it clear that complexity could be generated as an [[emergence|emergent]] feature of extended systems with simple local interactions. Over a similar period of time, [[Benoît Mandelbrot]]'s large body of work on [[fractals]] showed that much complexity in nature could be described by certain ubiquitous mathematical laws, while the extensive study of [[phase transition]]s carried out in the 1960s and 1970s showed how [[scale invariance|scale invariant]] phenomena such as [[fractals]] and [[power law]]s emerged at the [[critical point (physics)|critical point]] between phases.<br />
<br />
Self-organized criticality is one of a number of important discoveries made in statistical physics and related fields over the latter half of the 20th century, discoveries which relate particularly to the study of complexity in nature. For example, the study of cellular automata, from the early discoveries of Stanislaw Ulam and John von Neumann through to John Conway's Game of Life and the extensive work of Stephen Wolfram, made it clear that complexity could be generated as an emergent feature of extended systems with simple local interactions. Over a similar period of time, Benoît Mandelbrot's large body of work on fractals showed that much complexity in nature could be described by certain ubiquitous mathematical laws, while the extensive study of phase transitions carried out in the 1960s and 1970s showed how scale invariant phenomena such as fractals and power laws emerged at the critical point between phases.<br />
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'''<font color="#ff8000"> 自组织临界性Self-organized criticality(SOC)</font>'''是20世纪下半叶统计物理学及相关领域的众多重要发现之一,这些发现尤其与研究自然界的复杂性有关。例如,元胞自动机的研究---- 从 Stanislaw Ulam 和约翰·冯·诺伊曼的早期发现到 John Conway 的生命游戏和 Stephen Wolfram 的大量工作---- 清楚地表明,复杂性可以作为具有简单局部相互作用的扩展系统的一个涌现特征而产生。在相似的时间段内,beno t Mandelbrot 关于分形的大量工作表明,自然界的许多复杂性可以用某些无处不在的数学定律来描述,而在20世纪60年代和70年代对相变的广泛研究表明,诸如分形和幂律等尺度不变现象是如何出现在相变的临界点上的。<br />
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The term ''self-organized criticality'' was firstly introduced by [[Per Bak|Bak]], [[Chao Tang|Tang]] and [[Kurt Wiesenfeld|Wiesenfeld]]'s 1987 paper, which clearly linked together those factors: a simple [[cellular automaton]] was shown to produce several characteristic features observed in natural complexity ([[fractal]] geometry, [[pink noise|pink (1/f) noise]] and [[power law]]s) in a way that could be linked to [[critical point (physics)|critical-point phenomena]]. Crucially, however, the paper emphasized that the complexity observed emerged in a robust manner that did not depend on finely tuned details of the system: variable parameters in the model could be changed widely without affecting the emergence of critical behavior: hence, ''[[self-organized]]'' criticality. Thus, the key result of BTW's paper was its discovery of a mechanism by which the emergence of complexity from simple local interactions could be ''spontaneous''&mdash;and therefore plausible as a source of natural complexity&mdash;rather than something that was only possible in artificial situations in which control parameters are tuned to precise critical values. The publication of this research sparked considerable interest from both theoreticians and experimentalists, producing some of the most cited papers in the scientific literature.<br />
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The term self-organized criticality was firstly introduced by Bak, Tang and Wiesenfeld's 1987 paper, which clearly linked together those factors: a simple cellular automaton was shown to produce several characteristic features observed in natural complexity (fractal geometry, pink (1/f) noise and power laws) in a way that could be linked to critical-point phenomena. Crucially, however, the paper emphasized that the complexity observed emerged in a robust manner that did not depend on finely tuned details of the system: variable parameters in the model could be changed widely without affecting the emergence of critical behavior: hence, self-organized criticality. Thus, the key result of BTW's paper was its discovery of a mechanism by which the emergence of complexity from simple local interactions could be spontaneous&mdash;and therefore plausible as a source of natural complexity&mdash;rather than something that was only possible in artificial situations in which control parameters are tuned to precise critical values. The publication of this research sparked considerable interest from both theoreticians and experimentalists, producing some of the most cited papers in the scientific literature.<br />
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'''<font color="#ff8000"> 自组织临界性Self-organized criticality(SOC)</font>'''这个术语最早由 Bak,Tang 和 Wiesenfeld 在1987年的论文中提出,这篇论文将这些因素清楚地联系在一起: 一个简单的细胞自动机被证明可以产生在自然复杂性中观察到的几个特征(分形几何、粉红噪声和幂律) ,这种方式可以与临界点现象联系起来。然而,关键的是,这篇论文强调,观察到的复杂性是以一种强有力的方式出现的,并不依赖于系统精细调整的细节: 模型中的可变参数可以被广泛改变,而不会影响临界行为的涌现: 因此,具有自组织临界性。因此,BTW 论文的关键结果是发现了一种机制,通过这种机制,从简单的局部相互作用中产生的复杂性可能是自发的---- 因此是合理的自然复杂性的来源---- 而不是只有在控制参数调整到精确的临界值的人工情况下才可能出现的东西。这项研究的发表引起了理论家和实验家的极大兴趣,产生了一些在科学文献中被引用最多的论文。<br />
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Due to BTW's metaphorical visualization of their model as a "[[Bak–Tang–Wiesenfeld sandpile|sandpile]]" on which new sand grains were being slowly sprinkled to cause "avalanches", much of the initial experimental work tended to focus on examining real avalanches in [[granular matter]], the most famous and extensive such study probably being the Oslo ricepile experiment{{Citation needed|date=March 2018}}. Other experiments include those carried out on magnetic-domain patterns, the [[Barkhausen effect]] and vortices in [[superconductors]]. <br />
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Due to BTW's metaphorical visualization of their model as a "sandpile" on which new sand grains were being slowly sprinkled to cause "avalanches", much of the initial experimental work tended to focus on examining real avalanches in granular matter, the most famous and extensive such study probably being the Oslo ricepile experiment. Other experiments include those carried out on magnetic-domain patterns, the Barkhausen effect and vortices in superconductors. <br />
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由于 BTW 将他们的模型比喻为一个“沙堆” ,在沙堆上缓慢地喷洒新的沙粒以引起“雪崩” ,所以最初的实验工作主要集中在研究颗粒物质中的真实雪崩,其中最著名和最广泛的研究可能是奥斯陆地震实验。其他实验还包括在磁畴图案、超导体中的巴克豪森效应和涡旋上进行的实验。<br />
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Early theoretical work included the development of a variety of alternative SOC-generating dynamics distinct from the BTW model, attempts to prove model properties analytically (including calculating the [[critical exponent]]s<ref name=Tang1988a><br />
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Early theoretical work included the development of a variety of alternative SOC-generating dynamics distinct from the BTW model, attempts to prove model properties analytically (including calculating the critical exponents<ref name=Tang1988a><br />
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早期的理论工作包括开发各种不同于 BTW 模型的 soc 生成动力学,试图解析证明模型的性质(包括计算临界指数,参见 tang1988a<br />
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{{cite journal<br />
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{{cite journal<br />
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{引用期刊<br />
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| author = [[Chao Tang|Tang, C.]] and [[Per Bak|Bak, P.]]<br />
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| author = Tang, C. and Bak, P.<br />
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作者 Tang,c. and Bak,p。<br />
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| year = 1988<br />
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| year = 1988<br />
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1988年<br />
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| title = Critical exponents and scaling relations for self-organized critical phenomena<br />
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| title = Critical exponents and scaling relations for self-organized critical phenomena<br />
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自组织临界现象的临界指数和标度关系<br />
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| journal = [[Physical Review Letters]]<br />
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| journal = Physical Review Letters<br />
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物理评论快报<br />
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| doi = 10.1103/PhysRevLett.60.2347<br />
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| doi = 10.1103/PhysRevLett.60.2347<br />
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10.1103 / physrvlett. 60.2347<br />
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| bibcode= 1988PhRvL..60.2347T<br />
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| bibcode= 1988PhRvL..60.2347T<br />
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{{cite journal<br />
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{引用期刊<br />
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| author = [[Chao Tang|Tang, C.]] and [[Per Bak|Bak, P.]]<br />
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| author = Tang, C. and Bak, P.<br />
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作者 Tang,c. and Bak,p。<br />
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| year = 1988<br />
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| year = 1988<br />
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| title = Mean field theory of self-organized critical phenomena<br />
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| title = Mean field theory of self-organized critical phenomena<br />
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自组织临界现象的平均场理论<br />
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| journal = [[Journal of Statistical Physics]]<br />
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| journal = Journal of Statistical Physics<br />
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统计物理学杂志<br />
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| bibcode= 1988JSP....51..797T<br />
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</ref>), and examination of the conditions necessary for SOC to emerge. One of the important issues for the latter investigation was whether [[conservation of energy]] was required in the local dynamical exchanges of models: the answer in general is no, but with (minor) reservations, as some exchange dynamics (such as those of BTW) do require local conservation at least on average. In the long term, key theoretical issues yet to be resolved include the calculation of the possible [[universality class]]es of SOC behavior and the question of whether it is possible to derive a general rule for determining if an arbitrary [[algorithm]] displays SOC.<br />
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</ref>), and examination of the conditions necessary for SOC to emerge. One of the important issues for the latter investigation was whether conservation of energy was required in the local dynamical exchanges of models: the answer in general is no, but with (minor) reservations, as some exchange dynamics (such as those of BTW) do require local conservation at least on average. In the long term, key theoretical issues yet to be resolved include the calculation of the possible universality classes of SOC behavior and the question of whether it is possible to derive a general rule for determining if an arbitrary algorithm displays SOC.<br />
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/ ref) ,以及研究出现 '''<font color="#ff8000"> SOC</font>'''的必要条件。后一项研究的一个重要问题是,在局部动态交换模型时是否需要能量守恒: 一般的答案是否定的,但有一些保留意见,因为一些交换动力学(如 BTW 的动态)确实需要局部至少平均的能量守恒。从长远来看,有待解决的关键理论问题包括 '''<font color="#ff8000"> SOC</font>''' 行为可能的普适性类的计算,以及是否有可能推导出一个确定任意算法是否显示 '''<font color="#ff8000"> SOC</font>''' 的一般规则的问题。<br />
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Alongside these largely lab-based approaches, many other investigations have centered around large-scale natural or social systems that are known (or suspected) to display [[scale invariance|scale-invariant]] behavior. Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: [[earthquakes]] (which, long before SOC was discovered, were known as a source of scale-invariant behavior such as the [[Gutenberg–Richter law]] describing the statistical distribution of earthquake size, and the [[Aftershock|Omori law]] describing the frequency of aftershocks<ref name=TurcotteSmalleySolla85><br />
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Alongside these largely lab-based approaches, many other investigations have centered around large-scale natural or social systems that are known (or suspected) to display scale-invariant behavior. Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: earthquakes (which, long before SOC was discovered, were known as a source of scale-invariant behavior such as the Gutenberg–Richter law describing the statistical distribution of earthquake size, and the Omori law describing the frequency of aftershocks<ref name=TurcotteSmalleySolla85><br />
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除了这些大部分基于实验室的方法,许多其他的研究都集中在大规模的自然或社会系统上,这些系统已经知道(或怀疑)表现出尺度不变的行为。虽然这些方法并不总是受到研究对象专家的欢迎(至少最初是这样) ,但 '''<font color="#ff8000"> SOC</font>''' 已经成为解释一些自然现象的强有力的候选者,包括: 地震(早在 '''<font color="#ff8000"> SOC</font>''' 被发现之前,地震就被认为是尺度不变行为的来源,例如描述地震大小统计分布的古腾堡-里克特定律,以及描述余震频率的描述余震的 Omori 定律,命名为 turcottesmalleysolla85<br />
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{引用期刊<br />
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|author1=Turcotte, D. L. |author2=Smalley, R. F., Jr. |author3=Solla, S. A. | year = 1985<br />
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|author1=Turcotte, D. L. |author2=Smalley, R. F., Jr. |author3=Solla, S. A. | year = 1985<br />
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1 Turcotte,D.l. | author2 Smalley,r. f. ,jr. | author3 Solla,s. a.1985年<br />
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| title = Collapse of loaded fractal trees<br />
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| title = Collapse of loaded fractal trees<br />
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负载分形树的崩溃<br />
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| journal = Nature <br />
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| journal = Nature <br />
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自然》杂志<br />
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| doi= 10.1038/313671a0<br />
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| doi= 10.1038/313671a0<br />
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| volume = 313<br />
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| 第671-672页 | bibcode 1985 / natur. 313. . 671 t<br />
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}}</ref><ref name=SmalleyTurcotteSolla85 />); [[solar flares]]; fluctuations in economic systems such as [[financial markets]] (references to SOC are common in [[econophysics]]); [[landscape formation]]; [[forest fires]]; [[landslides]]; [[epidemics]]; neuronal avalanches in the cortex;<ref name="Beggs2003" /><ref name=Poil2012><br />
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}}</ref>); solar flares; fluctuations in economic systems such as financial markets (references to SOC are common in econophysics); landscape formation; forest fires; landslides; epidemics; neuronal avalanches in the cortex;<ref name=Poil2012><br />
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太阳耀斑; 经济系统的波动,比如金融市场(经济物理学中经常提到 SOC) ; 景观形成; 森林火灾; 滑坡; 流行病; 大脑皮层的神经雪崩; 参考名为 poil2012<br />
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|author1=Poil, SS |author2=Hardstone, R |author3=Mansvelder, HD |author4=Linkenkaer-Hansen, K | title = Critical-state dynamics of avalanches and oscillations jointly emerge from balanced excitation/inhibition in neuronal networks<br />
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|author1=Poil, SS |author2=Hardstone, R |author3=Mansvelder, HD |author4=Linkenkaer-Hansen, K | title = Critical-state dynamics of avalanches and oscillations jointly emerge from balanced excitation/inhibition in neuronal networks<br />
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1 Poil,SS | author2 Hardstone,r | author3 mansveder,HD | author4 Linkenkaer-Hansen,k | title 雪崩和振荡的临界状态动力学联合出现在神经元网络的平衡兴奋 / 抑制中<br />
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| volume = 32<br />
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| doi 10.1523 / jneurosci. 5990-11.2012<br />
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| journal = Journal of Neuroscience<br />
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| journal = Journal of Neuroscience<br />
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}}</ref> 1/f noise in the amplitude of electrophysiological signals;<ref name=LinkenkaerHansen2001 /> and [[biological evolution]] (where SOC has been invoked, for example, as the dynamical mechanism behind the theory of "[[punctuated equilibrium|punctuated equilibria]]" put forward by [[Niles Eldredge]] and [[Stephen Jay Gould]]). These "applied" investigations of SOC have included both modelling (either developing new models or adapting existing ones to the specifics of a given natural system) and extensive data analysis to determine the existence and/or characteristics of natural scaling laws.<br />
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}}</ref> 1/f noise in the amplitude of electrophysiological signals; and biological evolution (where SOC has been invoked, for example, as the dynamical mechanism behind the theory of "punctuated equilibria" put forward by Niles Eldredge and Stephen Jay Gould). These "applied" investigations of SOC have included both modelling (either developing new models or adapting existing ones to the specifics of a given natural system) and extensive data analysis to determine the existence and/or characteristics of natural scaling laws.<br />
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{} / ref 电生理信号振幅的1 / f 噪声,以及生物进化(其中 SOC 已被调用,例如,作为背后的动力机制的理论“间断平衡”由 Niles Eldredge 和史蒂芬·古尔德提出)。对SOC的这些”应用”研究既包括建模(开发新模型或使现有模型适应特定自然系统的具体情况) ,也包括广泛的数据分析,以确定是否存在和 / 或具有自然幂率的特点。<br />
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In addition, SOC has been applied to computational algorithms. Recently, it has been found that the avalanches from an SOC process, like the BTW model, make effective patterns in a random search for optimal solutions on graphs.<ref name=Hoffmann2018><br />
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In addition, SOC has been applied to computational algorithms. Recently, it has been found that the avalanches from an SOC process, like the BTW model, make effective patterns in a random search for optimal solutions on graphs.<ref name=Hoffmann2018><br />
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此外,SOC 已经应用于计算算法。最近,人们发现来自 SOC 过程的雪崩,如 BTW 模型,在图的最优解的随机搜索中形成有效的模式。 参考名称 hoffmann2018<br />
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{引用期刊<br />
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| author = [[H. Hoffmann|Hoffmann, H.]] and [[D. W. Payton|Payton, D. W.]]<br />
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| author = Hoffmann, H. and Payton, D. W.<br />
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| title = Optimization by Self-Organized Criticality<br />
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| title = Optimization by Self-Organized Criticality<br />
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最佳化作者: 自组织临界性<br />
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| journal = [[Scientific Reports]]<br />
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| journal = Scientific Reports<br />
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| doi=10.1038/s41598-018-20275-7<br />
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| doi=10.1038/s41598-018-20275-7<br />
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10.1038 / s41598-018-20275-7<br />
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| pmid = 29402956<br />
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| pmid = 29402956<br />
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| pmc = 5799203<br />
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| pmc = 5799203<br />
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| bibcode = 2018NatSR...8.2358H<br />
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An example of such an optimization problem is [[graph coloring]]. The SOC process apparently helps the optimization from getting stuck in a [[local optimum]] without the use of any [[Simulated_annealing|annealing]] scheme, as suggested by previous work on [[extremal optimization]].<br />
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An example of such an optimization problem is graph coloring. The SOC process apparently helps the optimization from getting stuck in a local optimum without the use of any annealing scheme, as suggested by previous work on extremal optimization.<br />
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图着色就是这种最佳化问题的一个例子。'''<font color="#ff8000"> SOC</font>''' 过程显然有助于避免优化陷入局部最优,而无需使用任何以前的极值优化工作所建议的退火方案。<br />
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The recent excitement generated by [[scale-free networks]] has raised some interesting new questions for SOC-related research: a number of different SOC models have been shown to generate such networks as an emergent phenomenon, as opposed to the simpler models proposed by network researchers where the network tends to be assumed to exist independently of any physical space or dynamics. While many single phenomena have been shown to exhibit scale-free properties over narrow ranges, a phenomenon offering by far a larger amount of data is solvent-accessible surface areas in globular proteins.<ref name=Moret2007><br />
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The recent excitement generated by scale-free networks has raised some interesting new questions for SOC-related research: a number of different SOC models have been shown to generate such networks as an emergent phenomenon, as opposed to the simpler models proposed by network researchers where the network tends to be assumed to exist independently of any physical space or dynamics. While many single phenomena have been shown to exhibit scale-free properties over narrow ranges, a phenomenon offering by far a larger amount of data is solvent-accessible surface areas in globular proteins.<ref name=Moret2007><br />
<br />
'''<font color="#ff8000"> 无标度网络Scale-free networks</font>'''最近引起的兴奋为 '''<font color="#ff8000"> SOC</font>'''相关研究提出了一些有趣的新问题: 许多不同的 '''<font color="#ff8000"> SOC</font>'''模型已经被证明是作为一种涌现现象产生这样的网络,而不是网络研究人员提出的更简单的模型,其中网络往往被假定独立于任何物理空间或动力学存在。虽然许多单一现象已被证明在狭窄的范围内表现出无标度特性,但是到目前为止提供了大量数据的现象是球状蛋白质中溶剂可及的表面区域。 参考名称 moret2007<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[M. A. Moret|Moret, M. A.]] and [[G. Zebende|Zebende, G.]]<br />
<br />
| author = Moret, M. A. and Zebende, G.<br />
<br />
作者: Moret,M.a. and Zebende,g。<br />
<br />
| year = 2007<br />
<br />
| year = 2007<br />
<br />
2007年<br />
<br />
| title = Amino acid hydrophobicity and accessible surface area<br />
<br />
| title = Amino acid hydrophobicity and accessible surface area<br />
<br />
氨基酸疏水性和可达表面积<br />
<br />
| journal = [[Phys. Rev. E]]<br />
<br />
| journal = Phys. Rev. E<br />
<br />
体育杂志。牧师。E<br />
<br />
| volume = 75<br />
<br />
| volume = 75<br />
<br />
第75卷<br />
<br />
| issue = 1<br />
<br />
| issue = 1<br />
<br />
第一期<br />
<br />
| pages = 011920<br />
<br />
| pages = 011920<br />
<br />
011920页<br />
<br />
| doi=10.1103/PhysRevE.75.011920<br />
<br />
| doi=10.1103/PhysRevE.75.011920<br />
<br />
10.1103 / physarve. 75.011920<br />
<br />
| pmid = 17358197<br />
<br />
| pmid = 17358197<br />
<br />
17358197<br />
<br />
| bibcode = 2007PhRvE..75a1920M<br />
<br />
| bibcode = 2007PhRvE..75a1920M<br />
<br />
2007 / phrve. . 75 / a1920M<br />
<br />
}}</ref><br />
<br />
}}</ref><br />
<br />
{} / ref<br />
<br />
These studies quantify the differential geometry of proteins, and resolve many evolutionary puzzles regarding the biological emergence of complexity.<ref name=Phillips2014><br />
<br />
These studies quantify the differential geometry of proteins, and resolve many evolutionary puzzles regarding the biological emergence of complexity.<ref name=Phillips2014><br />
<br />
这些研究量化了蛋白质的微分几何,并解决了许多关于生物复杂性出现的进化之谜<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = Phillips, J. C.<br />
<br />
| author = Phillips, J. C.<br />
<br />
作者: 菲利普斯。<br />
<br />
| year = 2014<br />
<br />
| year = 2014<br />
<br />
2014年<br />
<br />
| title = Fractals and self-organized criticality in proteins<br />
<br />
| title = Fractals and self-organized criticality in proteins<br />
<br />
标题蛋白质中的分形和自组织临界性<br />
<br />
| journal = Physica A<br />
<br />
| journal = Physica A<br />
<br />
物理学杂志 a<br />
<br />
| volume = 415<br />
<br />
| volume = 415<br />
<br />
第415卷<br />
<br />
| pages = 440–448 <br />
<br />
| pages = 440–448 <br />
<br />
第440-448页<br />
<br />
| doi=10.1016/j.physa.2014.08.034<br />
<br />
| doi=10.1016/j.physa.2014.08.034<br />
<br />
| doi 10.1016 / j.physa. 2014.08.034<br />
<br />
| bibcode = 2014PhyA..415..440P<br />
<br />
| bibcode = 2014PhyA..415..440P<br />
<br />
| bibcode 2014PhyA. . 415. . 440 p<br />
<br />
| author-link = J. C. Phillips<br />
<br />
| author-link = J. C. Phillips<br />
<br />
作者链接 J.c. 菲利普斯<br />
<br />
}}</ref><br />
<br />
}}</ref><br />
<br />
{} / ref<br />
<br />
<br />
<br />
<br />
<br />
Despite the considerable interest and research output generated from the SOC hypothesis, there remains no general agreement with regards to its mechanisms in abstract mathematical form. Bak Tang and Wiesenfeld based their hypothesis on the behavior of their sandpile model.<ref name=Bak1987/> However,<br />
<br />
Despite the considerable interest and research output generated from the SOC hypothesis, there remains no general agreement with regards to its mechanisms in abstract mathematical form. Bak Tang and Wiesenfeld based their hypothesis on the behavior of their sandpile model. However,<br />
<br />
尽管 SOC 假说引起了相当大的兴趣和研究成果,但是关于其抽象数学形式的机制仍然没有普遍的一致性。和 Wiesenfeld 基于他们的沙堆模型的行为建立了他们的假设。然而,<br />
<br />
it has been argued that this model would actually generate 1/f<sup>2</sup> noise rather than 1/f noise.<ref name=Jensen1989><br />
<br />
it has been argued that this model would actually generate 1/f<sup>2</sup> noise rather than 1/f noise.<ref name=Jensen1989><br />
<br />
有人认为,这种模型实际上会产生1 / f sup 2 / sup 噪声而不是1 / f 噪声<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[H. J. Jensen|Jensen, H. J.]], [[K. Christensen|Christensen, K.]] and [[H. C. Fogedby|Fogedby, H. C.]]<br />
<br />
| author = Jensen, H. J., Christensen, K. and Fogedby, H. C.<br />
<br />
作者 Jensen,h. j. ,Christensen,k. and fogeby,h. c。<br />
<br />
| year = 1989<br />
<br />
| year = 1989<br />
<br />
1989年<br />
<br />
| title = 1/f noise, distribution of lifetimes, and a pile of sand<br />
<br />
| title = 1/f noise, distribution of lifetimes, and a pile of sand<br />
<br />
标题1 / f 噪音,寿命分布,和一堆沙子<br />
<br />
| journal = [[Phys. Rev. B]]<br />
<br />
| journal = Phys. Rev. B<br />
<br />
体育杂志。牧师。B<br />
<br />
| volume = 40<br />
<br />
| volume = 40<br />
<br />
第40卷<br />
<br />
| issue = 10<br />
<br />
| issue = 10<br />
<br />
第10期<br />
<br />
| pages = 7425–7427<br />
<br />
| pages = 7425–7427<br />
<br />
第7425-7427页<br />
<br />
| doi=10.1103/physrevb.40.7425<br />
<br />
| doi=10.1103/physrevb.40.7425<br />
<br />
10.1103 / physirevb. 40.7425<br />
<br />
| pmid = 9991162<br />
<br />
| pmid = 9991162<br />
<br />
9991162<br />
<br />
|bibcode = 1989PhRvB..40.7425J }}<br />
<br />
|bibcode = 1989PhRvB..40.7425J }}<br />
<br />
1989 / phrvb. 40.7425 j }<br />
<br />
</ref><br />
<br />
</ref><br />
<br />
/ 参考<br />
<br />
This claim was based on untested scaling assumptions, and a more rigorous analysis showed that sandpile models <br />
<br />
This claim was based on untested scaling assumptions, and a more rigorous analysis showed that sandpile models <br />
<br />
这种说法是基于未经测试的比例假设,更严格的分析表明沙堆模型<br />
<br />
generally produce 1/f<sup>a</sup> spectra, with a<2. <ref name=Laurson2005><br />
<br />
generally produce 1/f<sup>a</sup> spectra, with a<2. <ref name=Laurson2005><br />
<br />
一般产生1 / f sup a / sup 光谱,其值为2。参考名称 laurson2005<br />
<br />
{{cite journal |author1=Laurson, Lasse |author2=Alava, Mikko J. |author3=Zapperi, Stefano |title=Letter: Power spectra of self-organized critical sand piles |journal=Journal of Statistical Mechanics: Theory and Experiment |volume=0511 |id=L001 |date=15 September 2005 }}</ref><br />
<br />
</ref><br />
<br />
/ 参考<br />
<br />
Other simulation models were proposed later that could produce true 1/f noise,<ref name=Maslov1999><br />
<br />
Other simulation models were proposed later that could produce true 1/f noise,<ref name=Maslov1999><br />
<br />
其他模拟模型后来被提出,可以产生真正的1 / f 噪声,参考名称 maslov1999<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[S. Maslov|Maslov, S.]], [[C. Tang|Tang, C.]] and [[Y. –C. Zhang|Zhang, Y. - C.]]<br />
<br />
| author = Maslov, S., Tang, C. and Zhang, Y. - C.<br />
<br />
作者 Maslov,s. ,Tang,c. and Zhang,y。- c.<br />
<br />
| year = 1999<br />
<br />
| year = 1999<br />
<br />
1999年<br />
<br />
| title = 1/f noise in Bak-Tang-Wiesenfeld models on narrow stripes<br />
<br />
| title = 1/f noise in Bak-Tang-Wiesenfeld models on narrow stripes<br />
<br />
| 标题1 / f Bak-Tang-Wiesenfeld 窄条纹模型的噪音<br />
<br />
| journal = [[Phys. Rev. Lett.]]<br />
<br />
| journal = Phys. Rev. Lett.<br />
<br />
体育杂志。牧师。莱特。<br />
<br />
| volume = 83<br />
<br />
| volume = 83<br />
<br />
第83卷<br />
<br />
| issue = 12<br />
<br />
| issue = 12<br />
<br />
第12期<br />
<br />
| pages = 2449–2452<br />
<br />
| pages = 2449–2452<br />
<br />
2449-2452页<br />
<br />
| doi=10.1103/physrevlett.83.2449<br />
<br />
| doi=10.1103/physrevlett.83.2449<br />
<br />
10.1103 / physrvlett. 83.2449<br />
<br />
|arxiv = cond-mat/9902074 |bibcode = 1999PhRvL..83.2449M }}<br />
<br />
|arxiv = cond-mat/9902074 |bibcode = 1999PhRvL..83.2449M }}<br />
<br />
| arxiv cond-mat / 9902074 | bibcode 1999PhRvL. . 83.2449 m }<br />
<br />
</ref> and experimental sandpile models were observed to yield 1/f noise.<ref name=Frette1996><br />
<br />
</ref> and experimental sandpile models were observed to yield 1/f noise.<ref name=Frette1996><br />
<br />
/ ref 和实验沙堆模型被观察到产生1 / f 噪音。参考名称 frette1996<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[V.Frette|Frette, V.]], [[K. Christiansen|Christinasen, K.]], [[A. Malthe-Sørenssen|Malthe-Sørenssen, A.]], [[J. Feder|Feder, J]], [[T. Jøssang|Jøssang, T]] and [[P. Meakin|Meaken, P]]<br />
<br />
| author = Frette, V., Christinasen, K., Malthe-Sørenssen, A., Feder, J, Jøssang, T and Meaken, P<br />
<br />
| author = Frette, V., Christinasen, K., Malthe-Sørenssen, A., Feder, J, Jøssang, T and Meaken, P<br />
<br />
| year = 1996<br />
<br />
| year = 1996<br />
<br />
1996年<br />
<br />
| title = Avalanche dynamics in a pile of rice<br />
<br />
| title = Avalanche dynamics in a pile of rice<br />
<br />
| 题目: 大米堆中的雪崩动力学<br />
<br />
| journal = [[Nature (journal)|Nature]]<br />
<br />
| journal = Nature<br />
<br />
自然》杂志<br />
<br />
| volume = 379<br />
<br />
| volume = 379<br />
<br />
第379卷<br />
<br />
| issue = 6560<br />
<br />
| issue = 6560<br />
<br />
第6560期<br />
<br />
| pages = 49–52<br />
<br />
| pages = 49–52<br />
<br />
第49-52页<br />
<br />
| doi =10.1038/379049a0 <br />
<br />
| doi =10.1038/379049a0 <br />
<br />
10.1038 / 379049a0<br />
<br />
| bibcode= 1996Natur.379...49F}}<br />
<br />
| bibcode= 1996Natur.379...49F}}<br />
<br />
1996 / natur. 379... 49F }<br />
<br />
</ref> In addition to the nonconservative theoretical model mentioned above, other theoretical models for SOC have been based upon [[information theory]]<ref name=Dewar2003><br />
<br />
</ref> In addition to the nonconservative theoretical model mentioned above, other theoretical models for SOC have been based upon information theory<ref name=Dewar2003><br />
<br />
除了上面提到的非保守理论模型之外,其他关于 SOC 的理论模型都是基于信息论,例如 dewar2003<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = Dewar, R.<br />
<br />
| author = Dewar, R.<br />
<br />
作者杜瓦,r。<br />
<br />
| year = 2003<br />
<br />
| year = 2003<br />
<br />
2003年<br />
<br />
| title = Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states<br />
<br />
| title = Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states<br />
<br />
非平衡态中涨落定理、最大产生熵和自组织临界性的信息论解释<br />
<br />
| journal =J. Phys. A: Math. Gen. <br />
<br />
| journal =J. Phys. A: Math. Gen. <br />
<br />
| j 杂志。女名女子名。答: 数学。将军。<br />
<br />
| volume = 36<br />
<br />
| volume = 36<br />
<br />
第36卷<br />
<br />
| pages =631&ndash;641<br />
<br />
| pages =631&ndash;641<br />
<br />
631-- 641<br />
<br />
| pmid = <br />
<br />
| pmid = <br />
<br />
我不会让你失望的<br />
<br />
| doi = 10.1088/0305-4470/36/3/303<br />
<br />
| doi = 10.1088/0305-4470/36/3/303<br />
<br />
10.1088 / 0305-4470 / 36 / 3 / 303<br />
<br />
| issue = 3<br />
<br />
| issue = 3<br />
<br />
第三期<br />
<br />
| pmc = <br />
<br />
| pmc = <br />
<br />
我会的,我会的,我会的<br />
<br />
|bibcode = 2003JPhA...36..631D|arxiv = cond-mat/0005382 | author-link = R Dewar<br />
<br />
|bibcode = 2003JPhA...36..631D|arxiv = cond-mat/0005382 | author-link = R Dewar<br />
<br />
| bibcode 2003JPhA... 36. . 631 d | arxiv cond-mat / 0005382 | author-link r Dewar<br />
<br />
}}</ref>, <br />
<br />
}}</ref>, <br />
<br />
} / ref,<br />
<br />
[[mean field theory]]<ref name=Vespignani1998><br />
<br />
mean field theory<ref name=Vespignani1998><br />
<br />
平均场理论参考名称 vespignani1998<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[Alessandro Vespignani|Vespignani, A.]], and [[Stefano Zapperi|Zapperi, S.]]<br />
<br />
| author = Vespignani, A., and Zapperi, S.<br />
<br />
作者 Vespignani,a,和 Zapperi,s。<br />
<br />
| year = 1998<br />
<br />
| year = 1998<br />
<br />
1998年<br />
<br />
| title = How self-organized criticality works: a unified mean-field picture<br />
<br />
| title = How self-organized criticality works: a unified mean-field picture<br />
<br />
标题自组织临界性如何工作: 一个统一的平均场图片<br />
<br />
| journal =Phys. Rev. E <br />
<br />
| journal =Phys. Rev. E <br />
<br />
体育杂志。牧师。E<br />
<br />
| volume = 57<br />
<br />
| volume = 57<br />
<br />
第57卷<br />
<br />
| pages =6345–6362<br />
<br />
| pages =6345–6362<br />
<br />
6345-6362页<br />
<br />
| pmid = <br />
<br />
| pmid = <br />
<br />
我不会让你失望的<br />
<br />
| doi = 10.1103/physreve.57.6345<br />
<br />
| doi = 10.1103/physreve.57.6345<br />
<br />
10.1103 / physorve. 57.6345<br />
<br />
| issue = 6<br />
<br />
| issue = 6<br />
<br />
第六期<br />
<br />
| pmc = <br />
<br />
| pmc = <br />
<br />
我会的,我会的,我会的<br />
<br />
| bibcode = 1998PhRvE..57.6345V<br />
<br />
| bibcode = 1998PhRvE..57.6345V<br />
<br />
| bibcode 1998PhRvE. . 57.6345 v<br />
<br />
| arxiv = cond-mat/9709192<br />
<br />
| arxiv = cond-mat/9709192<br />
<br />
| arxiv = cond-mat/9709192<br />
<br />
| hdl = 2047/d20002173<br />
<br />
| hdl = 2047/d20002173<br />
<br />
2047 / d20002173<br />
<br />
}}</ref>,<br />
<br />
}}</ref>,<br />
<br />
} / ref,<br />
<br />
the [[convergence of random variables]]<ref name=Kendal2015><br />
<br />
the convergence of random variables<ref name=Kendal2015><br />
<br />
随机变量的收敛裁判名称 kendal 2015<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = Kendal, WS<br />
<br />
| author = Kendal, WS<br />
<br />
作者 Kendal,WS<br />
<br />
| year = 2015<br />
<br />
| year = 2015<br />
<br />
2015年<br />
<br />
| title = Self-organized criticality attributed to a central limit-like convergence effect<br />
<br />
| title = Self-organized criticality attributed to a central limit-like convergence effect<br />
<br />
| 标题自组织临界性归因于类似中心极限的聚合效应<br />
<br />
| journal =Physica A <br />
<br />
| journal =Physica A <br />
<br />
物理学杂志 a<br />
<br />
| volume = 421<br />
<br />
| volume = 421<br />
<br />
第421卷<br />
<br />
| pages =141&ndash;150<br />
<br />
| pages =141&ndash;150<br />
<br />
141-- 150页<br />
<br />
| pmid = <br />
<br />
| pmid = <br />
<br />
我不会让你失望的<br />
<br />
| doi = 10.1016/j.physa.2014.11.035<br />
<br />
| doi = 10.1016/j.physa.2014.11.035<br />
<br />
| doi 10.1016 / j.physa. 2014.11.035<br />
<br />
| issue = <br />
<br />
| issue = <br />
<br />
发行<br />
<br />
| pmc = <br />
<br />
| pmc = <br />
<br />
我会的,我会的,我会的<br />
<br />
|bibcode =2015PhyA..421..141K | author-link = Wayne Kendal<br />
<br />
|bibcode =2015PhyA..421..141K | author-link = Wayne Kendal<br />
<br />
| bibcode 2015PhyA. . 421. . 141 k | 作者链接 Wayne Kendal<br />
<br />
}}</ref>,<br />
<br />
}}</ref>,<br />
<br />
} / ref,<br />
<br />
and cluster formation.<ref name=Hoffmann2018b><br />
<br />
and cluster formation.<ref name=Hoffmann2018b><br />
<br />
和簇的形成。参考名称 hoffmann2018b<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = Hoffmann, H.<br />
<br />
| author = Hoffmann, H.<br />
<br />
作者: 霍夫曼。<br />
<br />
| year = 2018<br />
<br />
| year = 2018<br />
<br />
2018年<br />
<br />
| title = Impact of Network Topology on Self-Organized Criticality<br />
<br />
| title = Impact of Network Topology on Self-Organized Criticality<br />
<br />
网络拓扑对自组织临界性的影响<br />
<br />
| journal = Phys. Rev. E <br />
<br />
| journal = Phys. Rev. E <br />
<br />
体育杂志。牧师。E<br />
<br />
| volume = 97<br />
<br />
| volume = 97<br />
<br />
第97卷<br />
<br />
| pages =022313<br />
<br />
| pages =022313<br />
<br />
022313页<br />
<br />
| pmid = 29548239<br />
<br />
| pmid = 29548239<br />
<br />
29548239<br />
<br />
| doi = 10.1103/PhysRevE.97.022313<br />
<br />
| doi = 10.1103/PhysRevE.97.022313<br />
<br />
10.1103 / physarve. 97.022313<br />
<br />
| issue = 2<br />
<br />
| issue = 2<br />
<br />
第二期<br />
<br />
| pmc = <br />
<br />
| pmc = <br />
<br />
我会的,我会的,我会的<br />
<br />
| bibcode =2018PhRvE..97b2313H <br />
<br />
| bibcode =2018PhRvE..97b2313H <br />
<br />
2018 / phrve. . 97 / b2313H<br />
<br />
| author-link = Heiko Hoffmann<br />
<br />
| author-link = Heiko Hoffmann<br />
<br />
作者: 海科 · 霍夫曼<br />
<br />
| doi-access = free<br />
<br />
| doi-access = free<br />
<br />
免费访问<br />
<br />
}}</ref> A continuous model of self-organised criticality is proposed by using [[tropical geometry]].<ref>{{Cite journal|last=Kalinin|first=N.|last2=Guzmán-Sáenz|first2=A.|last3=Prieto|first3=Y.|last4=Shkolnikov|first4=M.|last5=Kalinina|first5=V.|last6=Lupercio|first6=E.|date=2018-08-15|title=Self-organized criticality and pattern emergence through the lens of tropical geometry|journal=Proceedings of the National Academy of Sciences|volume=115|issue=35|language=en|pages=E8135–E8142|doi=10.1073/pnas.1805847115|issn=0027-8424|pmid=30111541|pmc=6126730|arxiv=1806.09153}}</ref><br />
<br />
}}</ref> A continuous model of self-organised criticality is proposed by using tropical geometry.<br />
<br />
{} / ref 一个'''<font color="#ff8000"> 自组织临界Self-organised criticality</font>'''的连续模型是通过使用热带几何来提出的。<br />
<br />
== Examples of self-organized critical dynamics自组织临界动力学的例子 ==<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
In chronological order of development:<br />
<br />
In chronological order of development:<br />
<br />
按发展时间顺序排列:<br />
<br />
<br />
<br />
<br />
<br />
* Stick-slip model of fault failure<ref name="TurcotteSmalleySolla85" /><ref name="SmalleyTurcotteSolla85" /><br />
<br />
*断层破坏的粘滑模型<ref name="TurcotteSmalleySolla85" /><ref name="SmalleyTurcotteSolla85" /><br />
<br />
*[[Abelian sandpile model|Bak–Tang–Wiesenfeld sandpile]]<br />
<br />
*[[阿贝尔沙堆模型| Bak–Tang–Wiesenfeld沙堆]]<br />
<br />
* [[Forest-fire model]]<br />
<br />
*[[森林火灾模型]]<br />
<br />
* [[Olami–Feder–Christensen model]]<br />
<br />
* [[奥拉米·费德·克里斯滕森模型]]<br />
<br />
* [[Bak–Sneppen model]]<br />
<br />
*[[背景模型]]<br />
<br />
== See also 参见==<br />
<br />
<br />
<br />
* [[Pink noise|1/f noise]]<br />
<br />
*[[粉红噪音| 1/f噪音]]<br />
<br />
* [[Complex system]]s<br />
<br />
* [[复杂系统]]s<br />
<br />
* [[Critical brain hypothesis]]<br />
<br />
*[[【关键大脑假说】]]<br />
<br />
* [[Critical exponents]]<br />
<br />
*[[临界指数]]<br />
<br />
* [[Detrended fluctuation analysis]], a method to detect power-law scaling in time series.<br />
<br />
*[[Detrended涨落分析]],一种检测中幂律标度的方法<br />
<br />
* [[Dual-phase evolution]], another process that contributes to self-organization in complex systems.<br />
<br />
* [[双相演化]],另一个有助于自我组织的过程<br />
<br />
* [[Fractal]]s<br />
<br />
* [[分形]]s;<br />
<br />
* [[Ilya Prigogine]], a systems scientist who helped formalize dissipative system behavior in general terms.<br />
<br />
*[[伊利亚·普里高津]],一位帮助将耗散系统形式化的系统科学家<br />
<br />
* [[Power law]]s<br />
<br />
*[[幂律]]s<br />
<br />
* [[Red Queen hypothesis]]<br />
<br />
*[[红皇后假说]]<br />
<br />
* [[Scale invariance]]<br />
<br />
* [[标度不变性]]<br />
<br />
* [[Self-organization]]<br />
<br />
* [[自组织]]<br />
<br />
* [[Self-organized criticality control]]<br />
<br />
*[[自组织临界控制]]<br />
<br />
==References参考资料==<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<references/><br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
== Further reading延伸阅读 ==<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = Adami, C.<br />
<br />
| author = Adami, C.<br />
<br />
作者: 阿达米。<br />
<br />
| year = 1995<br />
<br />
| year = 1995<br />
<br />
1995年<br />
<br />
| title = Self-organized criticality in living systems<br />
<br />
| title = Self-organized criticality in living systems<br />
<br />
| 生命系统中的自组织临界性<br />
<br />
| journal = [[Physics Letters A]]<br />
<br />
| journal = Physics Letters A<br />
<br />
物理学快报<br />
<br />
| volume = 203<br />
<br />
| volume = 203<br />
<br />
第203卷<br />
<br />
| issue = 1<br />
<br />
| issue = 1<br />
<br />
第一期<br />
<br />
| pages = 29&ndash;32<br />
<br />
| pages = 29&ndash;32<br />
<br />
29-- 32页<br />
<br />
| doi = 10.1016/0375-9601(95)00372-A<br />
<br />
| doi = 10.1016/0375-9601(95)00372-A<br />
<br />
| doi 10.1016 / 0375-9601(95)00372-A<br />
<br />
|bibcode = 1995PhLA..203...29A | arxiv = adap-org/9401001<br />
<br />
|bibcode = 1995PhLA..203...29A | arxiv = adap-org/9401001<br />
<br />
|bibcode = 1995PhLA..203...29A | arxiv = adap-org/9401001<br />
<br />
| citeseerx = 10.1.1.456.9543<br />
<br />
| citeseerx = 10.1.1.456.9543<br />
<br />
10.1.1.456.9543<br />
<br />
| author-link = Adami, C<br />
<br />
| author-link = Adami, C<br />
<br />
| 作者链接阿达米,c<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite book<br />
<br />
<br />
<br />
| author = Bak, P.<br />
<br />
| author = Bak, P.<br />
<br />
作者 Bak,p。<br />
<br />
| year = 1996<br />
<br />
| year = 1996<br />
<br />
1996年<br />
<br />
| title = How Nature Works: The Science of Self-Organized Criticality<br />
<br />
| title = How Nature Works: The Science of Self-Organized Criticality<br />
<br />
自然如何运作: 自组织临界性的科学<br />
<br />
| publisher = Copernicus<br />
<br />
| publisher = Copernicus<br />
<br />
出版商哥白尼<br />
<br />
| location = New York<br />
<br />
| location = New York<br />
<br />
| 地点: 纽约<br />
<br />
| isbn = 978-0-387-94791-4<br />
<br />
| isbn = 978-0-387-94791-4<br />
<br />
[国际标准图书编号978-0-387-94791-4]<br />
<br />
| author-link = Per Bak<br />
<br />
| author-link = Per Bak<br />
<br />
| 作者链接 Per Bak<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = [[Per Bak|Bak, P.]] and [[Maya Paczuski|Paczuski, M.]]<br />
<br />
| author = Bak, P. and Paczuski, M.<br />
<br />
作者 Bak,p. and Paczuski,m。<br />
<br />
| year = 1995<br />
<br />
| year = 1995<br />
<br />
1995年<br />
<br />
| title = Complexity, contingency, and criticality<br />
<br />
| title = Complexity, contingency, and criticality<br />
<br />
| 标题复杂性、偶然性和临界性<br />
<br />
| journal = [[Proceedings of the National Academy of Sciences|Proceedings of the National Academy of Sciences of the USA]]<br />
<br />
| journal = Proceedings of the National Academy of Sciences of the USA<br />
<br />
美国美国国家科学院院刊杂志<br />
<br />
| volume = 92<br />
<br />
| volume = 92<br />
<br />
第92卷<br />
<br />
| pages = 6689&ndash;6696<br />
<br />
| pages = 6689&ndash;6696<br />
<br />
6689-- 6696<br />
<br />
| url = http://pnas.org/cgi/content/abstract/92/15/6689<br />
<br />
| url = http://pnas.org/cgi/content/abstract/92/15/6689<br />
<br />
Http://pnas.org/cgi/content/abstract/92/15/6689<br />
<br />
| doi = 10.1073/pnas.92.15.6689<br />
<br />
| doi = 10.1073/pnas.92.15.6689<br />
<br />
10.1073 / pnas. 92.15.6689<br />
<br />
| pmid = 11607561<br />
<br />
| pmid = 11607561<br />
<br />
11607561<br />
<br />
| issue = 15<br />
<br />
| issue = 15<br />
<br />
第15期<br />
<br />
| pmc = 41396<br />
<br />
| pmc = 41396<br />
<br />
41396<br />
<br />
|bibcode = 1995PNAS...92.6689B }}<br />
<br />
|bibcode = 1995PNAS...92.6689B }}<br />
<br />
92.6689 b }<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = [[Per Bak|Bak, P.]] and [[Kim Sneppen|Sneppen, K.]]<br />
<br />
| author = Bak, P. and Sneppen, K.<br />
<br />
作者 Bak,p. and Sneppen,k。<br />
<br />
| year = 1993<br />
<br />
| year = 1993<br />
<br />
1993年<br />
<br />
| title = Punctuated equilibrium and criticality in a simple model of evolution <br />
<br />
| title = Punctuated equilibrium and criticality in a simple model of evolution <br />
<br />
| 简单演化模型中的间断平衡和临界性<br />
<br />
| journal = [[Physical Review Letters]]<br />
<br />
| journal = Physical Review Letters<br />
<br />
物理评论快报<br />
<br />
| volume = 71<br />
<br />
| volume = 71<br />
<br />
第71卷<br />
<br />
| issue = 24<br />
<br />
| issue = 24<br />
<br />
第24期<br />
<br />
| pages = 4083&ndash;4086<br />
<br />
| pages = 4083&ndash;4086<br />
<br />
4083-- 4086<br />
<br />
| doi = 10.1103/PhysRevLett.71.4083<br />
<br />
| doi = 10.1103/PhysRevLett.71.4083<br />
<br />
10.1103 / physrvlett. 71.4083<br />
<br />
| pmid=10055149<br />
<br />
| pmid=10055149<br />
<br />
10055149<br />
<br />
| bibcode=1993PhRvL..71.4083B}}<br />
<br />
| bibcode=1993PhRvL..71.4083B}}<br />
<br />
1993 phrvl. . 71.4083 b }<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = [[Per Bak|Bak, P.]], [[Chao Tang|Tang, C.]] and [[Kurt Wiesenfeld|Wiesenfeld, K.]]<br />
<br />
| author = Bak, P., Tang, C. and Wiesenfeld, K.<br />
<br />
作者 Bak,p. ,Tang,c. and Wiesenfeld,k。<br />
<br />
| year = 1987<br />
<br />
| year = 1987<br />
<br />
1987年<br />
<br />
| title = Self-organized criticality: an explanation of <math>1/f</math> noise<br />
<br />
| title = Self-organized criticality: an explanation of <math>1/f</math> noise<br />
<br />
| 题目自组织临界性: 数学噪音的解释<br />
<br />
| journal = [[Physical Review Letters]]<br />
<br />
| journal = Physical Review Letters<br />
<br />
物理评论快报<br />
<br />
| volume = 59<br />
<br />
| volume = 59<br />
<br />
第59卷<br />
<br />
| issue = 4<br />
<br />
| issue = 4<br />
<br />
第四期<br />
<br />
| pages = 381&ndash;384<br />
<br />
| pages = 381&ndash;384<br />
<br />
381-- 384<br />
<br />
| doi = 10.1103/PhysRevLett.59.381<br />
<br />
| doi = 10.1103/PhysRevLett.59.381<br />
<br />
10.1103 / physrvlett. 59.381<br />
<br />
| pmid = 10035754<br />
<br />
| pmid = 10035754<br />
<br />
10035754<br />
<br />
| bibcode=1987PhRvL..59..381B}}<br />
<br />
| bibcode=1987PhRvL..59..381B}}<br />
<br />
1987 / phrvl. . 59. . 381 b }<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = [[Per Bak|Bak, P.]], [[Chao Tang|Tang, C.]] and [[Kurt Wiesenfeld|Wiesenfeld, K.]]<br />
<br />
| author = Bak, P., Tang, C. and Wiesenfeld, K.<br />
<br />
作者 Bak,p. ,Tang,c. and Wiesenfeld,k。<br />
<br />
| year = 1988<br />
<br />
| year = 1988<br />
<br />
1988年<br />
<br />
| title = Self-organized criticality<br />
<br />
| title = Self-organized criticality<br />
<br />
标题自组织临界性<br />
<br />
| journal = [[Physical Review A]]<br />
<br />
| journal = Physical Review A<br />
<br />
物理评论 a 期刊<br />
<br />
| volume = 38<br />
<br />
| volume = 38<br />
<br />
第38卷<br />
<br />
| issue = 1<br />
<br />
| issue = 1<br />
<br />
第一期<br />
<br />
| pages = 364&ndash;374<br />
<br />
| pages = 364&ndash;374<br />
<br />
364-- 374<br />
<br />
| doi = 10.1103/PhysRevA.38.364<br />
<br />
| doi = 10.1103/PhysRevA.38.364<br />
<br />
10.1103 / PhysRevA. 38.364<br />
<br />
| pmid = 9900174<br />
<br />
| pmid = 9900174<br />
<br />
9900174<br />
<br />
|bibcode = 1988PhRvA..38..364B }} [https://archive.is/20130415140421/http://www.papercore.org/PerBak1987 Papercore summary].<br />
<br />
|bibcode = 1988PhRvA..38..364B }} [https://archive.is/20130415140421/http://www.papercore.org/PerBak1987 Papercore summary].<br />
<br />
| bibcode 1988PhRvA. . 38. . 364 b }[ https://archive.is/20130415140421/http://www.Papercore.org/perbak1987文件核心摘要]。<br />
<br />
<br />
<br />
<br />
<br />
* {{cite book<br />
<br />
<br />
<br />
| author = Buchanan, M.<br />
<br />
| author = Buchanan, M.<br />
<br />
作者: 布坎南。<br />
<br />
| year = 2000<br />
<br />
| year = 2000<br />
<br />
2000年<br />
<br />
| title = Ubiquity<br />
<br />
| title = Ubiquity<br />
<br />
标题: Ubiquity<br />
<br />
| publisher = Weidenfeld &amp; Nicolson<br />
<br />
| publisher = Weidenfeld &amp; Nicolson<br />
<br />
| publisher = Weidenfeld &amp; Nicolson<br />
<br />
| location = London<br />
<br />
| location = London<br />
<br />
地点: 伦敦<br />
<br />
| isbn = 978-0-7538-1297-6<br />
<br />
| isbn = 978-0-7538-1297-6<br />
<br />
[国际标准图书编号978-0-7538-1297-6]<br />
<br />
| author-link = Mark Buchanan<br />
<br />
| author-link = Mark Buchanan<br />
<br />
马克 · 布坎南<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite book<br />
<br />
<br />
<br />
| author = Jensen, H. J.<br />
<br />
| author = Jensen, H. J.<br />
<br />
作者 Jensen,h. j。<br />
<br />
| year = 1998<br />
<br />
| year = 1998<br />
<br />
1998年<br />
<br />
| title = Self-Organized Criticality<br />
<br />
| title = Self-Organized Criticality<br />
<br />
标题自组织临界性<br />
<br />
| publisher = [[Cambridge University Press]]<br />
<br />
| publisher = Cambridge University Press<br />
<br />
出版商剑桥大学出版社<br />
<br />
| location = Cambridge<br />
<br />
| location = Cambridge<br />
<br />
| 地点: 剑桥<br />
<br />
| isbn = 978-0-521-48371-1<br />
<br />
| isbn = 978-0-521-48371-1<br />
<br />
[国际标准图书编号978-0-521-48371-1]<br />
<br />
| author-link = Henrik Jeldtoft Jensen<br />
<br />
| author-link = Henrik Jeldtoft Jensen<br />
<br />
作者: 亨里克 · 耶尔德托夫特 · 詹森<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = Katz, J. I.<br />
<br />
| author = Katz, J. I.<br />
<br />
作者 Katz,j. i。<br />
<br />
| year = 1986<br />
<br />
| year = 1986<br />
<br />
1986年<br />
<br />
| title = A model of propagating brittle failure in heterogeneous media<br />
<br />
| title = A model of propagating brittle failure in heterogeneous media<br />
<br />
在非均匀介质中传播脆性破坏的模型<br />
<br />
| journal = Journal of Geophysical Research<br />
<br />
| journal = Journal of Geophysical Research<br />
<br />
地球物理研究期刊<br />
<br />
| bibcode = 1986JGR....9110412K<br />
<br />
| bibcode = 1986JGR....9110412K<br />
<br />
| bibcode 1986JGR... 9110412K<br />
<br />
| doi = 10.1029/JB091iB10p10412<br />
<br />
| doi = 10.1029/JB091iB10p10412<br />
<br />
| doi 10.1029 / JB091iB10p10412<br />
<br />
| volume = 91<br />
<br />
| volume = 91<br />
<br />
第91卷<br />
<br />
| issue = B10<br />
<br />
| issue = B10<br />
<br />
第10期<br />
<br />
| pages = 10412<br />
<br />
| pages = 10412<br />
<br />
10412页<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = Kron, T./Grund, T.<br />
<br />
| author = Kron, T./Grund, T.<br />
<br />
作者: Kron t. / Grund t。<br />
<br />
| year = 2009<br />
<br />
| year = 2009<br />
<br />
2009年<br />
<br />
| title = Society as a Selforganized Critical System<br />
<br />
| title = Society as a Selforganized Critical System<br />
<br />
作为一个自组织的批判系统的社会<br />
<br />
| journal = Cybernetics and Human Knowing<br />
<br />
| journal = Cybernetics and Human Knowing<br />
<br />
控制论与人类认知<br />
<br />
| volume = 16<br />
<br />
| volume = 16<br />
<br />
第16卷<br />
<br />
| pages = 65–82<br />
<br />
| pages = 65–82<br />
<br />
第65-82页<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{Cite book<br />
<br />
<br />
<br />
| author = Paczuski, M.<br />
<br />
| author = Paczuski, M.<br />
<br />
作者: 帕祖斯基。<br />
<br />
| year = 2005<br />
<br />
| year = 2005<br />
<br />
2005年<br />
<br />
| title = Networks as renormalized models for emergent behavior in physical systems<br />
<br />
| title = Networks as renormalized models for emergent behavior in physical systems<br />
<br />
作为物理系统中突发行为的重整化模型的网络<br />
<br />
| journal = Complexity<br />
<br />
| journal = Complexity<br />
<br />
杂志复杂性<br />
<br />
| pages = 363–374<br />
<br />
| pages = 363–374<br />
<br />
第363-374页<br />
<br />
| arxiv = physics/0502028<br />
<br />
| arxiv = physics/0502028<br />
<br />
| arxiv physics / 0502028<br />
<br />
|bibcode = 2005cmn..conf..363P |doi = 10.1142/9789812701558_0042<br />
<br />
|bibcode = 2005cmn..conf..363P |doi = 10.1142/9789812701558_0042<br />
<br />
2005 / cmn. conf. 363 p | doi 10.1142 / 97898127015580042<br />
<br />
| series = The Science and Culture Series – Physics<br />
<br />
| series = The Science and Culture Series – Physics<br />
<br />
| 科学与文化系列-物理学<br />
<br />
| isbn = 978-981-256-525-9 | citeseerx = 10.1.1.261.9886<br />
<br />
| isbn = 978-981-256-525-9 | citeseerx = 10.1.1.261.9886<br />
<br />
| isbn 978-981-256-525-9 | citeserx 10.1.1.261.9886<br />
<br />
| author-link = Maya Paczuski<br />
<br />
| author-link = Maya Paczuski<br />
<br />
| 作者链接 Maya Paczuski<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite book<br />
<br />
<br />
<br />
| author = Turcotte, D. L.<br />
<br />
| author = Turcotte, D. L.<br />
<br />
作者: Turcotte,D.l。<br />
<br />
| year = 1997<br />
<br />
| year = 1997<br />
<br />
1997年<br />
<br />
| title = Fractals and Chaos in Geology and Geophysics<br />
<br />
| title = Fractals and Chaos in Geology and Geophysics<br />
<br />
地质学与地球物理学中的分形与混沌<br />
<br />
| publisher = [[Cambridge University Press]]<br />
<br />
| publisher = Cambridge University Press<br />
<br />
出版商剑桥大学出版社<br />
<br />
| location = Cambridge<br />
<br />
| location = Cambridge<br />
<br />
| 地点: 剑桥<br />
<br />
| isbn = 978-0-521-56733-6<br />
<br />
| isbn = 978-0-521-56733-6<br />
<br />
[国际标准图书馆编号978-0-521-56733-6]<br />
<br />
| author-link = Donald L. Turcotte<br />
<br />
| author-link = Donald L. Turcotte<br />
<br />
作者: Donald l. Turcotte<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = Turcotte, D. L.<br />
<br />
| author = Turcotte, D. L.<br />
<br />
作者: Turcotte,D.l。<br />
<br />
| year = 1999<br />
<br />
| year = 1999<br />
<br />
1999年<br />
<br />
| title = Self-organized criticality<br />
<br />
| title = Self-organized criticality<br />
<br />
标题自组织临界性<br />
<br />
| journal = [[Reports on Progress in Physics]]<br />
<br />
| journal = Reports on Progress in Physics<br />
<br />
物理学进展报告<br />
<br />
| volume = 62<br />
<br />
| volume = 62<br />
<br />
第62卷<br />
<br />
| issue = 10<br />
<br />
| issue = 10<br />
<br />
第10期<br />
<br />
| pages = 1377&ndash;1429<br />
<br />
| pages = 1377&ndash;1429<br />
<br />
13771429页<br />
<br />
| doi = 10.1088/0034-4885/62/10/201<br />
<br />
| doi = 10.1088/0034-4885/62/10/201<br />
<br />
10.1088 / 0034-4885 / 62 / 10 / 201<br />
<br />
|bibcode = 1999RPPh...62.1377T | author-link = Donald L. Turcotte<br />
<br />
|bibcode = 1999RPPh...62.1377T | author-link = Donald L. Turcotte<br />
<br />
| bibcode 1999RPPh... 62.1377 t | 作者链接 Donald l. Turcotte<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = Md. Nurujjaman/A. N. Sekar Iyengar<br />
<br />
| author = Md. Nurujjaman/A. N. Sekar Iyengar<br />
<br />
作者马里兰大学。Nurujjaman / a.N. Sekar Iyengar<br />
<br />
| year = 2007<br />
<br />
| year = 2007<br />
<br />
2007年<br />
<br />
| title = Realization of {SOC} behavior in a dc glow discharge plasma<br />
<br />
| title = Realization of {SOC} behavior in a dc glow discharge plasma<br />
<br />
直流辉光放电等离子体{ SOC }行为的实现<br />
<br />
| journal = [[Physics Letters A]]<br />
<br />
| journal = Physics Letters A<br />
<br />
物理学快报<br />
<br />
| volume = 360<br />
<br />
| volume = 360<br />
<br />
第360卷<br />
<br />
| issue = 6<br />
<br />
| issue = 6<br />
<br />
第六期<br />
<br />
| pages = 717&ndash;721<br />
<br />
| pages = 717&ndash;721<br />
<br />
717-- 721页<br />
<br />
|arxiv = physics/0611069 |bibcode = 2007PhLA..360..717N |doi = 10.1016/j.physleta.2006.09.005 | author-link = Md. Nurujjaman/A. N. Sekar Iyengar<br />
<br />
|arxiv = physics/0611069 |bibcode = 2007PhLA..360..717N |doi = 10.1016/j.physleta.2006.09.005 | author-link = Md. Nurujjaman/A. N. Sekar Iyengar<br />
<br />
| arxiv physics / 0611069 | bibcode 2007 phla. . 360. . 717 n | doi 10.1016 / j.physleta. 2006.09.005 | author-link md.Nurujjaman / a.N. Sekar Iyengar<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
*[http://xstructure.inr.ac.ru/x-bin/theme2.py?arxiv=cond-mat&level=1&index1=20771 Self-organized criticality on arxiv.org]<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
[[Category:Critical phenomena]]<br />
<br />
Category:Critical phenomena<br />
<br />
范畴: 关键现象<br />
<br />
[[Category:Applied and interdisciplinary physics]]<br />
<br />
Category:Applied and interdisciplinary physics<br />
<br />
类别: 应用和跨学科物理学<br />
<br />
[[Category:Chaos theory]]<br />
<br />
Category:Chaos theory<br />
<br />
范畴: 混沌理论<br />
<br />
[[Category:Self-organization]]<br />
<br />
Category:Self-organization<br />
<br />
类别: 自我组织<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Self-organized criticality]]. Its edit history can be viewed at [[自组织临界性/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E8%87%AA%E7%BB%84%E7%BB%87%E4%B8%B4%E7%95%8C%E6%80%A7&diff=21921自组织临界性2021-02-20T15:16:37Z<p>Jxzhou:/* Overview 概览 */</p>
<hr />
<div>此词条暂由水流心不竞初译,未经审校,带来阅读不便,请见谅。<br />
<br />
In [[physics]], '''self-organized criticality''' ('''SOC''') is a property of [[dynamical system]]s that have a [[critical phenomena|critical point]] as an [[attractor]]. Their macroscopic behavior thus displays the spatial or temporal [[scale invariance|scale-invariance]] characteristic of the [[critical point (physics)|critical point]] of a [[phase transition]], but without the need to tune control parameters to a precise value, because the system, effectively, tunes itself as it evolves towards criticality.<br />
<br />
In physics, self-organized criticality (SOC) is a property of dynamical systems that have a critical point as an attractor. Their macroscopic behavior thus displays the spatial or temporal scale-invariance characteristic of the critical point of a phase transition, but without the need to tune control parameters to a precise value, because the system, effectively, tunes itself as it evolves towards criticality.<br />
<br />
在物理学中,'''<font color="#ff8000"> 自组织临界性Self-organized criticality (SOC)</font>'''是动力系统的一种特性,动力系统有一个临界点作为'''<font color="#ff8000"> 吸引子Attractor</font>'''。它们的宏观行为因此显示了相变临界点的空间或时间尺度不变特性,但不需要把控制参数调整到一个精确的值,因为系统在趋向于临界状态时有效地自我调整。<br />
<br />
<br />
<br />
<br />
<br />
The concept was put forward by [[Per Bak]], [[Chao Tang]] and [[Kurt Wiesenfeld]] ("BTW") in a paper<ref name=Bak1987><br />
<br />
The concept was put forward by Per Bak, Chao Tang and Kurt Wiesenfeld ("BTW") in a paper<ref name=Bak1987><br />
<br />
这个概念是由 Per Bak,Chao Tang 和 Kurt Wiesenfeld (“ BTW”)在一篇名为 bak1987的论文中提出的<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[Per Bak|Bak, P.]], [[Chao Tang|Tang, C.]] and [[Kurt Wiesenfeld|Wiesenfeld, K.]]<br />
<br />
| author = Bak, P., Tang, C. and Wiesenfeld, K.<br />
<br />
作者 Bak,p. ,Tang,c. and Wiesenfeld,k。<br />
<br />
| year = 1987<br />
<br />
| year = 1987<br />
<br />
1987年<br />
<br />
| title = Self-organized criticality: an explanation of 1/''f'' noise<br />
<br />
| title = Self-organized criticality: an explanation of 1/f noise<br />
<br />
自组织临界性: 1 / f 噪音的解释<br />
<br />
| journal = [[Physical Review Letters]]<br />
<br />
| journal = Physical Review Letters<br />
<br />
物理评论快报<br />
<br />
| volume = 59<br />
<br />
| volume = 59<br />
<br />
第59卷<br />
<br />
| issue = 4<br />
<br />
| issue = 4<br />
<br />
第四期<br />
<br />
| pages = 381&ndash;384<br />
<br />
| pages = 381&ndash;384<br />
<br />
381-- 384<br />
<br />
| doi = 10.1103/PhysRevLett.59.381<br />
<br />
| doi = 10.1103/PhysRevLett.59.381<br />
<br />
10.1103 / physrvlett. 59.381<br />
<br />
| pmid = 10035754<br />
<br />
| pmid = 10035754<br />
<br />
10035754<br />
<br />
| bibcode=1987PhRvL..59..381B<br />
<br />
| bibcode=1987PhRvL..59..381B<br />
<br />
| bibcode 1987PhRvL. . 59. . 381 b<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
Papercore summary: [https://archive.is/20130704122906/http://papercore.org/Bak1987 http://papercore.org/Bak1987].</ref> <br />
<br />
Papercore summary: [https://archive.is/20130704122906/http://papercore.org/Bak1987 http://papercore.org/Bak1987].</ref> <br />
<br />
论文摘要: [ https://archive.is/20130704122906/http://Papercore.org/bak1987 http://Papercore.org/bak1987] / 参考<br />
<br />
published in 1987 in ''[[Physical Review Letters]]'', and is considered to be one of the mechanisms by which [[complexity]]<ref name=Bak1995><br />
<br />
published in 1987 in Physical Review Letters, and is considered to be one of the mechanisms by which complexity<ref name=Bak1995><br />
<br />
1987年发表在《物理评论快报》上,被认为是复杂性的机制之一<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[Per Bak|Bak, P.]], and [[Maya Paczuski|Paczuski, M.]]<br />
<br />
| author = Bak, P., and Paczuski, M.<br />
<br />
作者 Bak,p,and Paczuski,m。<br />
<br />
| year = 1995<br />
<br />
| year = 1995<br />
<br />
1995年<br />
<br />
| title = Complexity, contingency, and criticality<br />
<br />
| title = Complexity, contingency, and criticality<br />
<br />
| 标题复杂性、偶然性和临界性<br />
<br />
| journal =Proc Natl Acad Sci U S A <br />
<br />
| journal =Proc Natl Acad Sci U S A <br />
<br />
美国科学促进协会<br />
<br />
| volume = 92<br />
<br />
| volume = 92<br />
<br />
第92卷<br />
<br />
| pages = 6689&ndash;6696<br />
<br />
| pages = 6689&ndash;6696<br />
<br />
6689-- 6696<br />
<br />
| pmid = 11607561<br />
<br />
| pmid = 11607561<br />
<br />
11607561<br />
<br />
| doi = 10.1073/pnas.92.15.6689<br />
<br />
| doi = 10.1073/pnas.92.15.6689<br />
<br />
10.1073 / pnas. 92.15.6689<br />
<br />
| issue = 15<br />
<br />
| issue = 15<br />
<br />
第15期<br />
<br />
| pmc = 41396<br />
<br />
| pmc = 41396<br />
<br />
41396<br />
<br />
|bibcode = 1995PNAS...92.6689B }}</ref> arises in nature. Its concepts have been applied across fields as diverse as [[geophysics]],<ref name=SmalleyTurcotteSolla85><br />
<br />
|bibcode = 1995PNAS...92.6689B }}</ref> arises in nature. Its concepts have been applied across fields as diverse as geophysics,<ref name=SmalleyTurcotteSolla85><br />
<br />
| bibcode 1995PNAS... 92.6689 b } / ref 在自然界中出现。它的概念已经被应用于各个领域,比如地球物理学,参考名称 smalleyturcottesolla85<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
|author1=Smalley, R. F., Jr. |author2=Turcotte, D. L. |author3=Solla, S. A. | year = 1985<br />
<br />
|author1=Smalley, R. F., Jr. |author2=Turcotte, D. L. |author3=Solla, S. A. | year = 1985<br />
<br />
1 Smalley,r. f. ,jr. | author2 Turcotte,d. l. | author3 Solla,s. a.1985年<br />
<br />
| title = A renormalization group approach to the stick-slip behavior of faults<br />
<br />
| title = A renormalization group approach to the stick-slip behavior of faults<br />
<br />
| 题目: 断层粘滑行为的重整化群方法<br />
<br />
| journal = Journal of Geophysical Research<br />
<br />
| journal = Journal of Geophysical Research<br />
<br />
地球物理研究期刊<br />
<br />
| bibcode = 1985JGR....90.1894S<br />
<br />
| bibcode = 1985JGR....90.1894S<br />
<br />
1985JGR... 90.1894 s<br />
<br />
| doi = 10.1029/JB090iB02p01894<br />
<br />
| doi = 10.1029/JB090iB02p01894<br />
<br />
| doi 10.1029 / JB090iB02p01894<br />
<br />
| volume = 90<br />
<br />
| volume = 90<br />
<br />
第90卷<br />
<br />
| issue = B2<br />
<br />
| issue = B2<br />
<br />
| 第二期<br />
<br />
| pages = 1894<br />
<br />
| pages = 1894<br />
<br />
1894页<br />
<br />
|url=https://semanticscholar.org/paper/6776d17957204c198e278bda98c935ab1cf8f22b }}</ref> [[physical cosmology]], [[evolutionary biology]] and [[ecology]], [[bio-inspired computing]] and [[optimization (mathematics)]], [[economics]], [[quantum gravity]], [[sociology]], [[solar physics]], [[plasma physics]], [[neurobiology]]<ref name=LinkenkaerHansen2001><br />
<br />
|url=https://semanticscholar.org/paper/6776d17957204c198e278bda98c935ab1cf8f22b }}</ref> physical cosmology, evolutionary biology and ecology, bio-inspired computing and optimization (mathematics), economics, quantum gravity, sociology, solar physics, plasma physics, neurobiology<ref name=LinkenkaerHansen2001><br />
<br />
[ https://semanticscholar.org/paper/6776d17957204c198e278bda98c935ab1cf8f22b ] / ref 物理宇宙学,进化生物学和生态学,生物启发计算和优化(数学) ,经济学,量子引力,社会学,太阳物理学,等离子物理学,神经生物学参考名称 linkenkaerhansen2001<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
|author1=K. Linkenkaer-Hansen |author2=V. V. Nikouline |author3=J. M. Palva |author4=R. J. Ilmoniemi. |last-author-amp=yes | year = 2001<br />
<br />
|author1=K. Linkenkaer-Hansen |author2=V. V. Nikouline |author3=J. M. Palva |author4=R. J. Ilmoniemi. |last-author-amp=yes | year = 2001<br />
<br />
1 k.Linkenkaer-hansen | author2 v.3 j.4 r.作者: j. Ilmoniemi。最后一个作者2001年<br />
<br />
| title = Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations<br />
<br />
| title = Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations<br />
<br />
人类大脑振荡中的长程时间相关性和标度行为<br />
<br />
| journal = J. Neurosci.<br />
<br />
| journal = J. Neurosci.<br />
<br />
作者: j. Neurosci。<br />
<br />
| volume = 21<br />
<br />
| volume = 21<br />
<br />
第21卷<br />
<br />
| pages = 1370&ndash;1377<br />
<br />
| pages = 1370&ndash;1377<br />
<br />
1370-- 1377<br />
<br />
| pmid = 11160408<br />
<br />
| pmid = 11160408<br />
<br />
11160408<br />
<br />
| issue = 4<br />
<br />
| issue = 4<br />
<br />
第四期<br />
<br />
|doi=10.1523/JNEUROSCI.21-04-01370.2001 |pmc=6762238 }}</ref><ref name=Beggs2003><br />
<br />
|doi=10.1523/JNEUROSCI.21-04-01370.2001 |pmc=6762238 }}</ref><ref name=Beggs2003><br />
<br />
| doi 10.1523 / jneurosci. 21-04-01370.2001 | pmc 6762238} / ref name begs2003<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
|author1=J. M. Beggs |author2=D. Plenz<br />
<br />
|author1=J. M. Beggs |author2=D. Plenz<br />
<br />
1 j.2 d.Plenz<br />
<br />
|lastauthoramp=yes | year = 2006<br />
<br />
|lastauthoramp=yes | year = 2006<br />
<br />
2006年<br />
<br />
| title = Neuronal Avalanches in Neocortical Circuits<br />
<br />
| title = Neuronal Avalanches in Neocortical Circuits<br />
<br />
新皮层神经回路中的神经雪崩<br />
<br />
| journal = J. Neurosci.<br />
<br />
| journal = J. Neurosci.<br />
<br />
作者: j. Neurosci。<br />
<br />
| volume = 23<br />
<br />
| volume = 23<br />
<br />
第23卷<br />
<br />
|issue=35<br />
<br />
|issue=35<br />
<br />
第35期<br />
<br />
|pages=11167–77<br />
<br />
|pages=11167–77<br />
<br />
第11167-77页<br />
<br />
|doi=10.1523/JNEUROSCI.23-35-11167.2003<br />
<br />
|doi=10.1523/JNEUROSCI.23-35-11167.2003<br />
<br />
10.1523 / jneurosci. 23-35-11167.2003<br />
<br />
|pmid=14657176<br />
<br />
|pmid=14657176<br />
<br />
14657176<br />
<br />
|pmc=6741045<br />
<br />
|pmc=6741045<br />
<br />
6741045<br />
<br />
}}</ref><ref name=Chialvo2004><br />
<br />
}}</ref><ref name=Chialvo2004><br />
<br />
} / ref ref name chialvo2004<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author =Chialvo, D. R.<br />
<br />
| author =Chialvo, D. R.<br />
<br />
作者 Chialvo,d. r。<br />
<br />
| year = 2004<br />
<br />
| year = 2004<br />
<br />
2004年<br />
<br />
| title = Critical brain networks<br />
<br />
| title = Critical brain networks<br />
<br />
关键的大脑网络<br />
<br />
| journal = Physica A<br />
<br />
| journal = Physica A<br />
<br />
物理学杂志 a<br />
<br />
| volume = 340<br />
<br />
| volume = 340<br />
<br />
第340卷<br />
<br />
| issue =4<br />
<br />
| issue =4<br />
<br />
第四期<br />
<br />
| pages = 756&ndash;765<br />
<br />
| pages = 756&ndash;765<br />
<br />
756-- 765<br />
<br />
| doi = 10.1016/j.physa.2004.05.064<br />
<br />
| doi = 10.1016/j.physa.2004.05.064<br />
<br />
10.1016 / j.physa. 2004.05.064<br />
<br />
|arxiv = cond-mat/0402538 |bibcode = 2004PhyA..340..756R | author-link = Dante R. Chialvo<br />
<br />
|arxiv = cond-mat/0402538 |bibcode = 2004PhyA..340..756R | author-link = Dante R. Chialvo<br />
<br />
| arxiv cond-mat / 0402538 | bibcode 2004PhyA. . 340. . 756 r | author-link Dante r. Chialvo<br />
<br />
}}</ref> and others.<br />
<br />
}}</ref> and others.<br />
<br />
} / ref and others.<br />
<br />
<br />
<br />
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SOC is typically observed in slowly driven [[non-equilibrium thermodynamics|non-equilibrium]] systems with many [[degrees of freedom (physics and chemistry)|degrees of freedom]] and strongly [[nonlinearity|nonlinear]] dynamics. Many individual examples have been identified since BTW's original paper, but to date there is no known set of general characteristics that ''guarantee'' a system will display SOC.<br />
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SOC is typically observed in slowly driven non-equilibrium systems with many degrees of freedom and strongly nonlinear dynamics. Many individual examples have been identified since BTW's original paper, but to date there is no known set of general characteristics that guarantee a system will display SOC.<br />
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'''<font color="#ff8000"> SOC</font>'''是典型的多自由度、强非线性动力学的缓慢驱动非平衡系统。自从 BTW 的原始论文以来,已经确定了许多单独的例子,但是到目前为止还没有一组已知的一般特征来保证一个系统将显示 '''<font color="#ff8000"> SOC</font>'''。<br />
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== Overview 概览==<br />
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Self-organized criticality is one of a number of important discoveries made in [[statistical physics]] and related fields over the latter half of the 20th century, discoveries which relate particularly to the study of [[complexity]] in nature. For example, the study of [[cellular automata]], from the early discoveries of [[Stanislaw Ulam]] and [[John von Neumann]] through to [[John Horton Conway|John Conway]]'s [[Conway's Game of Life|Game of Life]] and the extensive work of [[Stephen Wolfram]], made it clear that complexity could be generated as an [[emergence|emergent]] feature of extended systems with simple local interactions. Over a similar period of time, [[Benoît Mandelbrot]]'s large body of work on [[fractals]] showed that much complexity in nature could be described by certain ubiquitous mathematical laws, while the extensive study of [[phase transition]]s carried out in the 1960s and 1970s showed how [[scale invariance|scale invariant]] phenomena such as [[fractals]] and [[power law]]s emerged at the [[critical point (physics)|critical point]] between phases.<br />
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Self-organized criticality is one of a number of important discoveries made in statistical physics and related fields over the latter half of the 20th century, discoveries which relate particularly to the study of complexity in nature. For example, the study of cellular automata, from the early discoveries of Stanislaw Ulam and John von Neumann through to John Conway's Game of Life and the extensive work of Stephen Wolfram, made it clear that complexity could be generated as an emergent feature of extended systems with simple local interactions. Over a similar period of time, Benoît Mandelbrot's large body of work on fractals showed that much complexity in nature could be described by certain ubiquitous mathematical laws, while the extensive study of phase transitions carried out in the 1960s and 1970s showed how scale invariant phenomena such as fractals and power laws emerged at the critical point between phases.<br />
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'''<font color="#ff8000"> 自组织临界性Self-organized criticality(SOC)</font>'''是20世纪下半叶统计物理学及相关领域的众多重要发现之一,这些发现尤其与研究自然界的复杂性有关。例如,元胞自动机的研究---- 从 Stanislaw Ulam 和约翰·冯·诺伊曼的早期发现到 John Conway 的生命游戏和 Stephen Wolfram 的大量工作---- 清楚地表明,复杂性可以作为具有简单局部相互作用的扩展系统的一个涌现特征而产生。在相似的时间段内,beno t Mandelbrot 关于分形的大量工作表明,自然界的许多复杂性可以用某些无处不在的数学定律来描述,而在20世纪60年代和70年代对相变的广泛研究表明,诸如分形和幂律等尺度不变现象是如何出现在相变的临界点上的。<br />
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The term ''self-organized criticality'' was firstly introduced by [[Per Bak|Bak]], [[Chao Tang|Tang]] and [[Kurt Wiesenfeld|Wiesenfeld]]'s 1987 paper, which clearly linked together those factors: a simple [[cellular automaton]] was shown to produce several characteristic features observed in natural complexity ([[fractal]] geometry, [[pink noise|pink (1/f) noise]] and [[power law]]s) in a way that could be linked to [[critical point (physics)|critical-point phenomena]]. Crucially, however, the paper emphasized that the complexity observed emerged in a robust manner that did not depend on finely tuned details of the system: variable parameters in the model could be changed widely without affecting the emergence of critical behavior: hence, ''[[self-organized]]'' criticality. Thus, the key result of BTW's paper was its discovery of a mechanism by which the emergence of complexity from simple local interactions could be ''spontaneous''&mdash;and therefore plausible as a source of natural complexity&mdash;rather than something that was only possible in artificial situations in which control parameters are tuned to precise critical values. The publication of this research sparked considerable interest from both theoreticians and experimentalists, producing some of the most cited papers in the scientific literature.<br />
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The term self-organized criticality was firstly introduced by Bak, Tang and Wiesenfeld's 1987 paper, which clearly linked together those factors: a simple cellular automaton was shown to produce several characteristic features observed in natural complexity (fractal geometry, pink (1/f) noise and power laws) in a way that could be linked to critical-point phenomena. Crucially, however, the paper emphasized that the complexity observed emerged in a robust manner that did not depend on finely tuned details of the system: variable parameters in the model could be changed widely without affecting the emergence of critical behavior: hence, self-organized criticality. Thus, the key result of BTW's paper was its discovery of a mechanism by which the emergence of complexity from simple local interactions could be spontaneous&mdash;and therefore plausible as a source of natural complexity&mdash;rather than something that was only possible in artificial situations in which control parameters are tuned to precise critical values. The publication of this research sparked considerable interest from both theoreticians and experimentalists, producing some of the most cited papers in the scientific literature.<br />
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'''<font color="#ff8000"> 自组织临界性Self-organized criticality(SOC)</font>'''这个术语最早由 Bak,Tang 和 Wiesenfeld 在1987年的论文中提出,这篇论文将这些因素清楚地联系在一起: 一个简单的细胞自动机被证明可以产生在自然复杂性中观察到的几个特征(分形几何、粉红噪声和幂律) ,这种方式可以与临界点现象联系起来。然而,关键的是,这篇论文强调,观察到的复杂性是以一种强有力的方式出现的,并不依赖于系统精细调整的细节: 模型中的可变参数可以被广泛改变,而不会影响临界行为的涌现: 因此,具有自组织临界性。因此,BTW 论文的关键结果是发现了一种机制,通过这种机制,从简单的局部相互作用中产生的复杂性可能是自发的---- 因此是合理的自然复杂性的来源---- 而不是只有在控制参数调整到精确的临界值的人工情况下才可能出现的东西。这项研究的发表引起了理论家和实验家的极大兴趣,产生了一些在科学文献中被引用最多的论文。<br />
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Due to BTW's metaphorical visualization of their model as a "[[Bak–Tang–Wiesenfeld sandpile|sandpile]]" on which new sand grains were being slowly sprinkled to cause "avalanches", much of the initial experimental work tended to focus on examining real avalanches in [[granular matter]], the most famous and extensive such study probably being the Oslo ricepile experiment{{Citation needed|date=March 2018}}. Other experiments include those carried out on magnetic-domain patterns, the [[Barkhausen effect]] and vortices in [[superconductors]]. <br />
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Due to BTW's metaphorical visualization of their model as a "sandpile" on which new sand grains were being slowly sprinkled to cause "avalanches", much of the initial experimental work tended to focus on examining real avalanches in granular matter, the most famous and extensive such study probably being the Oslo ricepile experiment. Other experiments include those carried out on magnetic-domain patterns, the Barkhausen effect and vortices in superconductors. <br />
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由于 BTW 将他们的模型比喻为一个“沙堆” ,在沙堆上缓慢地喷洒新的沙粒以引起“雪崩” ,所以最初的实验工作主要集中在研究颗粒物质中的真实雪崩,其中最著名和最广泛的研究可能是奥斯陆地震实验。其他实验还包括在磁畴图案、超导体中的巴克豪森效应和涡旋上进行的实验。<br />
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Early theoretical work included the development of a variety of alternative SOC-generating dynamics distinct from the BTW model, attempts to prove model properties analytically (including calculating the [[critical exponent]]s<ref name=Tang1988a><br />
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Early theoretical work included the development of a variety of alternative SOC-generating dynamics distinct from the BTW model, attempts to prove model properties analytically (including calculating the critical exponents<ref name=Tang1988a><br />
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早期的理论工作包括开发各种不同于 BTW 模型的 soc 生成动力学,试图解析证明模型的性质(包括计算临界指数,参见 tang1988a<br />
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{{cite journal<br />
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{{cite journal<br />
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{引用期刊<br />
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| author = [[Chao Tang|Tang, C.]] and [[Per Bak|Bak, P.]]<br />
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| author = Tang, C. and Bak, P.<br />
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作者 Tang,c. and Bak,p。<br />
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| year = 1988<br />
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| year = 1988<br />
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1988年<br />
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| title = Critical exponents and scaling relations for self-organized critical phenomena<br />
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| title = Critical exponents and scaling relations for self-organized critical phenomena<br />
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自组织临界现象的临界指数和标度关系<br />
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| journal = [[Physical Review Letters]]<br />
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| journal = Physical Review Letters<br />
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物理评论快报<br />
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| volume = 60<br />
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| pages = 2347&ndash;2350<br />
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| doi = 10.1103/PhysRevLett.60.2347<br />
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| doi = 10.1103/PhysRevLett.60.2347<br />
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10.1103 / physrvlett. 60.2347<br />
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| bibcode= 1988PhRvL..60.2347T<br />
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| bibcode= 1988PhRvL..60.2347T<br />
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1988 / phrvl. 60.2347 t<br />
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</ref><ref name=Tang1988b><br />
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</ref><ref name=Tang1988b><br />
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/ ref / name tang1988b<br />
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{{cite journal<br />
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{{cite journal<br />
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{引用期刊<br />
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| author = [[Chao Tang|Tang, C.]] and [[Per Bak|Bak, P.]]<br />
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| author = Tang, C. and Bak, P.<br />
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作者 Tang,c. and Bak,p。<br />
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| year = 1988<br />
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| year = 1988<br />
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1988年<br />
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| title = Mean field theory of self-organized critical phenomena<br />
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| title = Mean field theory of self-organized critical phenomena<br />
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自组织临界现象的平均场理论<br />
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| journal = [[Journal of Statistical Physics]]<br />
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| journal = Journal of Statistical Physics<br />
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统计物理学杂志<br />
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| volume = 51<br />
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| pages = 797&ndash;802<br />
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| doi = 10.1007/BF01014884<br />
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| bibcode= 1988JSP....51..797T<br />
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| bibcode= 1988JSP....51..797T<br />
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1988JSP... 51. . 797 t<br />
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| url = https://zenodo.org/record/1232502<br />
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Https://zenodo.org/record/1232502<br />
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| type = Submitted manuscript<br />
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| type = Submitted manuscript<br />
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| 打印提交的手稿<br />
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</ref>), and examination of the conditions necessary for SOC to emerge. One of the important issues for the latter investigation was whether [[conservation of energy]] was required in the local dynamical exchanges of models: the answer in general is no, but with (minor) reservations, as some exchange dynamics (such as those of BTW) do require local conservation at least on average. In the long term, key theoretical issues yet to be resolved include the calculation of the possible [[universality class]]es of SOC behavior and the question of whether it is possible to derive a general rule for determining if an arbitrary [[algorithm]] displays SOC.<br />
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</ref>), and examination of the conditions necessary for SOC to emerge. One of the important issues for the latter investigation was whether conservation of energy was required in the local dynamical exchanges of models: the answer in general is no, but with (minor) reservations, as some exchange dynamics (such as those of BTW) do require local conservation at least on average. In the long term, key theoretical issues yet to be resolved include the calculation of the possible universality classes of SOC behavior and the question of whether it is possible to derive a general rule for determining if an arbitrary algorithm displays SOC.<br />
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/ ref) ,以及研究出现 '''<font color="#ff8000"> SOC</font>'''的必要条件。后一项研究的一个重要问题是,在局部动态交换模型时是否需要能量守恒: 一般的答案是否定的,但有一些保留意见,因为一些交换动力学(如 BTW 的动态)确实需要局部至少平均的能量守恒。从长远来看,有待解决的关键理论问题包括 '''<font color="#ff8000"> SOC</font>''' 行为可能的普适性类的计算,以及是否有可能推导出一个确定任意算法是否显示 '''<font color="#ff8000"> SOC</font>''' 的一般规则的问题。<br />
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Alongside these largely lab-based approaches, many other investigations have centered around large-scale natural or social systems that are known (or suspected) to display [[scale invariance|scale-invariant]] behavior. Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: [[earthquakes]] (which, long before SOC was discovered, were known as a source of scale-invariant behavior such as the [[Gutenberg–Richter law]] describing the statistical distribution of earthquake size, and the [[Aftershock|Omori law]] describing the frequency of aftershocks<ref name=TurcotteSmalleySolla85><br />
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Alongside these largely lab-based approaches, many other investigations have centered around large-scale natural or social systems that are known (or suspected) to display scale-invariant behavior. Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: earthquakes (which, long before SOC was discovered, were known as a source of scale-invariant behavior such as the Gutenberg–Richter law describing the statistical distribution of earthquake size, and the Omori law describing the frequency of aftershocks<ref name=TurcotteSmalleySolla85><br />
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除了这些大部分基于实验室的方法,许多其他的研究都集中在大规模的自然或社会系统上,这些系统已经知道(或怀疑)表现出尺度不变的行为。虽然这些方法并不总是受到研究对象专家的欢迎(至少最初是这样) ,但 '''<font color="#ff8000"> SOC</font>''' 已经成为解释一些自然现象的强有力的候选者,包括: 地震(早在 '''<font color="#ff8000"> SOC</font>''' 被发现之前,地震就被认为是尺度不变行为的来源,例如描述地震大小统计分布的古腾堡-里克特定律,以及描述余震频率的描述余震的 Omori 定律,命名为 turcottesmalleysolla85<br />
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{{cite journal<br />
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{引用期刊<br />
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|author1=Turcotte, D. L. |author2=Smalley, R. F., Jr. |author3=Solla, S. A. | year = 1985<br />
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|author1=Turcotte, D. L. |author2=Smalley, R. F., Jr. |author3=Solla, S. A. | year = 1985<br />
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1 Turcotte,D.l. | author2 Smalley,r. f. ,jr. | author3 Solla,s. a.1985年<br />
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| title = Collapse of loaded fractal trees<br />
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| title = Collapse of loaded fractal trees<br />
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负载分形树的崩溃<br />
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| journal = Nature <br />
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| journal = Nature <br />
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自然》杂志<br />
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| doi= 10.1038/313671a0<br />
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| doi= 10.1038/313671a0<br />
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10.1038 / 313671a0<br />
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| volume = 313<br />
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| volume = 313<br />
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第313卷<br />
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| issue = 6004<br />
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| pages = 671–672|bibcode = 1985Natur.313..671T <br />
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| pages = 671–672|bibcode = 1985Natur.313..671T <br />
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| 第671-672页 | bibcode 1985 / natur. 313. . 671 t<br />
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}}</ref><ref name=SmalleyTurcotteSolla85 />); [[solar flares]]; fluctuations in economic systems such as [[financial markets]] (references to SOC are common in [[econophysics]]); [[landscape formation]]; [[forest fires]]; [[landslides]]; [[epidemics]]; neuronal avalanches in the cortex;<ref name="Beggs2003" /><ref name=Poil2012><br />
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}}</ref>); solar flares; fluctuations in economic systems such as financial markets (references to SOC are common in econophysics); landscape formation; forest fires; landslides; epidemics; neuronal avalanches in the cortex;<ref name=Poil2012><br />
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太阳耀斑; 经济系统的波动,比如金融市场(经济物理学中经常提到 SOC) ; 景观形成; 森林火灾; 滑坡; 流行病; 大脑皮层的神经雪崩; 参考名为 poil2012<br />
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{引用期刊<br />
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|date=Jul 2012<br />
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|author1=Poil, SS |author2=Hardstone, R |author3=Mansvelder, HD |author4=Linkenkaer-Hansen, K | title = Critical-state dynamics of avalanches and oscillations jointly emerge from balanced excitation/inhibition in neuronal networks<br />
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|author1=Poil, SS |author2=Hardstone, R |author3=Mansvelder, HD |author4=Linkenkaer-Hansen, K | title = Critical-state dynamics of avalanches and oscillations jointly emerge from balanced excitation/inhibition in neuronal networks<br />
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1 Poil,SS | author2 Hardstone,r | author3 mansveder,HD | author4 Linkenkaer-Hansen,k | title 雪崩和振荡的临界状态动力学联合出现在神经元网络的平衡兴奋 / 抑制中<br />
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| volume = 32<br />
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| volume = 32<br />
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| issue = 29<br />
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| pages = 9817–23 <br />
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| doi = 10.1523/JNEUROSCI.5990-11.2012<br />
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| doi = 10.1523/JNEUROSCI.5990-11.2012<br />
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| doi 10.1523 / jneurosci. 5990-11.2012<br />
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| journal = Journal of Neuroscience<br />
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| journal = Journal of Neuroscience<br />
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神经科学杂志<br />
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| pmc=3553543<br />
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| pmc=3553543<br />
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3553543<br />
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}}</ref> 1/f noise in the amplitude of electrophysiological signals;<ref name=LinkenkaerHansen2001 /> and [[biological evolution]] (where SOC has been invoked, for example, as the dynamical mechanism behind the theory of "[[punctuated equilibrium|punctuated equilibria]]" put forward by [[Niles Eldredge]] and [[Stephen Jay Gould]]). These "applied" investigations of SOC have included both modelling (either developing new models or adapting existing ones to the specifics of a given natural system) and extensive data analysis to determine the existence and/or characteristics of natural scaling laws.<br />
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}}</ref> 1/f noise in the amplitude of electrophysiological signals; and biological evolution (where SOC has been invoked, for example, as the dynamical mechanism behind the theory of "punctuated equilibria" put forward by Niles Eldredge and Stephen Jay Gould). These "applied" investigations of SOC have included both modelling (either developing new models or adapting existing ones to the specifics of a given natural system) and extensive data analysis to determine the existence and/or characteristics of natural scaling laws.<br />
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{} / ref 1 / f 噪声在电生理信号的振幅,以及生物进化(其中 SOC 已被调用,例如,作为背后的动力机制的理论“间断平衡”由 Niles Eldredge 和史蒂芬·古尔德提出)。对土壤有机碳的这些”应用”研究既包括建模(开发新模型或使现有模型适应特定自然系统的具体情况) ,也包括广泛的数据分析,以确定是否存在和 / 或具有自然定标法的特点。<br />
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In addition, SOC has been applied to computational algorithms. Recently, it has been found that the avalanches from an SOC process, like the BTW model, make effective patterns in a random search for optimal solutions on graphs.<ref name=Hoffmann2018><br />
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In addition, SOC has been applied to computational algorithms. Recently, it has been found that the avalanches from an SOC process, like the BTW model, make effective patterns in a random search for optimal solutions on graphs.<ref name=Hoffmann2018><br />
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此外,SOC 已经应用于计算算法。最近,人们发现来自 SOC 过程的雪崩,如 BTW 模型,在图的最优解的随机搜索中形成有效的模式。 参考名称 hoffmann2018<br />
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{{cite journal<br />
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{引用期刊<br />
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| author = [[H. Hoffmann|Hoffmann, H.]] and [[D. W. Payton|Payton, D. W.]]<br />
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| author = Hoffmann, H. and Payton, D. W.<br />
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作者: 霍夫曼 h. 和佩顿 d. w。<br />
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| year = 2018<br />
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| year = 2018<br />
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2018年<br />
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| title = Optimization by Self-Organized Criticality<br />
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| title = Optimization by Self-Organized Criticality<br />
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最佳化作者: 自组织临界性<br />
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| journal = [[Scientific Reports]]<br />
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| journal = Scientific Reports<br />
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科学报告<br />
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| volume = 8<br />
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| pages = 2358<br />
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| pages = 2358<br />
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2358页<br />
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| doi=10.1038/s41598-018-20275-7<br />
<br />
| doi=10.1038/s41598-018-20275-7<br />
<br />
10.1038 / s41598-018-20275-7<br />
<br />
| pmid = 29402956<br />
<br />
| pmid = 29402956<br />
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29402956<br />
<br />
| pmc = 5799203<br />
<br />
| pmc = 5799203<br />
<br />
5799203<br />
<br />
| bibcode = 2018NatSR...8.2358H<br />
<br />
| bibcode = 2018NatSR...8.2358H<br />
<br />
| bibcode 2018NatSR... 8.2358 h<br />
<br />
}}</ref> <br />
<br />
}}</ref> <br />
<br />
{} / ref<br />
<br />
An example of such an optimization problem is [[graph coloring]]. The SOC process apparently helps the optimization from getting stuck in a [[local optimum]] without the use of any [[Simulated_annealing|annealing]] scheme, as suggested by previous work on [[extremal optimization]].<br />
<br />
An example of such an optimization problem is graph coloring. The SOC process apparently helps the optimization from getting stuck in a local optimum without the use of any annealing scheme, as suggested by previous work on extremal optimization.<br />
<br />
图着色就是这种最佳化问题的一个例子。'''<font color="#ff8000"> SOC</font>''' 过程显然有助于优化陷入局部最优,而无需使用任何退火方案,正如以前的极值优化工作所建议的。<br />
<br />
<br />
<br />
<br />
<br />
The recent excitement generated by [[scale-free networks]] has raised some interesting new questions for SOC-related research: a number of different SOC models have been shown to generate such networks as an emergent phenomenon, as opposed to the simpler models proposed by network researchers where the network tends to be assumed to exist independently of any physical space or dynamics. While many single phenomena have been shown to exhibit scale-free properties over narrow ranges, a phenomenon offering by far a larger amount of data is solvent-accessible surface areas in globular proteins.<ref name=Moret2007><br />
<br />
The recent excitement generated by scale-free networks has raised some interesting new questions for SOC-related research: a number of different SOC models have been shown to generate such networks as an emergent phenomenon, as opposed to the simpler models proposed by network researchers where the network tends to be assumed to exist independently of any physical space or dynamics. While many single phenomena have been shown to exhibit scale-free properties over narrow ranges, a phenomenon offering by far a larger amount of data is solvent-accessible surface areas in globular proteins.<ref name=Moret2007><br />
<br />
'''<font color="#ff8000"> 无标度网络Scale-free networks</font>'''最近引起的兴奋为 '''<font color="#ff8000"> SOC</font>'''相关研究提出了一些有趣的新问题: 许多不同的 '''<font color="#ff8000"> SOC</font>'''模型已经被证明是作为一种涌现现象产生这样的网络,而不是网络研究人员提出的更简单的模型,其中网络往往被假定独立于任何物理空间或动力学存在。虽然许多单一现象已被证明在狭窄的范围内表现出无标度特性,但是到目前为止提供了大量数据的现象是球状蛋白质中溶剂可及的表面区域。 参考名称 moret2007<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[M. A. Moret|Moret, M. A.]] and [[G. Zebende|Zebende, G.]]<br />
<br />
| author = Moret, M. A. and Zebende, G.<br />
<br />
作者: Moret,M.a. and Zebende,g。<br />
<br />
| year = 2007<br />
<br />
| year = 2007<br />
<br />
2007年<br />
<br />
| title = Amino acid hydrophobicity and accessible surface area<br />
<br />
| title = Amino acid hydrophobicity and accessible surface area<br />
<br />
氨基酸疏水性和可达表面积<br />
<br />
| journal = [[Phys. Rev. E]]<br />
<br />
| journal = Phys. Rev. E<br />
<br />
体育杂志。牧师。E<br />
<br />
| volume = 75<br />
<br />
| volume = 75<br />
<br />
第75卷<br />
<br />
| issue = 1<br />
<br />
| issue = 1<br />
<br />
第一期<br />
<br />
| pages = 011920<br />
<br />
| pages = 011920<br />
<br />
011920页<br />
<br />
| doi=10.1103/PhysRevE.75.011920<br />
<br />
| doi=10.1103/PhysRevE.75.011920<br />
<br />
10.1103 / physarve. 75.011920<br />
<br />
| pmid = 17358197<br />
<br />
| pmid = 17358197<br />
<br />
17358197<br />
<br />
| bibcode = 2007PhRvE..75a1920M<br />
<br />
| bibcode = 2007PhRvE..75a1920M<br />
<br />
2007 / phrve. . 75 / a1920M<br />
<br />
}}</ref><br />
<br />
}}</ref><br />
<br />
{} / ref<br />
<br />
These studies quantify the differential geometry of proteins, and resolve many evolutionary puzzles regarding the biological emergence of complexity.<ref name=Phillips2014><br />
<br />
These studies quantify the differential geometry of proteins, and resolve many evolutionary puzzles regarding the biological emergence of complexity.<ref name=Phillips2014><br />
<br />
这些研究量化了蛋白质的微分几何,并解决了许多关于生物复杂性出现的进化之谜<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = Phillips, J. C.<br />
<br />
| author = Phillips, J. C.<br />
<br />
作者: 菲利普斯。<br />
<br />
| year = 2014<br />
<br />
| year = 2014<br />
<br />
2014年<br />
<br />
| title = Fractals and self-organized criticality in proteins<br />
<br />
| title = Fractals and self-organized criticality in proteins<br />
<br />
标题蛋白质中的分形和自组织临界性<br />
<br />
| journal = Physica A<br />
<br />
| journal = Physica A<br />
<br />
物理学杂志 a<br />
<br />
| volume = 415<br />
<br />
| volume = 415<br />
<br />
第415卷<br />
<br />
| pages = 440–448 <br />
<br />
| pages = 440–448 <br />
<br />
第440-448页<br />
<br />
| doi=10.1016/j.physa.2014.08.034<br />
<br />
| doi=10.1016/j.physa.2014.08.034<br />
<br />
| doi 10.1016 / j.physa. 2014.08.034<br />
<br />
| bibcode = 2014PhyA..415..440P<br />
<br />
| bibcode = 2014PhyA..415..440P<br />
<br />
| bibcode 2014PhyA. . 415. . 440 p<br />
<br />
| author-link = J. C. Phillips<br />
<br />
| author-link = J. C. Phillips<br />
<br />
作者链接 J.c. 菲利普斯<br />
<br />
}}</ref><br />
<br />
}}</ref><br />
<br />
{} / ref<br />
<br />
<br />
<br />
<br />
<br />
Despite the considerable interest and research output generated from the SOC hypothesis, there remains no general agreement with regards to its mechanisms in abstract mathematical form. Bak Tang and Wiesenfeld based their hypothesis on the behavior of their sandpile model.<ref name=Bak1987/> However,<br />
<br />
Despite the considerable interest and research output generated from the SOC hypothesis, there remains no general agreement with regards to its mechanisms in abstract mathematical form. Bak Tang and Wiesenfeld based their hypothesis on the behavior of their sandpile model. However,<br />
<br />
尽管 SOC 假说引起了相当大的兴趣和研究成果,但是关于其抽象数学形式的机制仍然没有普遍的一致性。和 Wiesenfeld 基于他们的沙堆模型的行为建立了他们的假设。然而,<br />
<br />
it has been argued that this model would actually generate 1/f<sup>2</sup> noise rather than 1/f noise.<ref name=Jensen1989><br />
<br />
it has been argued that this model would actually generate 1/f<sup>2</sup> noise rather than 1/f noise.<ref name=Jensen1989><br />
<br />
有人认为,这种模型实际上会产生1 / f sup 2 / sup 噪声而不是1 / f 噪声<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[H. J. Jensen|Jensen, H. J.]], [[K. Christensen|Christensen, K.]] and [[H. C. Fogedby|Fogedby, H. C.]]<br />
<br />
| author = Jensen, H. J., Christensen, K. and Fogedby, H. C.<br />
<br />
作者 Jensen,h. j. ,Christensen,k. and fogeby,h. c。<br />
<br />
| year = 1989<br />
<br />
| year = 1989<br />
<br />
1989年<br />
<br />
| title = 1/f noise, distribution of lifetimes, and a pile of sand<br />
<br />
| title = 1/f noise, distribution of lifetimes, and a pile of sand<br />
<br />
标题1 / f 噪音,寿命分布,和一堆沙子<br />
<br />
| journal = [[Phys. Rev. B]]<br />
<br />
| journal = Phys. Rev. B<br />
<br />
体育杂志。牧师。B<br />
<br />
| volume = 40<br />
<br />
| volume = 40<br />
<br />
第40卷<br />
<br />
| issue = 10<br />
<br />
| issue = 10<br />
<br />
第10期<br />
<br />
| pages = 7425–7427<br />
<br />
| pages = 7425–7427<br />
<br />
第7425-7427页<br />
<br />
| doi=10.1103/physrevb.40.7425<br />
<br />
| doi=10.1103/physrevb.40.7425<br />
<br />
10.1103 / physirevb. 40.7425<br />
<br />
| pmid = 9991162<br />
<br />
| pmid = 9991162<br />
<br />
9991162<br />
<br />
|bibcode = 1989PhRvB..40.7425J }}<br />
<br />
|bibcode = 1989PhRvB..40.7425J }}<br />
<br />
1989 / phrvb. 40.7425 j }<br />
<br />
</ref><br />
<br />
</ref><br />
<br />
/ 参考<br />
<br />
This claim was based on untested scaling assumptions, and a more rigorous analysis showed that sandpile models <br />
<br />
This claim was based on untested scaling assumptions, and a more rigorous analysis showed that sandpile models <br />
<br />
这种说法是基于未经测试的比例假设,更严格的分析表明沙堆模型<br />
<br />
generally produce 1/f<sup>a</sup> spectra, with a<2. <ref name=Laurson2005><br />
<br />
generally produce 1/f<sup>a</sup> spectra, with a<2. <ref name=Laurson2005><br />
<br />
一般产生1 / f sup a / sup 光谱,其值为2。参考名称 laurson2005<br />
<br />
{{cite journal |author1=Laurson, Lasse |author2=Alava, Mikko J. |author3=Zapperi, Stefano |title=Letter: Power spectra of self-organized critical sand piles |journal=Journal of Statistical Mechanics: Theory and Experiment |volume=0511 |id=L001 |date=15 September 2005 }}</ref><br />
<br />
</ref><br />
<br />
/ 参考<br />
<br />
Other simulation models were proposed later that could produce true 1/f noise,<ref name=Maslov1999><br />
<br />
Other simulation models were proposed later that could produce true 1/f noise,<ref name=Maslov1999><br />
<br />
其他模拟模型后来被提出,可以产生真正的1 / f 噪声,参考名称 maslov1999<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[S. Maslov|Maslov, S.]], [[C. Tang|Tang, C.]] and [[Y. –C. Zhang|Zhang, Y. - C.]]<br />
<br />
| author = Maslov, S., Tang, C. and Zhang, Y. - C.<br />
<br />
作者 Maslov,s. ,Tang,c. and Zhang,y。- c.<br />
<br />
| year = 1999<br />
<br />
| year = 1999<br />
<br />
1999年<br />
<br />
| title = 1/f noise in Bak-Tang-Wiesenfeld models on narrow stripes<br />
<br />
| title = 1/f noise in Bak-Tang-Wiesenfeld models on narrow stripes<br />
<br />
| 标题1 / f Bak-Tang-Wiesenfeld 窄条纹模型的噪音<br />
<br />
| journal = [[Phys. Rev. Lett.]]<br />
<br />
| journal = Phys. Rev. Lett.<br />
<br />
体育杂志。牧师。莱特。<br />
<br />
| volume = 83<br />
<br />
| volume = 83<br />
<br />
第83卷<br />
<br />
| issue = 12<br />
<br />
| issue = 12<br />
<br />
第12期<br />
<br />
| pages = 2449–2452<br />
<br />
| pages = 2449–2452<br />
<br />
2449-2452页<br />
<br />
| doi=10.1103/physrevlett.83.2449<br />
<br />
| doi=10.1103/physrevlett.83.2449<br />
<br />
10.1103 / physrvlett. 83.2449<br />
<br />
|arxiv = cond-mat/9902074 |bibcode = 1999PhRvL..83.2449M }}<br />
<br />
|arxiv = cond-mat/9902074 |bibcode = 1999PhRvL..83.2449M }}<br />
<br />
| arxiv cond-mat / 9902074 | bibcode 1999PhRvL. . 83.2449 m }<br />
<br />
</ref> and experimental sandpile models were observed to yield 1/f noise.<ref name=Frette1996><br />
<br />
</ref> and experimental sandpile models were observed to yield 1/f noise.<ref name=Frette1996><br />
<br />
/ ref 和实验沙堆模型被观察到产生1 / f 噪音。参考名称 frette1996<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[V.Frette|Frette, V.]], [[K. Christiansen|Christinasen, K.]], [[A. Malthe-Sørenssen|Malthe-Sørenssen, A.]], [[J. Feder|Feder, J]], [[T. Jøssang|Jøssang, T]] and [[P. Meakin|Meaken, P]]<br />
<br />
| author = Frette, V., Christinasen, K., Malthe-Sørenssen, A., Feder, J, Jøssang, T and Meaken, P<br />
<br />
| author = Frette, V., Christinasen, K., Malthe-Sørenssen, A., Feder, J, Jøssang, T and Meaken, P<br />
<br />
| year = 1996<br />
<br />
| year = 1996<br />
<br />
1996年<br />
<br />
| title = Avalanche dynamics in a pile of rice<br />
<br />
| title = Avalanche dynamics in a pile of rice<br />
<br />
| 题目: 大米堆中的雪崩动力学<br />
<br />
| journal = [[Nature (journal)|Nature]]<br />
<br />
| journal = Nature<br />
<br />
自然》杂志<br />
<br />
| volume = 379<br />
<br />
| volume = 379<br />
<br />
第379卷<br />
<br />
| issue = 6560<br />
<br />
| issue = 6560<br />
<br />
第6560期<br />
<br />
| pages = 49–52<br />
<br />
| pages = 49–52<br />
<br />
第49-52页<br />
<br />
| doi =10.1038/379049a0 <br />
<br />
| doi =10.1038/379049a0 <br />
<br />
10.1038 / 379049a0<br />
<br />
| bibcode= 1996Natur.379...49F}}<br />
<br />
| bibcode= 1996Natur.379...49F}}<br />
<br />
1996 / natur. 379... 49F }<br />
<br />
</ref> In addition to the nonconservative theoretical model mentioned above, other theoretical models for SOC have been based upon [[information theory]]<ref name=Dewar2003><br />
<br />
</ref> In addition to the nonconservative theoretical model mentioned above, other theoretical models for SOC have been based upon information theory<ref name=Dewar2003><br />
<br />
除了上面提到的非保守理论模型之外,其他关于 SOC 的理论模型都是基于信息论,例如 dewar2003<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = Dewar, R.<br />
<br />
| author = Dewar, R.<br />
<br />
作者杜瓦,r。<br />
<br />
| year = 2003<br />
<br />
| year = 2003<br />
<br />
2003年<br />
<br />
| title = Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states<br />
<br />
| title = Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states<br />
<br />
非平衡态中涨落定理、最大产生熵和自组织临界性的信息论解释<br />
<br />
| journal =J. Phys. A: Math. Gen. <br />
<br />
| journal =J. Phys. A: Math. Gen. <br />
<br />
| j 杂志。女名女子名。答: 数学。将军。<br />
<br />
| volume = 36<br />
<br />
| volume = 36<br />
<br />
第36卷<br />
<br />
| pages =631&ndash;641<br />
<br />
| pages =631&ndash;641<br />
<br />
631-- 641<br />
<br />
| pmid = <br />
<br />
| pmid = <br />
<br />
我不会让你失望的<br />
<br />
| doi = 10.1088/0305-4470/36/3/303<br />
<br />
| doi = 10.1088/0305-4470/36/3/303<br />
<br />
10.1088 / 0305-4470 / 36 / 3 / 303<br />
<br />
| issue = 3<br />
<br />
| issue = 3<br />
<br />
第三期<br />
<br />
| pmc = <br />
<br />
| pmc = <br />
<br />
我会的,我会的,我会的<br />
<br />
|bibcode = 2003JPhA...36..631D|arxiv = cond-mat/0005382 | author-link = R Dewar<br />
<br />
|bibcode = 2003JPhA...36..631D|arxiv = cond-mat/0005382 | author-link = R Dewar<br />
<br />
| bibcode 2003JPhA... 36. . 631 d | arxiv cond-mat / 0005382 | author-link r Dewar<br />
<br />
}}</ref>, <br />
<br />
}}</ref>, <br />
<br />
} / ref,<br />
<br />
[[mean field theory]]<ref name=Vespignani1998><br />
<br />
mean field theory<ref name=Vespignani1998><br />
<br />
平均场理论参考名称 vespignani1998<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[Alessandro Vespignani|Vespignani, A.]], and [[Stefano Zapperi|Zapperi, S.]]<br />
<br />
| author = Vespignani, A., and Zapperi, S.<br />
<br />
作者 Vespignani,a,和 Zapperi,s。<br />
<br />
| year = 1998<br />
<br />
| year = 1998<br />
<br />
1998年<br />
<br />
| title = How self-organized criticality works: a unified mean-field picture<br />
<br />
| title = How self-organized criticality works: a unified mean-field picture<br />
<br />
标题自组织临界性如何工作: 一个统一的平均场图片<br />
<br />
| journal =Phys. Rev. E <br />
<br />
| journal =Phys. Rev. E <br />
<br />
体育杂志。牧师。E<br />
<br />
| volume = 57<br />
<br />
| volume = 57<br />
<br />
第57卷<br />
<br />
| pages =6345–6362<br />
<br />
| pages =6345–6362<br />
<br />
6345-6362页<br />
<br />
| pmid = <br />
<br />
| pmid = <br />
<br />
我不会让你失望的<br />
<br />
| doi = 10.1103/physreve.57.6345<br />
<br />
| doi = 10.1103/physreve.57.6345<br />
<br />
10.1103 / physorve. 57.6345<br />
<br />
| issue = 6<br />
<br />
| issue = 6<br />
<br />
第六期<br />
<br />
| pmc = <br />
<br />
| pmc = <br />
<br />
我会的,我会的,我会的<br />
<br />
| bibcode = 1998PhRvE..57.6345V<br />
<br />
| bibcode = 1998PhRvE..57.6345V<br />
<br />
| bibcode 1998PhRvE. . 57.6345 v<br />
<br />
| arxiv = cond-mat/9709192<br />
<br />
| arxiv = cond-mat/9709192<br />
<br />
| arxiv = cond-mat/9709192<br />
<br />
| hdl = 2047/d20002173<br />
<br />
| hdl = 2047/d20002173<br />
<br />
2047 / d20002173<br />
<br />
}}</ref>,<br />
<br />
}}</ref>,<br />
<br />
} / ref,<br />
<br />
the [[convergence of random variables]]<ref name=Kendal2015><br />
<br />
the convergence of random variables<ref name=Kendal2015><br />
<br />
随机变量的收敛裁判名称 kendal 2015<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = Kendal, WS<br />
<br />
| author = Kendal, WS<br />
<br />
作者 Kendal,WS<br />
<br />
| year = 2015<br />
<br />
| year = 2015<br />
<br />
2015年<br />
<br />
| title = Self-organized criticality attributed to a central limit-like convergence effect<br />
<br />
| title = Self-organized criticality attributed to a central limit-like convergence effect<br />
<br />
| 标题自组织临界性归因于类似中心极限的聚合效应<br />
<br />
| journal =Physica A <br />
<br />
| journal =Physica A <br />
<br />
物理学杂志 a<br />
<br />
| volume = 421<br />
<br />
| volume = 421<br />
<br />
第421卷<br />
<br />
| pages =141&ndash;150<br />
<br />
| pages =141&ndash;150<br />
<br />
141-- 150页<br />
<br />
| pmid = <br />
<br />
| pmid = <br />
<br />
我不会让你失望的<br />
<br />
| doi = 10.1016/j.physa.2014.11.035<br />
<br />
| doi = 10.1016/j.physa.2014.11.035<br />
<br />
| doi 10.1016 / j.physa. 2014.11.035<br />
<br />
| issue = <br />
<br />
| issue = <br />
<br />
发行<br />
<br />
| pmc = <br />
<br />
| pmc = <br />
<br />
我会的,我会的,我会的<br />
<br />
|bibcode =2015PhyA..421..141K | author-link = Wayne Kendal<br />
<br />
|bibcode =2015PhyA..421..141K | author-link = Wayne Kendal<br />
<br />
| bibcode 2015PhyA. . 421. . 141 k | 作者链接 Wayne Kendal<br />
<br />
}}</ref>,<br />
<br />
}}</ref>,<br />
<br />
} / ref,<br />
<br />
and cluster formation.<ref name=Hoffmann2018b><br />
<br />
and cluster formation.<ref name=Hoffmann2018b><br />
<br />
和簇的形成。参考名称 hoffmann2018b<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = Hoffmann, H.<br />
<br />
| author = Hoffmann, H.<br />
<br />
作者: 霍夫曼。<br />
<br />
| year = 2018<br />
<br />
| year = 2018<br />
<br />
2018年<br />
<br />
| title = Impact of Network Topology on Self-Organized Criticality<br />
<br />
| title = Impact of Network Topology on Self-Organized Criticality<br />
<br />
网络拓扑对自组织临界性的影响<br />
<br />
| journal = Phys. Rev. E <br />
<br />
| journal = Phys. Rev. E <br />
<br />
体育杂志。牧师。E<br />
<br />
| volume = 97<br />
<br />
| volume = 97<br />
<br />
第97卷<br />
<br />
| pages =022313<br />
<br />
| pages =022313<br />
<br />
022313页<br />
<br />
| pmid = 29548239<br />
<br />
| pmid = 29548239<br />
<br />
29548239<br />
<br />
| doi = 10.1103/PhysRevE.97.022313<br />
<br />
| doi = 10.1103/PhysRevE.97.022313<br />
<br />
10.1103 / physarve. 97.022313<br />
<br />
| issue = 2<br />
<br />
| issue = 2<br />
<br />
第二期<br />
<br />
| pmc = <br />
<br />
| pmc = <br />
<br />
我会的,我会的,我会的<br />
<br />
| bibcode =2018PhRvE..97b2313H <br />
<br />
| bibcode =2018PhRvE..97b2313H <br />
<br />
2018 / phrve. . 97 / b2313H<br />
<br />
| author-link = Heiko Hoffmann<br />
<br />
| author-link = Heiko Hoffmann<br />
<br />
作者: 海科 · 霍夫曼<br />
<br />
| doi-access = free<br />
<br />
| doi-access = free<br />
<br />
免费访问<br />
<br />
}}</ref> A continuous model of self-organised criticality is proposed by using [[tropical geometry]].<ref>{{Cite journal|last=Kalinin|first=N.|last2=Guzmán-Sáenz|first2=A.|last3=Prieto|first3=Y.|last4=Shkolnikov|first4=M.|last5=Kalinina|first5=V.|last6=Lupercio|first6=E.|date=2018-08-15|title=Self-organized criticality and pattern emergence through the lens of tropical geometry|journal=Proceedings of the National Academy of Sciences|volume=115|issue=35|language=en|pages=E8135–E8142|doi=10.1073/pnas.1805847115|issn=0027-8424|pmid=30111541|pmc=6126730|arxiv=1806.09153}}</ref><br />
<br />
}}</ref> A continuous model of self-organised criticality is proposed by using tropical geometry.<br />
<br />
{} / ref 一个'''<font color="#ff8000"> 自组织临界Self-organised criticality</font>'''的连续模型是通过使用热带几何来提出的。<br />
<br />
== Examples of self-organized critical dynamics自组织临界动力学的例子 ==<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
In chronological order of development:<br />
<br />
In chronological order of development:<br />
<br />
按发展时间顺序排列:<br />
<br />
<br />
<br />
<br />
<br />
* Stick-slip model of fault failure<ref name="TurcotteSmalleySolla85" /><ref name="SmalleyTurcotteSolla85" /><br />
<br />
*断层破坏的粘滑模型<ref name="TurcotteSmalleySolla85" /><ref name="SmalleyTurcotteSolla85" /><br />
<br />
*[[Abelian sandpile model|Bak–Tang–Wiesenfeld sandpile]]<br />
<br />
*[[阿贝尔沙堆模型| Bak–Tang–Wiesenfeld沙堆]]<br />
<br />
* [[Forest-fire model]]<br />
<br />
*[[森林火灾模型]]<br />
<br />
* [[Olami–Feder–Christensen model]]<br />
<br />
* [[奥拉米·费德·克里斯滕森模型]]<br />
<br />
* [[Bak–Sneppen model]]<br />
<br />
*[[背景模型]]<br />
<br />
== See also 参见==<br />
<br />
<br />
<br />
* [[Pink noise|1/f noise]]<br />
<br />
*[[粉红噪音| 1/f噪音]]<br />
<br />
* [[Complex system]]s<br />
<br />
* [[复杂系统]]s<br />
<br />
* [[Critical brain hypothesis]]<br />
<br />
*[[【关键大脑假说】]]<br />
<br />
* [[Critical exponents]]<br />
<br />
*[[临界指数]]<br />
<br />
* [[Detrended fluctuation analysis]], a method to detect power-law scaling in time series.<br />
<br />
*[[Detrended涨落分析]],一种检测中幂律标度的方法<br />
<br />
* [[Dual-phase evolution]], another process that contributes to self-organization in complex systems.<br />
<br />
* [[双相演化]],另一个有助于自我组织的过程<br />
<br />
* [[Fractal]]s<br />
<br />
* [[分形]]s;<br />
<br />
* [[Ilya Prigogine]], a systems scientist who helped formalize dissipative system behavior in general terms.<br />
<br />
*[[伊利亚·普里高津]],一位帮助将耗散系统形式化的系统科学家<br />
<br />
* [[Power law]]s<br />
<br />
*[[幂律]]s<br />
<br />
* [[Red Queen hypothesis]]<br />
<br />
*[[红皇后假说]]<br />
<br />
* [[Scale invariance]]<br />
<br />
* [[标度不变性]]<br />
<br />
* [[Self-organization]]<br />
<br />
* [[自组织]]<br />
<br />
* [[Self-organized criticality control]]<br />
<br />
*[[自组织临界控制]]<br />
<br />
==References参考资料==<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<references/><br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
== Further reading延伸阅读 ==<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = Adami, C.<br />
<br />
| author = Adami, C.<br />
<br />
作者: 阿达米。<br />
<br />
| year = 1995<br />
<br />
| year = 1995<br />
<br />
1995年<br />
<br />
| title = Self-organized criticality in living systems<br />
<br />
| title = Self-organized criticality in living systems<br />
<br />
| 生命系统中的自组织临界性<br />
<br />
| journal = [[Physics Letters A]]<br />
<br />
| journal = Physics Letters A<br />
<br />
物理学快报<br />
<br />
| volume = 203<br />
<br />
| volume = 203<br />
<br />
第203卷<br />
<br />
| issue = 1<br />
<br />
| issue = 1<br />
<br />
第一期<br />
<br />
| pages = 29&ndash;32<br />
<br />
| pages = 29&ndash;32<br />
<br />
29-- 32页<br />
<br />
| doi = 10.1016/0375-9601(95)00372-A<br />
<br />
| doi = 10.1016/0375-9601(95)00372-A<br />
<br />
| doi 10.1016 / 0375-9601(95)00372-A<br />
<br />
|bibcode = 1995PhLA..203...29A | arxiv = adap-org/9401001<br />
<br />
|bibcode = 1995PhLA..203...29A | arxiv = adap-org/9401001<br />
<br />
|bibcode = 1995PhLA..203...29A | arxiv = adap-org/9401001<br />
<br />
| citeseerx = 10.1.1.456.9543<br />
<br />
| citeseerx = 10.1.1.456.9543<br />
<br />
10.1.1.456.9543<br />
<br />
| author-link = Adami, C<br />
<br />
| author-link = Adami, C<br />
<br />
| 作者链接阿达米,c<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite book<br />
<br />
<br />
<br />
| author = Bak, P.<br />
<br />
| author = Bak, P.<br />
<br />
作者 Bak,p。<br />
<br />
| year = 1996<br />
<br />
| year = 1996<br />
<br />
1996年<br />
<br />
| title = How Nature Works: The Science of Self-Organized Criticality<br />
<br />
| title = How Nature Works: The Science of Self-Organized Criticality<br />
<br />
自然如何运作: 自组织临界性的科学<br />
<br />
| publisher = Copernicus<br />
<br />
| publisher = Copernicus<br />
<br />
出版商哥白尼<br />
<br />
| location = New York<br />
<br />
| location = New York<br />
<br />
| 地点: 纽约<br />
<br />
| isbn = 978-0-387-94791-4<br />
<br />
| isbn = 978-0-387-94791-4<br />
<br />
[国际标准图书编号978-0-387-94791-4]<br />
<br />
| author-link = Per Bak<br />
<br />
| author-link = Per Bak<br />
<br />
| 作者链接 Per Bak<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = [[Per Bak|Bak, P.]] and [[Maya Paczuski|Paczuski, M.]]<br />
<br />
| author = Bak, P. and Paczuski, M.<br />
<br />
作者 Bak,p. and Paczuski,m。<br />
<br />
| year = 1995<br />
<br />
| year = 1995<br />
<br />
1995年<br />
<br />
| title = Complexity, contingency, and criticality<br />
<br />
| title = Complexity, contingency, and criticality<br />
<br />
| 标题复杂性、偶然性和临界性<br />
<br />
| journal = [[Proceedings of the National Academy of Sciences|Proceedings of the National Academy of Sciences of the USA]]<br />
<br />
| journal = Proceedings of the National Academy of Sciences of the USA<br />
<br />
美国美国国家科学院院刊杂志<br />
<br />
| volume = 92<br />
<br />
| volume = 92<br />
<br />
第92卷<br />
<br />
| pages = 6689&ndash;6696<br />
<br />
| pages = 6689&ndash;6696<br />
<br />
6689-- 6696<br />
<br />
| url = http://pnas.org/cgi/content/abstract/92/15/6689<br />
<br />
| url = http://pnas.org/cgi/content/abstract/92/15/6689<br />
<br />
Http://pnas.org/cgi/content/abstract/92/15/6689<br />
<br />
| doi = 10.1073/pnas.92.15.6689<br />
<br />
| doi = 10.1073/pnas.92.15.6689<br />
<br />
10.1073 / pnas. 92.15.6689<br />
<br />
| pmid = 11607561<br />
<br />
| pmid = 11607561<br />
<br />
11607561<br />
<br />
| issue = 15<br />
<br />
| issue = 15<br />
<br />
第15期<br />
<br />
| pmc = 41396<br />
<br />
| pmc = 41396<br />
<br />
41396<br />
<br />
|bibcode = 1995PNAS...92.6689B }}<br />
<br />
|bibcode = 1995PNAS...92.6689B }}<br />
<br />
92.6689 b }<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = [[Per Bak|Bak, P.]] and [[Kim Sneppen|Sneppen, K.]]<br />
<br />
| author = Bak, P. and Sneppen, K.<br />
<br />
作者 Bak,p. and Sneppen,k。<br />
<br />
| year = 1993<br />
<br />
| year = 1993<br />
<br />
1993年<br />
<br />
| title = Punctuated equilibrium and criticality in a simple model of evolution <br />
<br />
| title = Punctuated equilibrium and criticality in a simple model of evolution <br />
<br />
| 简单演化模型中的间断平衡和临界性<br />
<br />
| journal = [[Physical Review Letters]]<br />
<br />
| journal = Physical Review Letters<br />
<br />
物理评论快报<br />
<br />
| volume = 71<br />
<br />
| volume = 71<br />
<br />
第71卷<br />
<br />
| issue = 24<br />
<br />
| issue = 24<br />
<br />
第24期<br />
<br />
| pages = 4083&ndash;4086<br />
<br />
| pages = 4083&ndash;4086<br />
<br />
4083-- 4086<br />
<br />
| doi = 10.1103/PhysRevLett.71.4083<br />
<br />
| doi = 10.1103/PhysRevLett.71.4083<br />
<br />
10.1103 / physrvlett. 71.4083<br />
<br />
| pmid=10055149<br />
<br />
| pmid=10055149<br />
<br />
10055149<br />
<br />
| bibcode=1993PhRvL..71.4083B}}<br />
<br />
| bibcode=1993PhRvL..71.4083B}}<br />
<br />
1993 phrvl. . 71.4083 b }<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = [[Per Bak|Bak, P.]], [[Chao Tang|Tang, C.]] and [[Kurt Wiesenfeld|Wiesenfeld, K.]]<br />
<br />
| author = Bak, P., Tang, C. and Wiesenfeld, K.<br />
<br />
作者 Bak,p. ,Tang,c. and Wiesenfeld,k。<br />
<br />
| year = 1987<br />
<br />
| year = 1987<br />
<br />
1987年<br />
<br />
| title = Self-organized criticality: an explanation of <math>1/f</math> noise<br />
<br />
| title = Self-organized criticality: an explanation of <math>1/f</math> noise<br />
<br />
| 题目自组织临界性: 数学噪音的解释<br />
<br />
| journal = [[Physical Review Letters]]<br />
<br />
| journal = Physical Review Letters<br />
<br />
物理评论快报<br />
<br />
| volume = 59<br />
<br />
| volume = 59<br />
<br />
第59卷<br />
<br />
| issue = 4<br />
<br />
| issue = 4<br />
<br />
第四期<br />
<br />
| pages = 381&ndash;384<br />
<br />
| pages = 381&ndash;384<br />
<br />
381-- 384<br />
<br />
| doi = 10.1103/PhysRevLett.59.381<br />
<br />
| doi = 10.1103/PhysRevLett.59.381<br />
<br />
10.1103 / physrvlett. 59.381<br />
<br />
| pmid = 10035754<br />
<br />
| pmid = 10035754<br />
<br />
10035754<br />
<br />
| bibcode=1987PhRvL..59..381B}}<br />
<br />
| bibcode=1987PhRvL..59..381B}}<br />
<br />
1987 / phrvl. . 59. . 381 b }<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = [[Per Bak|Bak, P.]], [[Chao Tang|Tang, C.]] and [[Kurt Wiesenfeld|Wiesenfeld, K.]]<br />
<br />
| author = Bak, P., Tang, C. and Wiesenfeld, K.<br />
<br />
作者 Bak,p. ,Tang,c. and Wiesenfeld,k。<br />
<br />
| year = 1988<br />
<br />
| year = 1988<br />
<br />
1988年<br />
<br />
| title = Self-organized criticality<br />
<br />
| title = Self-organized criticality<br />
<br />
标题自组织临界性<br />
<br />
| journal = [[Physical Review A]]<br />
<br />
| journal = Physical Review A<br />
<br />
物理评论 a 期刊<br />
<br />
| volume = 38<br />
<br />
| volume = 38<br />
<br />
第38卷<br />
<br />
| issue = 1<br />
<br />
| issue = 1<br />
<br />
第一期<br />
<br />
| pages = 364&ndash;374<br />
<br />
| pages = 364&ndash;374<br />
<br />
364-- 374<br />
<br />
| doi = 10.1103/PhysRevA.38.364<br />
<br />
| doi = 10.1103/PhysRevA.38.364<br />
<br />
10.1103 / PhysRevA. 38.364<br />
<br />
| pmid = 9900174<br />
<br />
| pmid = 9900174<br />
<br />
9900174<br />
<br />
|bibcode = 1988PhRvA..38..364B }} [https://archive.is/20130415140421/http://www.papercore.org/PerBak1987 Papercore summary].<br />
<br />
|bibcode = 1988PhRvA..38..364B }} [https://archive.is/20130415140421/http://www.papercore.org/PerBak1987 Papercore summary].<br />
<br />
| bibcode 1988PhRvA. . 38. . 364 b }[ https://archive.is/20130415140421/http://www.Papercore.org/perbak1987文件核心摘要]。<br />
<br />
<br />
<br />
<br />
<br />
* {{cite book<br />
<br />
<br />
<br />
| author = Buchanan, M.<br />
<br />
| author = Buchanan, M.<br />
<br />
作者: 布坎南。<br />
<br />
| year = 2000<br />
<br />
| year = 2000<br />
<br />
2000年<br />
<br />
| title = Ubiquity<br />
<br />
| title = Ubiquity<br />
<br />
标题: Ubiquity<br />
<br />
| publisher = Weidenfeld &amp; Nicolson<br />
<br />
| publisher = Weidenfeld &amp; Nicolson<br />
<br />
| publisher = Weidenfeld &amp; Nicolson<br />
<br />
| location = London<br />
<br />
| location = London<br />
<br />
地点: 伦敦<br />
<br />
| isbn = 978-0-7538-1297-6<br />
<br />
| isbn = 978-0-7538-1297-6<br />
<br />
[国际标准图书编号978-0-7538-1297-6]<br />
<br />
| author-link = Mark Buchanan<br />
<br />
| author-link = Mark Buchanan<br />
<br />
马克 · 布坎南<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite book<br />
<br />
<br />
<br />
| author = Jensen, H. J.<br />
<br />
| author = Jensen, H. J.<br />
<br />
作者 Jensen,h. j。<br />
<br />
| year = 1998<br />
<br />
| year = 1998<br />
<br />
1998年<br />
<br />
| title = Self-Organized Criticality<br />
<br />
| title = Self-Organized Criticality<br />
<br />
标题自组织临界性<br />
<br />
| publisher = [[Cambridge University Press]]<br />
<br />
| publisher = Cambridge University Press<br />
<br />
出版商剑桥大学出版社<br />
<br />
| location = Cambridge<br />
<br />
| location = Cambridge<br />
<br />
| 地点: 剑桥<br />
<br />
| isbn = 978-0-521-48371-1<br />
<br />
| isbn = 978-0-521-48371-1<br />
<br />
[国际标准图书编号978-0-521-48371-1]<br />
<br />
| author-link = Henrik Jeldtoft Jensen<br />
<br />
| author-link = Henrik Jeldtoft Jensen<br />
<br />
作者: 亨里克 · 耶尔德托夫特 · 詹森<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = Katz, J. I.<br />
<br />
| author = Katz, J. I.<br />
<br />
作者 Katz,j. i。<br />
<br />
| year = 1986<br />
<br />
| year = 1986<br />
<br />
1986年<br />
<br />
| title = A model of propagating brittle failure in heterogeneous media<br />
<br />
| title = A model of propagating brittle failure in heterogeneous media<br />
<br />
在非均匀介质中传播脆性破坏的模型<br />
<br />
| journal = Journal of Geophysical Research<br />
<br />
| journal = Journal of Geophysical Research<br />
<br />
地球物理研究期刊<br />
<br />
| bibcode = 1986JGR....9110412K<br />
<br />
| bibcode = 1986JGR....9110412K<br />
<br />
| bibcode 1986JGR... 9110412K<br />
<br />
| doi = 10.1029/JB091iB10p10412<br />
<br />
| doi = 10.1029/JB091iB10p10412<br />
<br />
| doi 10.1029 / JB091iB10p10412<br />
<br />
| volume = 91<br />
<br />
| volume = 91<br />
<br />
第91卷<br />
<br />
| issue = B10<br />
<br />
| issue = B10<br />
<br />
第10期<br />
<br />
| pages = 10412<br />
<br />
| pages = 10412<br />
<br />
10412页<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = Kron, T./Grund, T.<br />
<br />
| author = Kron, T./Grund, T.<br />
<br />
作者: Kron t. / Grund t。<br />
<br />
| year = 2009<br />
<br />
| year = 2009<br />
<br />
2009年<br />
<br />
| title = Society as a Selforganized Critical System<br />
<br />
| title = Society as a Selforganized Critical System<br />
<br />
作为一个自组织的批判系统的社会<br />
<br />
| journal = Cybernetics and Human Knowing<br />
<br />
| journal = Cybernetics and Human Knowing<br />
<br />
控制论与人类认知<br />
<br />
| volume = 16<br />
<br />
| volume = 16<br />
<br />
第16卷<br />
<br />
| pages = 65–82<br />
<br />
| pages = 65–82<br />
<br />
第65-82页<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{Cite book<br />
<br />
<br />
<br />
| author = Paczuski, M.<br />
<br />
| author = Paczuski, M.<br />
<br />
作者: 帕祖斯基。<br />
<br />
| year = 2005<br />
<br />
| year = 2005<br />
<br />
2005年<br />
<br />
| title = Networks as renormalized models for emergent behavior in physical systems<br />
<br />
| title = Networks as renormalized models for emergent behavior in physical systems<br />
<br />
作为物理系统中突发行为的重整化模型的网络<br />
<br />
| journal = Complexity<br />
<br />
| journal = Complexity<br />
<br />
杂志复杂性<br />
<br />
| pages = 363–374<br />
<br />
| pages = 363–374<br />
<br />
第363-374页<br />
<br />
| arxiv = physics/0502028<br />
<br />
| arxiv = physics/0502028<br />
<br />
| arxiv physics / 0502028<br />
<br />
|bibcode = 2005cmn..conf..363P |doi = 10.1142/9789812701558_0042<br />
<br />
|bibcode = 2005cmn..conf..363P |doi = 10.1142/9789812701558_0042<br />
<br />
2005 / cmn. conf. 363 p | doi 10.1142 / 97898127015580042<br />
<br />
| series = The Science and Culture Series – Physics<br />
<br />
| series = The Science and Culture Series – Physics<br />
<br />
| 科学与文化系列-物理学<br />
<br />
| isbn = 978-981-256-525-9 | citeseerx = 10.1.1.261.9886<br />
<br />
| isbn = 978-981-256-525-9 | citeseerx = 10.1.1.261.9886<br />
<br />
| isbn 978-981-256-525-9 | citeserx 10.1.1.261.9886<br />
<br />
| author-link = Maya Paczuski<br />
<br />
| author-link = Maya Paczuski<br />
<br />
| 作者链接 Maya Paczuski<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite book<br />
<br />
<br />
<br />
| author = Turcotte, D. L.<br />
<br />
| author = Turcotte, D. L.<br />
<br />
作者: Turcotte,D.l。<br />
<br />
| year = 1997<br />
<br />
| year = 1997<br />
<br />
1997年<br />
<br />
| title = Fractals and Chaos in Geology and Geophysics<br />
<br />
| title = Fractals and Chaos in Geology and Geophysics<br />
<br />
地质学与地球物理学中的分形与混沌<br />
<br />
| publisher = [[Cambridge University Press]]<br />
<br />
| publisher = Cambridge University Press<br />
<br />
出版商剑桥大学出版社<br />
<br />
| location = Cambridge<br />
<br />
| location = Cambridge<br />
<br />
| 地点: 剑桥<br />
<br />
| isbn = 978-0-521-56733-6<br />
<br />
| isbn = 978-0-521-56733-6<br />
<br />
[国际标准图书馆编号978-0-521-56733-6]<br />
<br />
| author-link = Donald L. Turcotte<br />
<br />
| author-link = Donald L. Turcotte<br />
<br />
作者: Donald l. Turcotte<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = Turcotte, D. L.<br />
<br />
| author = Turcotte, D. L.<br />
<br />
作者: Turcotte,D.l。<br />
<br />
| year = 1999<br />
<br />
| year = 1999<br />
<br />
1999年<br />
<br />
| title = Self-organized criticality<br />
<br />
| title = Self-organized criticality<br />
<br />
标题自组织临界性<br />
<br />
| journal = [[Reports on Progress in Physics]]<br />
<br />
| journal = Reports on Progress in Physics<br />
<br />
物理学进展报告<br />
<br />
| volume = 62<br />
<br />
| volume = 62<br />
<br />
第62卷<br />
<br />
| issue = 10<br />
<br />
| issue = 10<br />
<br />
第10期<br />
<br />
| pages = 1377&ndash;1429<br />
<br />
| pages = 1377&ndash;1429<br />
<br />
13771429页<br />
<br />
| doi = 10.1088/0034-4885/62/10/201<br />
<br />
| doi = 10.1088/0034-4885/62/10/201<br />
<br />
10.1088 / 0034-4885 / 62 / 10 / 201<br />
<br />
|bibcode = 1999RPPh...62.1377T | author-link = Donald L. Turcotte<br />
<br />
|bibcode = 1999RPPh...62.1377T | author-link = Donald L. Turcotte<br />
<br />
| bibcode 1999RPPh... 62.1377 t | 作者链接 Donald l. Turcotte<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = Md. Nurujjaman/A. N. Sekar Iyengar<br />
<br />
| author = Md. Nurujjaman/A. N. Sekar Iyengar<br />
<br />
作者马里兰大学。Nurujjaman / a.N. Sekar Iyengar<br />
<br />
| year = 2007<br />
<br />
| year = 2007<br />
<br />
2007年<br />
<br />
| title = Realization of {SOC} behavior in a dc glow discharge plasma<br />
<br />
| title = Realization of {SOC} behavior in a dc glow discharge plasma<br />
<br />
直流辉光放电等离子体{ SOC }行为的实现<br />
<br />
| journal = [[Physics Letters A]]<br />
<br />
| journal = Physics Letters A<br />
<br />
物理学快报<br />
<br />
| volume = 360<br />
<br />
| volume = 360<br />
<br />
第360卷<br />
<br />
| issue = 6<br />
<br />
| issue = 6<br />
<br />
第六期<br />
<br />
| pages = 717&ndash;721<br />
<br />
| pages = 717&ndash;721<br />
<br />
717-- 721页<br />
<br />
|arxiv = physics/0611069 |bibcode = 2007PhLA..360..717N |doi = 10.1016/j.physleta.2006.09.005 | author-link = Md. Nurujjaman/A. N. Sekar Iyengar<br />
<br />
|arxiv = physics/0611069 |bibcode = 2007PhLA..360..717N |doi = 10.1016/j.physleta.2006.09.005 | author-link = Md. Nurujjaman/A. N. Sekar Iyengar<br />
<br />
| arxiv physics / 0611069 | bibcode 2007 phla. . 360. . 717 n | doi 10.1016 / j.physleta. 2006.09.005 | author-link md.Nurujjaman / a.N. Sekar Iyengar<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
*[http://xstructure.inr.ac.ru/x-bin/theme2.py?arxiv=cond-mat&level=1&index1=20771 Self-organized criticality on arxiv.org]<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
[[Category:Critical phenomena]]<br />
<br />
Category:Critical phenomena<br />
<br />
范畴: 关键现象<br />
<br />
[[Category:Applied and interdisciplinary physics]]<br />
<br />
Category:Applied and interdisciplinary physics<br />
<br />
类别: 应用和跨学科物理学<br />
<br />
[[Category:Chaos theory]]<br />
<br />
Category:Chaos theory<br />
<br />
范畴: 混沌理论<br />
<br />
[[Category:Self-organization]]<br />
<br />
Category:Self-organization<br />
<br />
类别: 自我组织<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Self-organized criticality]]. Its edit history can be viewed at [[自组织临界性/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E8%87%AA%E7%BB%84%E7%BB%87%E4%B8%B4%E7%95%8C%E6%80%A7&diff=21916自组织临界性2021-02-20T12:26:56Z<p>Jxzhou:/* Overview 概览 */</p>
<hr />
<div>此词条暂由水流心不竞初译,未经审校,带来阅读不便,请见谅。<br />
<br />
In [[physics]], '''self-organized criticality''' ('''SOC''') is a property of [[dynamical system]]s that have a [[critical phenomena|critical point]] as an [[attractor]]. Their macroscopic behavior thus displays the spatial or temporal [[scale invariance|scale-invariance]] characteristic of the [[critical point (physics)|critical point]] of a [[phase transition]], but without the need to tune control parameters to a precise value, because the system, effectively, tunes itself as it evolves towards criticality.<br />
<br />
In physics, self-organized criticality (SOC) is a property of dynamical systems that have a critical point as an attractor. Their macroscopic behavior thus displays the spatial or temporal scale-invariance characteristic of the critical point of a phase transition, but without the need to tune control parameters to a precise value, because the system, effectively, tunes itself as it evolves towards criticality.<br />
<br />
在物理学中,'''<font color="#ff8000"> 自组织临界性Self-organized criticality (SOC)</font>'''是动力系统的一种特性,动力系统有一个临界点作为'''<font color="#ff8000"> 吸引子Attractor</font>'''。它们的宏观行为因此显示了相变临界点的空间或时间尺度不变特性,但不需要把控制参数调整到一个精确的值,因为系统在趋向于临界状态时有效地自我调整。<br />
<br />
<br />
<br />
<br />
<br />
The concept was put forward by [[Per Bak]], [[Chao Tang]] and [[Kurt Wiesenfeld]] ("BTW") in a paper<ref name=Bak1987><br />
<br />
The concept was put forward by Per Bak, Chao Tang and Kurt Wiesenfeld ("BTW") in a paper<ref name=Bak1987><br />
<br />
这个概念是由 Per Bak,Chao Tang 和 Kurt Wiesenfeld (“ BTW”)在一篇名为 bak1987的论文中提出的<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[Per Bak|Bak, P.]], [[Chao Tang|Tang, C.]] and [[Kurt Wiesenfeld|Wiesenfeld, K.]]<br />
<br />
| author = Bak, P., Tang, C. and Wiesenfeld, K.<br />
<br />
作者 Bak,p. ,Tang,c. and Wiesenfeld,k。<br />
<br />
| year = 1987<br />
<br />
| year = 1987<br />
<br />
1987年<br />
<br />
| title = Self-organized criticality: an explanation of 1/''f'' noise<br />
<br />
| title = Self-organized criticality: an explanation of 1/f noise<br />
<br />
自组织临界性: 1 / f 噪音的解释<br />
<br />
| journal = [[Physical Review Letters]]<br />
<br />
| journal = Physical Review Letters<br />
<br />
物理评论快报<br />
<br />
| volume = 59<br />
<br />
| volume = 59<br />
<br />
第59卷<br />
<br />
| issue = 4<br />
<br />
| issue = 4<br />
<br />
第四期<br />
<br />
| pages = 381&ndash;384<br />
<br />
| pages = 381&ndash;384<br />
<br />
381-- 384<br />
<br />
| doi = 10.1103/PhysRevLett.59.381<br />
<br />
| doi = 10.1103/PhysRevLett.59.381<br />
<br />
10.1103 / physrvlett. 59.381<br />
<br />
| pmid = 10035754<br />
<br />
| pmid = 10035754<br />
<br />
10035754<br />
<br />
| bibcode=1987PhRvL..59..381B<br />
<br />
| bibcode=1987PhRvL..59..381B<br />
<br />
| bibcode 1987PhRvL. . 59. . 381 b<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
Papercore summary: [https://archive.is/20130704122906/http://papercore.org/Bak1987 http://papercore.org/Bak1987].</ref> <br />
<br />
Papercore summary: [https://archive.is/20130704122906/http://papercore.org/Bak1987 http://papercore.org/Bak1987].</ref> <br />
<br />
论文摘要: [ https://archive.is/20130704122906/http://Papercore.org/bak1987 http://Papercore.org/bak1987] / 参考<br />
<br />
published in 1987 in ''[[Physical Review Letters]]'', and is considered to be one of the mechanisms by which [[complexity]]<ref name=Bak1995><br />
<br />
published in 1987 in Physical Review Letters, and is considered to be one of the mechanisms by which complexity<ref name=Bak1995><br />
<br />
1987年发表在《物理评论快报》上,被认为是复杂性的机制之一<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[Per Bak|Bak, P.]], and [[Maya Paczuski|Paczuski, M.]]<br />
<br />
| author = Bak, P., and Paczuski, M.<br />
<br />
作者 Bak,p,and Paczuski,m。<br />
<br />
| year = 1995<br />
<br />
| year = 1995<br />
<br />
1995年<br />
<br />
| title = Complexity, contingency, and criticality<br />
<br />
| title = Complexity, contingency, and criticality<br />
<br />
| 标题复杂性、偶然性和临界性<br />
<br />
| journal =Proc Natl Acad Sci U S A <br />
<br />
| journal =Proc Natl Acad Sci U S A <br />
<br />
美国科学促进协会<br />
<br />
| volume = 92<br />
<br />
| volume = 92<br />
<br />
第92卷<br />
<br />
| pages = 6689&ndash;6696<br />
<br />
| pages = 6689&ndash;6696<br />
<br />
6689-- 6696<br />
<br />
| pmid = 11607561<br />
<br />
| pmid = 11607561<br />
<br />
11607561<br />
<br />
| doi = 10.1073/pnas.92.15.6689<br />
<br />
| doi = 10.1073/pnas.92.15.6689<br />
<br />
10.1073 / pnas. 92.15.6689<br />
<br />
| issue = 15<br />
<br />
| issue = 15<br />
<br />
第15期<br />
<br />
| pmc = 41396<br />
<br />
| pmc = 41396<br />
<br />
41396<br />
<br />
|bibcode = 1995PNAS...92.6689B }}</ref> arises in nature. Its concepts have been applied across fields as diverse as [[geophysics]],<ref name=SmalleyTurcotteSolla85><br />
<br />
|bibcode = 1995PNAS...92.6689B }}</ref> arises in nature. Its concepts have been applied across fields as diverse as geophysics,<ref name=SmalleyTurcotteSolla85><br />
<br />
| bibcode 1995PNAS... 92.6689 b } / ref 在自然界中出现。它的概念已经被应用于各个领域,比如地球物理学,参考名称 smalleyturcottesolla85<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
|author1=Smalley, R. F., Jr. |author2=Turcotte, D. L. |author3=Solla, S. A. | year = 1985<br />
<br />
|author1=Smalley, R. F., Jr. |author2=Turcotte, D. L. |author3=Solla, S. A. | year = 1985<br />
<br />
1 Smalley,r. f. ,jr. | author2 Turcotte,d. l. | author3 Solla,s. a.1985年<br />
<br />
| title = A renormalization group approach to the stick-slip behavior of faults<br />
<br />
| title = A renormalization group approach to the stick-slip behavior of faults<br />
<br />
| 题目: 断层粘滑行为的重整化群方法<br />
<br />
| journal = Journal of Geophysical Research<br />
<br />
| journal = Journal of Geophysical Research<br />
<br />
地球物理研究期刊<br />
<br />
| bibcode = 1985JGR....90.1894S<br />
<br />
| bibcode = 1985JGR....90.1894S<br />
<br />
1985JGR... 90.1894 s<br />
<br />
| doi = 10.1029/JB090iB02p01894<br />
<br />
| doi = 10.1029/JB090iB02p01894<br />
<br />
| doi 10.1029 / JB090iB02p01894<br />
<br />
| volume = 90<br />
<br />
| volume = 90<br />
<br />
第90卷<br />
<br />
| issue = B2<br />
<br />
| issue = B2<br />
<br />
| 第二期<br />
<br />
| pages = 1894<br />
<br />
| pages = 1894<br />
<br />
1894页<br />
<br />
|url=https://semanticscholar.org/paper/6776d17957204c198e278bda98c935ab1cf8f22b }}</ref> [[physical cosmology]], [[evolutionary biology]] and [[ecology]], [[bio-inspired computing]] and [[optimization (mathematics)]], [[economics]], [[quantum gravity]], [[sociology]], [[solar physics]], [[plasma physics]], [[neurobiology]]<ref name=LinkenkaerHansen2001><br />
<br />
|url=https://semanticscholar.org/paper/6776d17957204c198e278bda98c935ab1cf8f22b }}</ref> physical cosmology, evolutionary biology and ecology, bio-inspired computing and optimization (mathematics), economics, quantum gravity, sociology, solar physics, plasma physics, neurobiology<ref name=LinkenkaerHansen2001><br />
<br />
[ https://semanticscholar.org/paper/6776d17957204c198e278bda98c935ab1cf8f22b ] / ref 物理宇宙学,进化生物学和生态学,生物启发计算和优化(数学) ,经济学,量子引力,社会学,太阳物理学,等离子物理学,神经生物学参考名称 linkenkaerhansen2001<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
|author1=K. Linkenkaer-Hansen |author2=V. V. Nikouline |author3=J. M. Palva |author4=R. J. Ilmoniemi. |last-author-amp=yes | year = 2001<br />
<br />
|author1=K. Linkenkaer-Hansen |author2=V. V. Nikouline |author3=J. M. Palva |author4=R. J. Ilmoniemi. |last-author-amp=yes | year = 2001<br />
<br />
1 k.Linkenkaer-hansen | author2 v.3 j.4 r.作者: j. Ilmoniemi。最后一个作者2001年<br />
<br />
| title = Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations<br />
<br />
| title = Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations<br />
<br />
人类大脑振荡中的长程时间相关性和标度行为<br />
<br />
| journal = J. Neurosci.<br />
<br />
| journal = J. Neurosci.<br />
<br />
作者: j. Neurosci。<br />
<br />
| volume = 21<br />
<br />
| volume = 21<br />
<br />
第21卷<br />
<br />
| pages = 1370&ndash;1377<br />
<br />
| pages = 1370&ndash;1377<br />
<br />
1370-- 1377<br />
<br />
| pmid = 11160408<br />
<br />
| pmid = 11160408<br />
<br />
11160408<br />
<br />
| issue = 4<br />
<br />
| issue = 4<br />
<br />
第四期<br />
<br />
|doi=10.1523/JNEUROSCI.21-04-01370.2001 |pmc=6762238 }}</ref><ref name=Beggs2003><br />
<br />
|doi=10.1523/JNEUROSCI.21-04-01370.2001 |pmc=6762238 }}</ref><ref name=Beggs2003><br />
<br />
| doi 10.1523 / jneurosci. 21-04-01370.2001 | pmc 6762238} / ref name begs2003<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
|author1=J. M. Beggs |author2=D. Plenz<br />
<br />
|author1=J. M. Beggs |author2=D. Plenz<br />
<br />
1 j.2 d.Plenz<br />
<br />
|lastauthoramp=yes | year = 2006<br />
<br />
|lastauthoramp=yes | year = 2006<br />
<br />
2006年<br />
<br />
| title = Neuronal Avalanches in Neocortical Circuits<br />
<br />
| title = Neuronal Avalanches in Neocortical Circuits<br />
<br />
新皮层神经回路中的神经雪崩<br />
<br />
| journal = J. Neurosci.<br />
<br />
| journal = J. Neurosci.<br />
<br />
作者: j. Neurosci。<br />
<br />
| volume = 23<br />
<br />
| volume = 23<br />
<br />
第23卷<br />
<br />
|issue=35<br />
<br />
|issue=35<br />
<br />
第35期<br />
<br />
|pages=11167–77<br />
<br />
|pages=11167–77<br />
<br />
第11167-77页<br />
<br />
|doi=10.1523/JNEUROSCI.23-35-11167.2003<br />
<br />
|doi=10.1523/JNEUROSCI.23-35-11167.2003<br />
<br />
10.1523 / jneurosci. 23-35-11167.2003<br />
<br />
|pmid=14657176<br />
<br />
|pmid=14657176<br />
<br />
14657176<br />
<br />
|pmc=6741045<br />
<br />
|pmc=6741045<br />
<br />
6741045<br />
<br />
}}</ref><ref name=Chialvo2004><br />
<br />
}}</ref><ref name=Chialvo2004><br />
<br />
} / ref ref name chialvo2004<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author =Chialvo, D. R.<br />
<br />
| author =Chialvo, D. R.<br />
<br />
作者 Chialvo,d. r。<br />
<br />
| year = 2004<br />
<br />
| year = 2004<br />
<br />
2004年<br />
<br />
| title = Critical brain networks<br />
<br />
| title = Critical brain networks<br />
<br />
关键的大脑网络<br />
<br />
| journal = Physica A<br />
<br />
| journal = Physica A<br />
<br />
物理学杂志 a<br />
<br />
| volume = 340<br />
<br />
| volume = 340<br />
<br />
第340卷<br />
<br />
| issue =4<br />
<br />
| issue =4<br />
<br />
第四期<br />
<br />
| pages = 756&ndash;765<br />
<br />
| pages = 756&ndash;765<br />
<br />
756-- 765<br />
<br />
| doi = 10.1016/j.physa.2004.05.064<br />
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| doi = 10.1016/j.physa.2004.05.064<br />
<br />
10.1016 / j.physa. 2004.05.064<br />
<br />
|arxiv = cond-mat/0402538 |bibcode = 2004PhyA..340..756R | author-link = Dante R. Chialvo<br />
<br />
|arxiv = cond-mat/0402538 |bibcode = 2004PhyA..340..756R | author-link = Dante R. Chialvo<br />
<br />
| arxiv cond-mat / 0402538 | bibcode 2004PhyA. . 340. . 756 r | author-link Dante r. Chialvo<br />
<br />
}}</ref> and others.<br />
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}}</ref> and others.<br />
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} / ref and others.<br />
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SOC is typically observed in slowly driven [[non-equilibrium thermodynamics|non-equilibrium]] systems with many [[degrees of freedom (physics and chemistry)|degrees of freedom]] and strongly [[nonlinearity|nonlinear]] dynamics. Many individual examples have been identified since BTW's original paper, but to date there is no known set of general characteristics that ''guarantee'' a system will display SOC.<br />
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SOC is typically observed in slowly driven non-equilibrium systems with many degrees of freedom and strongly nonlinear dynamics. Many individual examples have been identified since BTW's original paper, but to date there is no known set of general characteristics that guarantee a system will display SOC.<br />
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'''<font color="#ff8000"> SOC</font>'''是典型的多自由度、强非线性动力学的缓慢驱动非平衡系统。自从 BTW 的原始论文以来,已经确定了许多单独的例子,但是到目前为止还没有一组已知的一般特征来保证一个系统将显示 '''<font color="#ff8000"> SOC</font>'''。<br />
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== Overview 概览==<br />
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Self-organized criticality is one of a number of important discoveries made in [[statistical physics]] and related fields over the latter half of the 20th century, discoveries which relate particularly to the study of [[complexity]] in nature. For example, the study of [[cellular automata]], from the early discoveries of [[Stanislaw Ulam]] and [[John von Neumann]] through to [[John Horton Conway|John Conway]]'s [[Conway's Game of Life|Game of Life]] and the extensive work of [[Stephen Wolfram]], made it clear that complexity could be generated as an [[emergence|emergent]] feature of extended systems with simple local interactions. Over a similar period of time, [[Benoît Mandelbrot]]'s large body of work on [[fractals]] showed that much complexity in nature could be described by certain ubiquitous mathematical laws, while the extensive study of [[phase transition]]s carried out in the 1960s and 1970s showed how [[scale invariance|scale invariant]] phenomena such as [[fractals]] and [[power law]]s emerged at the [[critical point (physics)|critical point]] between phases.<br />
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Self-organized criticality is one of a number of important discoveries made in statistical physics and related fields over the latter half of the 20th century, discoveries which relate particularly to the study of complexity in nature. For example, the study of cellular automata, from the early discoveries of Stanislaw Ulam and John von Neumann through to John Conway's Game of Life and the extensive work of Stephen Wolfram, made it clear that complexity could be generated as an emergent feature of extended systems with simple local interactions. Over a similar period of time, Benoît Mandelbrot's large body of work on fractals showed that much complexity in nature could be described by certain ubiquitous mathematical laws, while the extensive study of phase transitions carried out in the 1960s and 1970s showed how scale invariant phenomena such as fractals and power laws emerged at the critical point between phases.<br />
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'''<font color="#ff8000"> 自组织临界性Self-organized criticality(SOC)</font>'''是20世纪下半叶统计物理学及相关领域的众多重要发现之一,这些发现尤其与研究自然界的复杂性有关。例如,元胞自动机的研究---- 从 Stanislaw Ulam 和约翰·冯·诺伊曼的早期发现到 John Conway 的生命游戏和 Stephen Wolfram 的大量工作---- 清楚地表明,复杂性可以作为具有简单局部相互作用的扩展系统的一个涌现特征而产生。在相似的时间段内,beno t Mandelbrot 关于分形的大量工作表明,自然界的许多复杂性可以用某些无处不在的数学定律来描述,而在20世纪60年代和70年代对相变的广泛研究表明,诸如分形和幂定律等尺度不变现象是如何出现在相变的临界点上的。<br />
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The term ''self-organized criticality'' was firstly introduced by [[Per Bak|Bak]], [[Chao Tang|Tang]] and [[Kurt Wiesenfeld|Wiesenfeld]]'s 1987 paper, which clearly linked together those factors: a simple [[cellular automaton]] was shown to produce several characteristic features observed in natural complexity ([[fractal]] geometry, [[pink noise|pink (1/f) noise]] and [[power law]]s) in a way that could be linked to [[critical point (physics)|critical-point phenomena]]. Crucially, however, the paper emphasized that the complexity observed emerged in a robust manner that did not depend on finely tuned details of the system: variable parameters in the model could be changed widely without affecting the emergence of critical behavior: hence, ''[[self-organized]]'' criticality. Thus, the key result of BTW's paper was its discovery of a mechanism by which the emergence of complexity from simple local interactions could be ''spontaneous''&mdash;and therefore plausible as a source of natural complexity&mdash;rather than something that was only possible in artificial situations in which control parameters are tuned to precise critical values. The publication of this research sparked considerable interest from both theoreticians and experimentalists, producing some of the most cited papers in the scientific literature.<br />
<br />
The term self-organized criticality was firstly introduced by Bak, Tang and Wiesenfeld's 1987 paper, which clearly linked together those factors: a simple cellular automaton was shown to produce several characteristic features observed in natural complexity (fractal geometry, pink (1/f) noise and power laws) in a way that could be linked to critical-point phenomena. Crucially, however, the paper emphasized that the complexity observed emerged in a robust manner that did not depend on finely tuned details of the system: variable parameters in the model could be changed widely without affecting the emergence of critical behavior: hence, self-organized criticality. Thus, the key result of BTW's paper was its discovery of a mechanism by which the emergence of complexity from simple local interactions could be spontaneous&mdash;and therefore plausible as a source of natural complexity&mdash;rather than something that was only possible in artificial situations in which control parameters are tuned to precise critical values. The publication of this research sparked considerable interest from both theoreticians and experimentalists, producing some of the most cited papers in the scientific literature.<br />
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'''<font color="#ff8000"> 自组织临界性Self-organized criticality(SOC)</font>'''这个术语最早由 Bak,Tang 和 Wiesenfeld 在1987年的论文中提出,这篇论文将这些因素清楚地联系在一起: 一个简单的细胞自动机被证明可以产生在自然复杂性中观察到的几个特征(分形几何、粉红噪声和幂定律) ,这种方式可以与临界点现象联系起来。然而,关键的是,这篇论文强调,观察到的复杂性是以一种强有力的方式出现的,并不依赖于系统精细调整的细节: 模型中的可变参数可以被广泛改变,而不会影响关键行为的出现: 因此,自组织临界性。因此,BTW 论文的关键结果是发现了一种机制,通过这种机制,从简单的局部相互作用中产生的复杂性可能是自发的---- 因此是合理的自然复杂性的来源---- 而不是只有在控制参数调整到精确的临界值的人工情况下才可能出现的东西。这项研究的发表引起了理论家和实验家的极大兴趣,产生了一些在科学文献中被引用最多的论文。<br />
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Due to BTW's metaphorical visualization of their model as a "[[Bak–Tang–Wiesenfeld sandpile|sandpile]]" on which new sand grains were being slowly sprinkled to cause "avalanches", much of the initial experimental work tended to focus on examining real avalanches in [[granular matter]], the most famous and extensive such study probably being the Oslo ricepile experiment{{Citation needed|date=March 2018}}. Other experiments include those carried out on magnetic-domain patterns, the [[Barkhausen effect]] and vortices in [[superconductors]]. <br />
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Due to BTW's metaphorical visualization of their model as a "sandpile" on which new sand grains were being slowly sprinkled to cause "avalanches", much of the initial experimental work tended to focus on examining real avalanches in granular matter, the most famous and extensive such study probably being the Oslo ricepile experiment. Other experiments include those carried out on magnetic-domain patterns, the Barkhausen effect and vortices in superconductors. <br />
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由于 BTW 将他们的模型比喻为一个“沙堆” ,在沙堆上缓慢地喷洒新的沙粒以引起“雪崩” ,所以最初的实验工作主要集中在研究颗粒物质中的真实雪崩,其中最著名和最广泛的研究可能是奥斯陆地震实验。其他实验还包括在磁畴图案、超导体中的巴克豪森效应和涡旋上进行的实验。<br />
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Early theoretical work included the development of a variety of alternative SOC-generating dynamics distinct from the BTW model, attempts to prove model properties analytically (including calculating the [[critical exponent]]s<ref name=Tang1988a><br />
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Early theoretical work included the development of a variety of alternative SOC-generating dynamics distinct from the BTW model, attempts to prove model properties analytically (including calculating the critical exponents<ref name=Tang1988a><br />
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早期的理论工作包括开发各种不同于 BTW 模型的 soc 生成动力学,试图通过分析证明模型的性质(包括计算临界指数,参见 tang1988a<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[Chao Tang|Tang, C.]] and [[Per Bak|Bak, P.]]<br />
<br />
| author = Tang, C. and Bak, P.<br />
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作者 Tang,c. and Bak,p。<br />
<br />
| year = 1988<br />
<br />
| year = 1988<br />
<br />
1988年<br />
<br />
| title = Critical exponents and scaling relations for self-organized critical phenomena<br />
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| title = Critical exponents and scaling relations for self-organized critical phenomena<br />
<br />
自组织临界现象的临界指数和标度关系<br />
<br />
| journal = [[Physical Review Letters]]<br />
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| journal = Physical Review Letters<br />
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物理评论快报<br />
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| volume = 60<br />
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| volume = 60<br />
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第60卷<br />
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| issue = 23<br />
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| issue = 23<br />
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第23期<br />
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| pages = 2347&ndash;2350<br />
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| pages = 2347&ndash;2350<br />
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2347-- 2350<br />
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| doi = 10.1103/PhysRevLett.60.2347<br />
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| doi = 10.1103/PhysRevLett.60.2347<br />
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10.1103 / physrvlett. 60.2347<br />
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| bibcode= 1988PhRvL..60.2347T<br />
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| bibcode= 1988PhRvL..60.2347T<br />
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1988 / phrvl. 60.2347 t<br />
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| pmid=10038328<br />
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| pmid=10038328<br />
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10038328<br />
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}}<br />
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</ref><ref name=Tang1988b><br />
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</ref><ref name=Tang1988b><br />
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/ ref / name tang1988b<br />
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{{cite journal<br />
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{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[Chao Tang|Tang, C.]] and [[Per Bak|Bak, P.]]<br />
<br />
| author = Tang, C. and Bak, P.<br />
<br />
作者 Tang,c. and Bak,p。<br />
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| year = 1988<br />
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| year = 1988<br />
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1988年<br />
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| title = Mean field theory of self-organized critical phenomena<br />
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| title = Mean field theory of self-organized critical phenomena<br />
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自组织临界现象的平均场理论<br />
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| journal = [[Journal of Statistical Physics]]<br />
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| journal = Journal of Statistical Physics<br />
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统计物理学杂志<br />
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| volume = 51<br />
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| volume = 51<br />
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第51卷<br />
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| issue = 5–6<br />
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| issue = 5–6<br />
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第5-6期<br />
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| pages = 797&ndash;802<br />
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| pages = 797&ndash;802<br />
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797802页<br />
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| doi = 10.1007/BF01014884<br />
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| doi = 10.1007/BF01014884<br />
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10.1007 / BF01014884<br />
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| bibcode= 1988JSP....51..797T<br />
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| bibcode= 1988JSP....51..797T<br />
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1988JSP... 51. . 797 t<br />
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| url = https://zenodo.org/record/1232502<br />
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| url = https://zenodo.org/record/1232502<br />
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Https://zenodo.org/record/1232502<br />
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| type = Submitted manuscript<br />
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| type = Submitted manuscript<br />
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| 打印提交的手稿<br />
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</ref>), and examination of the conditions necessary for SOC to emerge. One of the important issues for the latter investigation was whether [[conservation of energy]] was required in the local dynamical exchanges of models: the answer in general is no, but with (minor) reservations, as some exchange dynamics (such as those of BTW) do require local conservation at least on average. In the long term, key theoretical issues yet to be resolved include the calculation of the possible [[universality class]]es of SOC behavior and the question of whether it is possible to derive a general rule for determining if an arbitrary [[algorithm]] displays SOC.<br />
<br />
</ref>), and examination of the conditions necessary for SOC to emerge. One of the important issues for the latter investigation was whether conservation of energy was required in the local dynamical exchanges of models: the answer in general is no, but with (minor) reservations, as some exchange dynamics (such as those of BTW) do require local conservation at least on average. In the long term, key theoretical issues yet to be resolved include the calculation of the possible universality classes of SOC behavior and the question of whether it is possible to derive a general rule for determining if an arbitrary algorithm displays SOC.<br />
<br />
/ ref) ,以及研究出现 '''<font color="#ff8000"> SOC</font>'''的必要条件。后一项研究的一个重要问题是,在局部动态交换模型时是否需要能量守恒: 一般的答案是否定的,但有一些保留意见,因为一些交换动态(如 BTW 的动态)确实需要局部至少平均的能量守恒。从长远来看,有待解决的关键理论问题包括 '''<font color="#ff8000"> SOC</font>''' 行为可能的普适性类的计算,以及是否有可能推导出一个确定任意算法是否显示 '''<font color="#ff8000"> SOC</font>''' 的一般规则的问题。<br />
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Alongside these largely lab-based approaches, many other investigations have centered around large-scale natural or social systems that are known (or suspected) to display [[scale invariance|scale-invariant]] behavior. Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: [[earthquakes]] (which, long before SOC was discovered, were known as a source of scale-invariant behavior such as the [[Gutenberg–Richter law]] describing the statistical distribution of earthquake size, and the [[Aftershock|Omori law]] describing the frequency of aftershocks<ref name=TurcotteSmalleySolla85><br />
<br />
Alongside these largely lab-based approaches, many other investigations have centered around large-scale natural or social systems that are known (or suspected) to display scale-invariant behavior. Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: earthquakes (which, long before SOC was discovered, were known as a source of scale-invariant behavior such as the Gutenberg–Richter law describing the statistical distribution of earthquake size, and the Omori law describing the frequency of aftershocks<ref name=TurcotteSmalleySolla85><br />
<br />
除了这些大部分基于实验室的方法,许多其他的研究都集中在大规模的自然或社会系统上,这些系统已经知道(或怀疑)表现出尺度不变的行为。虽然这些方法并不总是受到研究对象专家的欢迎(至少最初是这样) ,但 '''<font color="#ff8000"> SOC</font>''' 已经成为解释一些自然现象的强有力的候选者,包括: 地震(早在 '''<font color="#ff8000"> SOC</font>''' 被发现之前,地震就被认为是尺度不变行为的来源,例如描述地震大小统计分布的古腾堡-里克特定律,以及描述余震频率的描述余震的 Omori 定律,命名为 turcottesmalleysolla85<br />
<br />
{{cite journal<br />
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{{cite journal<br />
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{引用期刊<br />
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|author1=Turcotte, D. L. |author2=Smalley, R. F., Jr. |author3=Solla, S. A. | year = 1985<br />
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|author1=Turcotte, D. L. |author2=Smalley, R. F., Jr. |author3=Solla, S. A. | year = 1985<br />
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1 Turcotte,D.l. | author2 Smalley,r. f. ,jr. | author3 Solla,s. a.1985年<br />
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| title = Collapse of loaded fractal trees<br />
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| title = Collapse of loaded fractal trees<br />
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负载分形树的崩溃<br />
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| journal = Nature <br />
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| journal = Nature <br />
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自然》杂志<br />
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| doi= 10.1038/313671a0<br />
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| doi= 10.1038/313671a0<br />
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10.1038 / 313671a0<br />
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| volume = 313<br />
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| volume = 313<br />
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第313卷<br />
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| issue = 6004<br />
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| issue = 6004<br />
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第6004期<br />
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| pages = 671–672|bibcode = 1985Natur.313..671T <br />
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| pages = 671–672|bibcode = 1985Natur.313..671T <br />
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| 第671-672页 | bibcode 1985 / natur. 313. . 671 t<br />
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}}</ref><ref name=SmalleyTurcotteSolla85 />); [[solar flares]]; fluctuations in economic systems such as [[financial markets]] (references to SOC are common in [[econophysics]]); [[landscape formation]]; [[forest fires]]; [[landslides]]; [[epidemics]]; neuronal avalanches in the cortex;<ref name="Beggs2003" /><ref name=Poil2012><br />
<br />
}}</ref>); solar flares; fluctuations in economic systems such as financial markets (references to SOC are common in econophysics); landscape formation; forest fires; landslides; epidemics; neuronal avalanches in the cortex;<ref name=Poil2012><br />
<br />
太阳耀斑; 经济系统的波动,比如金融市场(经济物理学中经常提到 SOC) ; 景观形成; 森林火灾; 滑坡; 流行病; 大脑皮层的神经雪崩; 参考名为 poil2012<br />
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{{cite journal<br />
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{{cite journal<br />
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{引用期刊<br />
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| pmid = 22815496<br />
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| pmid = 22815496<br />
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22815496<br />
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|date=Jul 2012<br />
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2012年7月<br />
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|author1=Poil, SS |author2=Hardstone, R |author3=Mansvelder, HD |author4=Linkenkaer-Hansen, K | title = Critical-state dynamics of avalanches and oscillations jointly emerge from balanced excitation/inhibition in neuronal networks<br />
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|author1=Poil, SS |author2=Hardstone, R |author3=Mansvelder, HD |author4=Linkenkaer-Hansen, K | title = Critical-state dynamics of avalanches and oscillations jointly emerge from balanced excitation/inhibition in neuronal networks<br />
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1 Poil,SS | author2 Hardstone,r | author3 mansveder,HD | author4 Linkenkaer-Hansen,k | title 雪崩和振荡的临界状态动力学联合出现在神经元网络的平衡兴奋 / 抑制中<br />
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| volume = 32<br />
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| volume = 32<br />
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第32卷<br />
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| issue = 29<br />
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| issue = 29<br />
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第29期<br />
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| pages = 9817–23 <br />
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| pages = 9817–23 <br />
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第9817-23页<br />
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| doi = 10.1523/JNEUROSCI.5990-11.2012<br />
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| doi = 10.1523/JNEUROSCI.5990-11.2012<br />
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| doi 10.1523 / jneurosci. 5990-11.2012<br />
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| journal = Journal of Neuroscience<br />
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| journal = Journal of Neuroscience<br />
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神经科学杂志<br />
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| pmc=3553543<br />
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| pmc=3553543<br />
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3553543<br />
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}}</ref> 1/f noise in the amplitude of electrophysiological signals;<ref name=LinkenkaerHansen2001 /> and [[biological evolution]] (where SOC has been invoked, for example, as the dynamical mechanism behind the theory of "[[punctuated equilibrium|punctuated equilibria]]" put forward by [[Niles Eldredge]] and [[Stephen Jay Gould]]). These "applied" investigations of SOC have included both modelling (either developing new models or adapting existing ones to the specifics of a given natural system) and extensive data analysis to determine the existence and/or characteristics of natural scaling laws.<br />
<br />
}}</ref> 1/f noise in the amplitude of electrophysiological signals; and biological evolution (where SOC has been invoked, for example, as the dynamical mechanism behind the theory of "punctuated equilibria" put forward by Niles Eldredge and Stephen Jay Gould). These "applied" investigations of SOC have included both modelling (either developing new models or adapting existing ones to the specifics of a given natural system) and extensive data analysis to determine the existence and/or characteristics of natural scaling laws.<br />
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{} / ref 1 / f 噪声在电生理信号的振幅,以及生物进化(其中 SOC 已被调用,例如,作为背后的动力机制的理论“间断平衡”由 Niles Eldredge 和史蒂芬·古尔德提出)。对土壤有机碳的这些”应用”研究既包括建模(开发新模型或使现有模型适应特定自然系统的具体情况) ,也包括广泛的数据分析,以确定是否存在和 / 或具有自然定标法的特点。<br />
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In addition, SOC has been applied to computational algorithms. Recently, it has been found that the avalanches from an SOC process, like the BTW model, make effective patterns in a random search for optimal solutions on graphs.<ref name=Hoffmann2018><br />
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In addition, SOC has been applied to computational algorithms. Recently, it has been found that the avalanches from an SOC process, like the BTW model, make effective patterns in a random search for optimal solutions on graphs.<ref name=Hoffmann2018><br />
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此外,SOC 已经应用于计算算法。最近,人们发现来自 SOC 过程的雪崩,如 BTW 模型,在图的最优解的随机搜索中形成有效的模式。 参考名称 hoffmann2018<br />
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{{cite journal<br />
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{{cite journal<br />
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{引用期刊<br />
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| author = [[H. Hoffmann|Hoffmann, H.]] and [[D. W. Payton|Payton, D. W.]]<br />
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| author = Hoffmann, H. and Payton, D. W.<br />
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作者: 霍夫曼 h. 和佩顿 d. w。<br />
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| year = 2018<br />
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| year = 2018<br />
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2018年<br />
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| title = Optimization by Self-Organized Criticality<br />
<br />
| title = Optimization by Self-Organized Criticality<br />
<br />
最佳化作者: 自组织临界性<br />
<br />
| journal = [[Scientific Reports]]<br />
<br />
| journal = Scientific Reports<br />
<br />
科学报告<br />
<br />
| volume = 8<br />
<br />
| volume = 8<br />
<br />
第八卷<br />
<br />
| issue = 1<br />
<br />
| issue = 1<br />
<br />
第一期<br />
<br />
| pages = 2358<br />
<br />
| pages = 2358<br />
<br />
2358页<br />
<br />
| doi=10.1038/s41598-018-20275-7<br />
<br />
| doi=10.1038/s41598-018-20275-7<br />
<br />
10.1038 / s41598-018-20275-7<br />
<br />
| pmid = 29402956<br />
<br />
| pmid = 29402956<br />
<br />
29402956<br />
<br />
| pmc = 5799203<br />
<br />
| pmc = 5799203<br />
<br />
5799203<br />
<br />
| bibcode = 2018NatSR...8.2358H<br />
<br />
| bibcode = 2018NatSR...8.2358H<br />
<br />
| bibcode 2018NatSR... 8.2358 h<br />
<br />
}}</ref> <br />
<br />
}}</ref> <br />
<br />
{} / ref<br />
<br />
An example of such an optimization problem is [[graph coloring]]. The SOC process apparently helps the optimization from getting stuck in a [[local optimum]] without the use of any [[Simulated_annealing|annealing]] scheme, as suggested by previous work on [[extremal optimization]].<br />
<br />
An example of such an optimization problem is graph coloring. The SOC process apparently helps the optimization from getting stuck in a local optimum without the use of any annealing scheme, as suggested by previous work on extremal optimization.<br />
<br />
图着色就是这种最佳化问题的一个例子。'''<font color="#ff8000"> SOC</font>''' 过程显然有助于优化陷入局部最优,而无需使用任何退火方案,正如以前的极值优化工作所建议的。<br />
<br />
<br />
<br />
<br />
<br />
The recent excitement generated by [[scale-free networks]] has raised some interesting new questions for SOC-related research: a number of different SOC models have been shown to generate such networks as an emergent phenomenon, as opposed to the simpler models proposed by network researchers where the network tends to be assumed to exist independently of any physical space or dynamics. While many single phenomena have been shown to exhibit scale-free properties over narrow ranges, a phenomenon offering by far a larger amount of data is solvent-accessible surface areas in globular proteins.<ref name=Moret2007><br />
<br />
The recent excitement generated by scale-free networks has raised some interesting new questions for SOC-related research: a number of different SOC models have been shown to generate such networks as an emergent phenomenon, as opposed to the simpler models proposed by network researchers where the network tends to be assumed to exist independently of any physical space or dynamics. While many single phenomena have been shown to exhibit scale-free properties over narrow ranges, a phenomenon offering by far a larger amount of data is solvent-accessible surface areas in globular proteins.<ref name=Moret2007><br />
<br />
'''<font color="#ff8000"> 无标度网络Scale-free networks</font>'''最近引起的兴奋为 '''<font color="#ff8000"> SOC</font>'''相关研究提出了一些有趣的新问题: 许多不同的 '''<font color="#ff8000"> SOC</font>'''模型已经被证明是作为一种涌现现象产生这样的网络,而不是网络研究人员提出的更简单的模型,其中网络往往被假定独立于任何物理空间或动力学存在。虽然许多单一现象已被证明在狭窄的范围内表现出无标度特性,但是到目前为止提供了大量数据的现象是球状蛋白质中溶剂可及的表面区域。 参考名称 moret2007<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[M. A. Moret|Moret, M. A.]] and [[G. Zebende|Zebende, G.]]<br />
<br />
| author = Moret, M. A. and Zebende, G.<br />
<br />
作者: Moret,M.a. and Zebende,g。<br />
<br />
| year = 2007<br />
<br />
| year = 2007<br />
<br />
2007年<br />
<br />
| title = Amino acid hydrophobicity and accessible surface area<br />
<br />
| title = Amino acid hydrophobicity and accessible surface area<br />
<br />
氨基酸疏水性和可达表面积<br />
<br />
| journal = [[Phys. Rev. E]]<br />
<br />
| journal = Phys. Rev. E<br />
<br />
体育杂志。牧师。E<br />
<br />
| volume = 75<br />
<br />
| volume = 75<br />
<br />
第75卷<br />
<br />
| issue = 1<br />
<br />
| issue = 1<br />
<br />
第一期<br />
<br />
| pages = 011920<br />
<br />
| pages = 011920<br />
<br />
011920页<br />
<br />
| doi=10.1103/PhysRevE.75.011920<br />
<br />
| doi=10.1103/PhysRevE.75.011920<br />
<br />
10.1103 / physarve. 75.011920<br />
<br />
| pmid = 17358197<br />
<br />
| pmid = 17358197<br />
<br />
17358197<br />
<br />
| bibcode = 2007PhRvE..75a1920M<br />
<br />
| bibcode = 2007PhRvE..75a1920M<br />
<br />
2007 / phrve. . 75 / a1920M<br />
<br />
}}</ref><br />
<br />
}}</ref><br />
<br />
{} / ref<br />
<br />
These studies quantify the differential geometry of proteins, and resolve many evolutionary puzzles regarding the biological emergence of complexity.<ref name=Phillips2014><br />
<br />
These studies quantify the differential geometry of proteins, and resolve many evolutionary puzzles regarding the biological emergence of complexity.<ref name=Phillips2014><br />
<br />
这些研究量化了蛋白质的微分几何,并解决了许多关于生物复杂性出现的进化之谜<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = Phillips, J. C.<br />
<br />
| author = Phillips, J. C.<br />
<br />
作者: 菲利普斯。<br />
<br />
| year = 2014<br />
<br />
| year = 2014<br />
<br />
2014年<br />
<br />
| title = Fractals and self-organized criticality in proteins<br />
<br />
| title = Fractals and self-organized criticality in proteins<br />
<br />
标题蛋白质中的分形和自组织临界性<br />
<br />
| journal = Physica A<br />
<br />
| journal = Physica A<br />
<br />
物理学杂志 a<br />
<br />
| volume = 415<br />
<br />
| volume = 415<br />
<br />
第415卷<br />
<br />
| pages = 440–448 <br />
<br />
| pages = 440–448 <br />
<br />
第440-448页<br />
<br />
| doi=10.1016/j.physa.2014.08.034<br />
<br />
| doi=10.1016/j.physa.2014.08.034<br />
<br />
| doi 10.1016 / j.physa. 2014.08.034<br />
<br />
| bibcode = 2014PhyA..415..440P<br />
<br />
| bibcode = 2014PhyA..415..440P<br />
<br />
| bibcode 2014PhyA. . 415. . 440 p<br />
<br />
| author-link = J. C. Phillips<br />
<br />
| author-link = J. C. Phillips<br />
<br />
作者链接 J.c. 菲利普斯<br />
<br />
}}</ref><br />
<br />
}}</ref><br />
<br />
{} / ref<br />
<br />
<br />
<br />
<br />
<br />
Despite the considerable interest and research output generated from the SOC hypothesis, there remains no general agreement with regards to its mechanisms in abstract mathematical form. Bak Tang and Wiesenfeld based their hypothesis on the behavior of their sandpile model.<ref name=Bak1987/> However,<br />
<br />
Despite the considerable interest and research output generated from the SOC hypothesis, there remains no general agreement with regards to its mechanisms in abstract mathematical form. Bak Tang and Wiesenfeld based their hypothesis on the behavior of their sandpile model. However,<br />
<br />
尽管 SOC 假说引起了相当大的兴趣和研究成果,但是关于其抽象数学形式的机制仍然没有普遍的一致性。和 Wiesenfeld 基于他们的沙堆模型的行为建立了他们的假设。然而,<br />
<br />
it has been argued that this model would actually generate 1/f<sup>2</sup> noise rather than 1/f noise.<ref name=Jensen1989><br />
<br />
it has been argued that this model would actually generate 1/f<sup>2</sup> noise rather than 1/f noise.<ref name=Jensen1989><br />
<br />
有人认为,这种模型实际上会产生1 / f sup 2 / sup 噪声而不是1 / f 噪声<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[H. J. Jensen|Jensen, H. J.]], [[K. Christensen|Christensen, K.]] and [[H. C. Fogedby|Fogedby, H. C.]]<br />
<br />
| author = Jensen, H. J., Christensen, K. and Fogedby, H. C.<br />
<br />
作者 Jensen,h. j. ,Christensen,k. and fogeby,h. c。<br />
<br />
| year = 1989<br />
<br />
| year = 1989<br />
<br />
1989年<br />
<br />
| title = 1/f noise, distribution of lifetimes, and a pile of sand<br />
<br />
| title = 1/f noise, distribution of lifetimes, and a pile of sand<br />
<br />
标题1 / f 噪音,寿命分布,和一堆沙子<br />
<br />
| journal = [[Phys. Rev. B]]<br />
<br />
| journal = Phys. Rev. B<br />
<br />
体育杂志。牧师。B<br />
<br />
| volume = 40<br />
<br />
| volume = 40<br />
<br />
第40卷<br />
<br />
| issue = 10<br />
<br />
| issue = 10<br />
<br />
第10期<br />
<br />
| pages = 7425–7427<br />
<br />
| pages = 7425–7427<br />
<br />
第7425-7427页<br />
<br />
| doi=10.1103/physrevb.40.7425<br />
<br />
| doi=10.1103/physrevb.40.7425<br />
<br />
10.1103 / physirevb. 40.7425<br />
<br />
| pmid = 9991162<br />
<br />
| pmid = 9991162<br />
<br />
9991162<br />
<br />
|bibcode = 1989PhRvB..40.7425J }}<br />
<br />
|bibcode = 1989PhRvB..40.7425J }}<br />
<br />
1989 / phrvb. 40.7425 j }<br />
<br />
</ref><br />
<br />
</ref><br />
<br />
/ 参考<br />
<br />
This claim was based on untested scaling assumptions, and a more rigorous analysis showed that sandpile models <br />
<br />
This claim was based on untested scaling assumptions, and a more rigorous analysis showed that sandpile models <br />
<br />
这种说法是基于未经测试的比例假设,更严格的分析表明沙堆模型<br />
<br />
generally produce 1/f<sup>a</sup> spectra, with a<2. <ref name=Laurson2005><br />
<br />
generally produce 1/f<sup>a</sup> spectra, with a<2. <ref name=Laurson2005><br />
<br />
一般产生1 / f sup a / sup 光谱,其值为2。参考名称 laurson2005<br />
<br />
{{cite journal |author1=Laurson, Lasse |author2=Alava, Mikko J. |author3=Zapperi, Stefano |title=Letter: Power spectra of self-organized critical sand piles |journal=Journal of Statistical Mechanics: Theory and Experiment |volume=0511 |id=L001 |date=15 September 2005 }}</ref><br />
<br />
</ref><br />
<br />
/ 参考<br />
<br />
Other simulation models were proposed later that could produce true 1/f noise,<ref name=Maslov1999><br />
<br />
Other simulation models were proposed later that could produce true 1/f noise,<ref name=Maslov1999><br />
<br />
其他模拟模型后来被提出,可以产生真正的1 / f 噪声,参考名称 maslov1999<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[S. Maslov|Maslov, S.]], [[C. Tang|Tang, C.]] and [[Y. –C. Zhang|Zhang, Y. - C.]]<br />
<br />
| author = Maslov, S., Tang, C. and Zhang, Y. - C.<br />
<br />
作者 Maslov,s. ,Tang,c. and Zhang,y。- c.<br />
<br />
| year = 1999<br />
<br />
| year = 1999<br />
<br />
1999年<br />
<br />
| title = 1/f noise in Bak-Tang-Wiesenfeld models on narrow stripes<br />
<br />
| title = 1/f noise in Bak-Tang-Wiesenfeld models on narrow stripes<br />
<br />
| 标题1 / f Bak-Tang-Wiesenfeld 窄条纹模型的噪音<br />
<br />
| journal = [[Phys. Rev. Lett.]]<br />
<br />
| journal = Phys. Rev. Lett.<br />
<br />
体育杂志。牧师。莱特。<br />
<br />
| volume = 83<br />
<br />
| volume = 83<br />
<br />
第83卷<br />
<br />
| issue = 12<br />
<br />
| issue = 12<br />
<br />
第12期<br />
<br />
| pages = 2449–2452<br />
<br />
| pages = 2449–2452<br />
<br />
2449-2452页<br />
<br />
| doi=10.1103/physrevlett.83.2449<br />
<br />
| doi=10.1103/physrevlett.83.2449<br />
<br />
10.1103 / physrvlett. 83.2449<br />
<br />
|arxiv = cond-mat/9902074 |bibcode = 1999PhRvL..83.2449M }}<br />
<br />
|arxiv = cond-mat/9902074 |bibcode = 1999PhRvL..83.2449M }}<br />
<br />
| arxiv cond-mat / 9902074 | bibcode 1999PhRvL. . 83.2449 m }<br />
<br />
</ref> and experimental sandpile models were observed to yield 1/f noise.<ref name=Frette1996><br />
<br />
</ref> and experimental sandpile models were observed to yield 1/f noise.<ref name=Frette1996><br />
<br />
/ ref 和实验沙堆模型被观察到产生1 / f 噪音。参考名称 frette1996<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[V.Frette|Frette, V.]], [[K. Christiansen|Christinasen, K.]], [[A. Malthe-Sørenssen|Malthe-Sørenssen, A.]], [[J. Feder|Feder, J]], [[T. Jøssang|Jøssang, T]] and [[P. Meakin|Meaken, P]]<br />
<br />
| author = Frette, V., Christinasen, K., Malthe-Sørenssen, A., Feder, J, Jøssang, T and Meaken, P<br />
<br />
| author = Frette, V., Christinasen, K., Malthe-Sørenssen, A., Feder, J, Jøssang, T and Meaken, P<br />
<br />
| year = 1996<br />
<br />
| year = 1996<br />
<br />
1996年<br />
<br />
| title = Avalanche dynamics in a pile of rice<br />
<br />
| title = Avalanche dynamics in a pile of rice<br />
<br />
| 题目: 大米堆中的雪崩动力学<br />
<br />
| journal = [[Nature (journal)|Nature]]<br />
<br />
| journal = Nature<br />
<br />
自然》杂志<br />
<br />
| volume = 379<br />
<br />
| volume = 379<br />
<br />
第379卷<br />
<br />
| issue = 6560<br />
<br />
| issue = 6560<br />
<br />
第6560期<br />
<br />
| pages = 49–52<br />
<br />
| pages = 49–52<br />
<br />
第49-52页<br />
<br />
| doi =10.1038/379049a0 <br />
<br />
| doi =10.1038/379049a0 <br />
<br />
10.1038 / 379049a0<br />
<br />
| bibcode= 1996Natur.379...49F}}<br />
<br />
| bibcode= 1996Natur.379...49F}}<br />
<br />
1996 / natur. 379... 49F }<br />
<br />
</ref> In addition to the nonconservative theoretical model mentioned above, other theoretical models for SOC have been based upon [[information theory]]<ref name=Dewar2003><br />
<br />
</ref> In addition to the nonconservative theoretical model mentioned above, other theoretical models for SOC have been based upon information theory<ref name=Dewar2003><br />
<br />
除了上面提到的非保守理论模型之外,其他关于 SOC 的理论模型都是基于信息论,例如 dewar2003<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = Dewar, R.<br />
<br />
| author = Dewar, R.<br />
<br />
作者杜瓦,r。<br />
<br />
| year = 2003<br />
<br />
| year = 2003<br />
<br />
2003年<br />
<br />
| title = Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states<br />
<br />
| title = Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states<br />
<br />
非平衡态中涨落定理、最大产生熵和自组织临界性的信息论解释<br />
<br />
| journal =J. Phys. A: Math. Gen. <br />
<br />
| journal =J. Phys. A: Math. Gen. <br />
<br />
| j 杂志。女名女子名。答: 数学。将军。<br />
<br />
| volume = 36<br />
<br />
| volume = 36<br />
<br />
第36卷<br />
<br />
| pages =631&ndash;641<br />
<br />
| pages =631&ndash;641<br />
<br />
631-- 641<br />
<br />
| pmid = <br />
<br />
| pmid = <br />
<br />
我不会让你失望的<br />
<br />
| doi = 10.1088/0305-4470/36/3/303<br />
<br />
| doi = 10.1088/0305-4470/36/3/303<br />
<br />
10.1088 / 0305-4470 / 36 / 3 / 303<br />
<br />
| issue = 3<br />
<br />
| issue = 3<br />
<br />
第三期<br />
<br />
| pmc = <br />
<br />
| pmc = <br />
<br />
我会的,我会的,我会的<br />
<br />
|bibcode = 2003JPhA...36..631D|arxiv = cond-mat/0005382 | author-link = R Dewar<br />
<br />
|bibcode = 2003JPhA...36..631D|arxiv = cond-mat/0005382 | author-link = R Dewar<br />
<br />
| bibcode 2003JPhA... 36. . 631 d | arxiv cond-mat / 0005382 | author-link r Dewar<br />
<br />
}}</ref>, <br />
<br />
}}</ref>, <br />
<br />
} / ref,<br />
<br />
[[mean field theory]]<ref name=Vespignani1998><br />
<br />
mean field theory<ref name=Vespignani1998><br />
<br />
平均场理论参考名称 vespignani1998<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = [[Alessandro Vespignani|Vespignani, A.]], and [[Stefano Zapperi|Zapperi, S.]]<br />
<br />
| author = Vespignani, A., and Zapperi, S.<br />
<br />
作者 Vespignani,a,和 Zapperi,s。<br />
<br />
| year = 1998<br />
<br />
| year = 1998<br />
<br />
1998年<br />
<br />
| title = How self-organized criticality works: a unified mean-field picture<br />
<br />
| title = How self-organized criticality works: a unified mean-field picture<br />
<br />
标题自组织临界性如何工作: 一个统一的平均场图片<br />
<br />
| journal =Phys. Rev. E <br />
<br />
| journal =Phys. Rev. E <br />
<br />
体育杂志。牧师。E<br />
<br />
| volume = 57<br />
<br />
| volume = 57<br />
<br />
第57卷<br />
<br />
| pages =6345–6362<br />
<br />
| pages =6345–6362<br />
<br />
6345-6362页<br />
<br />
| pmid = <br />
<br />
| pmid = <br />
<br />
我不会让你失望的<br />
<br />
| doi = 10.1103/physreve.57.6345<br />
<br />
| doi = 10.1103/physreve.57.6345<br />
<br />
10.1103 / physorve. 57.6345<br />
<br />
| issue = 6<br />
<br />
| issue = 6<br />
<br />
第六期<br />
<br />
| pmc = <br />
<br />
| pmc = <br />
<br />
我会的,我会的,我会的<br />
<br />
| bibcode = 1998PhRvE..57.6345V<br />
<br />
| bibcode = 1998PhRvE..57.6345V<br />
<br />
| bibcode 1998PhRvE. . 57.6345 v<br />
<br />
| arxiv = cond-mat/9709192<br />
<br />
| arxiv = cond-mat/9709192<br />
<br />
| arxiv = cond-mat/9709192<br />
<br />
| hdl = 2047/d20002173<br />
<br />
| hdl = 2047/d20002173<br />
<br />
2047 / d20002173<br />
<br />
}}</ref>,<br />
<br />
}}</ref>,<br />
<br />
} / ref,<br />
<br />
the [[convergence of random variables]]<ref name=Kendal2015><br />
<br />
the convergence of random variables<ref name=Kendal2015><br />
<br />
随机变量的收敛裁判名称 kendal 2015<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = Kendal, WS<br />
<br />
| author = Kendal, WS<br />
<br />
作者 Kendal,WS<br />
<br />
| year = 2015<br />
<br />
| year = 2015<br />
<br />
2015年<br />
<br />
| title = Self-organized criticality attributed to a central limit-like convergence effect<br />
<br />
| title = Self-organized criticality attributed to a central limit-like convergence effect<br />
<br />
| 标题自组织临界性归因于类似中心极限的聚合效应<br />
<br />
| journal =Physica A <br />
<br />
| journal =Physica A <br />
<br />
物理学杂志 a<br />
<br />
| volume = 421<br />
<br />
| volume = 421<br />
<br />
第421卷<br />
<br />
| pages =141&ndash;150<br />
<br />
| pages =141&ndash;150<br />
<br />
141-- 150页<br />
<br />
| pmid = <br />
<br />
| pmid = <br />
<br />
我不会让你失望的<br />
<br />
| doi = 10.1016/j.physa.2014.11.035<br />
<br />
| doi = 10.1016/j.physa.2014.11.035<br />
<br />
| doi 10.1016 / j.physa. 2014.11.035<br />
<br />
| issue = <br />
<br />
| issue = <br />
<br />
发行<br />
<br />
| pmc = <br />
<br />
| pmc = <br />
<br />
我会的,我会的,我会的<br />
<br />
|bibcode =2015PhyA..421..141K | author-link = Wayne Kendal<br />
<br />
|bibcode =2015PhyA..421..141K | author-link = Wayne Kendal<br />
<br />
| bibcode 2015PhyA. . 421. . 141 k | 作者链接 Wayne Kendal<br />
<br />
}}</ref>,<br />
<br />
}}</ref>,<br />
<br />
} / ref,<br />
<br />
and cluster formation.<ref name=Hoffmann2018b><br />
<br />
and cluster formation.<ref name=Hoffmann2018b><br />
<br />
和簇的形成。参考名称 hoffmann2018b<br />
<br />
{{cite journal<br />
<br />
{{cite journal<br />
<br />
{引用期刊<br />
<br />
| author = Hoffmann, H.<br />
<br />
| author = Hoffmann, H.<br />
<br />
作者: 霍夫曼。<br />
<br />
| year = 2018<br />
<br />
| year = 2018<br />
<br />
2018年<br />
<br />
| title = Impact of Network Topology on Self-Organized Criticality<br />
<br />
| title = Impact of Network Topology on Self-Organized Criticality<br />
<br />
网络拓扑对自组织临界性的影响<br />
<br />
| journal = Phys. Rev. E <br />
<br />
| journal = Phys. Rev. E <br />
<br />
体育杂志。牧师。E<br />
<br />
| volume = 97<br />
<br />
| volume = 97<br />
<br />
第97卷<br />
<br />
| pages =022313<br />
<br />
| pages =022313<br />
<br />
022313页<br />
<br />
| pmid = 29548239<br />
<br />
| pmid = 29548239<br />
<br />
29548239<br />
<br />
| doi = 10.1103/PhysRevE.97.022313<br />
<br />
| doi = 10.1103/PhysRevE.97.022313<br />
<br />
10.1103 / physarve. 97.022313<br />
<br />
| issue = 2<br />
<br />
| issue = 2<br />
<br />
第二期<br />
<br />
| pmc = <br />
<br />
| pmc = <br />
<br />
我会的,我会的,我会的<br />
<br />
| bibcode =2018PhRvE..97b2313H <br />
<br />
| bibcode =2018PhRvE..97b2313H <br />
<br />
2018 / phrve. . 97 / b2313H<br />
<br />
| author-link = Heiko Hoffmann<br />
<br />
| author-link = Heiko Hoffmann<br />
<br />
作者: 海科 · 霍夫曼<br />
<br />
| doi-access = free<br />
<br />
| doi-access = free<br />
<br />
免费访问<br />
<br />
}}</ref> A continuous model of self-organised criticality is proposed by using [[tropical geometry]].<ref>{{Cite journal|last=Kalinin|first=N.|last2=Guzmán-Sáenz|first2=A.|last3=Prieto|first3=Y.|last4=Shkolnikov|first4=M.|last5=Kalinina|first5=V.|last6=Lupercio|first6=E.|date=2018-08-15|title=Self-organized criticality and pattern emergence through the lens of tropical geometry|journal=Proceedings of the National Academy of Sciences|volume=115|issue=35|language=en|pages=E8135–E8142|doi=10.1073/pnas.1805847115|issn=0027-8424|pmid=30111541|pmc=6126730|arxiv=1806.09153}}</ref><br />
<br />
}}</ref> A continuous model of self-organised criticality is proposed by using tropical geometry.<br />
<br />
{} / ref 一个'''<font color="#ff8000"> 自组织临界Self-organised criticality</font>'''的连续模型是通过使用热带几何来提出的。<br />
<br />
== Examples of self-organized critical dynamics自组织临界动力学的例子 ==<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
In chronological order of development:<br />
<br />
In chronological order of development:<br />
<br />
按发展时间顺序排列:<br />
<br />
<br />
<br />
<br />
<br />
* Stick-slip model of fault failure<ref name="TurcotteSmalleySolla85" /><ref name="SmalleyTurcotteSolla85" /><br />
<br />
*断层破坏的粘滑模型<ref name="TurcotteSmalleySolla85" /><ref name="SmalleyTurcotteSolla85" /><br />
<br />
*[[Abelian sandpile model|Bak–Tang–Wiesenfeld sandpile]]<br />
<br />
*[[阿贝尔沙堆模型| Bak–Tang–Wiesenfeld沙堆]]<br />
<br />
* [[Forest-fire model]]<br />
<br />
*[[森林火灾模型]]<br />
<br />
* [[Olami–Feder–Christensen model]]<br />
<br />
* [[奥拉米·费德·克里斯滕森模型]]<br />
<br />
* [[Bak–Sneppen model]]<br />
<br />
*[[背景模型]]<br />
<br />
== See also 参见==<br />
<br />
<br />
<br />
* [[Pink noise|1/f noise]]<br />
<br />
*[[粉红噪音| 1/f噪音]]<br />
<br />
* [[Complex system]]s<br />
<br />
* [[复杂系统]]s<br />
<br />
* [[Critical brain hypothesis]]<br />
<br />
*[[【关键大脑假说】]]<br />
<br />
* [[Critical exponents]]<br />
<br />
*[[临界指数]]<br />
<br />
* [[Detrended fluctuation analysis]], a method to detect power-law scaling in time series.<br />
<br />
*[[Detrended涨落分析]],一种检测中幂律标度的方法<br />
<br />
* [[Dual-phase evolution]], another process that contributes to self-organization in complex systems.<br />
<br />
* [[双相演化]],另一个有助于自我组织的过程<br />
<br />
* [[Fractal]]s<br />
<br />
* [[分形]]s;<br />
<br />
* [[Ilya Prigogine]], a systems scientist who helped formalize dissipative system behavior in general terms.<br />
<br />
*[[伊利亚·普里高津]],一位帮助将耗散系统形式化的系统科学家<br />
<br />
* [[Power law]]s<br />
<br />
*[[幂律]]s<br />
<br />
* [[Red Queen hypothesis]]<br />
<br />
*[[红皇后假说]]<br />
<br />
* [[Scale invariance]]<br />
<br />
* [[标度不变性]]<br />
<br />
* [[Self-organization]]<br />
<br />
* [[自组织]]<br />
<br />
* [[Self-organized criticality control]]<br />
<br />
*[[自组织临界控制]]<br />
<br />
==References参考资料==<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<references/><br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
== Further reading延伸阅读 ==<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = Adami, C.<br />
<br />
| author = Adami, C.<br />
<br />
作者: 阿达米。<br />
<br />
| year = 1995<br />
<br />
| year = 1995<br />
<br />
1995年<br />
<br />
| title = Self-organized criticality in living systems<br />
<br />
| title = Self-organized criticality in living systems<br />
<br />
| 生命系统中的自组织临界性<br />
<br />
| journal = [[Physics Letters A]]<br />
<br />
| journal = Physics Letters A<br />
<br />
物理学快报<br />
<br />
| volume = 203<br />
<br />
| volume = 203<br />
<br />
第203卷<br />
<br />
| issue = 1<br />
<br />
| issue = 1<br />
<br />
第一期<br />
<br />
| pages = 29&ndash;32<br />
<br />
| pages = 29&ndash;32<br />
<br />
29-- 32页<br />
<br />
| doi = 10.1016/0375-9601(95)00372-A<br />
<br />
| doi = 10.1016/0375-9601(95)00372-A<br />
<br />
| doi 10.1016 / 0375-9601(95)00372-A<br />
<br />
|bibcode = 1995PhLA..203...29A | arxiv = adap-org/9401001<br />
<br />
|bibcode = 1995PhLA..203...29A | arxiv = adap-org/9401001<br />
<br />
|bibcode = 1995PhLA..203...29A | arxiv = adap-org/9401001<br />
<br />
| citeseerx = 10.1.1.456.9543<br />
<br />
| citeseerx = 10.1.1.456.9543<br />
<br />
10.1.1.456.9543<br />
<br />
| author-link = Adami, C<br />
<br />
| author-link = Adami, C<br />
<br />
| 作者链接阿达米,c<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite book<br />
<br />
<br />
<br />
| author = Bak, P.<br />
<br />
| author = Bak, P.<br />
<br />
作者 Bak,p。<br />
<br />
| year = 1996<br />
<br />
| year = 1996<br />
<br />
1996年<br />
<br />
| title = How Nature Works: The Science of Self-Organized Criticality<br />
<br />
| title = How Nature Works: The Science of Self-Organized Criticality<br />
<br />
自然如何运作: 自组织临界性的科学<br />
<br />
| publisher = Copernicus<br />
<br />
| publisher = Copernicus<br />
<br />
出版商哥白尼<br />
<br />
| location = New York<br />
<br />
| location = New York<br />
<br />
| 地点: 纽约<br />
<br />
| isbn = 978-0-387-94791-4<br />
<br />
| isbn = 978-0-387-94791-4<br />
<br />
[国际标准图书编号978-0-387-94791-4]<br />
<br />
| author-link = Per Bak<br />
<br />
| author-link = Per Bak<br />
<br />
| 作者链接 Per Bak<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = [[Per Bak|Bak, P.]] and [[Maya Paczuski|Paczuski, M.]]<br />
<br />
| author = Bak, P. and Paczuski, M.<br />
<br />
作者 Bak,p. and Paczuski,m。<br />
<br />
| year = 1995<br />
<br />
| year = 1995<br />
<br />
1995年<br />
<br />
| title = Complexity, contingency, and criticality<br />
<br />
| title = Complexity, contingency, and criticality<br />
<br />
| 标题复杂性、偶然性和临界性<br />
<br />
| journal = [[Proceedings of the National Academy of Sciences|Proceedings of the National Academy of Sciences of the USA]]<br />
<br />
| journal = Proceedings of the National Academy of Sciences of the USA<br />
<br />
美国美国国家科学院院刊杂志<br />
<br />
| volume = 92<br />
<br />
| volume = 92<br />
<br />
第92卷<br />
<br />
| pages = 6689&ndash;6696<br />
<br />
| pages = 6689&ndash;6696<br />
<br />
6689-- 6696<br />
<br />
| url = http://pnas.org/cgi/content/abstract/92/15/6689<br />
<br />
| url = http://pnas.org/cgi/content/abstract/92/15/6689<br />
<br />
Http://pnas.org/cgi/content/abstract/92/15/6689<br />
<br />
| doi = 10.1073/pnas.92.15.6689<br />
<br />
| doi = 10.1073/pnas.92.15.6689<br />
<br />
10.1073 / pnas. 92.15.6689<br />
<br />
| pmid = 11607561<br />
<br />
| pmid = 11607561<br />
<br />
11607561<br />
<br />
| issue = 15<br />
<br />
| issue = 15<br />
<br />
第15期<br />
<br />
| pmc = 41396<br />
<br />
| pmc = 41396<br />
<br />
41396<br />
<br />
|bibcode = 1995PNAS...92.6689B }}<br />
<br />
|bibcode = 1995PNAS...92.6689B }}<br />
<br />
92.6689 b }<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = [[Per Bak|Bak, P.]] and [[Kim Sneppen|Sneppen, K.]]<br />
<br />
| author = Bak, P. and Sneppen, K.<br />
<br />
作者 Bak,p. and Sneppen,k。<br />
<br />
| year = 1993<br />
<br />
| year = 1993<br />
<br />
1993年<br />
<br />
| title = Punctuated equilibrium and criticality in a simple model of evolution <br />
<br />
| title = Punctuated equilibrium and criticality in a simple model of evolution <br />
<br />
| 简单演化模型中的间断平衡和临界性<br />
<br />
| journal = [[Physical Review Letters]]<br />
<br />
| journal = Physical Review Letters<br />
<br />
物理评论快报<br />
<br />
| volume = 71<br />
<br />
| volume = 71<br />
<br />
第71卷<br />
<br />
| issue = 24<br />
<br />
| issue = 24<br />
<br />
第24期<br />
<br />
| pages = 4083&ndash;4086<br />
<br />
| pages = 4083&ndash;4086<br />
<br />
4083-- 4086<br />
<br />
| doi = 10.1103/PhysRevLett.71.4083<br />
<br />
| doi = 10.1103/PhysRevLett.71.4083<br />
<br />
10.1103 / physrvlett. 71.4083<br />
<br />
| pmid=10055149<br />
<br />
| pmid=10055149<br />
<br />
10055149<br />
<br />
| bibcode=1993PhRvL..71.4083B}}<br />
<br />
| bibcode=1993PhRvL..71.4083B}}<br />
<br />
1993 phrvl. . 71.4083 b }<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = [[Per Bak|Bak, P.]], [[Chao Tang|Tang, C.]] and [[Kurt Wiesenfeld|Wiesenfeld, K.]]<br />
<br />
| author = Bak, P., Tang, C. and Wiesenfeld, K.<br />
<br />
作者 Bak,p. ,Tang,c. and Wiesenfeld,k。<br />
<br />
| year = 1987<br />
<br />
| year = 1987<br />
<br />
1987年<br />
<br />
| title = Self-organized criticality: an explanation of <math>1/f</math> noise<br />
<br />
| title = Self-organized criticality: an explanation of <math>1/f</math> noise<br />
<br />
| 题目自组织临界性: 数学噪音的解释<br />
<br />
| journal = [[Physical Review Letters]]<br />
<br />
| journal = Physical Review Letters<br />
<br />
物理评论快报<br />
<br />
| volume = 59<br />
<br />
| volume = 59<br />
<br />
第59卷<br />
<br />
| issue = 4<br />
<br />
| issue = 4<br />
<br />
第四期<br />
<br />
| pages = 381&ndash;384<br />
<br />
| pages = 381&ndash;384<br />
<br />
381-- 384<br />
<br />
| doi = 10.1103/PhysRevLett.59.381<br />
<br />
| doi = 10.1103/PhysRevLett.59.381<br />
<br />
10.1103 / physrvlett. 59.381<br />
<br />
| pmid = 10035754<br />
<br />
| pmid = 10035754<br />
<br />
10035754<br />
<br />
| bibcode=1987PhRvL..59..381B}}<br />
<br />
| bibcode=1987PhRvL..59..381B}}<br />
<br />
1987 / phrvl. . 59. . 381 b }<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = [[Per Bak|Bak, P.]], [[Chao Tang|Tang, C.]] and [[Kurt Wiesenfeld|Wiesenfeld, K.]]<br />
<br />
| author = Bak, P., Tang, C. and Wiesenfeld, K.<br />
<br />
作者 Bak,p. ,Tang,c. and Wiesenfeld,k。<br />
<br />
| year = 1988<br />
<br />
| year = 1988<br />
<br />
1988年<br />
<br />
| title = Self-organized criticality<br />
<br />
| title = Self-organized criticality<br />
<br />
标题自组织临界性<br />
<br />
| journal = [[Physical Review A]]<br />
<br />
| journal = Physical Review A<br />
<br />
物理评论 a 期刊<br />
<br />
| volume = 38<br />
<br />
| volume = 38<br />
<br />
第38卷<br />
<br />
| issue = 1<br />
<br />
| issue = 1<br />
<br />
第一期<br />
<br />
| pages = 364&ndash;374<br />
<br />
| pages = 364&ndash;374<br />
<br />
364-- 374<br />
<br />
| doi = 10.1103/PhysRevA.38.364<br />
<br />
| doi = 10.1103/PhysRevA.38.364<br />
<br />
10.1103 / PhysRevA. 38.364<br />
<br />
| pmid = 9900174<br />
<br />
| pmid = 9900174<br />
<br />
9900174<br />
<br />
|bibcode = 1988PhRvA..38..364B }} [https://archive.is/20130415140421/http://www.papercore.org/PerBak1987 Papercore summary].<br />
<br />
|bibcode = 1988PhRvA..38..364B }} [https://archive.is/20130415140421/http://www.papercore.org/PerBak1987 Papercore summary].<br />
<br />
| bibcode 1988PhRvA. . 38. . 364 b }[ https://archive.is/20130415140421/http://www.Papercore.org/perbak1987文件核心摘要]。<br />
<br />
<br />
<br />
<br />
<br />
* {{cite book<br />
<br />
<br />
<br />
| author = Buchanan, M.<br />
<br />
| author = Buchanan, M.<br />
<br />
作者: 布坎南。<br />
<br />
| year = 2000<br />
<br />
| year = 2000<br />
<br />
2000年<br />
<br />
| title = Ubiquity<br />
<br />
| title = Ubiquity<br />
<br />
标题: Ubiquity<br />
<br />
| publisher = Weidenfeld &amp; Nicolson<br />
<br />
| publisher = Weidenfeld &amp; Nicolson<br />
<br />
| publisher = Weidenfeld &amp; Nicolson<br />
<br />
| location = London<br />
<br />
| location = London<br />
<br />
地点: 伦敦<br />
<br />
| isbn = 978-0-7538-1297-6<br />
<br />
| isbn = 978-0-7538-1297-6<br />
<br />
[国际标准图书编号978-0-7538-1297-6]<br />
<br />
| author-link = Mark Buchanan<br />
<br />
| author-link = Mark Buchanan<br />
<br />
马克 · 布坎南<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite book<br />
<br />
<br />
<br />
| author = Jensen, H. J.<br />
<br />
| author = Jensen, H. J.<br />
<br />
作者 Jensen,h. j。<br />
<br />
| year = 1998<br />
<br />
| year = 1998<br />
<br />
1998年<br />
<br />
| title = Self-Organized Criticality<br />
<br />
| title = Self-Organized Criticality<br />
<br />
标题自组织临界性<br />
<br />
| publisher = [[Cambridge University Press]]<br />
<br />
| publisher = Cambridge University Press<br />
<br />
出版商剑桥大学出版社<br />
<br />
| location = Cambridge<br />
<br />
| location = Cambridge<br />
<br />
| 地点: 剑桥<br />
<br />
| isbn = 978-0-521-48371-1<br />
<br />
| isbn = 978-0-521-48371-1<br />
<br />
[国际标准图书编号978-0-521-48371-1]<br />
<br />
| author-link = Henrik Jeldtoft Jensen<br />
<br />
| author-link = Henrik Jeldtoft Jensen<br />
<br />
作者: 亨里克 · 耶尔德托夫特 · 詹森<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = Katz, J. I.<br />
<br />
| author = Katz, J. I.<br />
<br />
作者 Katz,j. i。<br />
<br />
| year = 1986<br />
<br />
| year = 1986<br />
<br />
1986年<br />
<br />
| title = A model of propagating brittle failure in heterogeneous media<br />
<br />
| title = A model of propagating brittle failure in heterogeneous media<br />
<br />
在非均匀介质中传播脆性破坏的模型<br />
<br />
| journal = Journal of Geophysical Research<br />
<br />
| journal = Journal of Geophysical Research<br />
<br />
地球物理研究期刊<br />
<br />
| bibcode = 1986JGR....9110412K<br />
<br />
| bibcode = 1986JGR....9110412K<br />
<br />
| bibcode 1986JGR... 9110412K<br />
<br />
| doi = 10.1029/JB091iB10p10412<br />
<br />
| doi = 10.1029/JB091iB10p10412<br />
<br />
| doi 10.1029 / JB091iB10p10412<br />
<br />
| volume = 91<br />
<br />
| volume = 91<br />
<br />
第91卷<br />
<br />
| issue = B10<br />
<br />
| issue = B10<br />
<br />
第10期<br />
<br />
| pages = 10412<br />
<br />
| pages = 10412<br />
<br />
10412页<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = Kron, T./Grund, T.<br />
<br />
| author = Kron, T./Grund, T.<br />
<br />
作者: Kron t. / Grund t。<br />
<br />
| year = 2009<br />
<br />
| year = 2009<br />
<br />
2009年<br />
<br />
| title = Society as a Selforganized Critical System<br />
<br />
| title = Society as a Selforganized Critical System<br />
<br />
作为一个自组织的批判系统的社会<br />
<br />
| journal = Cybernetics and Human Knowing<br />
<br />
| journal = Cybernetics and Human Knowing<br />
<br />
控制论与人类认知<br />
<br />
| volume = 16<br />
<br />
| volume = 16<br />
<br />
第16卷<br />
<br />
| pages = 65–82<br />
<br />
| pages = 65–82<br />
<br />
第65-82页<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{Cite book<br />
<br />
<br />
<br />
| author = Paczuski, M.<br />
<br />
| author = Paczuski, M.<br />
<br />
作者: 帕祖斯基。<br />
<br />
| year = 2005<br />
<br />
| year = 2005<br />
<br />
2005年<br />
<br />
| title = Networks as renormalized models for emergent behavior in physical systems<br />
<br />
| title = Networks as renormalized models for emergent behavior in physical systems<br />
<br />
作为物理系统中突发行为的重整化模型的网络<br />
<br />
| journal = Complexity<br />
<br />
| journal = Complexity<br />
<br />
杂志复杂性<br />
<br />
| pages = 363–374<br />
<br />
| pages = 363–374<br />
<br />
第363-374页<br />
<br />
| arxiv = physics/0502028<br />
<br />
| arxiv = physics/0502028<br />
<br />
| arxiv physics / 0502028<br />
<br />
|bibcode = 2005cmn..conf..363P |doi = 10.1142/9789812701558_0042<br />
<br />
|bibcode = 2005cmn..conf..363P |doi = 10.1142/9789812701558_0042<br />
<br />
2005 / cmn. conf. 363 p | doi 10.1142 / 97898127015580042<br />
<br />
| series = The Science and Culture Series – Physics<br />
<br />
| series = The Science and Culture Series – Physics<br />
<br />
| 科学与文化系列-物理学<br />
<br />
| isbn = 978-981-256-525-9 | citeseerx = 10.1.1.261.9886<br />
<br />
| isbn = 978-981-256-525-9 | citeseerx = 10.1.1.261.9886<br />
<br />
| isbn 978-981-256-525-9 | citeserx 10.1.1.261.9886<br />
<br />
| author-link = Maya Paczuski<br />
<br />
| author-link = Maya Paczuski<br />
<br />
| 作者链接 Maya Paczuski<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite book<br />
<br />
<br />
<br />
| author = Turcotte, D. L.<br />
<br />
| author = Turcotte, D. L.<br />
<br />
作者: Turcotte,D.l。<br />
<br />
| year = 1997<br />
<br />
| year = 1997<br />
<br />
1997年<br />
<br />
| title = Fractals and Chaos in Geology and Geophysics<br />
<br />
| title = Fractals and Chaos in Geology and Geophysics<br />
<br />
地质学与地球物理学中的分形与混沌<br />
<br />
| publisher = [[Cambridge University Press]]<br />
<br />
| publisher = Cambridge University Press<br />
<br />
出版商剑桥大学出版社<br />
<br />
| location = Cambridge<br />
<br />
| location = Cambridge<br />
<br />
| 地点: 剑桥<br />
<br />
| isbn = 978-0-521-56733-6<br />
<br />
| isbn = 978-0-521-56733-6<br />
<br />
[国际标准图书馆编号978-0-521-56733-6]<br />
<br />
| author-link = Donald L. Turcotte<br />
<br />
| author-link = Donald L. Turcotte<br />
<br />
作者: Donald l. Turcotte<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = Turcotte, D. L.<br />
<br />
| author = Turcotte, D. L.<br />
<br />
作者: Turcotte,D.l。<br />
<br />
| year = 1999<br />
<br />
| year = 1999<br />
<br />
1999年<br />
<br />
| title = Self-organized criticality<br />
<br />
| title = Self-organized criticality<br />
<br />
标题自组织临界性<br />
<br />
| journal = [[Reports on Progress in Physics]]<br />
<br />
| journal = Reports on Progress in Physics<br />
<br />
物理学进展报告<br />
<br />
| volume = 62<br />
<br />
| volume = 62<br />
<br />
第62卷<br />
<br />
| issue = 10<br />
<br />
| issue = 10<br />
<br />
第10期<br />
<br />
| pages = 1377&ndash;1429<br />
<br />
| pages = 1377&ndash;1429<br />
<br />
13771429页<br />
<br />
| doi = 10.1088/0034-4885/62/10/201<br />
<br />
| doi = 10.1088/0034-4885/62/10/201<br />
<br />
10.1088 / 0034-4885 / 62 / 10 / 201<br />
<br />
|bibcode = 1999RPPh...62.1377T | author-link = Donald L. Turcotte<br />
<br />
|bibcode = 1999RPPh...62.1377T | author-link = Donald L. Turcotte<br />
<br />
| bibcode 1999RPPh... 62.1377 t | 作者链接 Donald l. Turcotte<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
* {{cite journal<br />
<br />
<br />
<br />
| author = Md. Nurujjaman/A. N. Sekar Iyengar<br />
<br />
| author = Md. Nurujjaman/A. N. Sekar Iyengar<br />
<br />
作者马里兰大学。Nurujjaman / a.N. Sekar Iyengar<br />
<br />
| year = 2007<br />
<br />
| year = 2007<br />
<br />
2007年<br />
<br />
| title = Realization of {SOC} behavior in a dc glow discharge plasma<br />
<br />
| title = Realization of {SOC} behavior in a dc glow discharge plasma<br />
<br />
直流辉光放电等离子体{ SOC }行为的实现<br />
<br />
| journal = [[Physics Letters A]]<br />
<br />
| journal = Physics Letters A<br />
<br />
物理学快报<br />
<br />
| volume = 360<br />
<br />
| volume = 360<br />
<br />
第360卷<br />
<br />
| issue = 6<br />
<br />
| issue = 6<br />
<br />
第六期<br />
<br />
| pages = 717&ndash;721<br />
<br />
| pages = 717&ndash;721<br />
<br />
717-- 721页<br />
<br />
|arxiv = physics/0611069 |bibcode = 2007PhLA..360..717N |doi = 10.1016/j.physleta.2006.09.005 | author-link = Md. Nurujjaman/A. N. Sekar Iyengar<br />
<br />
|arxiv = physics/0611069 |bibcode = 2007PhLA..360..717N |doi = 10.1016/j.physleta.2006.09.005 | author-link = Md. Nurujjaman/A. N. Sekar Iyengar<br />
<br />
| arxiv physics / 0611069 | bibcode 2007 phla. . 360. . 717 n | doi 10.1016 / j.physleta. 2006.09.005 | author-link md.Nurujjaman / a.N. Sekar Iyengar<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
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*[http://xstructure.inr.ac.ru/x-bin/theme2.py?arxiv=cond-mat&level=1&index1=20771 Self-organized criticality on arxiv.org]<br />
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[[Category:Critical phenomena]]<br />
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Category:Critical phenomena<br />
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范畴: 关键现象<br />
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[[Category:Applied and interdisciplinary physics]]<br />
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Category:Applied and interdisciplinary physics<br />
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类别: 应用和跨学科物理学<br />
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[[Category:Chaos theory]]<br />
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Category:Chaos theory<br />
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范畴: 混沌理论<br />
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[[Category:Self-organization]]<br />
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Category:Self-organization<br />
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类别: 自我组织<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Self-organized criticality]]. Its edit history can be viewed at [[自组织临界性/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E7%83%AD%E5%8A%9B%E5%AD%A6&diff=21884热力学2021-02-19T13:35:00Z<p>Jxzhou:</p>
<hr />
<div>此词条暂由jxzhou翻译,未经人工整理和审校,带来阅读不便,请见谅。<br />
<br />
{{short description|Physics of heat, work, and temperature}}<br />
{{Use dmy dates|date=February 2016}}<br />
[[File:Carnot engine (hot body - working body - cold body).jpg|thumb|300px|right|Annotated color version of the original 1824 [[Carnot heat engine]] showing the hot body (boiler), working body (system, steam), and cold body (water), the letters labeled according to the stopping points in [[Carnot cycle]].]]<br />
{{Thermodynamics}}<br />
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'''Thermodynamics''' is a branch of [[physics]] that deals with [[heat]], [[Work (thermodynamics)|work]], and [[temperature]], and their relation to [[energy]], [[radiation]], and physical properties of [[matter]]. The behavior of these quantities is governed by the four [[laws of thermodynamics]] which convey a quantitative description using measurable macroscopic [[physical quantity|physical quantities]], but may be explained in terms of [[microscopic]] constituents by [[statistical mechanics]]. Thermodynamics applies to a wide variety of topics in [[science]] and [[engineering]], especially [[physical chemistry]], [[chemical engineering]] and [[mechanical engineering]], but also in other complex fields such as [[meteorology]].<br />
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热力学是物理学的一个分支,研究热和温度,以及它们与能量、功、辐射和物质性质的关系。这些量的行为是由4个热力学定律控制的,它们用可测量的宏观物理量传递了一个定量描述,但是可以用微观成分来解释统计力学。热力学适用于科学和工程中的各种各样的课题,尤其是物理化学、化学工程和机械工程,但也适用于气象学这样复杂的领域。<br />
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Historically, thermodynamics developed out of a desire to increase the [[thermodynamic efficiency|efficiency]] of early [[steam engine]]s, particularly through the work of French physicist [[Nicolas Léonard Sadi Carnot]] (1824) who believed that engine efficiency was the key that could help France win the [[Napoleonic Wars]].<ref>{{cite book | last = Clausius | first = Rudolf | title = On the Motive Power of Heat, and on the Laws which can be deduced from it for the Theory of Heat | publisher = Poggendorff's Annalen der Physik, LXXIX (Dover Reprint) | year = 1850 | isbn = 978-0-486-59065-3}}</ref> Scots-Irish physicist [[William Thomson, 1st Baron Kelvin|Lord Kelvin]] was the first to formulate a concise definition of thermodynamics in 1854<ref name=kelvin1854>{{cite book<br />
|title=Mathematical and Physical Papers<br />
|author= William Thomson, LL.D. D.C.L., F.R.S.<br />
|location=London, Cambridge<br />
|year=1882<br />
|volume=1<br />
|page=232<br />
|publisher=C.J. Clay, M.A. & Son, Cambridge University Press<br />
|url=https://books.google.com/books?id=nWMSAAAAIAAJ&q=On+an+Absolute+Thermometric+Scale+Founded+on+Carnot%E2%80%99s+Theory&pg=PA100<br />
}}</ref> which stated, "Thermo-dynamics is the subject of the relation of heat to forces acting between contiguous parts of bodies, and the relation of heat to electrical agency."<br />
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“热力学的主题是热量与物体相邻部分之间作用力的关系,以及热量与电能的关系。”<br />
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The initial application of thermodynamics to [[mechanical heat engine]]s was quickly extended to the study of chemical compounds and chemical reactions. [[Chemical thermodynamics]] studies the nature of the role of [[entropy]] in the process of [[chemical reaction]]s and has provided the bulk of expansion and knowledge of the field.<ref name="Gibbs 1876">{{cite book|author=Gibbs, Willard, J.|title=Transactions of the Connecticut Academy of Arts and Sciences|volume=III|pages=[https://archive.org/details/transactions03conn/page/108 108]–248, 343–524|year=1874–1878|url=https://archive.org/details/transactions03conn|publisher=New Haven}}</ref><ref name="Duhem 1886">Duhem, P.M.M. (1886). ''Le Potential Thermodynamique et ses Applications'', Hermann, Paris.</ref><ref name="Lewis Randall 1923">{{cite book | last1=Lewis | first1=Gilbert N. | last2=Randall | first2=Merle | title=Thermodynamics and the Free Energy of Chemical Substances | url=https://archive.org/details/thermodynamicsfr00gnle | publisher=McGraw-Hill Book Co. Inc. | year=1923}}</ref><ref name="Guggenheim 1933">Guggenheim, E.A. (1933). ''Modern Thermodynamics by the Methods of J.W. Gibbs'', Methuen, London.</ref><ref name="Guggenheim 1949/1967">Guggenheim, E.A. (1949/1967). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', 1st edition 1949, 5th edition 1967, North-Holland, Amsterdam.</ref><ref>{{cite book | author=Ilya Prigogine, I. & Defay, R., translated by D.H. Everett| title=Chemical Thermodynamics | year=1954 | publisher=Longmans, Green & Co., London. Includes classical non-equilibrium thermodynamics.}}<br />
</ref><ref name=Fermi>{{cite book<br />
|title=Thermodynamics<br />
|author=Enrico Fermi<br />
|url=https://books.google.com/books?id=VEZ1ljsT3IwC&q=thermodynamics<br />
|isbn=978-0486603612<br />
|publisher=Courier Dover Publications<br />
|year=1956<br />
|page=ix<br />
|oclc=230763036}}</ref><ref name="Perrot" >{{cite book | author=Perrot, Pierre | title=A to Z of Thermodynamics | publisher=Oxford University Press | year=1998 | isbn=978-0-19-856552-9 | oclc=123283342}}</ref><ref>{{cite book | author=Clark, John, O.E.| title=The Essential Dictionary of Science | publisher=Barnes & Noble Books | year=2004 | isbn=978-0-7607-4616-5 | oclc=58732844}}</ref> Other formulations of thermodynamics emerged. [[Statistical thermodynamics]], or statistical mechanics, concerns itself with [[statistics|statistical]] predictions of the collective motion of particles from their microscopic behavior. In 1909, [[Constantin Carathéodory]] presented a purely mathematical approach in an [[axiomatic]] formulation, a description often referred to as ''geometrical thermodynamics''.<br />
<br />
热力学的其他公式出现了。统计热力学,或称统计力学热力学,从微观角度对粒子的集体运动进行统计预测。在1909年,康斯坦丁·卡拉西奥多里提出了一个纯粹的数学方法在一个公理化的公式,一个描述通常被称为几何热力学。<br />
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==Introduction==<br />
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引言<br />
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A description of any thermodynamic system employs the four [[laws of thermodynamics]] that form an axiomatic basis. The first law specifies that energy can be exchanged between physical systems as [[heat]] and [[Mechanical work|work]].<ref>{{cite book | author=Van Ness, H.C. | title=Understanding Thermodynamics | publisher=Dover Publications, Inc. | year=1983 | origyear=1969 | isbn=9780486632773 | oclc=8846081 | url-access=registration | url=https://archive.org/details/understandingthe00vann }}</ref> The second law defines the existence of a quantity called [[entropy]], that describes the direction, thermodynamically, that a system can evolve and quantifies the state of order of a system and that can be used to quantify the useful work that can be extracted from the system.<ref>{{cite book | author=Dugdale, J.S. | title=Entropy and its Physical Meaning | publisher=Taylor and Francis | year=1998 | isbn=978-0-7484-0569-5 | oclc=36457809}}</ref><br />
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A description of any thermodynamic system employs the four laws of thermodynamics that form an axiomatic basis. The first law specifies that energy can be exchanged between physical systems as heat and work. The second law defines the existence of a quantity called entropy, that describes the direction, thermodynamically, that a system can evolve and quantifies the state of order of a system and that can be used to quantify the useful work that can be extracted from the system.<br />
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任何热力学系统的描述都采用了构成公理基础的4个热力学定律。第一定律规定能量可以在物理系统之间以热和功的形式进行交换。第二定律定义了一个叫做熵的量的存在,这个量描述了一个系统可以进化和量化一个系统的有序状态的方向,可以用来量化可以从系统中提取的有用功。<br />
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In thermodynamics, interactions between large ensembles of objects are studied and categorized. Central to this are the concepts of the thermodynamic ''[[System (thermodynamics)|system]]'' and its ''[[Surroundings (thermodynamics)|surroundings]]''. A system is composed of particles, whose average motions define its properties, and those properties are in turn related to one another through [[Equation of state|equations of state]]. Properties can be combined to express [[internal energy]] and [[thermodynamic potential]]s, which are useful for determining conditions for [[Dynamic equilibrium|equilibrium]] and [[spontaneous process]]es.<br />
<br />
In thermodynamics, interactions between large ensembles of objects are studied and categorized. Central to this are the concepts of the thermodynamic system and its surroundings. A system is composed of particles, whose average motions define its properties, and those properties are in turn related to one another through equations of state. Properties can be combined to express internal energy and thermodynamic potentials, which are useful for determining conditions for equilibrium and spontaneous processes.<br />
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在热力学中,研究和分类了物体大系综之间的相互作用。其核心是热力学系统及其周围环境的概念。一个系统是由粒子组成的,粒子的平均运动决定了它的性质,而这些性质又通过状态方程彼此相关。性质可以结合起来表示内能和热力学势,这对于确定平衡和自发过程的条件是有用的。<br />
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With these tools, thermodynamics can be used to describe how systems respond to changes in their environment. This can be applied to a wide variety of topics in [[science]] and [[engineering]], such as [[engine]]s, [[phase transition]]s, [[chemical reaction]]s, [[transport phenomena]], and even [[black hole]]s. The results of thermodynamics are essential for other fields of [[physics]] and for [[chemistry]], [[chemical engineering]], [[corrosion engineering]], [[aerospace engineering]], [[mechanical engineering]], [[cell biology]], [[biomedical engineering]], [[materials science]], and [[economics]], to name a few.<ref>{{Cite book | last1=Smith | first1=J.M. | last2=Van Ness | first2=H.C. | last3=Abbott | first3=M.M. | title=Introduction to Chemical Engineering Thermodynamics | journal=Journal of Chemical Education | volume=27 | issue=10 | page=584 | year=2005 | isbn=978-0-07-310445-4 | oclc=56491111| bibcode=1950JChEd..27..584S | doi=10.1021/ed027p584.3 }}</ref><ref>{{cite book | author=Haynie, Donald, T. | title=Biological Thermodynamics | publisher=Cambridge University Press | year=2001 | isbn=978-0-521-79549-4 | oclc=43993556}}</ref><br />
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With these tools, thermodynamics can be used to describe how systems respond to changes in their environment. This can be applied to a wide variety of topics in science and engineering, such as engines, phase transitions, chemical reactions, transport phenomena, and even black holes. The results of thermodynamics are essential for other fields of physics and for chemistry, chemical engineering, corrosion engineering, aerospace engineering, mechanical engineering, cell biology, biomedical engineering, materials science, and economics, to name a few.<br />
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有了这些工具,热力学可以用来描述系统如何响应环境中的变化。这可以应用于科学和工程的各种主题,如引擎,相变,化学反应,传输现象,甚至黑洞。热力学的结果对于物理学、化学、化学工程、腐蚀工程、航空航天工业奖、机械工程、细胞生物学、生物医学工程、材料科学和经济学等其他领域都是必不可少的。<br />
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This article is focused mainly on classical thermodynamics which primarily studies systems in [[thermodynamic equilibrium]]. [[Non-equilibrium thermodynamics]] is often treated as an extension of the classical treatment, but statistical mechanics has brought many advances to that field.<br />
<br />
This article is focused mainly on classical thermodynamics which primarily studies systems in thermodynamic equilibrium. Non-equilibrium thermodynamics is often treated as an extension of the classical treatment, but statistical mechanics has brought many advances to that field.<br />
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这篇文章主要关注经典热力学,它主要研究热力学平衡中的系统。非平衡态热力学通常被视为古典治疗的延伸,但是统计力学已经在这个领域带来了许多进步。<br />
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[[File:Eight founding schools.png|400px|thumb|The [[thermodynamicist]]s representative of the original eight founding schools of thermodynamics. The schools with the most-lasting effect in founding the modern versions of thermodynamics are the Berlin school, particularly as established in [[Rudolf Clausius]]’s 1865 textbook ''The Mechanical Theory of Heat'', the Vienna school, with the [[statistical mechanics]] of [[Ludwig Boltzmann]], and the Gibbsian school at Yale University, American engineer [[Willard Gibbs]]' 1876 ''[[On the Equilibrium of Heterogeneous Substances]]'' launching [[chemical thermodynamics]].<ref name="autogenerated1">[http://www.eoht.info/page/Schools+of+thermodynamics Schools of thermodynamics] – EoHT.info.</ref>]]<br />
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The [[thermodynamicists representative of the original eight founding schools of thermodynamics. The schools with the most-lasting effect in founding the modern versions of thermodynamics are the Berlin school, particularly as established in Rudolf Clausius’s 1865 textbook The Mechanical Theory of Heat, the Vienna school, with the statistical mechanics of Ludwig Boltzmann, and the Gibbsian school at Yale University, American engineer Willard Gibbs' 1876 On the Equilibrium of Heterogeneous Substances launching chemical thermodynamics.]]<br />
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代表热力学最初八个学派的热力学学者。在建立现代版本的热力学方面影响最深远的学校是柏林学派,特别是由 Rudolf Clausius 在1865年的教科书《热力学的机械理论》中建立的维也纳学派,与统计力学路德维希·玻尔兹曼合作的维也纳学派,以及耶鲁大学的 Gibbsian 学派,美国工程师 Willard Gibbs 在1876年建立的关于多相物质平衡化学热力学<br />
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==History==<br />
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==History==<br />
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历史<br />
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The [[history of thermodynamics]] as a scientific discipline generally begins with [[Otto von Guericke]] who, in 1650, built and designed the world's first [[vacuum pump]] and demonstrated a [[vacuum]] using his [[Magdeburg hemispheres]]. Guericke was driven to make a vacuum in order to disprove [[Aristotle]]'s long-held supposition that 'nature abhors a vacuum'. Shortly after Guericke, the English physicist and chemist [[Robert Boyle]] had learned of Guericke's designs and, in 1656, in coordination with English scientist [[Robert Hooke]], built an air pump.<ref>{{cite book | author=Partington, J.R. | title=A Short History of Chemistry | url=https://archive.org/details/shorthistoryofch0000part_q6h4 | url-access=registration | publisher=Dover | year=1989 | isbn= | oclc=19353301| author-link=J. R. Partington }}</ref> Using this pump, Boyle and Hooke noticed a correlation between [[pressure]], [[temperature]], and [[Volume (thermodynamics)|volume]]. In time, [[Boyle's Law]] was formulated, which states that pressure and volume are [[inverse proportion|inversely proportional]]. Then, in 1679, based on these concepts, an associate of Boyle's named [[Denis Papin]] built a [[steam digester]], which was a closed vessel with a tightly fitting lid that confined steam until a high pressure was generated.<br />
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The history of thermodynamics as a scientific discipline generally begins with Otto von Guericke who, in 1650, built and designed the world's first vacuum pump and demonstrated a vacuum using his Magdeburg hemispheres. Guericke was driven to make a vacuum in order to disprove Aristotle's long-held supposition that 'nature abhors a vacuum'. Shortly after Guericke, the English physicist and chemist Robert Boyle had learned of Guericke's designs and, in 1656, in coordination with English scientist Robert Hooke, built an air pump. Using this pump, Boyle and Hooke noticed a correlation between pressure, temperature, and volume. In time, Boyle's Law was formulated, which states that pressure and volume are inversely proportional. Then, in 1679, based on these concepts, an associate of Boyle's named Denis Papin built a steam digester, which was a closed vessel with a tightly fitting lid that confined steam until a high pressure was generated.<br />
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热力学史作为一门科学学科通常始于1650年的奥托·冯·格里克,他建造并设计了世界上第一台真空泵,并用他的马德堡半球展示了真空。格里克被迫制造一个真空,以反驳亚里士多德长期以来的假设,即“自然憎恶真空”。在格里克之后不久,英国物理学家和化学家罗伯特 · 波义耳听说了格里克的设计,并在1656年与英国科学家罗伯特 · 胡克合作制造了一个空气泵。波义耳和胡克利用这台泵,注意到了压力、温度和体积之间的关系。随着时间的推移,波义耳定律被公式化了,它指出压强和体积成反比。然后,在1679年,基于这些概念,波义耳的一位名叫丹尼斯 · 帕平的合伙人建造了一个蒸汽消化器,这是一个封闭的容器,有一个紧密的盖子,将蒸汽封闭起来,直到产生高压。<br />
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Later designs implemented a steam release valve that kept the machine from exploding. By watching the valve rhythmically move up and down, Papin conceived of the idea of a [[piston]] and a cylinder engine. He did not, however, follow through with his design. Nevertheless, in 1697, based on Papin's designs, engineer [[Thomas Savery]] built the first engine, followed by [[Thomas Newcomen]] in 1712. Although these early engines were crude and inefficient, they attracted the attention of the leading scientists of the time.<br />
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Later designs implemented a steam release valve that kept the machine from exploding. By watching the valve rhythmically move up and down, Papin conceived of the idea of a piston and a cylinder engine. He did not, however, follow through with his design. Nevertheless, in 1697, based on Papin's designs, engineer Thomas Savery built the first engine, followed by Thomas Newcomen in 1712. Although these early engines were crude and inefficient, they attracted the attention of the leading scientists of the time.<br />
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后来的设计实现了一个蒸汽释放阀,以防止机器爆炸。通过观察阀门有节奏地上下运动,帕平构思了活塞和汽缸发动机的概念。然而,他并没有坚持他的设计。然而,在1697年,根据帕平的设计,工程师托马斯 · 萨维里制造了第一台发动机,随后在1712年托马斯 · 纽科门制造了第一台发动机。虽然这些早期的发动机粗糙和低效,他们吸引了当时的主要科学家的注意。<br />
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The fundamental concepts of [[heat capacity]] and [[latent heat]], which were necessary for the development of thermodynamics, were developed by Professor [[Joseph Black]] at the University of Glasgow, where [[James Watt]] was employed as an instrument maker. Black and Watt performed experiments together, but it was Watt who conceived the idea of the [[Watt steam engine#Separate condenser|external condenser]] which resulted in a large increase in [[steam engine]] efficiency.<ref>The Newcomen engine was improved from 1711 until Watt's work, making the efficiency comparison subject to qualification, but the increase from the 1865 version was on the order of 100%.</ref> Drawing on all the previous work led [[Nicolas Léonard Sadi Carnot|Sadi Carnot]], the "father of thermodynamics", to publish ''[[Reflections on the Motive Power of Fire]]'' (1824), a discourse on heat, power, energy and engine efficiency. The book outlined the basic energetic relations between the [[Carnot engine]], the [[Carnot cycle]], and '''motive power'''. It marked the start of thermodynamics as a modern science.<ref name="Perrot" /><br />
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The fundamental concepts of heat capacity and latent heat, which were necessary for the development of thermodynamics, were developed by Professor Joseph Black at the University of Glasgow, where James Watt was employed as an instrument maker. Black and Watt performed experiments together, but it was Watt who conceived the idea of the external condenser which resulted in a large increase in steam engine efficiency. Drawing on all the previous work led Sadi Carnot, the "father of thermodynamics", to publish Reflections on the Motive Power of Fire (1824), a discourse on heat, power, energy and engine efficiency. The book outlined the basic energetic relations between the Carnot engine, the Carnot cycle, and motive power. It marked the start of thermodynamics as a modern science.<br />
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热容量和潜热的基本概念是热力学发展所必需的,是由格拉斯哥大学的 Joseph Black 教授提出来的,James Watt 是那里的一个仪器制造商。布莱克和瓦特一起进行实验,但是瓦特提出了外部冷凝器的概念,从而大大提高了蒸汽机的效率。根据以前所有的工作,“热力学之父”萨迪 · 卡诺发表了《论火的动力(1824年) ,一篇关于热、动力、能源和发动机效率的论文。这本书概述了卡诺发动机、卡诺循环和动力之间的基本能量关系。它标志着热力学作为一门现代科学的开始。<br />
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The first thermodynamic textbook was written in 1859 by [[William John Macquorn Rankine|William Rankine]], originally trained as a physicist and a civil and mechanical engineering professor at the [[University of Glasgow]].<ref>{{cite book |author1=Cengel, Yunus A. |author2=Boles, Michael A. | title=Thermodynamics – an Engineering Approach | publisher=McGraw-Hill | year=2005 | isbn=978-0-07-310768-4}}</ref> The first and second laws of thermodynamics emerged simultaneously in the 1850s, primarily out of the works of [[William John Macquorn Rankine|William Rankine]], [[Rudolf Clausius]], and [[William Thomson, 1st Baron Kelvin|William Thomson]] (Lord Kelvin).<ref name = "NKS note b">''[[A New Kind of Science]]'' [https://www.wolframscience.com/nks/notes-9-3--history-of-thermodynamics/ Note (b) for Irreversibility and the Second Law of Thermodynamics]</ref><br />
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The first thermodynamic textbook was written in 1859 by William Rankine, originally trained as a physicist and a civil and mechanical engineering professor at the University of Glasgow. The first and second laws of thermodynamics emerged simultaneously in the 1850s, primarily out of the works of William Rankine, Rudolf Clausius, and William Thomson (Lord Kelvin).<br />
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第一本热力学教科书是 William Rankine 在1859年写的,他最初是格拉斯哥大学的物理学家和土木机械工程教授。第一个和第二个热力学定律同时出现在19世纪50年代,主要出自 William Rankine,Rudolf Clausius 和 William Thomson (Lord Kelvin)的作品。<br />
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The foundations of statistical thermodynamics were set out by physicists such as [[James Clerk Maxwell]], [[Ludwig Boltzmann]], [[Max Planck]], [[Rudolf Clausius]] and [[Josiah Willard Gibbs|J. Willard Gibbs]].<br />
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The foundations of statistical thermodynamics were set out by physicists such as James Clerk Maxwell, Ludwig Boltzmann, Max Planck, Rudolf Clausius and J. Willard Gibbs.<br />
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统计热力学的基础是由物理学家建立的,如詹姆斯·克拉克·麦克斯韦,路德维希·玻尔兹曼,马克斯 · 普朗克,Rudolf Clausius 和 j. Willard Gibbs。<br />
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During the years 1873–76 the American mathematical physicist [[Josiah Willard Gibbs]] published a series of three papers, the most famous being ''[[On the Equilibrium of Heterogeneous Substances]]'',<ref name="Gibbs 1876"/> in which he showed how [[thermodynamic processes]], including [[chemical reaction]]s, could be graphically analyzed, by studying the [[energy]], [[entropy]], [[Volume (thermodynamics)|volume]], [[temperature]] and [[pressure]] of the [[thermodynamic system]] in such a manner, one can determine if a process would occur spontaneously.<ref>{{cite book | author=Gibbs, Willard | title=The Scientific Papers of J. Willard Gibbs, Volume One: Thermodynamics | publisher=Ox Bow Press | year=1993 | isbn=978-0-918024-77-0 | oclc=27974820}}</ref> Also [[Pierre Duhem]] in the 19th century wrote about chemical thermodynamics.<ref name="Duhem 1886"/> During the early 20th century, chemists such as [[Gilbert N. Lewis]], [[Merle Randall]],<ref name="Lewis Randall 1923"/> and [[E. A. Guggenheim]]<ref name="Guggenheim 1933"/><ref name="Guggenheim 1949/1967"/> applied the mathematical methods of Gibbs to the analysis of chemical processes.<br />
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During the years 1873–76 the American mathematical physicist Josiah Willard Gibbs published a series of three papers, the most famous being On the Equilibrium of Heterogeneous Substances, Also Pierre Duhem in the 19th century wrote about chemical thermodynamics. During the early 20th century, chemists such as Gilbert N. Lewis, Merle Randall, and E. A. Guggenheim applied the mathematical methods of Gibbs to the analysis of chemical processes.<br />
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在1873年至1876年间,美国数学物理学家约西亚·威拉德·吉布斯发表了一系列的3篇论文,其中最著名的是关于多相物质平衡,也是 Pierre Duhem 在19世纪写的关于化学热力学的论文。在20世纪早期,化学家如吉尔伯特·牛顿·路易斯,Merle Randall 和 e. a. Guggenheim 将吉布斯的数学方法应用于化学过程的分析。<br />
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==Etymology==<br />
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==Etymology==<br />
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词源学<br />
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这个术语的历史是丰富的,需要更多的补充<br />
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The etymology of ''thermodynamics'' has an intricate history.<ref name=eoht>{{cite web<br />
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The etymology of thermodynamics has an intricate history.<ref name=eoht>{{cite web<br />
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热力学的词源有一个错综复杂的历史<br />
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|url=http://www.eoht.info/page/Thermo-dynamics<br />
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|title=Thermodynamics (etymology)<br />
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| 题目: 热力学(词源)<br />
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}}</ref> It was first spelled in a hyphenated form as an adjective (''thermo-dynamic'') and from 1854 to 1868 as the noun ''thermo-dynamics'' to represent the science of generalized heat engines.<ref name=eoht/><br />
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}}</ref> It was first spelled in a hyphenated form as an adjective (thermo-dynamic) and from 1854 to 1868 as the noun thermo-dynamics to represent the science of generalized heat engines.<br />
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它最初以连字符的形式作为形容词(热力学)拼写,从1854年到1868年作为名词热力学来代表广义热发动机的科学。<br />
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American [[Biophysics|biophysicist]] Donald Haynie claims that ''thermodynamics'' was coined in 1840 from the [[Greek language|Greek]] root [[wikt:θέρμη|θέρμη]] ''therme,'' meaning “heat”, and [[wikt:δύναμις|δύναμις]] ''dynamis,'' meaning “power”.<ref>{{cite book<br />
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American biophysicist Donald Haynie claims that thermodynamics was coined in 1840 from the Greek root θέρμη therme, meaning “heat”, and δύναμις dynamis, meaning “power”.<ref>{{cite book<br />
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美国生物物理学家唐纳德 · 海尼声称,热力学是在1840年从希腊词根 therme (意思是“热”)和 dynamis (意思是“力”)创造出来的。 文档{ cite book<br />
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生物热力学<br />
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剑桥大学出版社<br />
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Pierre Perrot claims that the term ''thermodynamics'' was coined by [[James Joule]] in 1858 to designate the science of relations between heat and power,<ref name="Perrot" /> however, Joule never used that term, but used instead the term ''perfect thermo-dynamic engine'' in reference to Thomson's 1849<ref name=kelvin1849/> phraseology.<ref name=eoht/><br />
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Pierre Perrot claims that the term thermodynamics was coined by James Joule in 1858 to designate the science of relations between heat and power, however, Joule never used that term, but used instead the term perfect thermo-dynamic engine in reference to Thomson's 1849 phraseology.<br />
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皮埃尔 · 佩罗声称,热力学这个术语是由詹姆斯 · 朱尔在1858年创造的,用来指代热量和能量之间关系的科学。然而,朱尔从来没有使用过这个术语,而是在汤姆森1849年的措辞中使用了完美热力学引擎这个术语。<br />
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By 1858, ''thermo-dynamics'', as a functional term, was used in [[William Thomson, 1st Baron Kelvin|William Thomson]]'s paper "An Account of Carnot's Theory of the Motive Power of Heat."<ref name=kelvin1849>Kelvin, William T. (1849) "An Account of Carnot's Theory of the Motive Power of Heat – with Numerical Results Deduced from Regnault's Experiments on Steam." ''Transactions of the Edinburg Royal Society, XVI. January 2.''[http://visualiseur.bnf.fr/Visualiseur?Destination=Gallica&O=NUMM-95118 Scanned Copy]</ref><br />
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By 1858, thermo-dynamics, as a functional term, was used in William Thomson's paper "An Account of Carnot's Theory of the Motive Power of Heat."<br />
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到1858年,热力学作为一个函数术语,被用于威廉 · 汤姆森的论文“卡诺的热动力理论的帐户。”<br />
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==Branches of thermodynamics==<br />
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==Branches of thermodynamics==<br />
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The study of thermodynamical systems has developed into several related branches, each using a different fundamental model as a theoretical or experimental basis, or applying the principles to varying types of systems.<br />
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The study of thermodynamical systems has developed into several related branches, each using a different fundamental model as a theoretical or experimental basis, or applying the principles to varying types of systems.<br />
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热力学系统的研究已经发展成为几个相关的分支,每个分支都使用不同的基本模型作为理论或实验基础,或者将这些原理应用于不同类型的系统。<br />
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===Classical thermodynamics===<br />
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===Classical thermodynamics===<br />
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经典热力学<br />
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Classical thermodynamics is the description of the states of thermodynamic systems at near-equilibrium, that uses macroscopic, measurable properties. It is used to model exchanges of energy, work and heat based on the [[laws of thermodynamics]]. The qualifier ''classical'' reflects the fact that it represents the first level of understanding of the subject as it developed in the 19th century and describes the changes of a system in terms of macroscopic empirical (large scale, and measurable) parameters. A microscopic interpretation of these concepts was later provided by the development of ''statistical mechanics''.<br />
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Classical thermodynamics is the description of the states of thermodynamic systems at near-equilibrium, that uses macroscopic, measurable properties. It is used to model exchanges of energy, work and heat based on the laws of thermodynamics. The qualifier classical reflects the fact that it represents the first level of understanding of the subject as it developed in the 19th century and describes the changes of a system in terms of macroscopic empirical (large scale, and measurable) parameters. A microscopic interpretation of these concepts was later provided by the development of statistical mechanics.<br />
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经典热力学是对近平衡态热力学系统状态的描述,它使用宏观的、可测量的性质。它被用来模拟能量、功和热量的交换,基于热力学定律。经典限定词反映了这样一个事实,即它代表了人们对这个学科在19世纪发展过程中的第一层次的理解,并且描述了一个系统在宏观经验(大尺度和可测量的)参数方面的变化。这些概念的微观解释后来由统计力学的发展提供。<br />
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===Statistical mechanics===<br />
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===Statistical mechanics===<br />
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[[Statistical mechanics]], also called statistical thermodynamics, emerged with the development of atomic and molecular theories in the late 19th century and early 20th century, and supplemented classical thermodynamics with an interpretation of the microscopic interactions between individual particles or quantum-mechanical states. This field relates the microscopic properties of individual atoms and molecules to the macroscopic, bulk properties of materials that can be observed on the human scale, thereby explaining classical thermodynamics as a natural result of statistics, classical mechanics, and [[Quantum mechanics|quantum theory]] at the microscopic level.<ref name= "NKS note b" /><br />
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Statistical mechanics, also called statistical thermodynamics, emerged with the development of atomic and molecular theories in the late 19th century and early 20th century, and supplemented classical thermodynamics with an interpretation of the microscopic interactions between individual particles or quantum-mechanical states. This field relates the microscopic properties of individual atoms and molecules to the macroscopic, bulk properties of materials that can be observed on the human scale, thereby explaining classical thermodynamics as a natural result of statistics, classical mechanics, and quantum theory at the microscopic level.<br />
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统计力学,又称统计热力学,在19世纪末20世纪初随着原子和分子理论的发展而出现,对单个粒子或量子力学状态之间的微观相互作用的解释补充了经典热力学。这个领域将单个原子和分子的微观属性与可以在人类尺度上观察到的物质的宏观体积属性联系起来,从而在微观层次上解释了经典热力学作为统计学、经典力学、量子理论的自然结果。<br />
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===Chemical thermodynamics===<br />
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[[Chemical thermodynamics]] is the study of the interrelation of [[energy]] with [[chemical reactions]] or with a physical change of [[thermodynamic state|state]] within the confines of the [[laws of thermodynamics]].<br />
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Chemical thermodynamics is the study of the interrelation of energy with chemical reactions or with a physical change of state within the confines of the laws of thermodynamics.<br />
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化学热力学是研究能量与化学反应或热力学定律范围内状态的物理变化之间的相互关系。<br />
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===Equilibrium thermodynamics===<br />
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===Equilibrium thermodynamics===<br />
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平衡热力学<br />
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[[Equilibrium thermodynamics]] is the study of transfers of matter and energy in systems or bodies that, by agencies in their surroundings, can be driven from one state of thermodynamic equilibrium to another. The term 'thermodynamic equilibrium' indicates a state of balance, in which all macroscopic flows are zero; in the case of the simplest systems or bodies, their intensive properties are homogeneous, and their pressures are perpendicular to their boundaries. In an equilibrium state there are no unbalanced potentials, or driving forces, between macroscopically distinct parts of the system. A central aim in equilibrium thermodynamics is: given a system in a well-defined initial equilibrium state, and given its surroundings, and given its constitutive walls, to calculate what will be the final equilibrium state of the system after a specified thermodynamic operation has changed its walls or surroundings.<br />
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Equilibrium thermodynamics is the study of transfers of matter and energy in systems or bodies that, by agencies in their surroundings, can be driven from one state of thermodynamic equilibrium to another. The term 'thermodynamic equilibrium' indicates a state of balance, in which all macroscopic flows are zero; in the case of the simplest systems or bodies, their intensive properties are homogeneous, and their pressures are perpendicular to their boundaries. In an equilibrium state there are no unbalanced potentials, or driving forces, between macroscopically distinct parts of the system. A central aim in equilibrium thermodynamics is: given a system in a well-defined initial equilibrium state, and given its surroundings, and given its constitutive walls, to calculate what will be the final equilibrium state of the system after a specified thermodynamic operation has changed its walls or surroundings.<br />
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平衡态热力学研究的是物质和能量在系统或物体中的转移,这些系统或物体在其周围的环境中,可以从一种热力学平衡状态转移到另一种状态。热力学平衡这个术语表示一种平衡状态,在这种状态下所有的宏观流动都是零; 对于最简单的系统或物体来说,它们的密集属性是均匀的,它们的压力垂直于它们的边界。在平衡状态下,系统宏观上截然不同的部分之间没有不平衡的势能或驱动力。平衡态热力学的一个中心目标是: 给定一个处于明确初始平衡状态的系统,给定其周围环境,给定其本构壁,计算在一个特定的热力学操作改变其周围或周围环境后,系统的最终平衡状态是什么。<br />
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[[Non-equilibrium thermodynamics]] is a branch of thermodynamics that deals with systems that are not in [[thermodynamic equilibrium]]. Most systems found in nature are not in thermodynamic equilibrium because they are not in stationary states, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are not in stationary states, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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非平衡态热力学是热力学的一个分支,主要研究非热力学平衡系统。自然界中发现的大多数系统都不在热力学平衡,因为它们不处于静止状态,并且不断不断地受到来自其他系统的物质和能量流动的影响。非平衡体系的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出目前已知的宏观热力学方法的范围。<br />
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--[[用户:厚朴|厚朴]]([[用户讨论:厚朴|讨论]]) 2020年7月20日 (一) 09:41 (CST)continuously and discontinuously的翻译是不是有些不恰当<br />
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==Laws of thermodynamics==<br />
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==Laws of thermodynamics==<br />
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热力学定律<br />
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{{Main|Laws of thermodynamics}}<br />
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Thermodynamics is principally based on a set of four laws which are universally valid when applied to systems that fall within the constraints implied by each. In the various theoretical descriptions of thermodynamics these laws may be expressed in seemingly differing forms, but the most prominent formulations are the following.<br />
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Thermodynamics is principally based on a set of four laws which are universally valid when applied to systems that fall within the constraints implied by each. In the various theoretical descriptions of thermodynamics these laws may be expressed in seemingly differing forms, but the most prominent formulations are the following.<br />
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热力学基本上是建立在一套四条定律的基础上的,这些定律在适用于每个定律所暗示的约束条件下的系统时是普遍有效的。在热力学的各种理论描述中,这些定律可能表现为看似不同的形式,但最突出的公式如下。<br />
--[[用户:厚朴|厚朴]]([[用户讨论:厚朴|讨论]]) 2020年7月20日 (一) 10:05 (CST) set翻译成一集 prominent翻译成著名?<br />
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===Zeroth Law===<br />
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===Zeroth Law===<br />
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第零定律<br />
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The [[zeroth law of thermodynamics]] states: ''If two systems are each in thermal equilibrium with a third, they are also in thermal equilibrium with each other.''<br />
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The zeroth law of thermodynamics states: If two systems are each in thermal equilibrium with a third, they are also in thermal equilibrium with each other.<br />
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美国热力学第零定律协会指出: 如果两个系统各有三分之一的热平衡,那么它们之间的热平衡也是一样的。<br />
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This statement implies that thermal equilibrium is an [[equivalence relation]] on the set of [[thermodynamic system]]s under consideration. Systems are said to be in equilibrium if the small, random exchanges between them (e.g. [[Brownian motion]]) do not lead to a net change in energy. This law is tacitly assumed in every measurement of temperature. Thus, if one seeks to decide whether two bodies are at the same [[temperature]], it is not necessary to bring them into contact and measure any changes of their observable properties in time.<ref>Moran, Michael J. and Howard N. Shapiro, 2008. ''Fundamentals of Engineering Thermodynamics''. 6th ed. Wiley and Sons: 16.</ref> The law provides an empirical definition of temperature, and justification for the construction of practical thermometers.<br />
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This statement implies that thermal equilibrium is an equivalence relation on the set of thermodynamic systems under consideration. Systems are said to be in equilibrium if the small, random exchanges between them (e.g. Brownian motion) do not lead to a net change in energy. This law is tacitly assumed in every measurement of temperature. Thus, if one seeks to decide whether two bodies are at the same temperature, it is not necessary to bring them into contact and measure any changes of their observable properties in time. The law provides an empirical definition of temperature, and justification for the construction of practical thermometers.<br />
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这种说法暗示了热平衡是热力学系统集合上的一个等价关系。如果系统之间的小的、随机的交换(例如:布朗运动)不会导致能量的净变化。这个定律在每次测量温度时都是默认的。因此,如果要确定两个物体是否处于同一温度,就没有必要使它们接触并及时测量它们可观测性质的任何变化。该定律提供了温度的经验定义,以及建造实用温度计的依据。<br />
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The zeroth law was not initially recognized as a separate law of thermodynamics, as its basis in thermodynamical equilibrium was implied in the other laws. The first, second, and third laws had been explicitly stated already, and found common acceptance in the physics community before the importance of the zeroth law for the definition of temperature was realized. As it was impractical to renumber the other laws, it was named the ''zeroth law''.<br />
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The zeroth law was not initially recognized as a separate law of thermodynamics, as its basis in thermodynamical equilibrium was implied in the other laws. The first, second, and third laws had been explicitly stated already, and found common acceptance in the physics community before the importance of the zeroth law for the definition of temperature was realized. As it was impractical to renumber the other laws, it was named the zeroth law.<br />
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第零定律最初并没有被认为是一个独立的热力学定律,因为它在热力学平衡中的基础在其他定律中也有暗示。第一定律、第二定律和第三定律在温度定义的第零定律的重要性被认识到之前已经被物理学界明确阐述,并且得到了普遍接受。由于对其他法律重新编号是不切实际的,因此将其命名为第零法律。<br />
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--[[用户:厚朴|厚朴]]([[用户讨论:厚朴|讨论]]) 2020年7月20日 (一) 10:05 (CST)法律 Law检查一遍<br />
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===First Law===<br />
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===First Law===<br />
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第一定律<br />
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The [[first law of thermodynamics]] states: ''In a process without transfer of matter, the change in [[internal energy]],'' {{math|Δ''U''}}'', of a [[thermodynamic system]] is equal to the energy gained as heat,'' {{math|''Q''}}'', less the thermodynamic work,'' {{math|''W''}}'', done by the system on its surroundings.''<ref>Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics, AIP Press, Woodbury NY, {{ISBN|0883187973}}, p. 79.</ref><ref group=nb>The sign convention (Q is heat supplied ''to'' the system as, W is work done ''by'' the system) is that of [[Rudolf Clausius]]. The opposite sign convention is customary in chemical thermodynamics.</ref><br />
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The first law of thermodynamics states: In a process without transfer of matter, the change in internal energy, , of a thermodynamic system is equal to the energy gained as heat, , less the thermodynamic work, , done by the system on its surroundings.<br />
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能量守恒定律指出: 在一个没有物质转移的过程中,一个热力学系统的内部能量的变化等于作为热量获得的能量,减去系统在其周围所做的热力学功。<br />
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:<math>\Delta U = Q - W</math>.<br />
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<math>\Delta U = Q - W</math>.<br />
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数学 Delta u q-w / 数学。<br />
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For processes that include transfer of matter, a further statement is needed: ''With due account of the respective fiducial reference states of the systems, when two systems, which may be of different chemical compositions, initially separated only by an impermeable wall, and otherwise isolated, are combined into a new system by the thermodynamic operation of removal of the wall, then''<br />
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For processes that include transfer of matter, a further statement is needed: With due account of the respective fiducial reference states of the systems, when two systems, which may be of different chemical compositions, initially separated only by an impermeable wall, and otherwise isolated, are combined into a new system by the thermodynamic operation of removal of the wall, then<br />
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对于包含物质转移的过程,需要进一步的陈述: 在适当考虑了系统各自的基准参考状态的情况下,当两个系统---- 它们可能是不同的化学成分,最初只是被不透水的墙隔开,或者是被隔离---- 通过移除热力学操作结合成一个新的系统时,那么<br />
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:<math>U_0 = U_1 + U_2</math>,<br />
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<math>U_0 = U_1 + U_2</math>,<br />
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数学 u 0 u 1 + u 2 / math,<br />
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''where'' {{math|''U''<sub>0</sub>}} ''denotes the internal energy of the combined system, and'' {{math|''U''<sub>1</sub>}} ''and'' {{math|''U''<sub>2</sub>}} ''denote the internal energies of the respective separated systems.''<br />
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where denotes the internal energy of the combined system, and and denote the internal energies of the respective separated systems.<br />
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其中表示组合系统的内能,并表示各自分离系统的内能。<br />
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Adapted for thermodynamics, this law is an expression of the principle of [[conservation of energy]], which states that energy can be transformed (changed from one form to another), but cannot be created or destroyed.<ref>Callen, H.B. (1960/1985).''Thermodynamics and an Introduction to Thermostatistics'', second edition, John Wiley & Sons, Hoboken NY, {{ISBN|9780471862567}}, pp. 11–13.</ref><br />
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Adapted for thermodynamics, this law is an expression of the principle of conservation of energy, which states that energy can be transformed (changed from one form to another), but cannot be created or destroyed.<br />
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这一定律适用于热力学,是能量守恒定律的一种表述,它指出能量可以转换(从一种形式转变为另一种形式) ,但不能被创造或破坏。<br />
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Internal energy is a principal property of the [[thermodynamic state]], while heat and work are modes of energy transfer by which a process may change this state. A change of internal energy of a system may be achieved by any combination of heat added or removed and work performed on or by the system. As a [[State function|function of state]], the internal energy does not depend on the manner, or on the path through intermediate steps, by which the system arrived at its state.<br />
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Internal energy is a principal property of the thermodynamic state, while heat and work are modes of energy transfer by which a process may change this state. A change of internal energy of a system may be achieved by any combination of heat added or removed and work performed on or by the system. As a function of state, the internal energy does not depend on the manner, or on the path through intermediate steps, by which the system arrived at its state.<br />
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内能是热力学状态的主要特性,而热和功是能量传递的方式,通过这种方式,一个过程可以改变这种状态。系统内部能量的变化可以通过加热或除热以及在系统上或由系统所做的功的任何组合来实现。作为状态的函数,内能并不依赖于系统到达其状态的方式或中间步骤的路径。<br />
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===Second Law===<br />
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===Second Law===<br />
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第二定律<br />
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The [[second law of thermodynamics]] states: ''Heat cannot spontaneously flow from a colder location to a hotter location.''<ref name= "NKS note b" /><br />
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The second law of thermodynamics states: Heat cannot spontaneously flow from a colder location to a hotter location.<br />
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热力学第二定律指出: 热量不能自发地从较冷的地方流向较热的地方。<br />
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This law is an expression of the universal principle of decay observable in nature. The second law is an observation of the fact that over time, differences in temperature, pressure, and chemical potential tend to even out in a physical system that is isolated from the outside world. [[Entropy]] is a measure of how much this process has progressed. The entropy of an isolated system which is not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium. However, principles guiding systems that are far from equilibrium are still debatable. One of such principles is the [[entropy production|maximum entropy production]] principle.<ref>{{cite journal|last1=Onsager|first1=Lars|title=Reciprocal Relations in Irreversible Processes|journal=Phys. Rev.|date=1931|volume=37|issue=405|pages=405–426|doi=10.1103/physrev.37.405|bibcode=1931PhRv...37..405O|doi-access=free}}</ref><ref>{{cite book|last1=Ziegler|first1=H.|title=An Introduction to Thermomechanics|date=1983|location=North Holland}}</ref> It states that non-equilibrium systems behave such a way as to maximize its entropy production.<ref>{{cite journal|last1=Belkin|first1=Andrey|last2=Hubler|first2=A.|last3=Bezryadin|first3=A.|title=Self-Assembled Wiggling Nano-Structures and the Principle of Maximum Entropy Production|journal=Sci. Rep.|date=2015|doi=10.1038/srep08323|pmid=25662746|pmc=4321171|bibcode=2015NatSR...5E8323B|volume=5|page=8323}}</ref><br />
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This law is an expression of the universal principle of decay observable in nature. The second law is an observation of the fact that over time, differences in temperature, pressure, and chemical potential tend to even out in a physical system that is isolated from the outside world. Entropy is a measure of how much this process has progressed. The entropy of an isolated system which is not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium. However, principles guiding systems that are far from equilibrium are still debatable. One of such principles is the maximum entropy production principle. It states that non-equilibrium systems behave such a way as to maximize its entropy production.<br />
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这个定律是可以在自然界观察到的衰变的普遍原理的一种表述。第二定律是对这样一个事实的观察: 随着时间的推移,在与外界隔绝的物理系统中,温度、压力和化学势的差异趋于均衡。熵是对这个过程进展程度的度量。不处于平衡状态的孤立系统的熵会随着时间的推移而增加,在平衡状态时达到最大值。然而,远离平衡的原则指导体系仍然是有争议的。其中一个原则就是最大产生熵原则。它指出,非平衡系统的行为方式使其产生熵最大化。<br />
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In classical thermodynamics, the second law is a basic postulate applicable to any system involving heat energy transfer; in statistical thermodynamics, the second law is a consequence of the assumed randomness of molecular chaos. There are many versions of the second law, but they all have the same effect, which is to explain the phenomenon of [[irreversibility]] in nature.<br />
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In classical thermodynamics, the second law is a basic postulate applicable to any system involving heat energy transfer; in statistical thermodynamics, the second law is a consequence of the assumed randomness of molecular chaos. There are many versions of the second law, but they all have the same effect, which is to explain the phenomenon of irreversibility in nature.<br />
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在经典热力学中,第二定律是适用于任何涉及热能传递的系统的基本假设; 在统计热力学中,第二定律是假定的分子混沌随机性的结果。第二定律有许多版本,但它们都具有同样的效果,即解释自然界中的不可逆现象。<br />
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===Third Law===<br />
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===Third Law===<br />
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第三定律<br />
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The [[third law of thermodynamics]] states: ''As the temperature of a system approaches absolute zero, all processes cease and the entropy of the system approaches a minimum value.''<br />
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The third law of thermodynamics states: As the temperature of a system approaches absolute zero, all processes cease and the entropy of the system approaches a minimum value.<br />
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热力学第三定律指出: 当一个系统的温度接近绝对零度时,所有的过程停止,系统的熵接近最小值。<br />
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This law of thermodynamics is a statistical law of nature regarding entropy and the impossibility of reaching [[absolute zero]] of temperature. This law provides an absolute reference point for the determination of entropy. The entropy determined relative to this point is the absolute entropy. Alternate definitions include "the entropy of all systems and of all states of a system is smallest at absolute zero," or equivalently "it is impossible to reach the absolute zero of temperature by any finite number of processes".<br />
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This law of thermodynamics is a statistical law of nature regarding entropy and the impossibility of reaching absolute zero of temperature. This law provides an absolute reference point for the determination of entropy. The entropy determined relative to this point is the absolute entropy. Alternate definitions include "the entropy of all systems and of all states of a system is smallest at absolute zero," or equivalently "it is impossible to reach the absolute zero of temperature by any finite number of processes".<br />
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这个热力学定律是关于熵和不可能达到绝对零度的自然统计法则。这个定律为确定熵提供了一个绝对的参考点。相对于这个点确定的熵就是绝对熵。替代定义包括”系统的所有系统和系统的所有状态的熵在绝对零度时最小” ,或相当于”任何有限数目的过程都不可能达到绝对零度”。<br />
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Absolute zero, at which all activity would stop if it were possible to achieve, is −273.15&nbsp;°C (degrees Celsius), or −459.67&nbsp;°F (degrees Fahrenheit), or 0 K (kelvin), or 0° R (degrees [[Rankine scale|Rankine]]).<br />
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Absolute zero, at which all activity would stop if it were possible to achieve, is −273.15&nbsp;°C (degrees Celsius), or −459.67&nbsp;°F (degrees Fahrenheit), or 0 K (kelvin), or 0° R (degrees Rankine).<br />
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绝对零度是-273.15摄氏度(摄氏度) ,或-459.67华氏度(华氏度) ,或0 k (开尔文) ,或0 r (朗肯度)。<br />
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==System models==<br />
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系统模型<br />
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[[File:system boundary.svg|200px|thumb|right|A diagram of a generic thermodynamic system]]<br />
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A diagram of a generic thermodynamic system<br />
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一个通用的热力学系统图表<br />
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An important concept in thermodynamics is the [[thermodynamic system]], which is a precisely defined region of the universe under study. Everything in the universe except the system is called the [[Environment (systems)|''surroundings'']]. A system is separated from the remainder of the universe by a [[Boundary (thermodynamic)|''boundary'']] which may be a physical boundary or notional, but which by convention defines a finite volume. Exchanges of [[Work (thermodynamics)|work]], [[heat]], or [[matter]] between the system and the surroundings take place across this boundary.<br />
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An important concept in thermodynamics is the thermodynamic system, which is a precisely defined region of the universe under study. Everything in the universe except the system is called the surroundings. A system is separated from the remainder of the universe by a boundary which may be a physical boundary or notional, but which by convention defines a finite volume. Exchanges of work, heat, or matter between the system and the surroundings take place across this boundary.<br />
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热力学中的一个重要概念是热力学系统,它是研究中的宇宙的一个精确定义的区域。除了这个系统之外,宇宙中的一切都被称为环境。一个系统通过一个边界从宇宙的其余部分中分离出来,这个边界可能是物理边界或者概念边界,但是按照惯例,它定义了一个有限的体积。系统和周围环境之间的功、热或物质的交换发生在这个边界上。<br />
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In practice, the boundary of a system is simply an imaginary dotted line drawn around a volume within which is going to be a change in the [[internal energy]] of that volume. Anything that passes across the boundary that effects a change in the internal energy of the system needs to be accounted for in the energy balance equation. The volume can be the region surrounding a single atom resonating energy, such as [[Max Planck]] defined in 1900; it can be a body of steam or air in a [[steam engine]], such as [[Nicolas Léonard Sadi Carnot|Sadi Carnot]] defined in 1824; it can be the body of a [[tropical cyclone]], such as [[Kerry Emanuel]] theorized in 1986 in the field of [[atmospheric thermodynamics]]; it could also be just one [[nuclide]] (i.e. a system of [[quark]]s) as hypothesized in [[quantum thermodynamics]], or the [[event horizon]] of a [[black hole thermodynamics|black hole]].<br />
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In practice, the boundary of a system is simply an imaginary dotted line drawn around a volume within which is going to be a change in the internal energy of that volume. Anything that passes across the boundary that effects a change in the internal energy of the system needs to be accounted for in the energy balance equation. The volume can be the region surrounding a single atom resonating energy, such as Max Planck defined in 1900; it can be a body of steam or air in a steam engine, such as Sadi Carnot defined in 1824; it can be the body of a tropical cyclone, such as Kerry Emanuel theorized in 1986 in the field of atmospheric thermodynamics; it could also be just one nuclide (i.e. a system of quarks) as hypothesized in quantum thermodynamics, or the event horizon of a black hole.<br />
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实际上,一个系统的边界只是一个虚构的虚线,它围绕着一个体积绘制,体积内部能量将发生变化。任何通过边界的影响系统内部能量的变化都需要在能量平衡方程中加以解释。体积可以是围绕单个原子共振能量的区域,如马克斯 · 普朗克在1900年定义的; 它可以是蒸汽机中的蒸汽体或空气体,如萨迪 · 卡诺在1824年定义的; 它可以是热带气旋的体,如 Kerry Emanuel 在1986年在大气热力学领域建立的理论; 它也可以只是一个核素(即:。量子热力学中假设的夸克系统,或黑洞的事件视界。<br />
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Boundaries are of four types: fixed, movable, real, and imaginary. For example, in an engine, a fixed boundary means the piston is locked at its position, within which a constant volume process might occur. If the piston is allowed to move that boundary is movable while the cylinder and cylinder head boundaries are fixed. For closed systems, boundaries are real while for open systems boundaries are often imaginary. In the case of a jet engine, a fixed imaginary boundary might be assumed at the intake of the engine, fixed boundaries along the surface of the case and a second fixed imaginary boundary across the exhaust nozzle.<br />
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Boundaries are of four types: fixed, movable, real, and imaginary. For example, in an engine, a fixed boundary means the piston is locked at its position, within which a constant volume process might occur. If the piston is allowed to move that boundary is movable while the cylinder and cylinder head boundaries are fixed. For closed systems, boundaries are real while for open systems boundaries are often imaginary. In the case of a jet engine, a fixed imaginary boundary might be assumed at the intake of the engine, fixed boundaries along the surface of the case and a second fixed imaginary boundary across the exhaust nozzle.<br />
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边界有四种类型: 固定的、可移动的、真实的和想象的。例如,在发动机中,一个固定的边界意味着活塞被锁定在它的位置,在那里可能发生一个定容过程。如果活塞允许移动,那么边界是可移动的,而气缸和气缸盖边界是固定的。对于封闭系统,边界是真实的,而对于开放系统,边界往往是虚构的。在喷气发动机的情况下,可以假定在发动机进气口处有一个固定的虚边界,沿着箱体表面有一个固定的边界,在排气喷嘴处有一个固定的虚边界。<br />
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Generally, thermodynamics distinguishes three classes of systems, defined in terms of what is allowed to cross their boundaries:<br />
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Generally, thermodynamics distinguishes three classes of systems, defined in terms of what is allowed to cross their boundaries:<br />
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一般来说,热力学区分了三类系统,根据允许什么跨越它们的边界来定义:<br />
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{{table of thermodynamic systems}}<br />
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As time passes in an isolated system, internal differences of pressures, densities, and temperatures tend to even out. A system in which all equalizing processes have gone to completion is said to be in a [[state (thermodynamic)|state]] of [[thermodynamic equilibrium]].<br />
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As time passes in an isolated system, internal differences of pressures, densities, and temperatures tend to even out. A system in which all equalizing processes have gone to completion is said to be in a state of thermodynamic equilibrium.<br />
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在一个孤立的系统中,随着时间的推移,压力、密度和温度的内部差异趋于平衡。一个所有均衡过程均已完成的系统被称为处于热力学平衡状态。<br />
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Once in thermodynamic equilibrium, a system's properties are, by definition, unchanging in time. Systems in equilibrium are much simpler and easier to understand than are systems which are not in equilibrium. Often, when analysing a dynamic thermodynamic process, the simplifying assumption is made that each intermediate state in the process is at equilibrium, producing thermodynamic processes which develop so slowly as to allow each intermediate step to be an equilibrium state and are said to be [[reversible process (thermodynamics)|reversible processes]].<br />
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Once in thermodynamic equilibrium, a system's properties are, by definition, unchanging in time. Systems in equilibrium are much simpler and easier to understand than are systems which are not in equilibrium. Often, when analysing a dynamic thermodynamic process, the simplifying assumption is made that each intermediate state in the process is at equilibrium, producing thermodynamic processes which develop so slowly as to allow each intermediate step to be an equilibrium state and are said to be reversible processes.<br />
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一旦进入热力学平衡,系统的属性,根据定义,在时间上是不变的。处于平衡状态的系统比不处于平衡状态的系统要简单得多,也更容易理解。通常,当分析一个动态热力学过程时,会做出这样的简化假设: 过程中的每一个居间态都处于平衡状态,产生的热力学过程发展得如此缓慢,以至于每一个中间步骤都是一个平衡状态,称之为可逆过程。<br />
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==States and processes==<br />
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==States and processes==<br />
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状态和过程<br />
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When a system is at equilibrium under a given set of conditions, it is said to be in a definite [[thermodynamic state]]. The state of the system can be described by a number of [[state function|state quantities]] that do not depend on the process by which the system arrived at its state. They are called [[intensive variable]]s or [[extensive variable]]s according to how they change when the size of the system changes. The properties of the system can be described by an [[equation of state]] which specifies the relationship between these variables. State may be thought of as the instantaneous quantitative description of a system with a set number of variables held constant.<br />
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When a system is at equilibrium under a given set of conditions, it is said to be in a definite thermodynamic state. The state of the system can be described by a number of state quantities that do not depend on the process by which the system arrived at its state. They are called intensive variables or extensive variables according to how they change when the size of the system changes. The properties of the system can be described by an equation of state which specifies the relationship between these variables. State may be thought of as the instantaneous quantitative description of a system with a set number of variables held constant.<br />
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当一个系统在一组给定的条件下处于平衡状态时,我们称之为处于一个确定的热力学状态。系统的状态可以用许多状态量来描述,这些状态量并不依赖于系统到达其状态的过程。它们被称为密集型变量或扩展型变量,这取决于它们在系统规模发生变化时的变化情况。系统的属性可以用一个状态方程来描述,它指定了这些变量之间的关系。状态可以被认为是一系列变量保持不变的系统的瞬时定量描述。<br />
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A [[thermodynamic process]] may be defined as the energetic evolution of a thermodynamic system proceeding from an initial state to a final state. It can be described by [[process function|process quantities]]. Typically, each thermodynamic process is distinguished from other processes in energetic character according to what parameters, such as temperature, pressure, or volume, etc., are held fixed; Furthermore, it is useful to group these processes into pairs, in which each variable held constant is one member of a [[conjugate variables (thermodynamics)|conjugate]] pair.<br />
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A thermodynamic process may be defined as the energetic evolution of a thermodynamic system proceeding from an initial state to a final state. It can be described by process quantities. Typically, each thermodynamic process is distinguished from other processes in energetic character according to what parameters, such as temperature, pressure, or volume, etc., are held fixed; Furthermore, it is useful to group these processes into pairs, in which each variable held constant is one member of a conjugate pair.<br />
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热力学过程可以被定义为热力学系统从初始状态到最终状态的能量演化。它可以用工艺量来描述。通常情况下,根据温度、压力、体积等参数的固定程度,每个热力学过程过程与能量特征中的其他过程是不同的; 此外,将这些过程分组成对也很有用,每个变量保持常数是一个共轭对的一个成员。<br />
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Several commonly studied thermodynamic processes are:<br />
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Several commonly studied thermodynamic processes are:<br />
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一些常见的研究热力学过程是:<br />
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* [[Adiabatic process]]: occurs without loss or gain of energy by [[heat]]<br />
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* [[Isenthalpic process]]: occurs at a constant [[enthalpy]]<br />
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* [[Isentropic process]]: a reversible adiabatic process, occurs at a constant [[entropy]]<br />
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* [[Isobaric process]]: occurs at constant [[pressure]]<br />
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* [[Isochoric process]]: occurs at constant [[Volume (thermodynamics)|volume]] (also called isometric/isovolumetric)<br />
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* [[Isothermal process]]: occurs at a constant [[temperature]]<br />
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* [[steady state|Steady state process]]: occurs without a change in the [[internal energy]]<br />
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== Instrumentation ==<br />
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== Instrumentation ==<br />
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仪器仪表<br />
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There are two types of [[thermodynamic instruments]], the '''meter''' and the '''reservoir'''. A thermodynamic meter is any device which measures any parameter of a [[thermodynamic system]]. In some cases, the thermodynamic parameter is actually defined in terms of an idealized measuring instrument. For example, the [[zeroth law of thermodynamics|zeroth law]] states that if two bodies are in thermal equilibrium with a third body, they are also in thermal equilibrium with each other. This principle, as noted by [[James Clerk Maxwell|James Maxwell]] in 1872, asserts that it is possible to measure temperature. An idealized [[thermometer]] is a sample of an ideal gas at constant pressure. From the [[ideal gas law]] ''pV=nRT'', the volume of such a sample can be used as an indicator of temperature; in this manner it defines temperature. Although pressure is defined mechanically, a pressure-measuring device, called a [[barometer]] may also be constructed from a sample of an ideal gas held at a constant temperature. A [[calorimeter]] is a device which is used to measure and define the internal energy of a system.<br />
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There are two types of thermodynamic instruments, the meter and the reservoir. A thermodynamic meter is any device which measures any parameter of a thermodynamic system. In some cases, the thermodynamic parameter is actually defined in terms of an idealized measuring instrument. For example, the zeroth law states that if two bodies are in thermal equilibrium with a third body, they are also in thermal equilibrium with each other. This principle, as noted by James Maxwell in 1872, asserts that it is possible to measure temperature. An idealized thermometer is a sample of an ideal gas at constant pressure. From the ideal gas law pV=nRT, the volume of such a sample can be used as an indicator of temperature; in this manner it defines temperature. Although pressure is defined mechanically, a pressure-measuring device, called a barometer may also be constructed from a sample of an ideal gas held at a constant temperature. A calorimeter is a device which is used to measure and define the internal energy of a system.<br />
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有两种类型的热力学设备,水表和水库。热力学仪表是测量热力学系统的任何参数的任何装置。在某些情况下,热力学参数实际上是用理想化的测量仪器来定义的。例如,第零定律指出,如果两个物体在热平衡中有第三个物体,那么它们也在热平衡中。正如詹姆斯 · 麦克斯韦尔在1872年指出的那样,这个原理断言测量温度是可能的。理想温度计是恒压下理想气体的样品。根据理想气体定律 pV nRT,这样一个样品的体积可以用作温度的指示器; 在这种方式下,它定义了温度。虽然压力是机械定义的,一个称为气压计的压力测量装置也可以由恒定温度下的理想气体样品构成。量热计是用来测量和定义系统内部能量的装置。<br />
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A thermodynamic reservoir is a system which is so large that its state parameters are not appreciably altered when it is brought into contact with the system of interest. When the reservoir is brought into contact with the system, the system is brought into equilibrium with the reservoir. For example, a pressure reservoir is a system at a particular pressure, which imposes that pressure upon the system to which it is mechanically connected. The Earth's atmosphere is often used as a pressure reservoir. If ocean water is used to cool a power plant, the ocean is often a temperature reservoir in the analysis of the power plant cycle.<br />
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A thermodynamic reservoir is a system which is so large that its state parameters are not appreciably altered when it is brought into contact with the system of interest. When the reservoir is brought into contact with the system, the system is brought into equilibrium with the reservoir. For example, a pressure reservoir is a system at a particular pressure, which imposes that pressure upon the system to which it is mechanically connected. The Earth's atmosphere is often used as a pressure reservoir. If ocean water is used to cool a power plant, the ocean is often a temperature reservoir in the analysis of the power plant cycle.<br />
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热力学储存器是这样一个系统,它的状态参数如此之大,当它与感兴趣的系统接触时,它的状态参数没有明显的改变。当油藏与系统接触时,系统与油藏达到平衡。例如,压力容器是一个处于特定压力下的系统,它对与之机械连接的系统施加压力。地球的大气层经常被用作压力储存器。如果用海水来冷却发电厂,在分析发电厂的循环过程中,海洋通常是一个温度储存库。<br />
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== Conjugate variables ==<br />
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== Conjugate variables ==<br />
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共轭变量<br />
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{{Main|Conjugate variables (thermodynamics)|l1=Conjugate variables}}<br />
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The central concept of thermodynamics is that of [[energy]], the ability to do [[Work (thermodynamics)|work]]. By the [[first law of thermodynamics|First Law]], the total energy of a system and its surroundings is conserved. Energy may be transferred into a system by heating, compression, or addition of matter, and extracted from a system by cooling, expansion, or extraction of matter. In [[mechanics]], for example, energy transfer equals the product of the force applied to a body and the resulting displacement.<br />
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The central concept of thermodynamics is that of energy, the ability to do work. By the First Law, the total energy of a system and its surroundings is conserved. Energy may be transferred into a system by heating, compression, or addition of matter, and extracted from a system by cooling, expansion, or extraction of matter. In mechanics, for example, energy transfer equals the product of the force applied to a body and the resulting displacement.<br />
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热力学的核心概念是能量,做功的能力。根据第一定律,系统及其周围环境的总能量是守恒的。能量可以通过加热、压缩或添加物质的方式转移到系统中,也可以通过冷却、膨胀或提取物质的方式从系统中提取。例如,在力学中,能量传递等于作用在物体上的力和由此产生的位移的乘积。<br />
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[[conjugate variables (thermodynamics)|Conjugate variables]] are pairs of thermodynamic concepts, with the first being akin to a "force" applied to some [[thermodynamic system]], the second being akin to the resulting "displacement," and the product of the two equalling the amount of energy transferred. The common conjugate variables are:<br />
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Conjugate variables are pairs of thermodynamic concepts, with the first being akin to a "force" applied to some thermodynamic system, the second being akin to the resulting "displacement," and the product of the two equalling the amount of energy transferred. The common conjugate variables are:<br />
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共轭变量是成对的热力学概念,第一个类似于施加在某些热力学系统上的“力” ,第二个类似于由此产生的“位移” ,两者的乘积等于所转移的能量。常见的共轭变量有:<br />
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* [[Pressure]]-[[Volume (thermodynamics)|volume]] (the [[Mechanics|mechanical]] parameters);<br />
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* [[Temperature]]-[[entropy]] (thermal parameters);<br />
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* [[Chemical potential]]-[[particle number]] (material parameters).<br />
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== Potentials ==<br />
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== Potentials ==<br />
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== Potentials ==<br />
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[[Thermodynamic potential]]s are different quantitative measures of the stored energy in a system. Potentials are used to measure the energy changes in systems as they evolve from an initial state to a final state. The potential used depends on the constraints of the system, such as constant temperature or pressure. For example, the Helmholtz and Gibbs energies are the energies available in a system to do useful work when the temperature and volume or the pressure and temperature are fixed, respectively.<br />
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Thermodynamic potentials are different quantitative measures of the stored energy in a system. Potentials are used to measure the energy changes in systems as they evolve from an initial state to a final state. The potential used depends on the constraints of the system, such as constant temperature or pressure. For example, the Helmholtz and Gibbs energies are the energies available in a system to do useful work when the temperature and volume or the pressure and temperature are fixed, respectively.<br />
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热力学势是体系中储存能量的不同定量度量。势能被用来测量系统从初始状态到最终状态的能量变化。所用的电位取决于系统的约束条件,如恒温或恒压。例如,亥姆霍兹能量和吉布斯能量是当温度和体积或压力和温度分别固定时,系统中可用于做有用功的能量。<br />
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The five most well known potentials are:<br />
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The five most well known potentials are:<br />
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五个最有名的潜力是:<br />
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{{table of thermodynamic potentials}}<br />
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where <math>T</math> is the [[thermodynamic temperature|temperature]], <math>S</math> the [[entropy]], <math>p</math> the [[pressure]], <math>V</math> the [[Volume (thermodynamics)|volume]], <math>\mu</math> the [[chemical potential]], <math>N</math> the number of particles in the system, and <math>i</math> is the count of particles types in the system.<br />
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where <math>T</math> is the temperature, <math>S</math> the entropy, <math>p</math> the pressure, <math>V</math> the volume, <math>\mu</math> the chemical potential, <math>N</math> the number of particles in the system, and <math>i</math> is the count of particles types in the system.<br />
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数学 t / math 是温度,数学 s / math 是熵,数学 p / math 是压力,数学 v / math 是体积,数学 mu / math 是化学势,数学 n / math 是系统中粒子的数量,数学 i / math 是系统中粒子类型的数量。<br />
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Thermodynamic potentials can be derived from the energy balance equation applied to a thermodynamic system. Other thermodynamic potentials can also be obtained through [[Legendre transformation]].<br />
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Thermodynamic potentials can be derived from the energy balance equation applied to a thermodynamic system. Other thermodynamic potentials can also be obtained through Legendre transformation.<br />
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热力学势可以从应用于热力学系统的能量平衡方程推导出来。其他热力学势也可以通过勒壤得转换得到。<br />
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== Applied fields ==<br />
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== Applied fields ==<br />
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应用领域<br />
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{{columns-list|colwidth=22em|<br />
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{{columns-list|colwidth=22em|<br />
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{ columns-list | colwidth 22em | <br />
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* [[Atmospheric thermodynamics]]<br />
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* [[Biological thermodynamics]]<br />
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* [[Black hole thermodynamics]]<br />
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* [[Chemical thermodynamics]]<br />
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* [[Classical thermodynamics]]<br />
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* [[Thermodynamic equilibrium|Equilibrium thermodynamics]]<br />
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* [[Industrial ecology]] (re: [[Exergy]])<br />
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* [[Maximum entropy thermodynamics]]<br />
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* [[Non-equilibrium thermodynamics]]<br />
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* [[Philosophy of thermal and statistical physics]]<br />
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* [[Psychrometrics]]<br />
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* [[Quantum thermodynamics]]<br />
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* [[Statistical thermodynamics]]<br />
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* [[Thermoeconomics]]<br />
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}}<br />
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}}<br />
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}}<br />
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== See also ==<br />
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== See also ==<br />
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参见<br />
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{{portal|Physics}}<br />
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* [[Thermodynamic process path]]<br />
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===Lists and timelines===<br />
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===Lists and timelines===<br />
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清单和时间线<br />
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* [[List of important publications in physics#Thermodynamics|List of important publications in thermodynamics]]<br />
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* [[List of textbooks in statistical mechanics|List of textbooks on thermodynamics and statistical mechanics]]<br />
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* [[List of thermal conductivities]]<br />
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* [[List of thermodynamic properties]]<br />
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* [[Table of thermodynamic equations]]<br />
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* [[Timeline of thermodynamics]]<br />
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== Notes ==<br />
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== Notes ==<br />
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注释<br />
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{{reflist|group=nb}}<br />
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==References==<br />
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==References==<br />
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参考资料<br />
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{{Reflist|35em}}<br />
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==Further reading==<br />
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==Further reading==<br />
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进一步阅读<br />
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* {{cite book|author1=Goldstein, Martin|author2=Inge F.|lastauthoramp=yes|title=The Refrigerator and the Universe|url=https://archive.org/details/refrigeratoruniv0000gold|url-access=registration|publisher=Harvard University Press|year=1993|isbn=978-0-674-75325-9|location=|pages=|oclc=32826343}} A nontechnical introduction, good on historical and interpretive matters.<br />
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* {{cite journal |last1=Kazakov |first1=Andrei |last2=Muzny |first2=Chris D. |last3=Chirico |first3=Robert D. |last4=Diky |first4=Vladimir V. |last5=Frenkel |first5=Michael |title=Web Thermo Tables – an On-Line Version of the TRC Thermodynamic Tables |journal=Journal of Research of the National Institute of Standards and Technology |volume=113 |issue=4 |year=2008 |pages=209–220 |issn=1044-677X |doi=10.6028/jres.113.016 |pmc=4651616 |pmid=27096122}}<br />
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* {{cite book|author=Gibbs J.W.|title=The Collected Works of J. Willard Gibbs Thermodynamics.|publisher=Longmans, Green and Co.|year=1928|isbn=|location=New York|pages=|oclc=}} Vol. 1, pp. 55–349.<br />
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* {{cite book|author=Guggenheim E.A.|title=Modern thermodynamics by the methods of Willard Gibbs|publisher=Methuen & co. ltd.|year=1933|isbn=|location=London|pages=|oclc=}}<br />
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* {{cite book|author=Denbigh K.|title=The Principles of Chemical Equilibrium: With Applications in Chemistry and Chemical Engineering.|publisher=Cambridge University Press|year=1981|isbn=|location=London|pages=|oclc=}}<br />
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* {{cite book|author=Stull, D.R., Westrum Jr., E.F. and Sinke, G.C.|title=The Chemical Thermodynamics of Organic Compounds.|publisher=John Wiley and Sons, Inc.|year=1969|isbn=|location=London|pages=|oclc=}}<br />
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* {{cite book|author=Bazarov I.P.|title=Thermodynamics: Textbook.|publisher=Lan publishing house|year=2010|isbn=978-5-8114-1003-3|location=St. Petersburg|page=384|oclc=}} 5th ed. (in Russian)<br />
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* {{cite book|author=Bawendi Moungi G., Alberty Robert A. and Silbey Robert J.|title=Physical Chemistry|publisher=J. Wiley & Sons, Incorporated|year=2004|isbn=|location=|pages=|oclc=}}<br />
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* {{cite book|author=Alberty Robert A.|title=Thermodynamics of Biochemical Reactions|publisher=Wiley-Interscience|year=2003|isbn=|location=|pages=|oclc=}}<br />
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* {{cite book|author=Alberty Robert A.|title=Biochemical Thermodynamics: Applications of Mathematica|journal=Methods of Biochemical Analysis|publisher=John Wiley & Sons, Inc.|year=2006|volume=48|isbn=978-0-471-75798-6|location=|pages=1–458|pmid=16878778|oclc=}}<br />
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The following titles are more technical:<br />
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The following titles are more technical:<br />
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下面的标题更具技术性:<br />
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* {{Cite book|title=Advanced Engineering Thermodynamics|last=Bejan|first=Adrian|publisher=Wiley|year=2016|isbn=978-1-119-05209-8|edition=4|location=|pages=}}<br />
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* {{cite book|author=Cengel, Yunus A., & Boles, Michael A.|title=Thermodynamics – an Engineering Approach|publisher=McGraw Hill|year=2002|isbn=978-0-07-238332-4|location=|pages=|oclc=45791449|url-access=registration|url=https://archive.org/details/thermodynamicsen00ceng_0}}<br />
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* {{cite book|author=Dunning-Davies, Jeremy|title=Concise Thermodynamics: Principles and Applications|publisher=Horwood Publishing|year=1997|isbn=978-1-8985-6315-0|location=|pages=|oclc=36025958}}<br />
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* {{cite book|author1=Kroemer, Herbert|author2=Kittel, Charles|lastauthoramp=yes|title=Thermal Physics|publisher=W.H. Freeman Company|year=1980|isbn=978-0-7167-1088-2|location=|pages=|oclc=32932988}}<br />
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== External links ==<br />
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== External links ==<br />
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外部链接<br />
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{{Wikibooks|Engineering Thermodynamics}}<br />
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{{wikiquote|Thermodynamics}}<br />
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* {{cite EB1911 |title=Thermodynamics |volume=26 |pages=808–814 |short=x |url=https://archive.org/details/encyclopaediabri26chisrich/page/808}}<br />
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* [http://tigger.uic.edu/~mansoori/Thermodynamic.Data.and.Property_html Thermodynamics Data & Property Calculation Websites]<br />
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* [http://tigger.uic.edu/~mansoori/Thermodynamics.Educational.Sites_html Thermodynamics Educational Websites]<br />
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* [http://scienceworld.wolfram.com/physics/topics/Thermodynamics.html Thermodynamics at ''ScienceWorld'']<br />
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* [http://www.wiley.com/legacy/college/boyer/0470003790/reviews/thermo/thermo_intro.htm Biochemistry Thermodynamics]<br />
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* [http://farside.ph.utexas.edu/teaching/sm1/lectures/lectures.html Thermodynamics and Statistical Mechanics]<br />
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* [https://web.archive.org/web/20090430200028/http://www.ent.ohiou.edu/~thermo/ Engineering Thermodynamics – A Graphical Approach]<br />
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* [http://farside.ph.utexas.edu/teaching/sm1/statmech.pdf Thermodynamics and Statistical Mechanics] by Richard Fitzpatrick<br />
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[[Category:Thermodynamics| ]]<br />
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类别: 化学工程<br />
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Category:Concepts in physics<br />
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分类: 物理概念<br />
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分类: 物理学的子领域<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Thermodynamics]]. Its edit history can be viewed at [[热力学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%B9%B3%E8%A1%A1%E7%83%AD%E5%8A%9B%E5%AD%A6&diff=21699平衡热力学2021-02-09T08:15:09Z<p>Jxzhou:/* Non-equilibrium */</p>
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<div>此词条暂由小竹凉翻译,翻译字数共5339,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{short description|State of thermodynamic system(s) where no net macroscopic flow of matter or energy occurs}}<br />
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'''Thermodynamic equilibrium''' is an [[axiomatic]] concept of [[thermodynamics]]. It is an internal [[State variables|state]] of a single [[thermodynamic system]], or a relation between several thermodynamic systems connected by more or less permeable or impermeable [[Thermodynamic system#Walls|walls]]. In thermodynamic equilibrium there are no net [[macroscopic]] [[Flow (mathematics)|flows]] of [[matter]] or of [[energy]], either within a system or between systems. <br />
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Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium there are no net macroscopic flows of matter or of energy, either within a system or between systems. <br />
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'''热力学平衡'''是'''<font color="#ff8000">热力学 Thermodynamics</font>'''的一个'''<font color="#ff8000">不言自明的 Axiomatic</font>'''概念。它是单个'''<font color="#ff8000">热力学系统 Thermodynamic System</font>'''的内部'''<font color="#ff8000">状态 State</font>''',或者是几个热力学系统之间通过或多或少的渗透或不渗透的'''<font color="#ff8000">壁 Wall</font>'''连接的关系。无论是在一个系统内还是在系统之间,在热力学平衡中不存在'''<font color="#ff8000">物质 Matter</font>'''或'''<font color="#ff8000">能量 Energy</font>'''的净'''<font color="#ff8000">宏观 Macroscopic</font>''' '''<font color="#ff8000">流动 Flow</font>'''。<br />
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In a system that is in its own state of internal thermodynamic equilibrium, no [[macroscopic]] change occurs. <br />
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In a system that is in its own state of internal thermodynamic equilibrium, no macroscopic change occurs. <br />
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在一个处于内部热力学平衡状态的系统中,不会发生'''<font color="#ff8000">宏观 Macroscopic</font>'''变化。<br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual [[Thermal equilibrium|thermal]], [[Mechanical equilibrium|mechanical]], [[Chemical equilibrium|chemical]], and [[Radiative equilibrium|radiative]] equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a [[thermodynamic operation]]. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a thermodynamic operation. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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相互热力学平衡的体系同时处于互相之间的'''<font color="#ff8000">热 Thermal</font>'''平衡、'''<font color="#ff8000">力学 Mechanical</font>'''平衡、'''<font color="#ff8000">化学 Chemical</font>'''平衡和'''<font color="#ff8000">辐射 Radiative</font>'''平衡。系统可以处于其中一种相互平衡状态,尽管其他状态未平衡。在热力学平衡中所有的平衡同时并且无限期地保持,直到被'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''打破。在一个宏观平衡中,微观交换是完全或几乎完全平衡的;这是对宏观平衡概念的物理解释。<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform [[temperature]]. Its [[Intensive and extensive properties|intensive properties]], other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform temperature. Its intensive properties, other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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一个处于内部热力学状态平衡的热力学系统具有空间均匀的'''<font color="#ff8000">温度 Temperature</font>'''。除了温度以外,它的'''<font color="#ff8000">强度性质 Intensive Properties</font>'''可以由于周围环境施加的不变的长程力场而导致空间不均匀性。<br />
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In systems that are at a state of [[non-equilibrium]] there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a '''meta-stable equilibrium'''.<br />
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In systems that are at a state of non-equilibrium there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a meta-stable equilibrium.<br />
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相比之下,处于'''<font color="#ff8000">非平衡状态 non-equilibrium</font>'''的系统中有物质或能量的净流动。如果这些变化可以在一个还没有发生的系统中被触发,那么这个系统就被称为处于一个'''亚稳定的平衡状态'''。<br />
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Though not a widely named a "law," it is an [[axiom]] of thermodynamics that there exist states of thermodynamic equilibrium. The [[second law of thermodynamics]] states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the [[entropy|entropies]] of the portions.<br />
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Though not a widely named a "law," it is an axiom of thermodynamics that there exist states of thermodynamic equilibrium. The second law of thermodynamics states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the entropies of the portions.<br />
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虽然不是一个广泛命名的“定律” ,但存在热力学平衡状态是一个热力学'''<font color="#ff8000">公理 Axiom</font>'''。'''<font color="#ff8000">热力学第二定律 second law of thermodynamics</font>'''指出,当一个物质体从一个平衡状态开始,在这个状态中,它的一部分被或多或少渗透或不渗透的分区保持在不同的状态,并且是孤立的,热力学操作移除分区或使分区更具渗透性,然后它会自发地达到自己内部热力学平衡的新状态,并伴随着部分'''<font color="#ff8000">熵 Entropy</font>'''的总和增加。<br />
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== Overview 概览==<br />
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{{Thermodynamics|cTopic=[[Thermodynamic system|Systems]]}}<br />
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Classical thermodynamics deals with states of [[dynamic equilibrium]]. The state of a system at thermodynamic equilibrium is the one for which some [[thermodynamic potential]] is minimized, or for which the [[entropy]] (''S'') is maximized, for specified conditions. One such potential is the [[Helmholtz free energy]] (''A''), for a system with surroundings at controlled constant temperature and volume:<br />
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Classical thermodynamics deals with states of dynamic equilibrium. The state of a system at thermodynamic equilibrium is the one for which some thermodynamic potential is minimized, or for which the entropy (S) is maximized, for specified conditions. One such potential is the Helmholtz free energy (A), for a system with surroundings at controlled constant temperature and volume:<br />
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经典热力学研究'''<font color="#ff8000">动态平衡 Dynamic Equilibrium</font>'''的状态。系统的热力学平衡状态是对于特定的条件,一些'''<font color="#ff8000">热力学势 Thermodynamic Potential</font>'''被最小化,或者'''<font color="#ff8000">熵 Entropy</font>'''(S)被最大化。对于一个周围环境温度和体积恒定的系统,其中一个这样的热力学势是'''<font color="#ff8000">亥姆霍兹自由能 Helmholtz Free Energy</font>'''(A):<br />
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:<math>A = U - TS</math><br />
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<math>A = U - TS</math><br />
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A = U-TS<br />
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Another potential, the [[Gibbs free energy]] (''G''), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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Another potential, the Gibbs free energy (G), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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在恒定温度和压力的系统中,另一个热力学势'''<font color="#ff8000">吉布斯自由能 Gibbs Free Energy</font>'''(G)在热力学平衡状态最小:<br />
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:<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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where ''T'' denotes the absolute thermodynamic temperature, ''P'' the pressure, ''S'' the entropy, ''V'' the volume, and ''U'' the internal energy of the system.<br />
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where T denotes the absolute thermodynamic temperature, P the pressure, S the entropy, V the volume, and U the internal energy of the system.<br />
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其中 T 表示热力学绝对温度,P 表示压强,S 表示熵,V 表示体积,U 表示体系的内能。<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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热力学平衡是一种独特的稳定定态,当系统长时间与周围环境相互作用时,它可以被接近或最终到达。上述势能是数学构造的热力学量,在特定的环境条件下最小化。<br />
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== Conditions 条件==<br />
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* For a completely isolated system, ''S'' is maximum at thermodynamic equilibrium. 对于一个完全孤立的系统,S在热力学平衡中取最大值。<br />
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* For a system with controlled constant temperature and volume, ''A'' is minimum at thermodynamic equilibrium. 对于一个恒定温度和体积的系统来说,A在热力学平衡中取最小值。<br />
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* For a system with controlled constant temperature and pressure, ''G'' is minimum at thermodynamic equilibrium. 对于一个恒温恒压的系统,G在热力学平衡中取最小值。<br />
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The various types of equilibriums are achieved as follows:<br />
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The various types of equilibriums are achieved as follows:<br />
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实现各种类型的平衡的方法如下:<br />
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*Two systems are in ''thermal equilibrium'' when their [[temperature]]s are the same. 当两个系统的'''<font color="#ff8000">温度 Temperature</font>'''相同时,它们就处于''热平衡状态''<br />
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*Two systems are in ''mechanical equilibrium'' when their [[pressure]]s are the same. 当两个体系的'''<font color="#ff8000">压力 Pressure</font>'''相同时,它们就处于''力学平衡''<br />
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*Two systems are in ''diffusive equilibrium'' when their [[chemical potential]]s are the same. 当两个题体系的'''<font color="#ff8000">化学势 Chemical Potential</font>'''相同时,它们就处于''扩散平衡''<br />
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*All [[forces]] are balanced and there is no significant external driving force.<br />
所有的'''<font color="#ff8000">力 Force</font>'''都是平衡的,没有明显的外部驱动力<br />
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==Relation of exchange equilibrium between systems 系统之间的交换均衡关系==<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability.<ref name="Nster_a">Münster, A. (1970), p. 49.</ref> When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability. When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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通常,热力学系统的周围环境也可以被看作是另一个热力学系统。在这种观点中,我们可以把系统及其周围环境看作是相互接触的两个系统,远程作用力也将它们联系在一起。系统的包围物是两个系统之间的接触面或边界。在热力学形式中,该表面被认为具有特定的渗透性质。例如,接触的表面可能被认为只能透热,使能量只能作为热传递。当远程力在时间上不发生变化,两个系统之间的热量传递减慢并最终永久停止时,这两个系统被称为热平衡; 这就是接触平衡的一个例子。其它类型的接触平衡可用其它类型的比渗透率来定义。当两个系统对于某一特定类型的渗透率处于接触平衡时,它们具有属于该特定类型渗透率的强变量的共同值。这种强度变量的例子有温度、压力、化学势。<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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接触平衡也可视为交换平衡。在接触平衡状态下,两系统之间某些量的传递速率存在零平衡。例如,对于只能透热的壁,内能作为热在两个系统之间的扩散速率是相等并反向的。两个系统之间的绝热壁只对作为功传递的能量有渗透作用; 在力学平衡,两个系统之间作为功的能量传递速率相等且相反。如果是一个简单的壁,那么通过它的体积转移率也是相等且相反的; 即它两边的压力是相等的。如果绝热壁比较复杂,有一种杠杆,有一个面积比,那么两个体系在交换平衡中的压力与体积交换比成反比,这使得转移率的零平衡作功。<br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<ref name="Planck 1914 40">[[Max Planck|Planck. M.]] (1914), p. 40.</ref><br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<br />
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辐射交换可以发生在两个不同的系统之间。当两个体系温度相同时,辐射交换平衡占优势。<br />
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==Thermodynamic state of internal equilibrium of a system 系统内部平衡的热力学状态==<br />
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A collection of matter may be entirely [[Isolated system|isolated]] from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium.<ref>Haase, R. (1971), p. 4.</ref><ref>Callen, H.B. (1960/1985), p. 26.</ref> (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics.<ref>{{Cite journal |doi = 10.1119/1.4914528|bibcode = 2015AmJPh..83..628M|title = Time and irreversibility in axiomatic thermodynamics|year = 2015|last1 = Marsland|first1 = Robert|last2 = Brown|first2 = Harvey R.|last3 = Valente|first3 = Giovanni|journal = American Journal of Physics|volume = 83|issue = 7|pages = 628–634}}</ref> One textbook<ref>[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963), p. 5.</ref> calls it the "zeroth law", remarking that the authors think this more befitting that title than its [[Zeroth law of thermodynamics|more customary definition]], which apparently was suggested by [[Ralph H. Fowler|Fowler]].)<br />
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A collection of matter may be entirely isolated from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium. (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics. One textbook calls it the "zeroth law", remarking that the authors think this more befitting that title than its more customary definition, which apparently was suggested by Fowler.)<br />
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物质的集合可能与其周围的环境完全'''<font color="#ff8000">孤立 Isolated</font>'''。如果它在无限长的时间内一直保持不受干扰,按照经典热力学假定,它处于一个没有发生任何变化,没有流动的状态,即内部平衡的热力学状态。(这种假设有时被称为“负第一”热力学定律,但并不常见。有教科书称之为“第零定律” ,作者'''<font color="#ff8000">福勒 Fowler</font>'''认为这个名称是'''<font color="#ff8000">更符合惯例的定义 More Customary Definition</font>'''。)<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a [[thermodynamic operation]] be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a thermodynamic operation be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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这种状态是所谓的经典热力学或平衡态热力学的主要关注点,因为它们是系统中被认为在这门学科中得到很好定义的唯一状态。一个与另一个系统处于接触平衡状态可以被一个'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''隔离,在隔离发生时,其内部不会发生任何变化。因此,一个与另一个系统处于接触平衡状态时也可以被视为处于其自身的内部热力学平衡状态。<br />
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==Multiple contact equilibrium 多点接触平衡==<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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热力学形式允许一个系统同时与其他多个系统接触,这些系统可能有也可能没有相互接触,且这些接触具有不同的渗透性。如果这些系统都与世界其他部分相互隔离,那么它们彼此之间就会达到各自的接触平衡。<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy.<ref name="Caratheodory">Carathéodory, C. (1909).</ref><ref>Prigogine, I. (1947), p. 48.</ref><ref>Landsberg, P. T. (1961), pp. 128–142.</ref><ref>Tisza, L. (1966), p. 108.</ref> Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy. Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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如果几个系统彼此之间没有绝热壁,但是它们与世界其他部分共同隔离,那么它们就会达到多重接触平衡状态,且有共同的温度,总的内能和熵。在众多强度量中,这是温度的一个独特性质。即使在远距离作用力存在的情况下,它也是有效的。(也就是说,没有“力”可以维持温度的差异。)举个例子,在热力学平衡的一个垂直的引力场系统中,顶部壁面的压力比底部壁面的压力小,但是各处的温度都是一样的。<br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural [[thermodynamic process]].<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), § 1.12.</ref> It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings.<ref>Levine, I.N. (1983), p. 40.</ref><ref>Lieb, E.H., Yngvason, J. (1999), pp. 17–18.</ref> The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of [[Second law of thermodynamics#Description#Kelvin statement|"inanimate" agency]]; a system in thermodynamic equilibrium is inanimate.<ref>[[William Thomson, 1st Baron Kelvin|Thomson, W.]] (1851).</ref><br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural thermodynamic process. It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings. The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of "inanimate" agency; a system in thermodynamic equilibrium is inanimate.<br />
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热力操作可能作为一个事件发生在周围环境的壁上,既不直接影响与周围环境联系的壁,也不直接影响其内部,且发生在一个明确的有限的时间内。例如,一个固定的绝热壁可以在环境中被放置或拆除。由于这种操作仅限于周围环境,系统可能会在一段时间内远离自身最初的内部状态---- 热力学平衡。根据热力学第二定律的说法,整体经历了变化并最终与周围环境达到了新的平衡。继Planck之后,这一连串的事件被称为自然'''<font color="#ff8000">热力学过程 Thermodynamic Process</font>'''。即使在这个过程中,当系统和周围环境都不处于明确的内部平衡状态时,存在着暂时偏离热力学平衡的现象,由于初始状态和最终状态都是热力学平衡的,这在平衡热力学中也是允许的。一个自然过程在其主要部分中以有限的速率进行,因此,它从根本上不同于虚构的准静态“过程”;即不在整个过程中无限缓慢地进行而且虚构地“可逆”。经典热力学允许,即使一个过程可能需要很长的时间才能达到热力学平衡,如果主要部分的过程是在一个有限的比率中,那么它被认为是自然的,并受制于热力学第二定律,即不可逆的。工程设计的机器、人工设备和操作是允许在周围环境中进行的。允许在环境中而不是在系统中进行此类操作和设备,是开尔文在他的一个热力学第二定律的陈述中提到'''<font color="#ff8000">无生命机构 Inanimate Agency</font>'''的原因; 在热力学平衡的系统是无生命的。<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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否则,热力操作可能会直接影响系统的壁。<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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通常可以很方便地假设周围的某些子系统比系统大得多,以至于这个过程只能影响周围子系统的强度变量,然后将这些子系统称为相关强度变量的储备库。<br />
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== Local and global equilibrium 局部和全局均衡==<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by [[intensive quantity|intensive]] parameters. As an example, [[temperature]] controls [[Heat equation|heat exchanges]]. ''Global thermodynamic equilibrium'' (GTE) means that those [[intensive quantity|intensive]] parameters are homogeneous throughout the whole system, while ''local thermodynamic equilibrium'' (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by intensive parameters. As an example, temperature controls heat exchanges. Global thermodynamic equilibrium (GTE) means that those intensive parameters are homogeneous throughout the whole system, while local thermodynamic equilibrium (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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区分全局性和局部性热力学平衡是很有用的。在热力学中,系统内部和系统与外部之间的交换是由'''<font color="#ff8000">强度 Intensive</font>'''参数控制的。例如,'''<font color="#ff8000">温度 Temperature</font>'''控制'''<font color="#ff8000">热交换 Heat Equation</font>'''。全局热力学平衡(GTE)意味着这些'''<font color="#ff8000">强度 Intensive</font>'''参数在整个系统中是均匀的,而局部热力学平衡(LTE)意味着这些强度参数在空间和时间上是变化的,但变化如此缓慢,以至于对于任何一点,人们都可以假设在该点的某个邻域存在热力学平衡。<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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如果对系统的描述要求强度参数的变化过大,那么这些强度参数的定义所依据的假设本身就会失效,系统将既不处于全局平衡,也不处于局部平衡。例如,粒子需要一定数量的碰撞来平衡其周围环境。如果在这些碰撞中移动的平均距离使它离开平衡邻域,它将永远不会平衡,也就不会有 LTE。根据定义,温度与平衡邻域的平均内部能量成正比。由于没有达到平衡邻域,温度的概念就不成立,温度也就变得无法定义。<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to [[massive]] particles. In a [[radiation|radiating]] gas, the [[photon]]s being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to massive particles. In a radiating gas, the photons being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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值得注意的是,这种局部平衡可能只适用于系统中的某个粒子子集。例如,LTE 通常只适用于'''<font color="#ff8000">大 Massive</font>'''质量粒子。在'''<font color="#ff8000">辐射 Radiation</font>'''气体中,被气体发射和吸收的'''<font color="#ff8000">光子 Photon</font>'''不需要彼此在一个热力学平衡内,或与气体中的大量粒子在一起,LTE 才能存在。在某些情况下,自由电子并不需要与大得多的原子或分子处于平衡状态,LTE 才能存在。<br />
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As an example, LTE will exist in a glass of water that contains a melting [[ice cube]]. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the [[Maxwell–Boltzmann distribution]] for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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As an example, LTE will exist in a glass of water that contains a melting ice cube. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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例如,LTE 将存在于一个装有正在融化的'''<font color="#ff8000">冰块 Ice Cube</font>'''的水杯中。玻璃杯内的温度可以在任何时候定义,但是离冰块近的地方要比离冰块远的地方冷。如果观察到位于给定点附近的分子的能量,它们将按照麦克斯韦-波兹曼分布在一定温度下的分布。如果观察到位于另一点附近的分子的能量,它们将按照'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''分布到另一个温度。<br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural [[transport phenomena]] may lead a system from local to global thermodynamic equilibrium. Going back to our example, the [[diffusion]] of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<ref>H.R. Griem, 2005</ref><br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural transport phenomena may lead a system from local to global thermodynamic equilibrium. Going back to our example, the diffusion of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<br />
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局部热力学平衡不需要局部或全局的平稳性。换句话说,每一个小区域不需要有一个恒定的温度。然而,它确实要求每个小的局部变化缓慢到足以维持其局部麦克斯韦-波尔兹曼速度分布。全局非平衡态只有通过系统与外界的交换才能保持稳定。例如,通过在水杯中不断添加细粉冰来补偿熔化,并持续排出融水,可以保持全局稳定的静态。自然'''<font color="#ff8000">输运现象 Transport Phenomena</font>'''会使一个局部热力学平衡系统逐渐达到全局的热力学平衡。回顾我们的例子,热量的扩散将导致我们的玻璃杯水流向全局热力学平衡,在这种状态下,玻璃杯的温度是完全均匀的。<br />
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==Reservations 保留意见==<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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学识渊博的笔者在热力学领域对热力学平衡描述时,经常对他们的描述附加条件或保留意见。有些笔者含蓄地保留了或多或少的空白,以待说明。<br />
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For example, one widely cited writer, [[Herbert Callen|H. B. Callen]] writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. ''Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!''"<ref>Callen, H.B. (1960/1985), p. 15.</ref><br />
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For example, one widely cited writer, H. B. Callen writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!"<br />
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例如,一位被广泛引用的作家'''<font color="#ff8000">H.B.卡伦 H.B.Callen</font>'''在这里写道: “实际上,很少有系统处于绝对和真正的平衡状态。”他提到了放射性过程,认为它们可能需要“宇宙时间才能完成,因此通常可以忽略”。他补充道: “在实践中,平衡的标准是循环的。在操作上,如果一个系统的性质一致地用热力学理论来描述,那么它就处于平衡状态! ”<br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<ref>Beattie, J.A., Oppenheim, I. (1979), p. 3.</ref><br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<br />
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J.A.贝蒂和 I.奥本海姆写道: “坚持对平衡定义的严格解释,将排除热力学应用于实际系统的所有状态。”<br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment",<ref>Callen, H.B. (1960/1985), p. 485.</ref> and cited by Adkins as having written a "classic text",<ref>Adkins, C.J. (1968/1983), p. ''xiii''.</ref> [[Brian Pippard|A.B. Pippard]] writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<ref>Pippard, A.B. (1957/1966), p. 6.</ref><br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment", and cited by Adkins as having written a "classic text", A.B. Pippard writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<br />
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Callen引用另一位作者的话说,他给出了“学术且严谨的论述” ,Adkins引用他的话说,他写了一本“经典著作”—— '''<font color="#ff8000">A.B.皮帕德 A.B.Pippard</font>'''在文中写道: “只要时间足够长,过冷水蒸汽最终会凝结,... ..。时间可能是漫长的,也许长达10年或者更长。就大多数目的而言,只要这种迅速的变化不是人为地刺激,这些系统就可以被视为处于平衡状态。”<br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster">Münster, A. (1970), p. 53.</ref><br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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另一位作者A.Münster,写道。他观察到热核反应发生的速度非常缓慢,以至于在热力学中可以忽略不计。他评论道: “‘绝对平衡’或‘所有可想象过程的平衡’的概念没有物理意义。”他说: “ ... 我们只能考虑特定过程和确定的实验条件下的平衡。”<br />
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According to [[László Tisza|L. Tisza]]: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<ref>Tisza, L. (1966), p. 119.</ref><br />
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According to L. Tisza: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<br />
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根据'''<font color="#ff8000">L.缇莎 L.Tisza</font>'''的说法: “ ... 在讨论接近绝对零度的现象时。经典理论的绝对预测变得特别模糊,因为在非平衡状态下发生冻结是非常普遍的。”<br />
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==Definitions 定义==<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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一个系统最普遍的热力学平衡是通过与周围环境的接触,允许所有化学物质和各种能量同时通过。热力学平衡中的系统可能以均匀加速度在空间中运动,但此时不能改变其形状或大小; 因此它是由空间中的刚性体积来定义的。它可能存在于外力场中,由远远大于系统本身的外部因素决定,因此系统内的事件不会对外力场产生相当大的影响。只有当外力场是均匀的,并且确定了它的均匀加速度,或者它处于一个非均匀力场中,但是由于表面的局部力,例如机械压力,使它保持静止时,这个系统才能处于热力学平衡。<br />
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Thermodynamic equilibrium is a [[primitive notion]] of the theory of thermodynamics. According to [[Philip M. Morse|P.M. Morse]]: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are ''not'' conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments."<ref>[[Philip M. Morse|Morse, P.M.]] (1969), p. 7.</ref> This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<ref>Bailyn, M. (1994), p. 20.</ref><br />
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Thermodynamic equilibrium is a primitive notion of the theory of thermodynamics. According to P.M. Morse: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are not conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments." This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<br />
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热力学平衡是热力学理论的一个'''<font color="#ff8000">基本概念 Primitive Notion</font>'''。'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''说: “应该强调的是,存在热力学状态这一事实,以及存在由平衡态唯一指定的热力学变量这一事实,并不是从某些哲学第一原理得出的逻辑结论。这些结论不可避免地来自两个多世纪的实验。”这意味着热力学平衡不能仅仅用热力学的其他理论概念来定义。M.Bailyn提出了一个基本的热力学定律理论,它定义并假设了热力学平衡的存在。<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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热力学平衡的教科书定义通常被仔细说明,并有些保留。<br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<ref>Münster, A. (1970), p. 52.</ref><br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<br />
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例如,A. Münster写道:“当一个孤立系统中没有以可测量的速率发生状态变化时,系统处于热力学平衡状态。”这里有两项保留:系统是孤立的;任何状态的变化都是不可测量的缓慢。他通过对在室温且没有催化剂的情况下混合氧和氢的说明,讨论了第二个条件。Münster指出,描述热力学平衡状态所需要的宏观变量比给定系统任何其他状态都少。这是部分,但不完全是,因为系统内和流过系统的所有流都是零。<br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in ''equilibrium''.<ref>Haase, R. (1971), pp. 3–4.</ref><br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in equilibrium.<br />
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R. Haase's的热力学演示并不从对热力学平衡的限制开始,因为他打算考虑非平衡态热力学。他考虑一个具有时间不变性质的任意系统。他通过切断除外力场以外的所有外部影响来测试它的热力学平衡。如果在绝缘之后,没有任何变化,他说,系统处于平衡状态。<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness".<ref>Callen, H.B. (1960/1985), p. 13.</ref> This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness". This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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在一个标题为“热力学平衡”的章节中,H.B. Callen在一个段落中定义了平衡状态.他指出,它们“是由系统内部的内在因素决定的”。它们是“终端状态” ,随着时间的推移,系统会以“冰川般缓慢”的速度朝着这个终端状态演化。这个说法并没有明确,对于热力学平衡系统必须是孤立的;;Callen也没有说明他所说的“内在因素”是什么意思。<br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<ref>Adkins, C.J. (1968/1983), p. ''7''.</ref><br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<br />
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另一位教科书作者,C.J.Adkins,明确允许热力学平衡在非孤立的系统中发生。然而,他的系统在物质转移方面是封闭的。他写道: “一般来说,热力学平衡的方法包括热和类似功的形式与周围环境的相互作用。”他将这种热力学平衡与只有通过热接触才能进行能量传递的热平衡相区别。<br />
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Another textbook author, [[J.R. Partington]], writes: "(i) ''An equilibrium state is one which is independent of time''." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..."<ref>Partington, J.R. (1949), p. 161.</ref> This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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Another textbook author, J.R. Partington, writes: "(i) An equilibrium state is one which is independent of time." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..." This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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另一位教科书作者'''<font color="#ff8000">J.R.帕廷顿 J.R.Partington</font>'''写道: “(i)平衡状态是独立于时间的状态。”但是,在提到“只是明显处于平衡状态”的系统时,他补充说: “这样的系统处于‘虚假平衡’状态。帕廷顿的陈述没有明确指出平衡是指一个孤立的系统。和Münster一样,Partington也指的是氧和氢的混合物。他补充说:“在一个真正的平衡状态,任何影响状态的外部条件的微小变化都会产生一个微小的状态变化... ... ”这个条件意味着热力学平衡必须在小的扰动下保持稳定; 这个要求对于热力学平衡的严格意义是必不可少的。<br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, ''thermodynamic—equilibrium.''"<ref>Crawford, F.H. (1963), p. 5.</ref><br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, thermodynamic—equilibrium."<br />
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在F.H.Crawford的一本学生教科书中,有一个标题为“热力学平衡”的章节。它区分了几种流动的驱动因素,然后说: “这些是孤立系统明显普遍趋向于完全机械、热、化学和电力状态的例子——或者简单地说,热力学平衡状态。”<br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in ''equilibrium''."<ref>Buchdahl, H.A. (1966), p. 8.</ref> Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being ''in equilibrium'' so long as experimental tests show that 'slow' transitions are in effect reversible."<ref>Buchdahl, H.A. (1966), p. 111.</ref> It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<ref>Adkins, C.J. (1968/1983), p. 8.</ref><br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in equilibrium." Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being in equilibrium so long as experimental tests show that 'slow' transitions are in effect reversible." It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<br />
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H.A. Buchdahl的一本关于经典热力学的专著考虑了热力学系统的平衡,而实际上并没有写热力学平衡一词。Buchdahl在提到封闭的物质交换系统时写道: “如果一个系统处于一个适当的静态状态,那么它将被称为处于平衡状态。”出于热力学描述的目的,Buchdahl的专著也讨论了非晶态玻璃。它说: “更准确地说,只要实验测试表明‘慢’跃迁实际上是可逆的,玻璃就可以被认为处于平衡状态。”通常来说不会将这一条件作为热力学平衡定义的一部分,而是假定相反的情况:如果热力学平衡中的一个物体受到足够慢的过程的影响,则该过程可被视为足够接近可逆,并且该物体在过程中足够接近热力学平衡。<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of ''contact equilibrium''. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by [[Constantin Carathéodory|C. Carathéodory]], and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster" /> Thermodynamic equilibrium for an open system means that, with respect to every relevant kind of selectively permeable wall, contact equilibrium exists when the respective intensive parameters of the system and surroundings are equal.<ref name="Nster_a" /> This definition does not consider the most general kind of thermodynamic equilibrium, which is through unselective contacts. This definition does not simply state that no current of matter or energy exists in the interior or at the boundaries; but it is compatible with the following definition, which does so state.<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of contact equilibrium. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by C. Carathéodory, and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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通过引入接触平衡的概念,A. Münster仔细地扩展了孤立系统热力学平衡的定义。这指定了在考虑非孤立系统的热力学平衡时允许的特定过程,并特别关心开放系统,这些开放系统可能从周围环境获得或丢失物质。感兴趣的系统和周围系统之间的接触平衡,通过一种特殊的壁与之接触,其余的连接系统是孤立的。这种特殊类型的壁也被'''<font color="#ff8000">C.喀喇西奥多里 C.Carathéodory</font>'''考虑过,其他作家也提到过。它们具有选择渗透性。它们可能只对机械功有渗透性,或者只对热有渗透性,或者只对某种特定的化学物质有渗透性。每个接触平衡定义了一个强度参数; 例如,只能透热的壁定义了一个经验温度。对于感兴趣的体系中每一种化学成分,都可以存在接触平衡。在接触平衡中,尽管有可能通过选择性渗透壁进行交换,但是感兴趣的系统是不变的,好像它处在孤立的热力学平衡。这个方案遵循的一般规则是: “ ... ... 我们只能考虑特定过程和特定实验条件下的平衡。”<br />
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[[Mark Zemansky|M. Zemansky]] also distinguishes mechanical, chemical, and thermal equilibrium. He then writes: "When the conditions for all three types of equilibrium are satisfied, the system is said to be in a state of thermodynamic equilibrium".<ref>[[Mark Zemansky|Zemansky, M.]] (1937/1968), p. 27.</ref><br />
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'''<font color="#ff8000">M.泽曼斯基 M.Zemansky</font>'''还区分了力学、化学和热平衡。他接着写道: “当这三种均衡的条件都满足时,系统就处于热力学平衡状态。”<br />
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P.M. Morse writes that thermodynamics is concerned with "states of thermodynamic equilibrium". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<br />
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[[Philip M. Morse|P.M. Morse]] writes that thermodynamics is concerned with "''states of thermodynamic equilibrium''". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<ref>[[Philip M. Morse|Morse, P.M.]] (1969), pp. 6, 37.</ref><br />
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'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''写道,热力学关注的是“热力学平衡状态”。在讨论物体与周围热源之间的热量传递时,他也使用了“热平衡”这个短语,尽管没有明确定义一个特殊的术语“热平衡”<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "full thermodynamic equilibrium state".<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "''full'' thermodynamic equilibrium state".<ref>Waldram, J.R. (1985), p. 5.</ref><br />
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J.R. Waldram写到了“一个明确的热力学状态”。他将一个系统定义为“当其观测量随时间停止变化时”的“热平衡”。但是在这个定义之下不久,他写到一块玻璃还没有达到“完全的热力学平衡状态”。<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, thermodynamic equilibrium is said to exist." He is not here considering the presence of an external force field.<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, ''thermodynamic equilibrium'' is said to exist." He is not here considering the presence of an external force field.<ref>Bailyn, M. (1994), p. 21.</ref><br />
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考虑到平衡状态,M.Bailyn写道: “每个强度变量都有自己的平衡类型。”然后他定义了热平衡、力学平衡和物质平衡。因此,他写道: “如果所有的强度变量都是一致的,那么热力学平衡就是存在的。”他在这里没有考虑外力场的存在。<br />
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J.G. Kirkwood and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of thermodynamic equilibrium if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<br />
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[[John Gamble Kirkwood|J.G. Kirkwood]] and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of ''thermodynamic equilibrium'' if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<ref>Kirkwood, J.G., Oppenheim, I. (1961), p. 2</ref><br />
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'''<font color="#ff8000">J.G.柯克伍德 J.G.Kirkwood</font>'''和 I.Oppenheim 将热力学平衡定义为: “一个系统处于热力学平衡状态,如果,在实验的时间内,(a)它强度特性与时间无关,(b)它的内部或与周围环境的边界处没有物质或能量流。”显然,他们没有把定义限制在孤立的或封闭的系统。它们不讨论“缓慢”发生变化的可能性,并且超出了分配给实验的时间范围。他们注意到,对于两个相接触的系统,存在一个强度性质的小子类,如果这个小子类的所有子类都相等,那么所有各自的强度性质都相等。只要满足其他一些条件,热力学平衡状态可以由这个子类定义。<br />
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==Characteristics of a state of internal thermodynamic equilibrium 内部热力学平衡状态的特征==<br />
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===Homogeneity in the absence of external forces 在没有外力的情况下的均匀性===<br />
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A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous.<ref name="Planck 1903 3"/> This means that the material in any small volume element of the system can be interchanged with the material of any other geometrically congruent volume element of the system, and the effect is to leave the system thermodynamically unchanged. In general, a strong external force field makes a system of a single phase in its own internal thermodynamic equilibrium inhomogeneous with respect to some [[Intensive and extensive properties|intensive variables]]. For example, a relatively dense component of a mixture can be concentrated by centrifugation.<br />
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在没有外力的情况下,由单一相组成的热力学系统,在其自身的内部热力学平衡中是均匀的。这意味着系统中任何小体积单元中的材料可以与系统中任何其他几何相等的体积单元中的材料互换,其效果是使系统在热力学上保持不变。一般来说,一个强外力场使得一个单相系统在其自身的内部热力学平衡中对于一些'''<font color="#ff8000">强度量 Intensive Variable</font>'''是不均匀的。例如,可以通过离心来浓缩混合物中相对密度较大的组分。<br />
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===Uniform temperature 均匀温度===<br />
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Such equilibrium inhomogeneity, induced by external forces, does not occur for the intensive variable [[temperature]]. According to [[Edward A. Guggenheim|E.A. Guggenheim]], "The most important conception of thermodynamics is temperature."<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), p.5.</ref> Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface."<ref name="Planck 1903 3">[[Max Planck|Planck, M.]] (1897/1927), p.3.</ref> As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.<br />
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这种由外力引起的平衡不均匀性,对于强度量'''<font color="#ff8000">温度 Temperature</font>'''不会发生。'''<font color="#ff8000">E.A.古根海姆 E.A. Guggenheim</font>'''认为,“热力学最重要的概念是温度。“Planck在介绍他的论文时,简要叙述了热、温度和热平衡,然后宣布: ”在下文中,我们将主要讨论任何形式的均匀、各向同性的物体,它们的物质具有相同的温度和密度,并受到到处垂直于表面的均匀压力的作用。和Carathéodory 一样,Planck将表面效应、外场和各向异性晶体排除在外。虽然Planck提到了温度,但并没有明确提到热力学平衡的概念。相比之下,Carathéodory关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ,虽然没有明确地使用短语‘热力学平衡’ ,也没有明确地假设存在一个温度来定义它。<br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform.<ref name="Planck 1914 40"/> This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers.<ref>Gibbs, J.W. (1876/1878), pp. 144-150.</ref><ref>[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966), pp. 127–130.</ref><ref>Münster, A. (1970), pp. 309–310.</ref><ref>Bailyn, M. (1994), pp. 254-256.</ref><ref>{{cite journal | last1 = Verkley | first1 = W.T.M. | last2 = Gerkema | first2 = T. | year = 2004 | title = On maximum entropy profiles | journal = J. Atmos. Sci. | volume = 61 | issue = 8| pages = 931–936 | doi=10.1175/1520-0469(2004)061<0931:omep>2.0.co;2| bibcode = 2004JAtS...61..931V | doi-access = free }}</ref><ref>{{cite journal | last1 = Akmaev | first1 = R.A. | year = 2008 | title = On the energetics of maximum-entropy temperature profiles | url = | journal = Q. J. R. Meteorol. Soc. | volume = 134 | issue = 630| pages = 187–197 | doi=10.1002/qj.209| bibcode = 2008QJRMS.134..187A }}</ref> Considerations of kinetic theory or statistical mechanics also support this statement.<ref>Maxwell, J.C. (1867).</ref><ref>Boltzmann, L. (1896/1964), p. 143.</ref><ref>Chapman, S., Cowling, T.G. (1939/1970), Section 4.14, pp. 75–78.</ref><ref>[[J. R. Partington|Partington, J.R.]] (1949), pp. 275–278.</ref><ref>{{cite journal | last1 = Coombes | first1 = C.A. | last2 = Laue | first2 = H. | year = 1985 | title = A paradox concerning the temperature distribution of a gas in a gravitational field | url = | journal = Am. J. Phys. | volume = 53 | issue = 3| pages = 272–273 | doi=10.1119/1.14138| bibcode = 1985AmJPh..53..272C }}</ref><ref>{{cite journal | last1 = Román | first1 = F.L. | last2 = White | first2 = J.A. | last3 = Velasco | first3 = S. | year = 1995 | title = Microcanonical single-particle distributions for an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 16 | issue = 2| pages = 83–90 | doi=10.1088/0143-0807/16/2/008| bibcode = 1995EJPh...16...83R }}</ref><ref>{{cite journal | last1 = Velasco | first1 = S. | last2 = Román | first2 = F.L. | last3 = White | first3 = J.A. | year = 1996 | title = On a paradox concerning the temperature distribution of an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 17 | issue = | pages = 43–44 | doi=10.1088/0143-0807/17/1/008}}</ref><br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform. This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers. Considerations of kinetic theory or statistical mechanics also support this statement.<br />
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热力学平衡系统内的温度在时间和空间上都是均匀的。在一个处于内部热力学平衡的系统中,不存在净的内部宏观流动。特别是,这意味着系统的所有局部都处于相互辐射交换平衡。这意味着系统的温度在空间上是均匀的。这在所有情况下都是如此,包括那些非均匀外力场。对于外部施加的引力场,这可以使用拉格郎日乘子法通过变分的计算在宏观热力学术语中证明。动力学理论或统计力学也支持这种说法。<br />
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In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium.<ref name="Fitts 43"/><br />
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为了使一个系统处于它自己的内部热力学平衡状态,它必须处于它自己的内部热平衡状态是必要不充分的; 一个系统在到达内部热平衡之前到达内部力学平衡是可能的。<br />
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===Number of real variables needed for specification 规范所需的实变量数目===<br />
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In his exposition of his scheme of closed system equilibrium thermodynamics, C. Carathéodory initially postulates that experiment reveals that a definite number of real variables define the states that are the points of the manifold of equilibria.<ref name="Caratheodory" /> In the words of Prigogine and Defay (1945): "It is a matter of experience that when we have specified a certain number of macroscopic properties of a system, then all the other properties are fixed."<ref>Prigogine, I., Defay, R. (1950/1954), p. 1.</ref><ref>Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005), p. 4.</ref> As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.<br />
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在他关于封闭系统平衡态热力学方案的论述中,C.Carathéodory 最初假定实验揭示了一定数量的实变量定义了作为平衡态流形点的状态。用 Prigogine 和 Defay (1945)的话说: “这是一个经验问题,当我们确定了一个系统一定数量的宏观属性时,那么所有其他属性都是固定的”。如上所述,A. Münster认为,定义热力学平衡所需的变量数量相对于给定孤立系统的任何状态来说都是最少的。如上所述,J.G. Kirkwood 和 I. Oppenheim 指出,热力学平衡状态可以由一个特殊子类的强度变量来定义,该子类中有一定数量的成员。<br />
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If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.<br />
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如果热力学平衡位于一个外力场中,那么通常只有温度在空间上是均匀的。如果外力场非零,温度以外的强度变量通常是不均匀的。在这种情况下,一般需要附加变量来描述空间非均匀性。<br />
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===Stability against small perturbations 对小扰动的稳定性===<br />
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As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.<br />
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如上所述,J.R. Partington 指出热力学平衡状态在小的瞬态扰动下是稳定的。如果没有这个条件,一般来说,研究热力学平衡系统的实验就会遇到严重的困难。<br />
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===Approach to thermodynamic equilibrium within an isolated system 孤立系统中的热力学平衡===<br />
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When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium. Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<br />
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When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium.<ref name="Fitts 43">Fitts, D.D. (1962), p. 43.</ref> Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<ref>Denbigh, K.G. (1951), p. 42.</ref><br />
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当一个物质体从不均匀的非平衡状态或化学非平衡状态开始,然后被孤立,它会自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如,在这种演化的许多情况下,内部力学平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是,在这种演化的许多情况下,热平衡的发展要比化学平衡快得多。<br />
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===Fluctuations within an isolated system in its own internal thermodynamic equilibrium 孤立系统内部热力学平衡的涨落===<br />
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In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
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在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
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To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics.<ref>Tschoegl, N.W. (2000). ''Fundamentals of Equilibrium and Steady-State Thermodynamics'', Elsevier, Amsterdam, {{ISBN|0-444-50426-5}}, p. 21.</ref> But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
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To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics. But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
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考虑孤立热力学系统中的涨落概念,一个方便的例子是由其内能、体积和质量组成等广延量表示的系统。根据定义,它们是不随时间变化的。根据定义,这些量与它们的共轭状态强度函数的时不变名义值相结合,包括逆温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广延量的值,不足以提供这些名义值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
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It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.<br />
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可以承认,在重复测量这些共轭强度状态函数时,发现它们的值随时间略有不同。这种可变性被认为是由于内部涨落。不同测量值平均到其名义值。<br />
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If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<ref>Buchdahl, H.A. (1966), p. 16.</ref><br />
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If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<br />
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如果系统真的像经典热力学所假定的那样是宏观的,那么系统的涨落很小以至于宏观上无法检测到。这就是所谓的热力学极限。实际上,物质的分子性质和动量转移的量子性质由于它们太小而看不见,已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中,平衡的涨落概念是不存在的。”<br />
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If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
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如果系统被重复细分,最终产生的系统足够小,可以表现出明显的涨落。这是一个介观层面的研究。涨落则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
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If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在涨落过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,并且需要量子统计力学。涨落可以变得相对占主导地位,测量问题变得重要。<br />
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The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
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"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有随时间变化趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的名义值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微涨落期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。除非已知属于平衡状态的名义值,否则根据单一的度量无法进行判断。<br />
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=== Thermal equilibrium 热平衡===<br />
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{{Main|Thermal equilibrium}}<br />
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An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process."<ref>Eu, B.C. (2002), page 13.</ref> This illustrates the importance for thermodynamics of the concept of temperature.<br />
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热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他考虑两个系统在热接触,一个是温度计,另一个是一个有几个不可逆过程的系统,产生非零的流; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在感兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。因此存在热平衡但是不存在热力学平衡。因此,Eu提出,即使在没有热力学平衡的情况下,也可以考虑应用热力学第零定律; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
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[[Thermal equilibrium]] is achieved when two systems in [[thermal contact]] with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<ref>[[Raj Pathria|R. K. Pathria]], 1996</ref><br />
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当两个相互'''<font color="#ff8000">热接触 Thermal Contact</font>'''的系统不再有净能量交换时,就会产生'''<font color="#ff8000">热平衡 Thermal Equilibrium</font>'''。因此,如果两个系统处于热平衡,那么它们的温度是相同的。<br />
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Thermal equilibrium occurs when a system's [[macroscopic]] thermal observables have ceased to change with time. For example, an [[ideal gas]] whose [[Distribution function (physics)|distribution function]] has stabilised to a specific [[Maxwell–Boltzmann distribution]] would be in thermal equilibrium. This outcome allows a single [[temperature]] and [[pressure]] to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<ref>de Groot, S.R., Mazur, P. (1962), p. 44.</ref><br />
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当一个系统的'''<font color="#ff8000">宏观 Macroscopic</font>'''热观测值不再随时间变化时,就会出现热平衡。例如,一种'''<font color="#ff8000">分布函数 Distribution Function</font>'''稳定到一个特定的'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''的'''<font color="#ff8000">理想气体 Ideal Gas</font>'''即处于热平衡状态。这个结果可以用单一的'''<font color="#ff8000">温度 Temperature</font>'''和'''<font color="#ff8000">压力 Pressure</font>'''来描述整个系统。对于一个孤立的物体来说,在达到热平衡之前达到力学平衡是很可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
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==Non-equilibrium 非平衡==<br />
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{{Main|Non-equilibrium thermodynamics}}<br />
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A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<ref>de Groot, S.R., Mazur, P. (1962), p. 43.</ref><br />
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一个系统内部状态的热力学平衡应该区别于一个非孤立系统的定态,后者的热力学参数在时间上不变,但是在系统内外有非零的宏观流,这些流在时间上是常数。<br />
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Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更一般的概念。许多自然系统在今天仍然超出了目前已知的宏观热力学方法的范围。<br />
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Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle.<ref>{{cite book|last1=Ziegler|first1=H.|title=An Introduction to Thermomechanics.|date=1983|location=North Holland, Amsterdam.}}</ref><ref>{{cite journal|last1=Onsager|first1=Lars|title=Reciprocal Relations in Irreversible Processes|journal=Phys. Rev.|date=1931|volume=37|issue=4|doi=10.1103/PhysRev.37.405|bibcode=1931PhRv...37..405O|pages=405–426|doi-access=free}}</ref> It states that a non-equilibrium system evolves such as to maximize its entropy production.<ref>{{cite book|last1=Kleidon|first1=A.|last2=et.|first2=al.|title=Non-equilibrium Thermodynamics and the Production of Entropy.|date=2005|edition=Heidelberg: Springer.}}</ref><ref>{{cite journal|last1=Belkin|first1=Andrey|last2=et.|first2=al.|title=Self-Assembled Wiggling Nano-Structures and the Principle of Maximum Entropy Production|journal=Sci. Rep.|doi=10.1038/srep08323|bibcode=2015NatSR...5E8323B|pmc=4321171|pmid=25662746|volume=5|year=2015|page=8323}}</ref><br />
<br />
规定哪些系统远离平衡的规则也是有争议的。这些系统的指导原则之一就是最大熵产生原则。它指出,非平衡系统进行演化以最大化其熵产生。<br />
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==See also ==<br />
<br />
{{Portal|Chemistry}}<br />
<br />
;Thermodynamic models 热力学模型<br />
<br />
{{colbegin}}<br />
<br />
* [[Non-random two-liquid model]] (NRTL model) - Phase equilibrium calculations 非随机两液模型(NRTL 模型)-相平衡计算<br />
<br />
* [[UNIQUAC]] model - Phase equilibrium calculations UNIQUAC 模型-相平衡计算<br />
<br />
* [[Time crystal]] 时间晶体<br />
<br />
{{colend}}<br />
<br />
;Topics in control theory 控制理论主题<br />
<br />
{{colbegin}}<br />
<br />
* [[Steady state]] 稳态<br />
<br />
* [[Transient state]] 瞬态<br />
<br />
* [[Coefficient diagram method]] 系数图法<br />
<br />
* [[Control reconfiguration]] 控制重构<br />
<br />
* [[Cut-insertion theorem]] 切入定理<br />
<br />
* [[Feedback]] 反馈<br />
<br />
* [[H infinity]] H 无限<br />
<br />
* [[Hankel singular value]] 汉克尔奇异值<br />
<br />
* [[Krener's theorem]] 克雷纳定理<br />
<br />
* [[Lead-lag compensator]] 超前滞后补偿器<br />
<br />
* [[Minor loop feedback]] 小循环反馈<br />
<br />
* [[Minor loop feedback|Multi-loop feedback]] 小循环反馈 | 多循环反馈<br />
<br />
* [[Positive systems]] 正向系统<br />
<br />
* [[Radial basis function]] 径向基底函数<br />
<br />
Other related topics<br />
<br />
其他相关话题<br />
<br />
* [[Root locus]] 根轨迹<br />
<br />
* [[Signal-flow graph]]s 信号流图<br />
<br />
* [[Stable polynomial]] 稳定多项式<br />
<br />
* [[State space representation]] 状态空间<br />
<br />
* [[Underactuation]] 欠驱动<br />
<br />
* [[Youla–Kucera parametrization]] 尤拉-库切拉参数化<br />
<br />
* [[Markov chain approximation method]] 马尔可夫链近似法<br />
<br />
{{colend}}<br />
<br />
;Other related topics<br />
其他相关话题<br />
<br />
{{colbegin}}<br />
<br />
* [[Automation and remote control]] 自动化和远程控制<br />
<br />
* [[Bond graph]] 键合图<br />
<br />
* [[Control engineering]] 控制工程<br />
<br />
* [[Control–feedback–abort loop]] 控制-反馈-中止循环<br />
<br />
* [[Controller (control theory)]] 控制器(控制理论)<br />
<br />
* [[Cybernetics]] 控制论<br />
<br />
* [[Intelligent control]] 智能控制<br />
<br />
* [[Mathematical system theory]] 数学系统论<br />
<br />
* [[Negative feedback amplifier]] 负反馈放大器<br />
<br />
* [[People in systems and control]] 系统和控制中的人<br />
<br />
* [[Perceptual control theory]] 知觉控制理论<br />
<br />
* [[Systems theory]] 系统论<br />
<br />
* [[Time scale calculus]] 时间尺度演算<br />
<br />
{{colend}}<br />
<br />
<br />
<br />
== 编者推荐 ==<br />
===集智文章推荐===<br />
<br />
====[https://swarma.org/?p=21322 什么是非平衡态热力学 | 集智百科]====<br />
非平衡态热力学 Non-equilibrium thermodynamics 是热力学的一个分支,研究某些不处于热力学平衡中的物理系统<br />
<br />
<br />
<br />
<br />
==General references==<br />
<br />
* Cesare Barbieri (2007) ''Fundamentals of Astronomy''. First Edition (QB43.3.B37 2006) CRC Press {{ISBN|0-7503-0886-9}}, {{ISBN|978-0-7503-0886-1}}<br />
<br />
* Hans R. Griem (2005) ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}<br />
<br />
* C. Michael Hogan, Leda C. Patmore and Harry Seidman (1973) ''Statistical Prediction of Dynamic Thermal Equilibrium Temperatures using Standard Meteorological Data Bases'', Second Edition (EPA-660/2-73-003 2006) United States Environmental Protection Agency Office of Research and Development, Washington, D.C. [http://library.wur.nl/WebQuery/catalog/lang/1851848]<br />
<br />
* F. Mandl (1988) ''Statistical Physics'', Second Edition, John Wiley & Sons<br />
<br />
<br />
<br />
==References==<br />
<br />
{{Reflist|colwidth=35em}}<br />
<br />
<br />
<br />
==Cited bibliography==<br />
<br />
<br />
<br />
*Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', third edition, McGraw-Hill, London, {{ISBN|0-521-25445-0}}.<br />
<br />
*Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, {{ISBN|0-88318-797-3}}.<br />
<br />
*Beattie, J.A., Oppenheim, I. (1979). ''Principles of Thermodynamics'', Elsevier Scientific Publishing, Amsterdam, {{ISBN|0-444-41806-7}}.<br />
<br />
*[[Ludwig Boltzmann|Boltzmann, L.]] (1896/1964). ''Lectures on Gas Theory'', translated by S.G. Brush, University of California Press, Berkeley.<br />
<br />
*Buchdahl, H.A. (1966). ''The Concepts of Classical Thermodynamics'', Cambridge University Press, Cambridge UK.<br />
<br />
*[[Herbert Callen|Callen, H.B.]] (1960/1985). ''Thermodynamics and an Introduction to Thermostatistics'', (1st edition 1960) 2nd edition 1985, Wiley, New York, {{ISBN|0-471-86256-8}}.<br />
<br />
*[[Constantin Carathéodory|Carathéodory, C.]] (1909). [https://web.archive.org/web/20160304213645/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0067&DMDID=DMDLOG_0033&L=1 Untersuchungen über die Grundlagen der Thermodynamik], ''[[Mathematische Annalen]]'', '''67''': 355–386. A translation may be found [http://neo-classical-physics.info/uploads/3/0/6/5/3065888/caratheodory_-_thermodynamics.pdf here]. Also a mostly reliable [https://books.google.com/books?id=xwBRAAAAMAAJ&q=Investigation+into+the+foundations translation is to be found] at Kestin, J. (1976). ''The Second Law of Thermodynamics'', Dowden, Hutchinson & Ross, Stroudsburg PA.<br />
<br />
*[[Sydney Chapman (mathematician)|Chapman, S.]], [[Thomas George Cowling|Cowling, T.G.]] (1939/1970). ''The Mathematical Theory of Non-uniform gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases'', third edition 1970, Cambridge University Press, London.<br />
<br />
*Crawford, F.H. (1963). ''Heat, Thermodynamics, and Statistical Physics'', Rupert Hart-Davis, London, Harcourt, Brace & World, Inc.<br />
<br />
*de Groot, S.R., Mazur, P. (1962). ''Non-equilibrium Thermodynamics'', North-Holland, Amsterdam. Reprinted (1984), Dover Publications Inc., New York, {{ISBN|0486647412}}.<br />
<br />
*Denbigh, K.G. (1951). ''Thermodynamics of the Steady State'', Methuen, London.<br />
<br />
*Eu, B.C. (2002). ''Generalized Thermodynamics. The Thermodynamics of Irreversible Processes and Generalized Hydrodynamics'', Kluwer Academic Publishers, Dordrecht, {{ISBN|1-4020-0788-4}}.<br />
<br />
*Fitts, D.D. (1962). ''Nonequilibrium thermodynamics. A Phenomenological Theory of Irreversible Processes in Fluid Systems'', McGraw-Hill, New York.<br />
<br />
*[[Josiah Willard Gibbs|Gibbs, J.W.]] (1876/1878). On the equilibrium of heterogeneous substances, ''Trans. Conn. Acad.'', '''3''': 108–248, 343–524, reprinted in ''The Collected Works of J. Willard Gibbs, Ph.D, LL. D.'', edited by W.R. Longley, R.G. Van Name, Longmans, Green & Co., New York, 1928, volume 1, pp.&nbsp;55–353.<br />
<br />
*Griem, H.R. (2005). ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}.<br />
<br />
*[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', fifth revised edition, North-Holland, Amsterdam.<br />
<br />
*Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of ''Thermodynamics'', pages 1–97 of volume 1, ed. W. Jost, of ''Physical Chemistry. An Advanced Treatise'', ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081.<br />
<br />
*[[John Gamble Kirkwood|Kirkwood, J.G.]], Oppenheim, I. (1961). ''Chemical Thermodynamics'', McGraw-Hill Book Company, New York.<br />
<br />
*Landsberg, P.T. (1961). ''Thermodynamics with Quantum Statistical Illustrations'', Interscience, New York.<br />
<br />
*{{cite journal |last1=Lieb |first1=E. H. |last2=Yngvason |first2=J. |year=1999 |title=The Physics and Mathematics of the Second Law of Thermodynamics |journal=Phys. Rep. |volume=310 |issue= 1|pages=1–96 |doi= 10.1016/S0370-1573(98)00082-9|arxiv = cond-mat/9708200 |bibcode = 1999PhR...310....1L |s2cid=119620408 }}<br />
<br />
*Levine, I.N. (1983), ''Physical Chemistry'', second edition, McGraw-Hill, New York, {{ISBN|978-0072538625}}.<br />
<br />
*{{cite journal | last1 = Maxwell | first1 = J.C. | authorlink = James Clerk Maxwell | year = 1867 | title = On the dynamical theory of gases | url = | journal = Phil. Trans. Roy. Soc. London | volume = 157 | issue = | pages = 49–88 }}<br />
<br />
*[[Philip M. Morse|Morse, P.M.]] (1969). ''Thermal Physics'', second edition, W.A. Benjamin, Inc, New York.<br />
<br />
*Münster, A. (1970). ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London.<br />
<br />
*[[J.R. Partington|Partington, J.R.]] (1949). ''An Advanced Treatise on Physical Chemistry'', volume 1, ''Fundamental Principles. The Properties of Gases'', Longmans, Green and Co., London.<br />
<br />
*[[Brian Pippard|Pippard, A.B.]] (1957/1966). ''The Elements of Classical Thermodynamics'', reprinted with corrections 1966, Cambridge University Press, London.<br />
<br />
* [[Max Planck|Planck. M.]] (1914). [https://archive.org/details/theoryofheatradi00planrich ''The Theory of Heat Radiation''], a translation by Masius, M. of the second German edition, P. Blakiston's Son & Co., Philadelphia.<br />
<br />
*[[Ilya Prigogine|Prigogine, I.]] (1947). ''Étude Thermodynamique des Phénomènes irréversibles'', Dunod, Paris, and Desoers, Liège.<br />
<br />
*[[Ilya Prigogine|Prigogine, I.]], Defay, R. (1950/1954). ''Chemical Thermodynamics'', Longmans, Green & Co, London.<br />
<br />
*Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005). ''Physical Chemistry'', fourth edition, Wiley, Hoboken NJ.<br />
<br />
*[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966). ''Elements of Thermodynamics'', Addison-Wesley Publishing, Reading MA.<br />
<br />
*{{cite journal|last=Thomson|first=W.|author-link=William Thomson, 1st Baron Kelvin|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Transactions of the Royal Society of Edinburgh|date=March 1851|volume=XX|issue=part II|pages=261–268; 289–298}} Also published in {{cite journal|last=Thomson|first=W.|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Phil. Mag. |date=December 1852 |volume=IV |series=4 |issue=22 |pages=8–21 |url=https://archive.org/details/londonedinburghp04maga |accessdate=25 June 2012}}<br />
<br />
*[[László Tisza|Tisza, L.]] (1966). ''Generalized Thermodynamics'', M.I.T Press, Cambridge MA.<br />
<br />
*[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963). ''Lectures in Statistical Mechanics'', American Mathematical Society, Providence RI.<br />
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*Waldram, J.R. (1985). ''The Theory of Thermodynamics'', Cambridge University Press, Cambridge UK, {{ISBN|0-521-24575-3}}.<br />
<br />
*[[Mark Zemansky|Zemansky, M.]] (1937/1968). ''Heat and Thermodynamics. An Intermediate Textbook'', fifth edition 1967, McGraw–Hill Book Company, New York.<br />
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<br />
<br />
== External links ==<br />
<br />
Category:Equilibrium chemistry<br />
<br />
类别: 平衡化学<br />
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*[http://ads.harvard.edu/books/1989fsa..book/AbookC15.pdf Breakdown of Local Thermodynamic Equilibrium] George W. Collins, The Fundamentals of Stellar Astrophysics, Chapter 15<br />
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Category:Thermodynamic cycles<br />
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类别: 热力循环<br />
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*[http://spiff.rit.edu/classes/phys440/lectures/lte/lte.html Thermodynamic Equilibrium, Local and otherwise] lecture by Michael Richmond<br />
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Category:Thermodynamic processes<br />
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类别: 热力学过程<br />
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*[http://journals.ametsoc.org/doi/abs/10.1175/1520-0469%281970%29027%3C0711:NLTEIC%3E2.0.CO%3B2 Non-Local Thermodynamic Equilibrium in Cloudy Planetary Atmospheres] Paper by R. E. Samueison quantifying the effects due to non-LTE in an atmosphere<br />
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Category:Thermodynamic systems<br />
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类别: 热力学系统<br />
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*[http://scienceworld.wolfram.com/physics/LocalThermodynamicEquilibrium.html Local Thermodynamic Equilibrium]<br />
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Category:Thermodynamics<br />
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分类: 热力学<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Thermodynamic equilibrium]]. Its edit history can be viewed at [[平衡热力学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%B9%B3%E8%A1%A1%E7%83%AD%E5%8A%9B%E5%AD%A6&diff=21698平衡热力学2021-02-09T08:08:23Z<p>Jxzhou:/* Thermal equilibrium */</p>
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<div>此词条暂由小竹凉翻译,翻译字数共5339,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{short description|State of thermodynamic system(s) where no net macroscopic flow of matter or energy occurs}}<br />
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'''Thermodynamic equilibrium''' is an [[axiomatic]] concept of [[thermodynamics]]. It is an internal [[State variables|state]] of a single [[thermodynamic system]], or a relation between several thermodynamic systems connected by more or less permeable or impermeable [[Thermodynamic system#Walls|walls]]. In thermodynamic equilibrium there are no net [[macroscopic]] [[Flow (mathematics)|flows]] of [[matter]] or of [[energy]], either within a system or between systems. <br />
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Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium there are no net macroscopic flows of matter or of energy, either within a system or between systems. <br />
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'''热力学平衡'''是'''<font color="#ff8000">热力学 Thermodynamics</font>'''的一个'''<font color="#ff8000">不言自明的 Axiomatic</font>'''概念。它是单个'''<font color="#ff8000">热力学系统 Thermodynamic System</font>'''的内部'''<font color="#ff8000">状态 State</font>''',或者是几个热力学系统之间通过或多或少的渗透或不渗透的'''<font color="#ff8000">壁 Wall</font>'''连接的关系。无论是在一个系统内还是在系统之间,在热力学平衡中不存在'''<font color="#ff8000">物质 Matter</font>'''或'''<font color="#ff8000">能量 Energy</font>'''的净'''<font color="#ff8000">宏观 Macroscopic</font>''' '''<font color="#ff8000">流动 Flow</font>'''。<br />
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In a system that is in its own state of internal thermodynamic equilibrium, no [[macroscopic]] change occurs. <br />
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In a system that is in its own state of internal thermodynamic equilibrium, no macroscopic change occurs. <br />
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在一个处于内部热力学平衡状态的系统中,不会发生'''<font color="#ff8000">宏观 Macroscopic</font>'''变化。<br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual [[Thermal equilibrium|thermal]], [[Mechanical equilibrium|mechanical]], [[Chemical equilibrium|chemical]], and [[Radiative equilibrium|radiative]] equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a [[thermodynamic operation]]. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a thermodynamic operation. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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相互热力学平衡的体系同时处于互相之间的'''<font color="#ff8000">热 Thermal</font>'''平衡、'''<font color="#ff8000">力学 Mechanical</font>'''平衡、'''<font color="#ff8000">化学 Chemical</font>'''平衡和'''<font color="#ff8000">辐射 Radiative</font>'''平衡。系统可以处于其中一种相互平衡状态,尽管其他状态未平衡。在热力学平衡中所有的平衡同时并且无限期地保持,直到被'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''打破。在一个宏观平衡中,微观交换是完全或几乎完全平衡的;这是对宏观平衡概念的物理解释。<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform [[temperature]]. Its [[Intensive and extensive properties|intensive properties]], other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform temperature. Its intensive properties, other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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一个处于内部热力学状态平衡的热力学系统具有空间均匀的'''<font color="#ff8000">温度 Temperature</font>'''。除了温度以外,它的'''<font color="#ff8000">强度性质 Intensive Properties</font>'''可以由于周围环境施加的不变的长程力场而导致空间不均匀性。<br />
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In systems that are at a state of [[non-equilibrium]] there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a '''meta-stable equilibrium'''.<br />
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In systems that are at a state of non-equilibrium there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a meta-stable equilibrium.<br />
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相比之下,处于'''<font color="#ff8000">非平衡状态 non-equilibrium</font>'''的系统中有物质或能量的净流动。如果这些变化可以在一个还没有发生的系统中被触发,那么这个系统就被称为处于一个'''亚稳定的平衡状态'''。<br />
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Though not a widely named a "law," it is an [[axiom]] of thermodynamics that there exist states of thermodynamic equilibrium. The [[second law of thermodynamics]] states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the [[entropy|entropies]] of the portions.<br />
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Though not a widely named a "law," it is an axiom of thermodynamics that there exist states of thermodynamic equilibrium. The second law of thermodynamics states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the entropies of the portions.<br />
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虽然不是一个广泛命名的“定律” ,但存在热力学平衡状态是一个热力学'''<font color="#ff8000">公理 Axiom</font>'''。'''<font color="#ff8000">热力学第二定律 second law of thermodynamics</font>'''指出,当一个物质体从一个平衡状态开始,在这个状态中,它的一部分被或多或少渗透或不渗透的分区保持在不同的状态,并且是孤立的,热力学操作移除分区或使分区更具渗透性,然后它会自发地达到自己内部热力学平衡的新状态,并伴随着部分'''<font color="#ff8000">熵 Entropy</font>'''的总和增加。<br />
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== Overview 概览==<br />
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{{Thermodynamics|cTopic=[[Thermodynamic system|Systems]]}}<br />
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Classical thermodynamics deals with states of [[dynamic equilibrium]]. The state of a system at thermodynamic equilibrium is the one for which some [[thermodynamic potential]] is minimized, or for which the [[entropy]] (''S'') is maximized, for specified conditions. One such potential is the [[Helmholtz free energy]] (''A''), for a system with surroundings at controlled constant temperature and volume:<br />
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Classical thermodynamics deals with states of dynamic equilibrium. The state of a system at thermodynamic equilibrium is the one for which some thermodynamic potential is minimized, or for which the entropy (S) is maximized, for specified conditions. One such potential is the Helmholtz free energy (A), for a system with surroundings at controlled constant temperature and volume:<br />
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经典热力学研究'''<font color="#ff8000">动态平衡 Dynamic Equilibrium</font>'''的状态。系统的热力学平衡状态是对于特定的条件,一些'''<font color="#ff8000">热力学势 Thermodynamic Potential</font>'''被最小化,或者'''<font color="#ff8000">熵 Entropy</font>'''(S)被最大化。对于一个周围环境温度和体积恒定的系统,其中一个这样的热力学势是'''<font color="#ff8000">亥姆霍兹自由能 Helmholtz Free Energy</font>'''(A):<br />
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:<math>A = U - TS</math><br />
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<math>A = U - TS</math><br />
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A = U-TS<br />
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Another potential, the [[Gibbs free energy]] (''G''), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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Another potential, the Gibbs free energy (G), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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在恒定温度和压力的系统中,另一个热力学势'''<font color="#ff8000">吉布斯自由能 Gibbs Free Energy</font>'''(G)在热力学平衡状态最小:<br />
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:<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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where ''T'' denotes the absolute thermodynamic temperature, ''P'' the pressure, ''S'' the entropy, ''V'' the volume, and ''U'' the internal energy of the system.<br />
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where T denotes the absolute thermodynamic temperature, P the pressure, S the entropy, V the volume, and U the internal energy of the system.<br />
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其中 T 表示热力学绝对温度,P 表示压强,S 表示熵,V 表示体积,U 表示体系的内能。<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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热力学平衡是一种独特的稳定定态,当系统长时间与周围环境相互作用时,它可以被接近或最终到达。上述势能是数学构造的热力学量,在特定的环境条件下最小化。<br />
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== Conditions 条件==<br />
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* For a completely isolated system, ''S'' is maximum at thermodynamic equilibrium. 对于一个完全孤立的系统,S在热力学平衡中取最大值。<br />
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* For a system with controlled constant temperature and volume, ''A'' is minimum at thermodynamic equilibrium. 对于一个恒定温度和体积的系统来说,A在热力学平衡中取最小值。<br />
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* For a system with controlled constant temperature and pressure, ''G'' is minimum at thermodynamic equilibrium. 对于一个恒温恒压的系统,G在热力学平衡中取最小值。<br />
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The various types of equilibriums are achieved as follows:<br />
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The various types of equilibriums are achieved as follows:<br />
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实现各种类型的平衡的方法如下:<br />
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*Two systems are in ''thermal equilibrium'' when their [[temperature]]s are the same. 当两个系统的'''<font color="#ff8000">温度 Temperature</font>'''相同时,它们就处于''热平衡状态''<br />
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*Two systems are in ''mechanical equilibrium'' when their [[pressure]]s are the same. 当两个体系的'''<font color="#ff8000">压力 Pressure</font>'''相同时,它们就处于''力学平衡''<br />
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*Two systems are in ''diffusive equilibrium'' when their [[chemical potential]]s are the same. 当两个题体系的'''<font color="#ff8000">化学势 Chemical Potential</font>'''相同时,它们就处于''扩散平衡''<br />
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*All [[forces]] are balanced and there is no significant external driving force.<br />
所有的'''<font color="#ff8000">力 Force</font>'''都是平衡的,没有明显的外部驱动力<br />
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==Relation of exchange equilibrium between systems 系统之间的交换均衡关系==<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability.<ref name="Nster_a">Münster, A. (1970), p. 49.</ref> When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability. When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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通常,热力学系统的周围环境也可以被看作是另一个热力学系统。在这种观点中,我们可以把系统及其周围环境看作是相互接触的两个系统,远程作用力也将它们联系在一起。系统的包围物是两个系统之间的接触面或边界。在热力学形式中,该表面被认为具有特定的渗透性质。例如,接触的表面可能被认为只能透热,使能量只能作为热传递。当远程力在时间上不发生变化,两个系统之间的热量传递减慢并最终永久停止时,这两个系统被称为热平衡; 这就是接触平衡的一个例子。其它类型的接触平衡可用其它类型的比渗透率来定义。当两个系统对于某一特定类型的渗透率处于接触平衡时,它们具有属于该特定类型渗透率的强变量的共同值。这种强度变量的例子有温度、压力、化学势。<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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接触平衡也可视为交换平衡。在接触平衡状态下,两系统之间某些量的传递速率存在零平衡。例如,对于只能透热的壁,内能作为热在两个系统之间的扩散速率是相等并反向的。两个系统之间的绝热壁只对作为功传递的能量有渗透作用; 在力学平衡,两个系统之间作为功的能量传递速率相等且相反。如果是一个简单的壁,那么通过它的体积转移率也是相等且相反的; 即它两边的压力是相等的。如果绝热壁比较复杂,有一种杠杆,有一个面积比,那么两个体系在交换平衡中的压力与体积交换比成反比,这使得转移率的零平衡作功。<br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<ref name="Planck 1914 40">[[Max Planck|Planck. M.]] (1914), p. 40.</ref><br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<br />
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辐射交换可以发生在两个不同的系统之间。当两个体系温度相同时,辐射交换平衡占优势。<br />
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==Thermodynamic state of internal equilibrium of a system 系统内部平衡的热力学状态==<br />
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A collection of matter may be entirely [[Isolated system|isolated]] from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium.<ref>Haase, R. (1971), p. 4.</ref><ref>Callen, H.B. (1960/1985), p. 26.</ref> (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics.<ref>{{Cite journal |doi = 10.1119/1.4914528|bibcode = 2015AmJPh..83..628M|title = Time and irreversibility in axiomatic thermodynamics|year = 2015|last1 = Marsland|first1 = Robert|last2 = Brown|first2 = Harvey R.|last3 = Valente|first3 = Giovanni|journal = American Journal of Physics|volume = 83|issue = 7|pages = 628–634}}</ref> One textbook<ref>[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963), p. 5.</ref> calls it the "zeroth law", remarking that the authors think this more befitting that title than its [[Zeroth law of thermodynamics|more customary definition]], which apparently was suggested by [[Ralph H. Fowler|Fowler]].)<br />
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A collection of matter may be entirely isolated from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium. (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics. One textbook calls it the "zeroth law", remarking that the authors think this more befitting that title than its more customary definition, which apparently was suggested by Fowler.)<br />
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物质的集合可能与其周围的环境完全'''<font color="#ff8000">孤立 Isolated</font>'''。如果它在无限长的时间内一直保持不受干扰,按照经典热力学假定,它处于一个没有发生任何变化,没有流动的状态,即内部平衡的热力学状态。(这种假设有时被称为“负第一”热力学定律,但并不常见。有教科书称之为“第零定律” ,作者'''<font color="#ff8000">福勒 Fowler</font>'''认为这个名称是'''<font color="#ff8000">更符合惯例的定义 More Customary Definition</font>'''。)<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a [[thermodynamic operation]] be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a thermodynamic operation be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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这种状态是所谓的经典热力学或平衡态热力学的主要关注点,因为它们是系统中被认为在这门学科中得到很好定义的唯一状态。一个与另一个系统处于接触平衡状态可以被一个'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''隔离,在隔离发生时,其内部不会发生任何变化。因此,一个与另一个系统处于接触平衡状态时也可以被视为处于其自身的内部热力学平衡状态。<br />
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==Multiple contact equilibrium 多点接触平衡==<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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热力学形式允许一个系统同时与其他多个系统接触,这些系统可能有也可能没有相互接触,且这些接触具有不同的渗透性。如果这些系统都与世界其他部分相互隔离,那么它们彼此之间就会达到各自的接触平衡。<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy.<ref name="Caratheodory">Carathéodory, C. (1909).</ref><ref>Prigogine, I. (1947), p. 48.</ref><ref>Landsberg, P. T. (1961), pp. 128–142.</ref><ref>Tisza, L. (1966), p. 108.</ref> Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy. Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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如果几个系统彼此之间没有绝热壁,但是它们与世界其他部分共同隔离,那么它们就会达到多重接触平衡状态,且有共同的温度,总的内能和熵。在众多强度量中,这是温度的一个独特性质。即使在远距离作用力存在的情况下,它也是有效的。(也就是说,没有“力”可以维持温度的差异。)举个例子,在热力学平衡的一个垂直的引力场系统中,顶部壁面的压力比底部壁面的压力小,但是各处的温度都是一样的。<br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural [[thermodynamic process]].<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), § 1.12.</ref> It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings.<ref>Levine, I.N. (1983), p. 40.</ref><ref>Lieb, E.H., Yngvason, J. (1999), pp. 17–18.</ref> The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of [[Second law of thermodynamics#Description#Kelvin statement|"inanimate" agency]]; a system in thermodynamic equilibrium is inanimate.<ref>[[William Thomson, 1st Baron Kelvin|Thomson, W.]] (1851).</ref><br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural thermodynamic process. It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings. The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of "inanimate" agency; a system in thermodynamic equilibrium is inanimate.<br />
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热力操作可能作为一个事件发生在周围环境的壁上,既不直接影响与周围环境联系的壁,也不直接影响其内部,且发生在一个明确的有限的时间内。例如,一个固定的绝热壁可以在环境中被放置或拆除。由于这种操作仅限于周围环境,系统可能会在一段时间内远离自身最初的内部状态---- 热力学平衡。根据热力学第二定律的说法,整体经历了变化并最终与周围环境达到了新的平衡。继Planck之后,这一连串的事件被称为自然'''<font color="#ff8000">热力学过程 Thermodynamic Process</font>'''。即使在这个过程中,当系统和周围环境都不处于明确的内部平衡状态时,存在着暂时偏离热力学平衡的现象,由于初始状态和最终状态都是热力学平衡的,这在平衡热力学中也是允许的。一个自然过程在其主要部分中以有限的速率进行,因此,它从根本上不同于虚构的准静态“过程”;即不在整个过程中无限缓慢地进行而且虚构地“可逆”。经典热力学允许,即使一个过程可能需要很长的时间才能达到热力学平衡,如果主要部分的过程是在一个有限的比率中,那么它被认为是自然的,并受制于热力学第二定律,即不可逆的。工程设计的机器、人工设备和操作是允许在周围环境中进行的。允许在环境中而不是在系统中进行此类操作和设备,是开尔文在他的一个热力学第二定律的陈述中提到'''<font color="#ff8000">无生命机构 Inanimate Agency</font>'''的原因; 在热力学平衡的系统是无生命的。<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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否则,热力操作可能会直接影响系统的壁。<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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通常可以很方便地假设周围的某些子系统比系统大得多,以至于这个过程只能影响周围子系统的强度变量,然后将这些子系统称为相关强度变量的储备库。<br />
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== Local and global equilibrium 局部和全局均衡==<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by [[intensive quantity|intensive]] parameters. As an example, [[temperature]] controls [[Heat equation|heat exchanges]]. ''Global thermodynamic equilibrium'' (GTE) means that those [[intensive quantity|intensive]] parameters are homogeneous throughout the whole system, while ''local thermodynamic equilibrium'' (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by intensive parameters. As an example, temperature controls heat exchanges. Global thermodynamic equilibrium (GTE) means that those intensive parameters are homogeneous throughout the whole system, while local thermodynamic equilibrium (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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区分全局性和局部性热力学平衡是很有用的。在热力学中,系统内部和系统与外部之间的交换是由'''<font color="#ff8000">强度 Intensive</font>'''参数控制的。例如,'''<font color="#ff8000">温度 Temperature</font>'''控制'''<font color="#ff8000">热交换 Heat Equation</font>'''。全局热力学平衡(GTE)意味着这些'''<font color="#ff8000">强度 Intensive</font>'''参数在整个系统中是均匀的,而局部热力学平衡(LTE)意味着这些强度参数在空间和时间上是变化的,但变化如此缓慢,以至于对于任何一点,人们都可以假设在该点的某个邻域存在热力学平衡。<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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如果对系统的描述要求强度参数的变化过大,那么这些强度参数的定义所依据的假设本身就会失效,系统将既不处于全局平衡,也不处于局部平衡。例如,粒子需要一定数量的碰撞来平衡其周围环境。如果在这些碰撞中移动的平均距离使它离开平衡邻域,它将永远不会平衡,也就不会有 LTE。根据定义,温度与平衡邻域的平均内部能量成正比。由于没有达到平衡邻域,温度的概念就不成立,温度也就变得无法定义。<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to [[massive]] particles. In a [[radiation|radiating]] gas, the [[photon]]s being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to massive particles. In a radiating gas, the photons being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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值得注意的是,这种局部平衡可能只适用于系统中的某个粒子子集。例如,LTE 通常只适用于'''<font color="#ff8000">大 Massive</font>'''质量粒子。在'''<font color="#ff8000">辐射 Radiation</font>'''气体中,被气体发射和吸收的'''<font color="#ff8000">光子 Photon</font>'''不需要彼此在一个热力学平衡内,或与气体中的大量粒子在一起,LTE 才能存在。在某些情况下,自由电子并不需要与大得多的原子或分子处于平衡状态,LTE 才能存在。<br />
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As an example, LTE will exist in a glass of water that contains a melting [[ice cube]]. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the [[Maxwell–Boltzmann distribution]] for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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As an example, LTE will exist in a glass of water that contains a melting ice cube. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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例如,LTE 将存在于一个装有正在融化的'''<font color="#ff8000">冰块 Ice Cube</font>'''的水杯中。玻璃杯内的温度可以在任何时候定义,但是离冰块近的地方要比离冰块远的地方冷。如果观察到位于给定点附近的分子的能量,它们将按照麦克斯韦-波兹曼分布在一定温度下的分布。如果观察到位于另一点附近的分子的能量,它们将按照'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''分布到另一个温度。<br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural [[transport phenomena]] may lead a system from local to global thermodynamic equilibrium. Going back to our example, the [[diffusion]] of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<ref>H.R. Griem, 2005</ref><br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural transport phenomena may lead a system from local to global thermodynamic equilibrium. Going back to our example, the diffusion of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<br />
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局部热力学平衡不需要局部或全局的平稳性。换句话说,每一个小区域不需要有一个恒定的温度。然而,它确实要求每个小的局部变化缓慢到足以维持其局部麦克斯韦-波尔兹曼速度分布。全局非平衡态只有通过系统与外界的交换才能保持稳定。例如,通过在水杯中不断添加细粉冰来补偿熔化,并持续排出融水,可以保持全局稳定的静态。自然'''<font color="#ff8000">输运现象 Transport Phenomena</font>'''会使一个局部热力学平衡系统逐渐达到全局的热力学平衡。回顾我们的例子,热量的扩散将导致我们的玻璃杯水流向全局热力学平衡,在这种状态下,玻璃杯的温度是完全均匀的。<br />
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==Reservations 保留意见==<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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学识渊博的笔者在热力学领域对热力学平衡描述时,经常对他们的描述附加条件或保留意见。有些笔者含蓄地保留了或多或少的空白,以待说明。<br />
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For example, one widely cited writer, [[Herbert Callen|H. B. Callen]] writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. ''Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!''"<ref>Callen, H.B. (1960/1985), p. 15.</ref><br />
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For example, one widely cited writer, H. B. Callen writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!"<br />
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例如,一位被广泛引用的作家'''<font color="#ff8000">H.B.卡伦 H.B.Callen</font>'''在这里写道: “实际上,很少有系统处于绝对和真正的平衡状态。”他提到了放射性过程,认为它们可能需要“宇宙时间才能完成,因此通常可以忽略”。他补充道: “在实践中,平衡的标准是循环的。在操作上,如果一个系统的性质一致地用热力学理论来描述,那么它就处于平衡状态! ”<br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<ref>Beattie, J.A., Oppenheim, I. (1979), p. 3.</ref><br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<br />
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J.A.贝蒂和 I.奥本海姆写道: “坚持对平衡定义的严格解释,将排除热力学应用于实际系统的所有状态。”<br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment",<ref>Callen, H.B. (1960/1985), p. 485.</ref> and cited by Adkins as having written a "classic text",<ref>Adkins, C.J. (1968/1983), p. ''xiii''.</ref> [[Brian Pippard|A.B. Pippard]] writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<ref>Pippard, A.B. (1957/1966), p. 6.</ref><br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment", and cited by Adkins as having written a "classic text", A.B. Pippard writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<br />
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Callen引用另一位作者的话说,他给出了“学术且严谨的论述” ,Adkins引用他的话说,他写了一本“经典著作”—— '''<font color="#ff8000">A.B.皮帕德 A.B.Pippard</font>'''在文中写道: “只要时间足够长,过冷水蒸汽最终会凝结,... ..。时间可能是漫长的,也许长达10年或者更长。就大多数目的而言,只要这种迅速的变化不是人为地刺激,这些系统就可以被视为处于平衡状态。”<br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster">Münster, A. (1970), p. 53.</ref><br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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另一位作者A.Münster,写道。他观察到热核反应发生的速度非常缓慢,以至于在热力学中可以忽略不计。他评论道: “‘绝对平衡’或‘所有可想象过程的平衡’的概念没有物理意义。”他说: “ ... 我们只能考虑特定过程和确定的实验条件下的平衡。”<br />
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According to [[László Tisza|L. Tisza]]: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<ref>Tisza, L. (1966), p. 119.</ref><br />
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According to L. Tisza: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<br />
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根据'''<font color="#ff8000">L.缇莎 L.Tisza</font>'''的说法: “ ... 在讨论接近绝对零度的现象时。经典理论的绝对预测变得特别模糊,因为在非平衡状态下发生冻结是非常普遍的。”<br />
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==Definitions 定义==<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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一个系统最普遍的热力学平衡是通过与周围环境的接触,允许所有化学物质和各种能量同时通过。热力学平衡中的系统可能以均匀加速度在空间中运动,但此时不能改变其形状或大小; 因此它是由空间中的刚性体积来定义的。它可能存在于外力场中,由远远大于系统本身的外部因素决定,因此系统内的事件不会对外力场产生相当大的影响。只有当外力场是均匀的,并且确定了它的均匀加速度,或者它处于一个非均匀力场中,但是由于表面的局部力,例如机械压力,使它保持静止时,这个系统才能处于热力学平衡。<br />
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Thermodynamic equilibrium is a [[primitive notion]] of the theory of thermodynamics. According to [[Philip M. Morse|P.M. Morse]]: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are ''not'' conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments."<ref>[[Philip M. Morse|Morse, P.M.]] (1969), p. 7.</ref> This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<ref>Bailyn, M. (1994), p. 20.</ref><br />
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Thermodynamic equilibrium is a primitive notion of the theory of thermodynamics. According to P.M. Morse: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are not conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments." This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<br />
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热力学平衡是热力学理论的一个'''<font color="#ff8000">基本概念 Primitive Notion</font>'''。'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''说: “应该强调的是,存在热力学状态这一事实,以及存在由平衡态唯一指定的热力学变量这一事实,并不是从某些哲学第一原理得出的逻辑结论。这些结论不可避免地来自两个多世纪的实验。”这意味着热力学平衡不能仅仅用热力学的其他理论概念来定义。M.Bailyn提出了一个基本的热力学定律理论,它定义并假设了热力学平衡的存在。<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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热力学平衡的教科书定义通常被仔细说明,并有些保留。<br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<ref>Münster, A. (1970), p. 52.</ref><br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<br />
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例如,A. Münster写道:“当一个孤立系统中没有以可测量的速率发生状态变化时,系统处于热力学平衡状态。”这里有两项保留:系统是孤立的;任何状态的变化都是不可测量的缓慢。他通过对在室温且没有催化剂的情况下混合氧和氢的说明,讨论了第二个条件。Münster指出,描述热力学平衡状态所需要的宏观变量比给定系统任何其他状态都少。这是部分,但不完全是,因为系统内和流过系统的所有流都是零。<br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in ''equilibrium''.<ref>Haase, R. (1971), pp. 3–4.</ref><br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in equilibrium.<br />
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R. Haase's的热力学演示并不从对热力学平衡的限制开始,因为他打算考虑非平衡态热力学。他考虑一个具有时间不变性质的任意系统。他通过切断除外力场以外的所有外部影响来测试它的热力学平衡。如果在绝缘之后,没有任何变化,他说,系统处于平衡状态。<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness".<ref>Callen, H.B. (1960/1985), p. 13.</ref> This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness". This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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在一个标题为“热力学平衡”的章节中,H.B. Callen在一个段落中定义了平衡状态.他指出,它们“是由系统内部的内在因素决定的”。它们是“终端状态” ,随着时间的推移,系统会以“冰川般缓慢”的速度朝着这个终端状态演化。这个说法并没有明确,对于热力学平衡系统必须是孤立的;;Callen也没有说明他所说的“内在因素”是什么意思。<br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<ref>Adkins, C.J. (1968/1983), p. ''7''.</ref><br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<br />
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另一位教科书作者,C.J.Adkins,明确允许热力学平衡在非孤立的系统中发生。然而,他的系统在物质转移方面是封闭的。他写道: “一般来说,热力学平衡的方法包括热和类似功的形式与周围环境的相互作用。”他将这种热力学平衡与只有通过热接触才能进行能量传递的热平衡相区别。<br />
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Another textbook author, [[J.R. Partington]], writes: "(i) ''An equilibrium state is one which is independent of time''." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..."<ref>Partington, J.R. (1949), p. 161.</ref> This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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Another textbook author, J.R. Partington, writes: "(i) An equilibrium state is one which is independent of time." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..." This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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另一位教科书作者'''<font color="#ff8000">J.R.帕廷顿 J.R.Partington</font>'''写道: “(i)平衡状态是独立于时间的状态。”但是,在提到“只是明显处于平衡状态”的系统时,他补充说: “这样的系统处于‘虚假平衡’状态。帕廷顿的陈述没有明确指出平衡是指一个孤立的系统。和Münster一样,Partington也指的是氧和氢的混合物。他补充说:“在一个真正的平衡状态,任何影响状态的外部条件的微小变化都会产生一个微小的状态变化... ... ”这个条件意味着热力学平衡必须在小的扰动下保持稳定; 这个要求对于热力学平衡的严格意义是必不可少的。<br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, ''thermodynamic—equilibrium.''"<ref>Crawford, F.H. (1963), p. 5.</ref><br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, thermodynamic—equilibrium."<br />
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在F.H.Crawford的一本学生教科书中,有一个标题为“热力学平衡”的章节。它区分了几种流动的驱动因素,然后说: “这些是孤立系统明显普遍趋向于完全机械、热、化学和电力状态的例子——或者简单地说,热力学平衡状态。”<br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in ''equilibrium''."<ref>Buchdahl, H.A. (1966), p. 8.</ref> Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being ''in equilibrium'' so long as experimental tests show that 'slow' transitions are in effect reversible."<ref>Buchdahl, H.A. (1966), p. 111.</ref> It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<ref>Adkins, C.J. (1968/1983), p. 8.</ref><br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in equilibrium." Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being in equilibrium so long as experimental tests show that 'slow' transitions are in effect reversible." It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<br />
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H.A. Buchdahl的一本关于经典热力学的专著考虑了热力学系统的平衡,而实际上并没有写热力学平衡一词。Buchdahl在提到封闭的物质交换系统时写道: “如果一个系统处于一个适当的静态状态,那么它将被称为处于平衡状态。”出于热力学描述的目的,Buchdahl的专著也讨论了非晶态玻璃。它说: “更准确地说,只要实验测试表明‘慢’跃迁实际上是可逆的,玻璃就可以被认为处于平衡状态。”通常来说不会将这一条件作为热力学平衡定义的一部分,而是假定相反的情况:如果热力学平衡中的一个物体受到足够慢的过程的影响,则该过程可被视为足够接近可逆,并且该物体在过程中足够接近热力学平衡。<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of ''contact equilibrium''. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by [[Constantin Carathéodory|C. Carathéodory]], and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster" /> Thermodynamic equilibrium for an open system means that, with respect to every relevant kind of selectively permeable wall, contact equilibrium exists when the respective intensive parameters of the system and surroundings are equal.<ref name="Nster_a" /> This definition does not consider the most general kind of thermodynamic equilibrium, which is through unselective contacts. This definition does not simply state that no current of matter or energy exists in the interior or at the boundaries; but it is compatible with the following definition, which does so state.<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of contact equilibrium. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by C. Carathéodory, and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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通过引入接触平衡的概念,A. Münster仔细地扩展了孤立系统热力学平衡的定义。这指定了在考虑非孤立系统的热力学平衡时允许的特定过程,并特别关心开放系统,这些开放系统可能从周围环境获得或丢失物质。感兴趣的系统和周围系统之间的接触平衡,通过一种特殊的壁与之接触,其余的连接系统是孤立的。这种特殊类型的壁也被'''<font color="#ff8000">C.喀喇西奥多里 C.Carathéodory</font>'''考虑过,其他作家也提到过。它们具有选择渗透性。它们可能只对机械功有渗透性,或者只对热有渗透性,或者只对某种特定的化学物质有渗透性。每个接触平衡定义了一个强度参数; 例如,只能透热的壁定义了一个经验温度。对于感兴趣的体系中每一种化学成分,都可以存在接触平衡。在接触平衡中,尽管有可能通过选择性渗透壁进行交换,但是感兴趣的系统是不变的,好像它处在孤立的热力学平衡。这个方案遵循的一般规则是: “ ... ... 我们只能考虑特定过程和特定实验条件下的平衡。”<br />
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[[Mark Zemansky|M. Zemansky]] also distinguishes mechanical, chemical, and thermal equilibrium. He then writes: "When the conditions for all three types of equilibrium are satisfied, the system is said to be in a state of thermodynamic equilibrium".<ref>[[Mark Zemansky|Zemansky, M.]] (1937/1968), p. 27.</ref><br />
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'''<font color="#ff8000">M.泽曼斯基 M.Zemansky</font>'''还区分了力学、化学和热平衡。他接着写道: “当这三种均衡的条件都满足时,系统就处于热力学平衡状态。”<br />
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P.M. Morse writes that thermodynamics is concerned with "states of thermodynamic equilibrium". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<br />
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[[Philip M. Morse|P.M. Morse]] writes that thermodynamics is concerned with "''states of thermodynamic equilibrium''". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<ref>[[Philip M. Morse|Morse, P.M.]] (1969), pp. 6, 37.</ref><br />
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'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''写道,热力学关注的是“热力学平衡状态”。在讨论物体与周围热源之间的热量传递时,他也使用了“热平衡”这个短语,尽管没有明确定义一个特殊的术语“热平衡”<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "full thermodynamic equilibrium state".<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "''full'' thermodynamic equilibrium state".<ref>Waldram, J.R. (1985), p. 5.</ref><br />
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J.R. Waldram写到了“一个明确的热力学状态”。他将一个系统定义为“当其观测量随时间停止变化时”的“热平衡”。但是在这个定义之下不久,他写到一块玻璃还没有达到“完全的热力学平衡状态”。<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, thermodynamic equilibrium is said to exist." He is not here considering the presence of an external force field.<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, ''thermodynamic equilibrium'' is said to exist." He is not here considering the presence of an external force field.<ref>Bailyn, M. (1994), p. 21.</ref><br />
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考虑到平衡状态,M.Bailyn写道: “每个强度变量都有自己的平衡类型。”然后他定义了热平衡、力学平衡和物质平衡。因此,他写道: “如果所有的强度变量都是一致的,那么热力学平衡就是存在的。”他在这里没有考虑外力场的存在。<br />
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J.G. Kirkwood and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of thermodynamic equilibrium if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<br />
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[[John Gamble Kirkwood|J.G. Kirkwood]] and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of ''thermodynamic equilibrium'' if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<ref>Kirkwood, J.G., Oppenheim, I. (1961), p. 2</ref><br />
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'''<font color="#ff8000">J.G.柯克伍德 J.G.Kirkwood</font>'''和 I.Oppenheim 将热力学平衡定义为: “一个系统处于热力学平衡状态,如果,在实验的时间内,(a)它强度特性与时间无关,(b)它的内部或与周围环境的边界处没有物质或能量流。”显然,他们没有把定义限制在孤立的或封闭的系统。它们不讨论“缓慢”发生变化的可能性,并且超出了分配给实验的时间范围。他们注意到,对于两个相接触的系统,存在一个强度性质的小子类,如果这个小子类的所有子类都相等,那么所有各自的强度性质都相等。只要满足其他一些条件,热力学平衡状态可以由这个子类定义。<br />
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==Characteristics of a state of internal thermodynamic equilibrium 内部热力学平衡状态的特征==<br />
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===Homogeneity in the absence of external forces 在没有外力的情况下的均匀性===<br />
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A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous.<ref name="Planck 1903 3"/> This means that the material in any small volume element of the system can be interchanged with the material of any other geometrically congruent volume element of the system, and the effect is to leave the system thermodynamically unchanged. In general, a strong external force field makes a system of a single phase in its own internal thermodynamic equilibrium inhomogeneous with respect to some [[Intensive and extensive properties|intensive variables]]. For example, a relatively dense component of a mixture can be concentrated by centrifugation.<br />
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在没有外力的情况下,由单一相组成的热力学系统,在其自身的内部热力学平衡中是均匀的。这意味着系统中任何小体积单元中的材料可以与系统中任何其他几何相等的体积单元中的材料互换,其效果是使系统在热力学上保持不变。一般来说,一个强外力场使得一个单相系统在其自身的内部热力学平衡中对于一些'''<font color="#ff8000">强度量 Intensive Variable</font>'''是不均匀的。例如,可以通过离心来浓缩混合物中相对密度较大的组分。<br />
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===Uniform temperature 均匀温度===<br />
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Such equilibrium inhomogeneity, induced by external forces, does not occur for the intensive variable [[temperature]]. According to [[Edward A. Guggenheim|E.A. Guggenheim]], "The most important conception of thermodynamics is temperature."<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), p.5.</ref> Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface."<ref name="Planck 1903 3">[[Max Planck|Planck, M.]] (1897/1927), p.3.</ref> As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.<br />
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这种由外力引起的平衡不均匀性,对于强度量'''<font color="#ff8000">温度 Temperature</font>'''不会发生。'''<font color="#ff8000">E.A.古根海姆 E.A. Guggenheim</font>'''认为,“热力学最重要的概念是温度。“Planck在介绍他的论文时,简要叙述了热、温度和热平衡,然后宣布: ”在下文中,我们将主要讨论任何形式的均匀、各向同性的物体,它们的物质具有相同的温度和密度,并受到到处垂直于表面的均匀压力的作用。和Carathéodory 一样,Planck将表面效应、外场和各向异性晶体排除在外。虽然Planck提到了温度,但并没有明确提到热力学平衡的概念。相比之下,Carathéodory关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ,虽然没有明确地使用短语‘热力学平衡’ ,也没有明确地假设存在一个温度来定义它。<br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform.<ref name="Planck 1914 40"/> This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers.<ref>Gibbs, J.W. (1876/1878), pp. 144-150.</ref><ref>[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966), pp. 127–130.</ref><ref>Münster, A. (1970), pp. 309–310.</ref><ref>Bailyn, M. (1994), pp. 254-256.</ref><ref>{{cite journal | last1 = Verkley | first1 = W.T.M. | last2 = Gerkema | first2 = T. | year = 2004 | title = On maximum entropy profiles | journal = J. Atmos. Sci. | volume = 61 | issue = 8| pages = 931–936 | doi=10.1175/1520-0469(2004)061<0931:omep>2.0.co;2| bibcode = 2004JAtS...61..931V | doi-access = free }}</ref><ref>{{cite journal | last1 = Akmaev | first1 = R.A. | year = 2008 | title = On the energetics of maximum-entropy temperature profiles | url = | journal = Q. J. R. Meteorol. Soc. | volume = 134 | issue = 630| pages = 187–197 | doi=10.1002/qj.209| bibcode = 2008QJRMS.134..187A }}</ref> Considerations of kinetic theory or statistical mechanics also support this statement.<ref>Maxwell, J.C. (1867).</ref><ref>Boltzmann, L. (1896/1964), p. 143.</ref><ref>Chapman, S., Cowling, T.G. (1939/1970), Section 4.14, pp. 75–78.</ref><ref>[[J. R. Partington|Partington, J.R.]] (1949), pp. 275–278.</ref><ref>{{cite journal | last1 = Coombes | first1 = C.A. | last2 = Laue | first2 = H. | year = 1985 | title = A paradox concerning the temperature distribution of a gas in a gravitational field | url = | journal = Am. J. Phys. | volume = 53 | issue = 3| pages = 272–273 | doi=10.1119/1.14138| bibcode = 1985AmJPh..53..272C }}</ref><ref>{{cite journal | last1 = Román | first1 = F.L. | last2 = White | first2 = J.A. | last3 = Velasco | first3 = S. | year = 1995 | title = Microcanonical single-particle distributions for an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 16 | issue = 2| pages = 83–90 | doi=10.1088/0143-0807/16/2/008| bibcode = 1995EJPh...16...83R }}</ref><ref>{{cite journal | last1 = Velasco | first1 = S. | last2 = Román | first2 = F.L. | last3 = White | first3 = J.A. | year = 1996 | title = On a paradox concerning the temperature distribution of an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 17 | issue = | pages = 43–44 | doi=10.1088/0143-0807/17/1/008}}</ref><br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform. This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers. Considerations of kinetic theory or statistical mechanics also support this statement.<br />
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热力学平衡系统内的温度在时间和空间上都是均匀的。在一个处于内部热力学平衡的系统中,不存在净的内部宏观流动。特别是,这意味着系统的所有局部都处于相互辐射交换平衡。这意味着系统的温度在空间上是均匀的。这在所有情况下都是如此,包括那些非均匀外力场。对于外部施加的引力场,这可以使用拉格郎日乘子法通过变分的计算在宏观热力学术语中证明。动力学理论或统计力学也支持这种说法。<br />
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In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium.<ref name="Fitts 43"/><br />
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为了使一个系统处于它自己的内部热力学平衡状态,它必须处于它自己的内部热平衡状态是必要不充分的; 一个系统在到达内部热平衡之前到达内部力学平衡是可能的。<br />
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===Number of real variables needed for specification 规范所需的实变量数目===<br />
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In his exposition of his scheme of closed system equilibrium thermodynamics, C. Carathéodory initially postulates that experiment reveals that a definite number of real variables define the states that are the points of the manifold of equilibria.<ref name="Caratheodory" /> In the words of Prigogine and Defay (1945): "It is a matter of experience that when we have specified a certain number of macroscopic properties of a system, then all the other properties are fixed."<ref>Prigogine, I., Defay, R. (1950/1954), p. 1.</ref><ref>Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005), p. 4.</ref> As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.<br />
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在他关于封闭系统平衡态热力学方案的论述中,C.Carathéodory 最初假定实验揭示了一定数量的实变量定义了作为平衡态流形点的状态。用 Prigogine 和 Defay (1945)的话说: “这是一个经验问题,当我们确定了一个系统一定数量的宏观属性时,那么所有其他属性都是固定的”。如上所述,A. Münster认为,定义热力学平衡所需的变量数量相对于给定孤立系统的任何状态来说都是最少的。如上所述,J.G. Kirkwood 和 I. Oppenheim 指出,热力学平衡状态可以由一个特殊子类的强度变量来定义,该子类中有一定数量的成员。<br />
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If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.<br />
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如果热力学平衡位于一个外力场中,那么通常只有温度在空间上是均匀的。如果外力场非零,温度以外的强度变量通常是不均匀的。在这种情况下,一般需要附加变量来描述空间非均匀性。<br />
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===Stability against small perturbations 对小扰动的稳定性===<br />
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As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.<br />
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如上所述,J.R. Partington 指出热力学平衡状态在小的瞬态扰动下是稳定的。如果没有这个条件,一般来说,研究热力学平衡系统的实验就会遇到严重的困难。<br />
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===Approach to thermodynamic equilibrium within an isolated system 孤立系统中的热力学平衡===<br />
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When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium. Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<br />
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When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium.<ref name="Fitts 43">Fitts, D.D. (1962), p. 43.</ref> Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<ref>Denbigh, K.G. (1951), p. 42.</ref><br />
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当一个物质体从不均匀的非平衡状态或化学非平衡状态开始,然后被孤立,它会自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如,在这种演化的许多情况下,内部力学平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是,在这种演化的许多情况下,热平衡的发展要比化学平衡快得多。<br />
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===Fluctuations within an isolated system in its own internal thermodynamic equilibrium 孤立系统内部热力学平衡的涨落===<br />
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In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
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在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
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To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics.<ref>Tschoegl, N.W. (2000). ''Fundamentals of Equilibrium and Steady-State Thermodynamics'', Elsevier, Amsterdam, {{ISBN|0-444-50426-5}}, p. 21.</ref> But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
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To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics. But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
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考虑孤立热力学系统中的涨落概念,一个方便的例子是由其内能、体积和质量组成等广延量表示的系统。根据定义,它们是不随时间变化的。根据定义,这些量与它们的共轭状态强度函数的时不变名义值相结合,包括逆温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广延量的值,不足以提供这些名义值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
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It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.<br />
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可以承认,在重复测量这些共轭强度状态函数时,发现它们的值随时间略有不同。这种可变性被认为是由于内部涨落。不同测量值平均到其名义值。<br />
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If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<ref>Buchdahl, H.A. (1966), p. 16.</ref><br />
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If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<br />
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如果系统真的像经典热力学所假定的那样是宏观的,那么系统的涨落很小以至于宏观上无法检测到。这就是所谓的热力学极限。实际上,物质的分子性质和动量转移的量子性质由于它们太小而看不见,已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中,平衡的涨落概念是不存在的。”<br />
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If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
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如果系统被重复细分,最终产生的系统足够小,可以表现出明显的涨落。这是一个介观层面的研究。涨落则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
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If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在涨落过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,并且需要量子统计力学。涨落可以变得相对占主导地位,测量问题变得重要。<br />
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The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
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"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有随时间变化趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的名义值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微涨落期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。除非已知属于平衡状态的名义值,否则根据单一的度量无法进行判断。<br />
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=== Thermal equilibrium 热平衡===<br />
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{{Main|Thermal equilibrium}}<br />
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An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process."<ref>Eu, B.C. (2002), page 13.</ref> This illustrates the importance for thermodynamics of the concept of temperature.<br />
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热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他考虑两个系统在热接触,一个是温度计,另一个是一个有几个不可逆过程的系统,产生非零的流; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在感兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。因此存在热平衡但是不存在热力学平衡。因此,Eu提出,即使在没有热力学平衡的情况下,也可以考虑应用热力学第零定律; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
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[[Thermal equilibrium]] is achieved when two systems in [[thermal contact]] with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<ref>[[Raj Pathria|R. K. Pathria]], 1996</ref><br />
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当两个相互'''<font color="#ff8000">热接触 Thermal Contact</font>'''的系统不再有净能量交换时,就会产生'''<font color="#ff8000">热平衡 Thermal Equilibrium</font>'''。因此,如果两个系统处于热平衡,那么它们的温度是相同的。<br />
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Thermal equilibrium occurs when a system's [[macroscopic]] thermal observables have ceased to change with time. For example, an [[ideal gas]] whose [[Distribution function (physics)|distribution function]] has stabilised to a specific [[Maxwell–Boltzmann distribution]] would be in thermal equilibrium. This outcome allows a single [[temperature]] and [[pressure]] to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<ref>de Groot, S.R., Mazur, P. (1962), p. 44.</ref><br />
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当一个系统的'''<font color="#ff8000">宏观 Macroscopic</font>'''热观测值不再随时间变化时,就会出现热平衡。例如,一种'''<font color="#ff8000">分布函数 Distribution Function</font>'''稳定到一个特定的'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''的'''<font color="#ff8000">理想气体 Ideal Gas</font>'''即处于热平衡状态。这个结果可以用单一的'''<font color="#ff8000">温度 Temperature</font>'''和'''<font color="#ff8000">压力 Pressure</font>'''来描述整个系统。对于一个孤立的物体来说,在达到热平衡之前达到力学平衡是很可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
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==Non-equilibrium==<br />
非平衡<br />
{{Main|Non-equilibrium thermodynamics}}<br />
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Thermodynamic models <br />
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热力学模型<br />
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A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<ref>de Groot, S.R., Mazur, P. (1962), p. 43.</ref><br />
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一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数<br />
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Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
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Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle.<ref>{{cite book|last1=Ziegler|first1=H.|title=An Introduction to Thermomechanics.|date=1983|location=North Holland, Amsterdam.}}</ref><ref>{{cite journal|last1=Onsager|first1=Lars|title=Reciprocal Relations in Irreversible Processes|journal=Phys. Rev.|date=1931|volume=37|issue=4|doi=10.1103/PhysRev.37.405|bibcode=1931PhRv...37..405O|pages=405–426|doi-access=free}}</ref> It states that a non-equilibrium system evolves such as to maximize its entropy production.<ref>{{cite book|last1=Kleidon|first1=A.|last2=et.|first2=al.|title=Non-equilibrium Thermodynamics and the Production of Entropy.|date=2005|edition=Heidelberg: Springer.}}</ref><ref>{{cite journal|last1=Belkin|first1=Andrey|last2=et.|first2=al.|title=Self-Assembled Wiggling Nano-Structures and the Principle of Maximum Entropy Production|journal=Sci. Rep.|doi=10.1038/srep08323|bibcode=2015NatSR...5E8323B|pmc=4321171|pmid=25662746|volume=5|year=2015|page=8323}}</ref><br />
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定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
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Topics in control theory<br />
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控制理论主题<br />
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==See also ==<br />
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{{Portal|Chemistry}}<br />
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;Thermodynamic models 热力学模型<br />
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* [[Non-random two-liquid model]] (NRTL model) - Phase equilibrium calculations 非随机两液模型(NRTL 模型)-相平衡计算<br />
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* [[UNIQUAC]] model - Phase equilibrium calculations UNIQUAC 模型-相平衡计算<br />
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* [[Time crystal]] 时间晶体<br />
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;Topics in control theory 控制理论主题<br />
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* [[Steady state]] 稳态<br />
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* [[Transient state]] 瞬态<br />
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* [[Coefficient diagram method]] 系数图法<br />
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* [[Control reconfiguration]] 控制重构<br />
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* [[Cut-insertion theorem]] 切入定理<br />
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* [[Feedback]] 反馈<br />
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* [[H infinity]] H 无限<br />
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* [[Hankel singular value]] 汉克尔奇异值<br />
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* [[Krener's theorem]] 克雷纳定理<br />
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* [[Lead-lag compensator]] 超前滞后补偿器<br />
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* [[Minor loop feedback]] 小循环反馈<br />
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* [[Minor loop feedback|Multi-loop feedback]] 小循环反馈 | 多循环反馈<br />
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* [[Positive systems]] 正向系统<br />
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* [[Radial basis function]] 径向基底函数<br />
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Other related topics<br />
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其他相关话题<br />
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* [[Root locus]] 根轨迹<br />
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* [[Signal-flow graph]]s 信号流图<br />
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* [[Stable polynomial]] 稳定多项式<br />
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* [[State space representation]] 状态空间<br />
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* [[Underactuation]] 欠驱动<br />
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* [[Youla–Kucera parametrization]] 尤拉-库切拉参数化<br />
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* [[Markov chain approximation method]] 马尔可夫链近似法<br />
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{{colend}}<br />
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;Other related topics<br />
其他相关话题<br />
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* [[Automation and remote control]] 自动化和远程控制<br />
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* [[Bond graph]] 键合图<br />
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* [[Control engineering]] 控制工程<br />
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* [[Control–feedback–abort loop]] 控制-反馈-中止循环<br />
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* [[Controller (control theory)]] 控制器(控制理论)<br />
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* [[Cybernetics]] 控制论<br />
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* [[Intelligent control]] 智能控制<br />
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* [[Mathematical system theory]] 数学系统论<br />
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* [[Negative feedback amplifier]] 负反馈放大器<br />
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* [[People in systems and control]] 系统和控制中的人<br />
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* [[Perceptual control theory]] 知觉控制理论<br />
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* [[Systems theory]] 系统论<br />
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* [[Time scale calculus]] 时间尺度演算<br />
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{{colend}}<br />
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== 编者推荐 ==<br />
===集智文章推荐===<br />
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====[https://swarma.org/?p=21322 什么是非平衡态热力学 | 集智百科]====<br />
非平衡态热力学 Non-equilibrium thermodynamics 是热力学的一个分支,研究某些不处于热力学平衡中的物理系统<br />
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==General references==<br />
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* Cesare Barbieri (2007) ''Fundamentals of Astronomy''. First Edition (QB43.3.B37 2006) CRC Press {{ISBN|0-7503-0886-9}}, {{ISBN|978-0-7503-0886-1}}<br />
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* Hans R. Griem (2005) ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}<br />
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* C. Michael Hogan, Leda C. Patmore and Harry Seidman (1973) ''Statistical Prediction of Dynamic Thermal Equilibrium Temperatures using Standard Meteorological Data Bases'', Second Edition (EPA-660/2-73-003 2006) United States Environmental Protection Agency Office of Research and Development, Washington, D.C. [http://library.wur.nl/WebQuery/catalog/lang/1851848]<br />
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* F. Mandl (1988) ''Statistical Physics'', Second Edition, John Wiley & Sons<br />
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==References==<br />
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{{Reflist|colwidth=35em}}<br />
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==Cited bibliography==<br />
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*Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', third edition, McGraw-Hill, London, {{ISBN|0-521-25445-0}}.<br />
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*Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, {{ISBN|0-88318-797-3}}.<br />
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*Beattie, J.A., Oppenheim, I. (1979). ''Principles of Thermodynamics'', Elsevier Scientific Publishing, Amsterdam, {{ISBN|0-444-41806-7}}.<br />
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*[[Ludwig Boltzmann|Boltzmann, L.]] (1896/1964). ''Lectures on Gas Theory'', translated by S.G. Brush, University of California Press, Berkeley.<br />
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*Buchdahl, H.A. (1966). ''The Concepts of Classical Thermodynamics'', Cambridge University Press, Cambridge UK.<br />
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*[[Herbert Callen|Callen, H.B.]] (1960/1985). ''Thermodynamics and an Introduction to Thermostatistics'', (1st edition 1960) 2nd edition 1985, Wiley, New York, {{ISBN|0-471-86256-8}}.<br />
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*[[Constantin Carathéodory|Carathéodory, C.]] (1909). [https://web.archive.org/web/20160304213645/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0067&DMDID=DMDLOG_0033&L=1 Untersuchungen über die Grundlagen der Thermodynamik], ''[[Mathematische Annalen]]'', '''67''': 355–386. A translation may be found [http://neo-classical-physics.info/uploads/3/0/6/5/3065888/caratheodory_-_thermodynamics.pdf here]. Also a mostly reliable [https://books.google.com/books?id=xwBRAAAAMAAJ&q=Investigation+into+the+foundations translation is to be found] at Kestin, J. (1976). ''The Second Law of Thermodynamics'', Dowden, Hutchinson & Ross, Stroudsburg PA.<br />
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*[[Sydney Chapman (mathematician)|Chapman, S.]], [[Thomas George Cowling|Cowling, T.G.]] (1939/1970). ''The Mathematical Theory of Non-uniform gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases'', third edition 1970, Cambridge University Press, London.<br />
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*Crawford, F.H. (1963). ''Heat, Thermodynamics, and Statistical Physics'', Rupert Hart-Davis, London, Harcourt, Brace & World, Inc.<br />
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*de Groot, S.R., Mazur, P. (1962). ''Non-equilibrium Thermodynamics'', North-Holland, Amsterdam. Reprinted (1984), Dover Publications Inc., New York, {{ISBN|0486647412}}.<br />
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*Denbigh, K.G. (1951). ''Thermodynamics of the Steady State'', Methuen, London.<br />
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*Eu, B.C. (2002). ''Generalized Thermodynamics. The Thermodynamics of Irreversible Processes and Generalized Hydrodynamics'', Kluwer Academic Publishers, Dordrecht, {{ISBN|1-4020-0788-4}}.<br />
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*Fitts, D.D. (1962). ''Nonequilibrium thermodynamics. A Phenomenological Theory of Irreversible Processes in Fluid Systems'', McGraw-Hill, New York.<br />
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*[[Josiah Willard Gibbs|Gibbs, J.W.]] (1876/1878). On the equilibrium of heterogeneous substances, ''Trans. Conn. Acad.'', '''3''': 108–248, 343–524, reprinted in ''The Collected Works of J. Willard Gibbs, Ph.D, LL. D.'', edited by W.R. Longley, R.G. Van Name, Longmans, Green & Co., New York, 1928, volume 1, pp.&nbsp;55–353.<br />
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*Griem, H.R. (2005). ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}.<br />
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*[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', fifth revised edition, North-Holland, Amsterdam.<br />
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*Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of ''Thermodynamics'', pages 1–97 of volume 1, ed. W. Jost, of ''Physical Chemistry. An Advanced Treatise'', ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081.<br />
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*[[John Gamble Kirkwood|Kirkwood, J.G.]], Oppenheim, I. (1961). ''Chemical Thermodynamics'', McGraw-Hill Book Company, New York.<br />
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*Landsberg, P.T. (1961). ''Thermodynamics with Quantum Statistical Illustrations'', Interscience, New York.<br />
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*{{cite journal |last1=Lieb |first1=E. H. |last2=Yngvason |first2=J. |year=1999 |title=The Physics and Mathematics of the Second Law of Thermodynamics |journal=Phys. Rep. |volume=310 |issue= 1|pages=1–96 |doi= 10.1016/S0370-1573(98)00082-9|arxiv = cond-mat/9708200 |bibcode = 1999PhR...310....1L |s2cid=119620408 }}<br />
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*Levine, I.N. (1983), ''Physical Chemistry'', second edition, McGraw-Hill, New York, {{ISBN|978-0072538625}}.<br />
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*{{cite journal | last1 = Maxwell | first1 = J.C. | authorlink = James Clerk Maxwell | year = 1867 | title = On the dynamical theory of gases | url = | journal = Phil. Trans. Roy. Soc. London | volume = 157 | issue = | pages = 49–88 }}<br />
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*[[Philip M. Morse|Morse, P.M.]] (1969). ''Thermal Physics'', second edition, W.A. Benjamin, Inc, New York.<br />
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*Münster, A. (1970). ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London.<br />
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*[[J.R. Partington|Partington, J.R.]] (1949). ''An Advanced Treatise on Physical Chemistry'', volume 1, ''Fundamental Principles. The Properties of Gases'', Longmans, Green and Co., London.<br />
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*[[Brian Pippard|Pippard, A.B.]] (1957/1966). ''The Elements of Classical Thermodynamics'', reprinted with corrections 1966, Cambridge University Press, London.<br />
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* [[Max Planck|Planck. M.]] (1914). [https://archive.org/details/theoryofheatradi00planrich ''The Theory of Heat Radiation''], a translation by Masius, M. of the second German edition, P. Blakiston's Son & Co., Philadelphia.<br />
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*[[Ilya Prigogine|Prigogine, I.]] (1947). ''Étude Thermodynamique des Phénomènes irréversibles'', Dunod, Paris, and Desoers, Liège.<br />
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*[[Ilya Prigogine|Prigogine, I.]], Defay, R. (1950/1954). ''Chemical Thermodynamics'', Longmans, Green & Co, London.<br />
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*Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005). ''Physical Chemistry'', fourth edition, Wiley, Hoboken NJ.<br />
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*[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966). ''Elements of Thermodynamics'', Addison-Wesley Publishing, Reading MA.<br />
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*{{cite journal|last=Thomson|first=W.|author-link=William Thomson, 1st Baron Kelvin|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Transactions of the Royal Society of Edinburgh|date=March 1851|volume=XX|issue=part II|pages=261–268; 289–298}} Also published in {{cite journal|last=Thomson|first=W.|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Phil. Mag. |date=December 1852 |volume=IV |series=4 |issue=22 |pages=8–21 |url=https://archive.org/details/londonedinburghp04maga |accessdate=25 June 2012}}<br />
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*[[László Tisza|Tisza, L.]] (1966). ''Generalized Thermodynamics'', M.I.T Press, Cambridge MA.<br />
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*[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963). ''Lectures in Statistical Mechanics'', American Mathematical Society, Providence RI.<br />
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*Waldram, J.R. (1985). ''The Theory of Thermodynamics'', Cambridge University Press, Cambridge UK, {{ISBN|0-521-24575-3}}.<br />
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*[[Mark Zemansky|Zemansky, M.]] (1937/1968). ''Heat and Thermodynamics. An Intermediate Textbook'', fifth edition 1967, McGraw–Hill Book Company, New York.<br />
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== External links ==<br />
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Category:Equilibrium chemistry<br />
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类别: 平衡化学<br />
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*[http://ads.harvard.edu/books/1989fsa..book/AbookC15.pdf Breakdown of Local Thermodynamic Equilibrium] George W. Collins, The Fundamentals of Stellar Astrophysics, Chapter 15<br />
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Category:Thermodynamic cycles<br />
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类别: 热力循环<br />
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*[http://spiff.rit.edu/classes/phys440/lectures/lte/lte.html Thermodynamic Equilibrium, Local and otherwise] lecture by Michael Richmond<br />
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Category:Thermodynamic processes<br />
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类别: 热力学过程<br />
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*[http://journals.ametsoc.org/doi/abs/10.1175/1520-0469%281970%29027%3C0711:NLTEIC%3E2.0.CO%3B2 Non-Local Thermodynamic Equilibrium in Cloudy Planetary Atmospheres] Paper by R. E. Samueison quantifying the effects due to non-LTE in an atmosphere<br />
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Category:Thermodynamic systems<br />
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类别: 热力学系统<br />
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*[http://scienceworld.wolfram.com/physics/LocalThermodynamicEquilibrium.html Local Thermodynamic Equilibrium]<br />
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Category:Thermodynamics<br />
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分类: 热力学<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Thermodynamic equilibrium]]. Its edit history can be viewed at [[平衡热力学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%B9%B3%E8%A1%A1%E7%83%AD%E5%8A%9B%E5%AD%A6&diff=21697平衡热力学2021-02-09T07:53:56Z<p>Jxzhou:/* Fluctuations within an isolated system in its own internal thermodynamic equilibrium 孤立系统内部热力学平衡的涨落 */</p>
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<div>此词条暂由小竹凉翻译,翻译字数共5339,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{short description|State of thermodynamic system(s) where no net macroscopic flow of matter or energy occurs}}<br />
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'''Thermodynamic equilibrium''' is an [[axiomatic]] concept of [[thermodynamics]]. It is an internal [[State variables|state]] of a single [[thermodynamic system]], or a relation between several thermodynamic systems connected by more or less permeable or impermeable [[Thermodynamic system#Walls|walls]]. In thermodynamic equilibrium there are no net [[macroscopic]] [[Flow (mathematics)|flows]] of [[matter]] or of [[energy]], either within a system or between systems. <br />
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Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium there are no net macroscopic flows of matter or of energy, either within a system or between systems. <br />
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'''热力学平衡'''是'''<font color="#ff8000">热力学 Thermodynamics</font>'''的一个'''<font color="#ff8000">不言自明的 Axiomatic</font>'''概念。它是单个'''<font color="#ff8000">热力学系统 Thermodynamic System</font>'''的内部'''<font color="#ff8000">状态 State</font>''',或者是几个热力学系统之间通过或多或少的渗透或不渗透的'''<font color="#ff8000">壁 Wall</font>'''连接的关系。无论是在一个系统内还是在系统之间,在热力学平衡中不存在'''<font color="#ff8000">物质 Matter</font>'''或'''<font color="#ff8000">能量 Energy</font>'''的净'''<font color="#ff8000">宏观 Macroscopic</font>''' '''<font color="#ff8000">流动 Flow</font>'''。<br />
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In a system that is in its own state of internal thermodynamic equilibrium, no [[macroscopic]] change occurs. <br />
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In a system that is in its own state of internal thermodynamic equilibrium, no macroscopic change occurs. <br />
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在一个处于内部热力学平衡状态的系统中,不会发生'''<font color="#ff8000">宏观 Macroscopic</font>'''变化。<br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual [[Thermal equilibrium|thermal]], [[Mechanical equilibrium|mechanical]], [[Chemical equilibrium|chemical]], and [[Radiative equilibrium|radiative]] equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a [[thermodynamic operation]]. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a thermodynamic operation. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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相互热力学平衡的体系同时处于互相之间的'''<font color="#ff8000">热 Thermal</font>'''平衡、'''<font color="#ff8000">力学 Mechanical</font>'''平衡、'''<font color="#ff8000">化学 Chemical</font>'''平衡和'''<font color="#ff8000">辐射 Radiative</font>'''平衡。系统可以处于其中一种相互平衡状态,尽管其他状态未平衡。在热力学平衡中所有的平衡同时并且无限期地保持,直到被'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''打破。在一个宏观平衡中,微观交换是完全或几乎完全平衡的;这是对宏观平衡概念的物理解释。<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform [[temperature]]. Its [[Intensive and extensive properties|intensive properties]], other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform temperature. Its intensive properties, other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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一个处于内部热力学状态平衡的热力学系统具有空间均匀的'''<font color="#ff8000">温度 Temperature</font>'''。除了温度以外,它的'''<font color="#ff8000">强度性质 Intensive Properties</font>'''可以由于周围环境施加的不变的长程力场而导致空间不均匀性。<br />
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In systems that are at a state of [[non-equilibrium]] there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a '''meta-stable equilibrium'''.<br />
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In systems that are at a state of non-equilibrium there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a meta-stable equilibrium.<br />
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相比之下,处于'''<font color="#ff8000">非平衡状态 non-equilibrium</font>'''的系统中有物质或能量的净流动。如果这些变化可以在一个还没有发生的系统中被触发,那么这个系统就被称为处于一个'''亚稳定的平衡状态'''。<br />
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Though not a widely named a "law," it is an [[axiom]] of thermodynamics that there exist states of thermodynamic equilibrium. The [[second law of thermodynamics]] states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the [[entropy|entropies]] of the portions.<br />
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Though not a widely named a "law," it is an axiom of thermodynamics that there exist states of thermodynamic equilibrium. The second law of thermodynamics states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the entropies of the portions.<br />
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虽然不是一个广泛命名的“定律” ,但存在热力学平衡状态是一个热力学'''<font color="#ff8000">公理 Axiom</font>'''。'''<font color="#ff8000">热力学第二定律 second law of thermodynamics</font>'''指出,当一个物质体从一个平衡状态开始,在这个状态中,它的一部分被或多或少渗透或不渗透的分区保持在不同的状态,并且是孤立的,热力学操作移除分区或使分区更具渗透性,然后它会自发地达到自己内部热力学平衡的新状态,并伴随着部分'''<font color="#ff8000">熵 Entropy</font>'''的总和增加。<br />
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== Overview 概览==<br />
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{{Thermodynamics|cTopic=[[Thermodynamic system|Systems]]}}<br />
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Classical thermodynamics deals with states of [[dynamic equilibrium]]. The state of a system at thermodynamic equilibrium is the one for which some [[thermodynamic potential]] is minimized, or for which the [[entropy]] (''S'') is maximized, for specified conditions. One such potential is the [[Helmholtz free energy]] (''A''), for a system with surroundings at controlled constant temperature and volume:<br />
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Classical thermodynamics deals with states of dynamic equilibrium. The state of a system at thermodynamic equilibrium is the one for which some thermodynamic potential is minimized, or for which the entropy (S) is maximized, for specified conditions. One such potential is the Helmholtz free energy (A), for a system with surroundings at controlled constant temperature and volume:<br />
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经典热力学研究'''<font color="#ff8000">动态平衡 Dynamic Equilibrium</font>'''的状态。系统的热力学平衡状态是对于特定的条件,一些'''<font color="#ff8000">热力学势 Thermodynamic Potential</font>'''被最小化,或者'''<font color="#ff8000">熵 Entropy</font>'''(S)被最大化。对于一个周围环境温度和体积恒定的系统,其中一个这样的热力学势是'''<font color="#ff8000">亥姆霍兹自由能 Helmholtz Free Energy</font>'''(A):<br />
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:<math>A = U - TS</math><br />
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<math>A = U - TS</math><br />
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A = U-TS<br />
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Another potential, the [[Gibbs free energy]] (''G''), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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Another potential, the Gibbs free energy (G), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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在恒定温度和压力的系统中,另一个热力学势'''<font color="#ff8000">吉布斯自由能 Gibbs Free Energy</font>'''(G)在热力学平衡状态最小:<br />
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:<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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where ''T'' denotes the absolute thermodynamic temperature, ''P'' the pressure, ''S'' the entropy, ''V'' the volume, and ''U'' the internal energy of the system.<br />
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where T denotes the absolute thermodynamic temperature, P the pressure, S the entropy, V the volume, and U the internal energy of the system.<br />
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其中 T 表示热力学绝对温度,P 表示压强,S 表示熵,V 表示体积,U 表示体系的内能。<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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热力学平衡是一种独特的稳定定态,当系统长时间与周围环境相互作用时,它可以被接近或最终到达。上述势能是数学构造的热力学量,在特定的环境条件下最小化。<br />
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== Conditions 条件==<br />
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* For a completely isolated system, ''S'' is maximum at thermodynamic equilibrium. 对于一个完全孤立的系统,S在热力学平衡中取最大值。<br />
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* For a system with controlled constant temperature and volume, ''A'' is minimum at thermodynamic equilibrium. 对于一个恒定温度和体积的系统来说,A在热力学平衡中取最小值。<br />
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* For a system with controlled constant temperature and pressure, ''G'' is minimum at thermodynamic equilibrium. 对于一个恒温恒压的系统,G在热力学平衡中取最小值。<br />
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The various types of equilibriums are achieved as follows:<br />
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The various types of equilibriums are achieved as follows:<br />
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实现各种类型的平衡的方法如下:<br />
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*Two systems are in ''thermal equilibrium'' when their [[temperature]]s are the same. 当两个系统的'''<font color="#ff8000">温度 Temperature</font>'''相同时,它们就处于''热平衡状态''<br />
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*Two systems are in ''mechanical equilibrium'' when their [[pressure]]s are the same. 当两个体系的'''<font color="#ff8000">压力 Pressure</font>'''相同时,它们就处于''力学平衡''<br />
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*Two systems are in ''diffusive equilibrium'' when their [[chemical potential]]s are the same. 当两个题体系的'''<font color="#ff8000">化学势 Chemical Potential</font>'''相同时,它们就处于''扩散平衡''<br />
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*All [[forces]] are balanced and there is no significant external driving force.<br />
所有的'''<font color="#ff8000">力 Force</font>'''都是平衡的,没有明显的外部驱动力<br />
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==Relation of exchange equilibrium between systems 系统之间的交换均衡关系==<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability.<ref name="Nster_a">Münster, A. (1970), p. 49.</ref> When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability. When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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通常,热力学系统的周围环境也可以被看作是另一个热力学系统。在这种观点中,我们可以把系统及其周围环境看作是相互接触的两个系统,远程作用力也将它们联系在一起。系统的包围物是两个系统之间的接触面或边界。在热力学形式中,该表面被认为具有特定的渗透性质。例如,接触的表面可能被认为只能透热,使能量只能作为热传递。当远程力在时间上不发生变化,两个系统之间的热量传递减慢并最终永久停止时,这两个系统被称为热平衡; 这就是接触平衡的一个例子。其它类型的接触平衡可用其它类型的比渗透率来定义。当两个系统对于某一特定类型的渗透率处于接触平衡时,它们具有属于该特定类型渗透率的强变量的共同值。这种强度变量的例子有温度、压力、化学势。<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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接触平衡也可视为交换平衡。在接触平衡状态下,两系统之间某些量的传递速率存在零平衡。例如,对于只能透热的壁,内能作为热在两个系统之间的扩散速率是相等并反向的。两个系统之间的绝热壁只对作为功传递的能量有渗透作用; 在力学平衡,两个系统之间作为功的能量传递速率相等且相反。如果是一个简单的壁,那么通过它的体积转移率也是相等且相反的; 即它两边的压力是相等的。如果绝热壁比较复杂,有一种杠杆,有一个面积比,那么两个体系在交换平衡中的压力与体积交换比成反比,这使得转移率的零平衡作功。<br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<ref name="Planck 1914 40">[[Max Planck|Planck. M.]] (1914), p. 40.</ref><br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<br />
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辐射交换可以发生在两个不同的系统之间。当两个体系温度相同时,辐射交换平衡占优势。<br />
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==Thermodynamic state of internal equilibrium of a system 系统内部平衡的热力学状态==<br />
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A collection of matter may be entirely [[Isolated system|isolated]] from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium.<ref>Haase, R. (1971), p. 4.</ref><ref>Callen, H.B. (1960/1985), p. 26.</ref> (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics.<ref>{{Cite journal |doi = 10.1119/1.4914528|bibcode = 2015AmJPh..83..628M|title = Time and irreversibility in axiomatic thermodynamics|year = 2015|last1 = Marsland|first1 = Robert|last2 = Brown|first2 = Harvey R.|last3 = Valente|first3 = Giovanni|journal = American Journal of Physics|volume = 83|issue = 7|pages = 628–634}}</ref> One textbook<ref>[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963), p. 5.</ref> calls it the "zeroth law", remarking that the authors think this more befitting that title than its [[Zeroth law of thermodynamics|more customary definition]], which apparently was suggested by [[Ralph H. Fowler|Fowler]].)<br />
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A collection of matter may be entirely isolated from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium. (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics. One textbook calls it the "zeroth law", remarking that the authors think this more befitting that title than its more customary definition, which apparently was suggested by Fowler.)<br />
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物质的集合可能与其周围的环境完全'''<font color="#ff8000">孤立 Isolated</font>'''。如果它在无限长的时间内一直保持不受干扰,按照经典热力学假定,它处于一个没有发生任何变化,没有流动的状态,即内部平衡的热力学状态。(这种假设有时被称为“负第一”热力学定律,但并不常见。有教科书称之为“第零定律” ,作者'''<font color="#ff8000">福勒 Fowler</font>'''认为这个名称是'''<font color="#ff8000">更符合惯例的定义 More Customary Definition</font>'''。)<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a [[thermodynamic operation]] be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a thermodynamic operation be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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这种状态是所谓的经典热力学或平衡态热力学的主要关注点,因为它们是系统中被认为在这门学科中得到很好定义的唯一状态。一个与另一个系统处于接触平衡状态可以被一个'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''隔离,在隔离发生时,其内部不会发生任何变化。因此,一个与另一个系统处于接触平衡状态时也可以被视为处于其自身的内部热力学平衡状态。<br />
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==Multiple contact equilibrium 多点接触平衡==<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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热力学形式允许一个系统同时与其他多个系统接触,这些系统可能有也可能没有相互接触,且这些接触具有不同的渗透性。如果这些系统都与世界其他部分相互隔离,那么它们彼此之间就会达到各自的接触平衡。<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy.<ref name="Caratheodory">Carathéodory, C. (1909).</ref><ref>Prigogine, I. (1947), p. 48.</ref><ref>Landsberg, P. T. (1961), pp. 128–142.</ref><ref>Tisza, L. (1966), p. 108.</ref> Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy. Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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如果几个系统彼此之间没有绝热壁,但是它们与世界其他部分共同隔离,那么它们就会达到多重接触平衡状态,且有共同的温度,总的内能和熵。在众多强度量中,这是温度的一个独特性质。即使在远距离作用力存在的情况下,它也是有效的。(也就是说,没有“力”可以维持温度的差异。)举个例子,在热力学平衡的一个垂直的引力场系统中,顶部壁面的压力比底部壁面的压力小,但是各处的温度都是一样的。<br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural [[thermodynamic process]].<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), § 1.12.</ref> It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings.<ref>Levine, I.N. (1983), p. 40.</ref><ref>Lieb, E.H., Yngvason, J. (1999), pp. 17–18.</ref> The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of [[Second law of thermodynamics#Description#Kelvin statement|"inanimate" agency]]; a system in thermodynamic equilibrium is inanimate.<ref>[[William Thomson, 1st Baron Kelvin|Thomson, W.]] (1851).</ref><br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural thermodynamic process. It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings. The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of "inanimate" agency; a system in thermodynamic equilibrium is inanimate.<br />
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热力操作可能作为一个事件发生在周围环境的壁上,既不直接影响与周围环境联系的壁,也不直接影响其内部,且发生在一个明确的有限的时间内。例如,一个固定的绝热壁可以在环境中被放置或拆除。由于这种操作仅限于周围环境,系统可能会在一段时间内远离自身最初的内部状态---- 热力学平衡。根据热力学第二定律的说法,整体经历了变化并最终与周围环境达到了新的平衡。继Planck之后,这一连串的事件被称为自然'''<font color="#ff8000">热力学过程 Thermodynamic Process</font>'''。即使在这个过程中,当系统和周围环境都不处于明确的内部平衡状态时,存在着暂时偏离热力学平衡的现象,由于初始状态和最终状态都是热力学平衡的,这在平衡热力学中也是允许的。一个自然过程在其主要部分中以有限的速率进行,因此,它从根本上不同于虚构的准静态“过程”;即不在整个过程中无限缓慢地进行而且虚构地“可逆”。经典热力学允许,即使一个过程可能需要很长的时间才能达到热力学平衡,如果主要部分的过程是在一个有限的比率中,那么它被认为是自然的,并受制于热力学第二定律,即不可逆的。工程设计的机器、人工设备和操作是允许在周围环境中进行的。允许在环境中而不是在系统中进行此类操作和设备,是开尔文在他的一个热力学第二定律的陈述中提到'''<font color="#ff8000">无生命机构 Inanimate Agency</font>'''的原因; 在热力学平衡的系统是无生命的。<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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否则,热力操作可能会直接影响系统的壁。<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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通常可以很方便地假设周围的某些子系统比系统大得多,以至于这个过程只能影响周围子系统的强度变量,然后将这些子系统称为相关强度变量的储备库。<br />
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== Local and global equilibrium 局部和全局均衡==<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by [[intensive quantity|intensive]] parameters. As an example, [[temperature]] controls [[Heat equation|heat exchanges]]. ''Global thermodynamic equilibrium'' (GTE) means that those [[intensive quantity|intensive]] parameters are homogeneous throughout the whole system, while ''local thermodynamic equilibrium'' (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by intensive parameters. As an example, temperature controls heat exchanges. Global thermodynamic equilibrium (GTE) means that those intensive parameters are homogeneous throughout the whole system, while local thermodynamic equilibrium (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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区分全局性和局部性热力学平衡是很有用的。在热力学中,系统内部和系统与外部之间的交换是由'''<font color="#ff8000">强度 Intensive</font>'''参数控制的。例如,'''<font color="#ff8000">温度 Temperature</font>'''控制'''<font color="#ff8000">热交换 Heat Equation</font>'''。全局热力学平衡(GTE)意味着这些'''<font color="#ff8000">强度 Intensive</font>'''参数在整个系统中是均匀的,而局部热力学平衡(LTE)意味着这些强度参数在空间和时间上是变化的,但变化如此缓慢,以至于对于任何一点,人们都可以假设在该点的某个邻域存在热力学平衡。<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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如果对系统的描述要求强度参数的变化过大,那么这些强度参数的定义所依据的假设本身就会失效,系统将既不处于全局平衡,也不处于局部平衡。例如,粒子需要一定数量的碰撞来平衡其周围环境。如果在这些碰撞中移动的平均距离使它离开平衡邻域,它将永远不会平衡,也就不会有 LTE。根据定义,温度与平衡邻域的平均内部能量成正比。由于没有达到平衡邻域,温度的概念就不成立,温度也就变得无法定义。<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to [[massive]] particles. In a [[radiation|radiating]] gas, the [[photon]]s being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to massive particles. In a radiating gas, the photons being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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值得注意的是,这种局部平衡可能只适用于系统中的某个粒子子集。例如,LTE 通常只适用于'''<font color="#ff8000">大 Massive</font>'''质量粒子。在'''<font color="#ff8000">辐射 Radiation</font>'''气体中,被气体发射和吸收的'''<font color="#ff8000">光子 Photon</font>'''不需要彼此在一个热力学平衡内,或与气体中的大量粒子在一起,LTE 才能存在。在某些情况下,自由电子并不需要与大得多的原子或分子处于平衡状态,LTE 才能存在。<br />
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As an example, LTE will exist in a glass of water that contains a melting [[ice cube]]. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the [[Maxwell–Boltzmann distribution]] for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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As an example, LTE will exist in a glass of water that contains a melting ice cube. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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例如,LTE 将存在于一个装有正在融化的'''<font color="#ff8000">冰块 Ice Cube</font>'''的水杯中。玻璃杯内的温度可以在任何时候定义,但是离冰块近的地方要比离冰块远的地方冷。如果观察到位于给定点附近的分子的能量,它们将按照麦克斯韦-波兹曼分布在一定温度下的分布。如果观察到位于另一点附近的分子的能量,它们将按照'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''分布到另一个温度。<br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural [[transport phenomena]] may lead a system from local to global thermodynamic equilibrium. Going back to our example, the [[diffusion]] of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<ref>H.R. Griem, 2005</ref><br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural transport phenomena may lead a system from local to global thermodynamic equilibrium. Going back to our example, the diffusion of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<br />
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局部热力学平衡不需要局部或全局的平稳性。换句话说,每一个小区域不需要有一个恒定的温度。然而,它确实要求每个小的局部变化缓慢到足以维持其局部麦克斯韦-波尔兹曼速度分布。全局非平衡态只有通过系统与外界的交换才能保持稳定。例如,通过在水杯中不断添加细粉冰来补偿熔化,并持续排出融水,可以保持全局稳定的静态。自然'''<font color="#ff8000">输运现象 Transport Phenomena</font>'''会使一个局部热力学平衡系统逐渐达到全局的热力学平衡。回顾我们的例子,热量的扩散将导致我们的玻璃杯水流向全局热力学平衡,在这种状态下,玻璃杯的温度是完全均匀的。<br />
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==Reservations 保留意见==<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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学识渊博的笔者在热力学领域对热力学平衡描述时,经常对他们的描述附加条件或保留意见。有些笔者含蓄地保留了或多或少的空白,以待说明。<br />
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For example, one widely cited writer, [[Herbert Callen|H. B. Callen]] writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. ''Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!''"<ref>Callen, H.B. (1960/1985), p. 15.</ref><br />
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For example, one widely cited writer, H. B. Callen writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!"<br />
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例如,一位被广泛引用的作家'''<font color="#ff8000">H.B.卡伦 H.B.Callen</font>'''在这里写道: “实际上,很少有系统处于绝对和真正的平衡状态。”他提到了放射性过程,认为它们可能需要“宇宙时间才能完成,因此通常可以忽略”。他补充道: “在实践中,平衡的标准是循环的。在操作上,如果一个系统的性质一致地用热力学理论来描述,那么它就处于平衡状态! ”<br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<ref>Beattie, J.A., Oppenheim, I. (1979), p. 3.</ref><br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<br />
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J.A.贝蒂和 I.奥本海姆写道: “坚持对平衡定义的严格解释,将排除热力学应用于实际系统的所有状态。”<br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment",<ref>Callen, H.B. (1960/1985), p. 485.</ref> and cited by Adkins as having written a "classic text",<ref>Adkins, C.J. (1968/1983), p. ''xiii''.</ref> [[Brian Pippard|A.B. Pippard]] writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<ref>Pippard, A.B. (1957/1966), p. 6.</ref><br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment", and cited by Adkins as having written a "classic text", A.B. Pippard writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<br />
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Callen引用另一位作者的话说,他给出了“学术且严谨的论述” ,Adkins引用他的话说,他写了一本“经典著作”—— '''<font color="#ff8000">A.B.皮帕德 A.B.Pippard</font>'''在文中写道: “只要时间足够长,过冷水蒸汽最终会凝结,... ..。时间可能是漫长的,也许长达10年或者更长。就大多数目的而言,只要这种迅速的变化不是人为地刺激,这些系统就可以被视为处于平衡状态。”<br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster">Münster, A. (1970), p. 53.</ref><br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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另一位作者A.Münster,写道。他观察到热核反应发生的速度非常缓慢,以至于在热力学中可以忽略不计。他评论道: “‘绝对平衡’或‘所有可想象过程的平衡’的概念没有物理意义。”他说: “ ... 我们只能考虑特定过程和确定的实验条件下的平衡。”<br />
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According to [[László Tisza|L. Tisza]]: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<ref>Tisza, L. (1966), p. 119.</ref><br />
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According to L. Tisza: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<br />
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根据'''<font color="#ff8000">L.缇莎 L.Tisza</font>'''的说法: “ ... 在讨论接近绝对零度的现象时。经典理论的绝对预测变得特别模糊,因为在非平衡状态下发生冻结是非常普遍的。”<br />
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==Definitions 定义==<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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一个系统最普遍的热力学平衡是通过与周围环境的接触,允许所有化学物质和各种能量同时通过。热力学平衡中的系统可能以均匀加速度在空间中运动,但此时不能改变其形状或大小; 因此它是由空间中的刚性体积来定义的。它可能存在于外力场中,由远远大于系统本身的外部因素决定,因此系统内的事件不会对外力场产生相当大的影响。只有当外力场是均匀的,并且确定了它的均匀加速度,或者它处于一个非均匀力场中,但是由于表面的局部力,例如机械压力,使它保持静止时,这个系统才能处于热力学平衡。<br />
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Thermodynamic equilibrium is a [[primitive notion]] of the theory of thermodynamics. According to [[Philip M. Morse|P.M. Morse]]: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are ''not'' conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments."<ref>[[Philip M. Morse|Morse, P.M.]] (1969), p. 7.</ref> This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<ref>Bailyn, M. (1994), p. 20.</ref><br />
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Thermodynamic equilibrium is a primitive notion of the theory of thermodynamics. According to P.M. Morse: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are not conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments." This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<br />
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热力学平衡是热力学理论的一个'''<font color="#ff8000">基本概念 Primitive Notion</font>'''。'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''说: “应该强调的是,存在热力学状态这一事实,以及存在由平衡态唯一指定的热力学变量这一事实,并不是从某些哲学第一原理得出的逻辑结论。这些结论不可避免地来自两个多世纪的实验。”这意味着热力学平衡不能仅仅用热力学的其他理论概念来定义。M.Bailyn提出了一个基本的热力学定律理论,它定义并假设了热力学平衡的存在。<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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热力学平衡的教科书定义通常被仔细说明,并有些保留。<br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<ref>Münster, A. (1970), p. 52.</ref><br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<br />
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例如,A. Münster写道:“当一个孤立系统中没有以可测量的速率发生状态变化时,系统处于热力学平衡状态。”这里有两项保留:系统是孤立的;任何状态的变化都是不可测量的缓慢。他通过对在室温且没有催化剂的情况下混合氧和氢的说明,讨论了第二个条件。Münster指出,描述热力学平衡状态所需要的宏观变量比给定系统任何其他状态都少。这是部分,但不完全是,因为系统内和流过系统的所有流都是零。<br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in ''equilibrium''.<ref>Haase, R. (1971), pp. 3–4.</ref><br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in equilibrium.<br />
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R. Haase's的热力学演示并不从对热力学平衡的限制开始,因为他打算考虑非平衡态热力学。他考虑一个具有时间不变性质的任意系统。他通过切断除外力场以外的所有外部影响来测试它的热力学平衡。如果在绝缘之后,没有任何变化,他说,系统处于平衡状态。<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness".<ref>Callen, H.B. (1960/1985), p. 13.</ref> This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness". This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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在一个标题为“热力学平衡”的章节中,H.B. Callen在一个段落中定义了平衡状态.他指出,它们“是由系统内部的内在因素决定的”。它们是“终端状态” ,随着时间的推移,系统会以“冰川般缓慢”的速度朝着这个终端状态演化。这个说法并没有明确,对于热力学平衡系统必须是孤立的;;Callen也没有说明他所说的“内在因素”是什么意思。<br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<ref>Adkins, C.J. (1968/1983), p. ''7''.</ref><br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<br />
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另一位教科书作者,C.J.Adkins,明确允许热力学平衡在非孤立的系统中发生。然而,他的系统在物质转移方面是封闭的。他写道: “一般来说,热力学平衡的方法包括热和类似功的形式与周围环境的相互作用。”他将这种热力学平衡与只有通过热接触才能进行能量传递的热平衡相区别。<br />
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Another textbook author, [[J.R. Partington]], writes: "(i) ''An equilibrium state is one which is independent of time''." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..."<ref>Partington, J.R. (1949), p. 161.</ref> This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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Another textbook author, J.R. Partington, writes: "(i) An equilibrium state is one which is independent of time." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..." This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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另一位教科书作者'''<font color="#ff8000">J.R.帕廷顿 J.R.Partington</font>'''写道: “(i)平衡状态是独立于时间的状态。”但是,在提到“只是明显处于平衡状态”的系统时,他补充说: “这样的系统处于‘虚假平衡’状态。帕廷顿的陈述没有明确指出平衡是指一个孤立的系统。和Münster一样,Partington也指的是氧和氢的混合物。他补充说:“在一个真正的平衡状态,任何影响状态的外部条件的微小变化都会产生一个微小的状态变化... ... ”这个条件意味着热力学平衡必须在小的扰动下保持稳定; 这个要求对于热力学平衡的严格意义是必不可少的。<br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, ''thermodynamic—equilibrium.''"<ref>Crawford, F.H. (1963), p. 5.</ref><br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, thermodynamic—equilibrium."<br />
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在F.H.Crawford的一本学生教科书中,有一个标题为“热力学平衡”的章节。它区分了几种流动的驱动因素,然后说: “这些是孤立系统明显普遍趋向于完全机械、热、化学和电力状态的例子——或者简单地说,热力学平衡状态。”<br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in ''equilibrium''."<ref>Buchdahl, H.A. (1966), p. 8.</ref> Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being ''in equilibrium'' so long as experimental tests show that 'slow' transitions are in effect reversible."<ref>Buchdahl, H.A. (1966), p. 111.</ref> It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<ref>Adkins, C.J. (1968/1983), p. 8.</ref><br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in equilibrium." Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being in equilibrium so long as experimental tests show that 'slow' transitions are in effect reversible." It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<br />
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H.A. Buchdahl的一本关于经典热力学的专著考虑了热力学系统的平衡,而实际上并没有写热力学平衡一词。Buchdahl在提到封闭的物质交换系统时写道: “如果一个系统处于一个适当的静态状态,那么它将被称为处于平衡状态。”出于热力学描述的目的,Buchdahl的专著也讨论了非晶态玻璃。它说: “更准确地说,只要实验测试表明‘慢’跃迁实际上是可逆的,玻璃就可以被认为处于平衡状态。”通常来说不会将这一条件作为热力学平衡定义的一部分,而是假定相反的情况:如果热力学平衡中的一个物体受到足够慢的过程的影响,则该过程可被视为足够接近可逆,并且该物体在过程中足够接近热力学平衡。<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of ''contact equilibrium''. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by [[Constantin Carathéodory|C. Carathéodory]], and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster" /> Thermodynamic equilibrium for an open system means that, with respect to every relevant kind of selectively permeable wall, contact equilibrium exists when the respective intensive parameters of the system and surroundings are equal.<ref name="Nster_a" /> This definition does not consider the most general kind of thermodynamic equilibrium, which is through unselective contacts. This definition does not simply state that no current of matter or energy exists in the interior or at the boundaries; but it is compatible with the following definition, which does so state.<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of contact equilibrium. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by C. Carathéodory, and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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通过引入接触平衡的概念,A. Münster仔细地扩展了孤立系统热力学平衡的定义。这指定了在考虑非孤立系统的热力学平衡时允许的特定过程,并特别关心开放系统,这些开放系统可能从周围环境获得或丢失物质。感兴趣的系统和周围系统之间的接触平衡,通过一种特殊的壁与之接触,其余的连接系统是孤立的。这种特殊类型的壁也被'''<font color="#ff8000">C.喀喇西奥多里 C.Carathéodory</font>'''考虑过,其他作家也提到过。它们具有选择渗透性。它们可能只对机械功有渗透性,或者只对热有渗透性,或者只对某种特定的化学物质有渗透性。每个接触平衡定义了一个强度参数; 例如,只能透热的壁定义了一个经验温度。对于感兴趣的体系中每一种化学成分,都可以存在接触平衡。在接触平衡中,尽管有可能通过选择性渗透壁进行交换,但是感兴趣的系统是不变的,好像它处在孤立的热力学平衡。这个方案遵循的一般规则是: “ ... ... 我们只能考虑特定过程和特定实验条件下的平衡。”<br />
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[[Mark Zemansky|M. Zemansky]] also distinguishes mechanical, chemical, and thermal equilibrium. He then writes: "When the conditions for all three types of equilibrium are satisfied, the system is said to be in a state of thermodynamic equilibrium".<ref>[[Mark Zemansky|Zemansky, M.]] (1937/1968), p. 27.</ref><br />
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'''<font color="#ff8000">M.泽曼斯基 M.Zemansky</font>'''还区分了力学、化学和热平衡。他接着写道: “当这三种均衡的条件都满足时,系统就处于热力学平衡状态。”<br />
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P.M. Morse writes that thermodynamics is concerned with "states of thermodynamic equilibrium". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<br />
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[[Philip M. Morse|P.M. Morse]] writes that thermodynamics is concerned with "''states of thermodynamic equilibrium''". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<ref>[[Philip M. Morse|Morse, P.M.]] (1969), pp. 6, 37.</ref><br />
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'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''写道,热力学关注的是“热力学平衡状态”。在讨论物体与周围热源之间的热量传递时,他也使用了“热平衡”这个短语,尽管没有明确定义一个特殊的术语“热平衡”<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "full thermodynamic equilibrium state".<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "''full'' thermodynamic equilibrium state".<ref>Waldram, J.R. (1985), p. 5.</ref><br />
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J.R. Waldram写到了“一个明确的热力学状态”。他将一个系统定义为“当其观测量随时间停止变化时”的“热平衡”。但是在这个定义之下不久,他写到一块玻璃还没有达到“完全的热力学平衡状态”。<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, thermodynamic equilibrium is said to exist." He is not here considering the presence of an external force field.<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, ''thermodynamic equilibrium'' is said to exist." He is not here considering the presence of an external force field.<ref>Bailyn, M. (1994), p. 21.</ref><br />
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考虑到平衡状态,M.Bailyn写道: “每个强度变量都有自己的平衡类型。”然后他定义了热平衡、力学平衡和物质平衡。因此,他写道: “如果所有的强度变量都是一致的,那么热力学平衡就是存在的。”他在这里没有考虑外力场的存在。<br />
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J.G. Kirkwood and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of thermodynamic equilibrium if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<br />
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[[John Gamble Kirkwood|J.G. Kirkwood]] and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of ''thermodynamic equilibrium'' if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<ref>Kirkwood, J.G., Oppenheim, I. (1961), p. 2</ref><br />
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'''<font color="#ff8000">J.G.柯克伍德 J.G.Kirkwood</font>'''和 I.Oppenheim 将热力学平衡定义为: “一个系统处于热力学平衡状态,如果,在实验的时间内,(a)它强度特性与时间无关,(b)它的内部或与周围环境的边界处没有物质或能量流。”显然,他们没有把定义限制在孤立的或封闭的系统。它们不讨论“缓慢”发生变化的可能性,并且超出了分配给实验的时间范围。他们注意到,对于两个相接触的系统,存在一个强度性质的小子类,如果这个小子类的所有子类都相等,那么所有各自的强度性质都相等。只要满足其他一些条件,热力学平衡状态可以由这个子类定义。<br />
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==Characteristics of a state of internal thermodynamic equilibrium 内部热力学平衡状态的特征==<br />
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===Homogeneity in the absence of external forces 在没有外力的情况下的均匀性===<br />
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A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous.<ref name="Planck 1903 3"/> This means that the material in any small volume element of the system can be interchanged with the material of any other geometrically congruent volume element of the system, and the effect is to leave the system thermodynamically unchanged. In general, a strong external force field makes a system of a single phase in its own internal thermodynamic equilibrium inhomogeneous with respect to some [[Intensive and extensive properties|intensive variables]]. For example, a relatively dense component of a mixture can be concentrated by centrifugation.<br />
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在没有外力的情况下,由单一相组成的热力学系统,在其自身的内部热力学平衡中是均匀的。这意味着系统中任何小体积单元中的材料可以与系统中任何其他几何相等的体积单元中的材料互换,其效果是使系统在热力学上保持不变。一般来说,一个强外力场使得一个单相系统在其自身的内部热力学平衡中对于一些'''<font color="#ff8000">强度量 Intensive Variable</font>'''是不均匀的。例如,可以通过离心来浓缩混合物中相对密度较大的组分。<br />
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===Uniform temperature 均匀温度===<br />
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Such equilibrium inhomogeneity, induced by external forces, does not occur for the intensive variable [[temperature]]. According to [[Edward A. Guggenheim|E.A. Guggenheim]], "The most important conception of thermodynamics is temperature."<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), p.5.</ref> Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface."<ref name="Planck 1903 3">[[Max Planck|Planck, M.]] (1897/1927), p.3.</ref> As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.<br />
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这种由外力引起的平衡不均匀性,对于强度量'''<font color="#ff8000">温度 Temperature</font>'''不会发生。'''<font color="#ff8000">E.A.古根海姆 E.A. Guggenheim</font>'''认为,“热力学最重要的概念是温度。“Planck在介绍他的论文时,简要叙述了热、温度和热平衡,然后宣布: ”在下文中,我们将主要讨论任何形式的均匀、各向同性的物体,它们的物质具有相同的温度和密度,并受到到处垂直于表面的均匀压力的作用。和Carathéodory 一样,Planck将表面效应、外场和各向异性晶体排除在外。虽然Planck提到了温度,但并没有明确提到热力学平衡的概念。相比之下,Carathéodory关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ,虽然没有明确地使用短语‘热力学平衡’ ,也没有明确地假设存在一个温度来定义它。<br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform.<ref name="Planck 1914 40"/> This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers.<ref>Gibbs, J.W. (1876/1878), pp. 144-150.</ref><ref>[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966), pp. 127–130.</ref><ref>Münster, A. (1970), pp. 309–310.</ref><ref>Bailyn, M. (1994), pp. 254-256.</ref><ref>{{cite journal | last1 = Verkley | first1 = W.T.M. | last2 = Gerkema | first2 = T. | year = 2004 | title = On maximum entropy profiles | journal = J. Atmos. Sci. | volume = 61 | issue = 8| pages = 931–936 | doi=10.1175/1520-0469(2004)061<0931:omep>2.0.co;2| bibcode = 2004JAtS...61..931V | doi-access = free }}</ref><ref>{{cite journal | last1 = Akmaev | first1 = R.A. | year = 2008 | title = On the energetics of maximum-entropy temperature profiles | url = | journal = Q. J. R. Meteorol. Soc. | volume = 134 | issue = 630| pages = 187–197 | doi=10.1002/qj.209| bibcode = 2008QJRMS.134..187A }}</ref> Considerations of kinetic theory or statistical mechanics also support this statement.<ref>Maxwell, J.C. (1867).</ref><ref>Boltzmann, L. (1896/1964), p. 143.</ref><ref>Chapman, S., Cowling, T.G. (1939/1970), Section 4.14, pp. 75–78.</ref><ref>[[J. R. Partington|Partington, J.R.]] (1949), pp. 275–278.</ref><ref>{{cite journal | last1 = Coombes | first1 = C.A. | last2 = Laue | first2 = H. | year = 1985 | title = A paradox concerning the temperature distribution of a gas in a gravitational field | url = | journal = Am. J. Phys. | volume = 53 | issue = 3| pages = 272–273 | doi=10.1119/1.14138| bibcode = 1985AmJPh..53..272C }}</ref><ref>{{cite journal | last1 = Román | first1 = F.L. | last2 = White | first2 = J.A. | last3 = Velasco | first3 = S. | year = 1995 | title = Microcanonical single-particle distributions for an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 16 | issue = 2| pages = 83–90 | doi=10.1088/0143-0807/16/2/008| bibcode = 1995EJPh...16...83R }}</ref><ref>{{cite journal | last1 = Velasco | first1 = S. | last2 = Román | first2 = F.L. | last3 = White | first3 = J.A. | year = 1996 | title = On a paradox concerning the temperature distribution of an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 17 | issue = | pages = 43–44 | doi=10.1088/0143-0807/17/1/008}}</ref><br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform. This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers. Considerations of kinetic theory or statistical mechanics also support this statement.<br />
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热力学平衡系统内的温度在时间和空间上都是均匀的。在一个处于内部热力学平衡的系统中,不存在净的内部宏观流动。特别是,这意味着系统的所有局部都处于相互辐射交换平衡。这意味着系统的温度在空间上是均匀的。这在所有情况下都是如此,包括那些非均匀外力场。对于外部施加的引力场,这可以使用拉格郎日乘子法通过变分的计算在宏观热力学术语中证明。动力学理论或统计力学也支持这种说法。<br />
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In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium.<ref name="Fitts 43"/><br />
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为了使一个系统处于它自己的内部热力学平衡状态,它必须处于它自己的内部热平衡状态是必要不充分的; 一个系统在到达内部热平衡之前到达内部力学平衡是可能的。<br />
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===Number of real variables needed for specification 规范所需的实变量数目===<br />
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In his exposition of his scheme of closed system equilibrium thermodynamics, C. Carathéodory initially postulates that experiment reveals that a definite number of real variables define the states that are the points of the manifold of equilibria.<ref name="Caratheodory" /> In the words of Prigogine and Defay (1945): "It is a matter of experience that when we have specified a certain number of macroscopic properties of a system, then all the other properties are fixed."<ref>Prigogine, I., Defay, R. (1950/1954), p. 1.</ref><ref>Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005), p. 4.</ref> As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.<br />
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在他关于封闭系统平衡态热力学方案的论述中,C.Carathéodory 最初假定实验揭示了一定数量的实变量定义了作为平衡态流形点的状态。用 Prigogine 和 Defay (1945)的话说: “这是一个经验问题,当我们确定了一个系统一定数量的宏观属性时,那么所有其他属性都是固定的”。如上所述,A. Münster认为,定义热力学平衡所需的变量数量相对于给定孤立系统的任何状态来说都是最少的。如上所述,J.G. Kirkwood 和 I. Oppenheim 指出,热力学平衡状态可以由一个特殊子类的强度变量来定义,该子类中有一定数量的成员。<br />
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If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.<br />
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如果热力学平衡位于一个外力场中,那么通常只有温度在空间上是均匀的。如果外力场非零,温度以外的强度变量通常是不均匀的。在这种情况下,一般需要附加变量来描述空间非均匀性。<br />
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===Stability against small perturbations 对小扰动的稳定性===<br />
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As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.<br />
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如上所述,J.R. Partington 指出热力学平衡状态在小的瞬态扰动下是稳定的。如果没有这个条件,一般来说,研究热力学平衡系统的实验就会遇到严重的困难。<br />
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===Approach to thermodynamic equilibrium within an isolated system 孤立系统中的热力学平衡===<br />
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When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium. Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<br />
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When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium.<ref name="Fitts 43">Fitts, D.D. (1962), p. 43.</ref> Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<ref>Denbigh, K.G. (1951), p. 42.</ref><br />
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当一个物质体从不均匀的非平衡状态或化学非平衡状态开始,然后被孤立,它会自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如,在这种演化的许多情况下,内部力学平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是,在这种演化的许多情况下,热平衡的发展要比化学平衡快得多。<br />
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===Fluctuations within an isolated system in its own internal thermodynamic equilibrium 孤立系统内部热力学平衡的涨落===<br />
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In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
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在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
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To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics.<ref>Tschoegl, N.W. (2000). ''Fundamentals of Equilibrium and Steady-State Thermodynamics'', Elsevier, Amsterdam, {{ISBN|0-444-50426-5}}, p. 21.</ref> But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
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To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics. But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
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考虑孤立热力学系统中的涨落概念,一个方便的例子是由其内能、体积和质量组成等广延量表示的系统。根据定义,它们是不随时间变化的。根据定义,这些量与它们的共轭状态强度函数的时不变名义值相结合,包括逆温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广延量的值,不足以提供这些名义值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
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It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.<br />
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可以承认,在重复测量这些共轭强度状态函数时,发现它们的值随时间略有不同。这种可变性被认为是由于内部涨落。不同测量值平均到其名义值。<br />
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If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<ref>Buchdahl, H.A. (1966), p. 16.</ref><br />
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If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<br />
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如果系统真的像经典热力学所假定的那样是宏观的,那么系统的涨落很小以至于宏观上无法检测到。这就是所谓的热力学极限。实际上,物质的分子性质和动量转移的量子性质由于它们太小而看不见,已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中,平衡的涨落概念是不存在的。”<br />
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If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
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如果系统被重复细分,最终产生的系统足够小,可以表现出明显的涨落。这是一个介观层面的研究。涨落则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
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If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在涨落过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,并且需要量子统计力学。涨落可以变得相对占主导地位,测量问题变得重要。<br />
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The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
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"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有随时间变化趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的名义值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微涨落期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。除非已知属于平衡状态的名义值,否则根据单一的度量无法进行判断。<br />
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=== Thermal equilibrium ===<br />
热平衡<br />
{{Main|Thermal equilibrium}}<br />
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An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process."<ref>Eu, B.C. (2002), page 13.</ref> This illustrates the importance for thermodynamics of the concept of temperature.<br />
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热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
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A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<br />
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一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数。<br />
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[[Thermal equilibrium]] is achieved when two systems in [[thermal contact]] with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<ref>[[Raj Pathria|R. K. Pathria]], 1996</ref><br />
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当两个相互'''<font color="#ff8000">热接触 Thermal Contact</font>'''的系统不再有净能量交换时,就会产生'''<font color="#ff8000">热平衡 Thermal Equilibrium</font>'''。因此,如果两个系统处于热平衡,那么它们的温度是相同的<br />
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Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
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Thermal equilibrium occurs when a system's [[macroscopic]] thermal observables have ceased to change with time. For example, an [[ideal gas]] whose [[Distribution function (physics)|distribution function]] has stabilised to a specific [[Maxwell–Boltzmann distribution]] would be in thermal equilibrium. This outcome allows a single [[temperature]] and [[pressure]] to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<ref>de Groot, S.R., Mazur, P. (1962), p. 44.</ref><br />
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当一个系统的'''<font color="#ff8000">宏观 Macroscopic</font>'''热观测值不再随时间变化时,就会出现热平衡。例如,一种'''<font color="#ff8000">分布函数 Distribution Function</font>'''稳定到一个特定的'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''的'''<font color="#ff8000">理想气体 Ideal Gas</font>'''即处于热平衡状态。这个结果可以将单一的'''<font color="#ff8000">温度 Temperature</font>'''和'''<font color="#ff8000">压力 Pressure</font>'''归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
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Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle. It states that a non-equilibrium system evolves such as to maximize its entropy production.<br />
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定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
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==Non-equilibrium==<br />
非平衡<br />
{{Main|Non-equilibrium thermodynamics}}<br />
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Thermodynamic models <br />
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热力学模型<br />
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A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<ref>de Groot, S.R., Mazur, P. (1962), p. 43.</ref><br />
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一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数<br />
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Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
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Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle.<ref>{{cite book|last1=Ziegler|first1=H.|title=An Introduction to Thermomechanics.|date=1983|location=North Holland, Amsterdam.}}</ref><ref>{{cite journal|last1=Onsager|first1=Lars|title=Reciprocal Relations in Irreversible Processes|journal=Phys. Rev.|date=1931|volume=37|issue=4|doi=10.1103/PhysRev.37.405|bibcode=1931PhRv...37..405O|pages=405–426|doi-access=free}}</ref> It states that a non-equilibrium system evolves such as to maximize its entropy production.<ref>{{cite book|last1=Kleidon|first1=A.|last2=et.|first2=al.|title=Non-equilibrium Thermodynamics and the Production of Entropy.|date=2005|edition=Heidelberg: Springer.}}</ref><ref>{{cite journal|last1=Belkin|first1=Andrey|last2=et.|first2=al.|title=Self-Assembled Wiggling Nano-Structures and the Principle of Maximum Entropy Production|journal=Sci. Rep.|doi=10.1038/srep08323|bibcode=2015NatSR...5E8323B|pmc=4321171|pmid=25662746|volume=5|year=2015|page=8323}}</ref><br />
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定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
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Topics in control theory<br />
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控制理论主题<br />
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==See also ==<br />
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{{Portal|Chemistry}}<br />
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;Thermodynamic models 热力学模型<br />
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{{colbegin}}<br />
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* [[Non-random two-liquid model]] (NRTL model) - Phase equilibrium calculations 非随机两液模型(NRTL 模型)-相平衡计算<br />
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* [[UNIQUAC]] model - Phase equilibrium calculations UNIQUAC 模型-相平衡计算<br />
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* [[Time crystal]] 时间晶体<br />
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{{colend}}<br />
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;Topics in control theory 控制理论主题<br />
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{{colbegin}}<br />
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* [[Steady state]] 稳态<br />
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* [[Transient state]] 瞬态<br />
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* [[Coefficient diagram method]] 系数图法<br />
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* [[Control reconfiguration]] 控制重构<br />
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* [[Cut-insertion theorem]] 切入定理<br />
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* [[Feedback]] 反馈<br />
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* [[H infinity]] H 无限<br />
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* [[Hankel singular value]] 汉克尔奇异值<br />
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* [[Krener's theorem]] 克雷纳定理<br />
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* [[Lead-lag compensator]] 超前滞后补偿器<br />
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* [[Minor loop feedback]] 小循环反馈<br />
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* [[Minor loop feedback|Multi-loop feedback]] 小循环反馈 | 多循环反馈<br />
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* [[Positive systems]] 正向系统<br />
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* [[Radial basis function]] 径向基底函数<br />
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Other related topics<br />
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其他相关话题<br />
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* [[Root locus]] 根轨迹<br />
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* [[Signal-flow graph]]s 信号流图<br />
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* [[Stable polynomial]] 稳定多项式<br />
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* [[State space representation]] 状态空间<br />
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* [[Underactuation]] 欠驱动<br />
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* [[Youla–Kucera parametrization]] 尤拉-库切拉参数化<br />
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* [[Markov chain approximation method]] 马尔可夫链近似法<br />
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{{colend}}<br />
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;Other related topics<br />
其他相关话题<br />
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{{colbegin}}<br />
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* [[Automation and remote control]] 自动化和远程控制<br />
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* [[Bond graph]] 键合图<br />
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* [[Control engineering]] 控制工程<br />
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* [[Control–feedback–abort loop]] 控制-反馈-中止循环<br />
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* [[Controller (control theory)]] 控制器(控制理论)<br />
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* [[Cybernetics]] 控制论<br />
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* [[Intelligent control]] 智能控制<br />
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* [[Mathematical system theory]] 数学系统论<br />
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* [[Negative feedback amplifier]] 负反馈放大器<br />
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* [[People in systems and control]] 系统和控制中的人<br />
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* [[Perceptual control theory]] 知觉控制理论<br />
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* [[Systems theory]] 系统论<br />
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* [[Time scale calculus]] 时间尺度演算<br />
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{{colend}}<br />
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== 编者推荐 ==<br />
===集智文章推荐===<br />
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====[https://swarma.org/?p=21322 什么是非平衡态热力学 | 集智百科]====<br />
非平衡态热力学 Non-equilibrium thermodynamics 是热力学的一个分支,研究某些不处于热力学平衡中的物理系统<br />
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==General references==<br />
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* Cesare Barbieri (2007) ''Fundamentals of Astronomy''. First Edition (QB43.3.B37 2006) CRC Press {{ISBN|0-7503-0886-9}}, {{ISBN|978-0-7503-0886-1}}<br />
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* Hans R. Griem (2005) ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}<br />
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* C. Michael Hogan, Leda C. Patmore and Harry Seidman (1973) ''Statistical Prediction of Dynamic Thermal Equilibrium Temperatures using Standard Meteorological Data Bases'', Second Edition (EPA-660/2-73-003 2006) United States Environmental Protection Agency Office of Research and Development, Washington, D.C. [http://library.wur.nl/WebQuery/catalog/lang/1851848]<br />
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* F. Mandl (1988) ''Statistical Physics'', Second Edition, John Wiley & Sons<br />
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==References==<br />
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{{Reflist|colwidth=35em}}<br />
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==Cited bibliography==<br />
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*Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', third edition, McGraw-Hill, London, {{ISBN|0-521-25445-0}}.<br />
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*Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, {{ISBN|0-88318-797-3}}.<br />
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*Beattie, J.A., Oppenheim, I. (1979). ''Principles of Thermodynamics'', Elsevier Scientific Publishing, Amsterdam, {{ISBN|0-444-41806-7}}.<br />
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*[[Ludwig Boltzmann|Boltzmann, L.]] (1896/1964). ''Lectures on Gas Theory'', translated by S.G. Brush, University of California Press, Berkeley.<br />
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*Buchdahl, H.A. (1966). ''The Concepts of Classical Thermodynamics'', Cambridge University Press, Cambridge UK.<br />
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*[[Herbert Callen|Callen, H.B.]] (1960/1985). ''Thermodynamics and an Introduction to Thermostatistics'', (1st edition 1960) 2nd edition 1985, Wiley, New York, {{ISBN|0-471-86256-8}}.<br />
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*[[Constantin Carathéodory|Carathéodory, C.]] (1909). [https://web.archive.org/web/20160304213645/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0067&DMDID=DMDLOG_0033&L=1 Untersuchungen über die Grundlagen der Thermodynamik], ''[[Mathematische Annalen]]'', '''67''': 355–386. A translation may be found [http://neo-classical-physics.info/uploads/3/0/6/5/3065888/caratheodory_-_thermodynamics.pdf here]. Also a mostly reliable [https://books.google.com/books?id=xwBRAAAAMAAJ&q=Investigation+into+the+foundations translation is to be found] at Kestin, J. (1976). ''The Second Law of Thermodynamics'', Dowden, Hutchinson & Ross, Stroudsburg PA.<br />
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*[[Sydney Chapman (mathematician)|Chapman, S.]], [[Thomas George Cowling|Cowling, T.G.]] (1939/1970). ''The Mathematical Theory of Non-uniform gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases'', third edition 1970, Cambridge University Press, London.<br />
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*Crawford, F.H. (1963). ''Heat, Thermodynamics, and Statistical Physics'', Rupert Hart-Davis, London, Harcourt, Brace & World, Inc.<br />
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*de Groot, S.R., Mazur, P. (1962). ''Non-equilibrium Thermodynamics'', North-Holland, Amsterdam. Reprinted (1984), Dover Publications Inc., New York, {{ISBN|0486647412}}.<br />
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*Denbigh, K.G. (1951). ''Thermodynamics of the Steady State'', Methuen, London.<br />
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*Eu, B.C. (2002). ''Generalized Thermodynamics. The Thermodynamics of Irreversible Processes and Generalized Hydrodynamics'', Kluwer Academic Publishers, Dordrecht, {{ISBN|1-4020-0788-4}}.<br />
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*Fitts, D.D. (1962). ''Nonequilibrium thermodynamics. A Phenomenological Theory of Irreversible Processes in Fluid Systems'', McGraw-Hill, New York.<br />
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*[[Josiah Willard Gibbs|Gibbs, J.W.]] (1876/1878). On the equilibrium of heterogeneous substances, ''Trans. Conn. Acad.'', '''3''': 108–248, 343–524, reprinted in ''The Collected Works of J. Willard Gibbs, Ph.D, LL. D.'', edited by W.R. Longley, R.G. Van Name, Longmans, Green & Co., New York, 1928, volume 1, pp.&nbsp;55–353.<br />
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*Griem, H.R. (2005). ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}.<br />
<br />
*[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', fifth revised edition, North-Holland, Amsterdam.<br />
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*Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of ''Thermodynamics'', pages 1–97 of volume 1, ed. W. Jost, of ''Physical Chemistry. An Advanced Treatise'', ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081.<br />
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*[[John Gamble Kirkwood|Kirkwood, J.G.]], Oppenheim, I. (1961). ''Chemical Thermodynamics'', McGraw-Hill Book Company, New York.<br />
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*Landsberg, P.T. (1961). ''Thermodynamics with Quantum Statistical Illustrations'', Interscience, New York.<br />
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*{{cite journal |last1=Lieb |first1=E. H. |last2=Yngvason |first2=J. |year=1999 |title=The Physics and Mathematics of the Second Law of Thermodynamics |journal=Phys. Rep. |volume=310 |issue= 1|pages=1–96 |doi= 10.1016/S0370-1573(98)00082-9|arxiv = cond-mat/9708200 |bibcode = 1999PhR...310....1L |s2cid=119620408 }}<br />
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*Levine, I.N. (1983), ''Physical Chemistry'', second edition, McGraw-Hill, New York, {{ISBN|978-0072538625}}.<br />
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*{{cite journal | last1 = Maxwell | first1 = J.C. | authorlink = James Clerk Maxwell | year = 1867 | title = On the dynamical theory of gases | url = | journal = Phil. Trans. Roy. Soc. London | volume = 157 | issue = | pages = 49–88 }}<br />
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*[[Philip M. Morse|Morse, P.M.]] (1969). ''Thermal Physics'', second edition, W.A. Benjamin, Inc, New York.<br />
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*Münster, A. (1970). ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London.<br />
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*[[J.R. Partington|Partington, J.R.]] (1949). ''An Advanced Treatise on Physical Chemistry'', volume 1, ''Fundamental Principles. The Properties of Gases'', Longmans, Green and Co., London.<br />
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*[[Brian Pippard|Pippard, A.B.]] (1957/1966). ''The Elements of Classical Thermodynamics'', reprinted with corrections 1966, Cambridge University Press, London.<br />
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* [[Max Planck|Planck. M.]] (1914). [https://archive.org/details/theoryofheatradi00planrich ''The Theory of Heat Radiation''], a translation by Masius, M. of the second German edition, P. Blakiston's Son & Co., Philadelphia.<br />
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*[[Ilya Prigogine|Prigogine, I.]] (1947). ''Étude Thermodynamique des Phénomènes irréversibles'', Dunod, Paris, and Desoers, Liège.<br />
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*[[Ilya Prigogine|Prigogine, I.]], Defay, R. (1950/1954). ''Chemical Thermodynamics'', Longmans, Green & Co, London.<br />
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*Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005). ''Physical Chemistry'', fourth edition, Wiley, Hoboken NJ.<br />
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*[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966). ''Elements of Thermodynamics'', Addison-Wesley Publishing, Reading MA.<br />
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*{{cite journal|last=Thomson|first=W.|author-link=William Thomson, 1st Baron Kelvin|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Transactions of the Royal Society of Edinburgh|date=March 1851|volume=XX|issue=part II|pages=261–268; 289–298}} Also published in {{cite journal|last=Thomson|first=W.|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Phil. Mag. |date=December 1852 |volume=IV |series=4 |issue=22 |pages=8–21 |url=https://archive.org/details/londonedinburghp04maga |accessdate=25 June 2012}}<br />
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*[[László Tisza|Tisza, L.]] (1966). ''Generalized Thermodynamics'', M.I.T Press, Cambridge MA.<br />
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*[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963). ''Lectures in Statistical Mechanics'', American Mathematical Society, Providence RI.<br />
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*Waldram, J.R. (1985). ''The Theory of Thermodynamics'', Cambridge University Press, Cambridge UK, {{ISBN|0-521-24575-3}}.<br />
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*[[Mark Zemansky|Zemansky, M.]] (1937/1968). ''Heat and Thermodynamics. An Intermediate Textbook'', fifth edition 1967, McGraw–Hill Book Company, New York.<br />
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== External links ==<br />
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Category:Equilibrium chemistry<br />
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类别: 平衡化学<br />
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*[http://ads.harvard.edu/books/1989fsa..book/AbookC15.pdf Breakdown of Local Thermodynamic Equilibrium] George W. Collins, The Fundamentals of Stellar Astrophysics, Chapter 15<br />
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Category:Thermodynamic cycles<br />
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类别: 热力循环<br />
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*[http://spiff.rit.edu/classes/phys440/lectures/lte/lte.html Thermodynamic Equilibrium, Local and otherwise] lecture by Michael Richmond<br />
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Category:Thermodynamic processes<br />
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类别: 热力学过程<br />
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*[http://journals.ametsoc.org/doi/abs/10.1175/1520-0469%281970%29027%3C0711:NLTEIC%3E2.0.CO%3B2 Non-Local Thermodynamic Equilibrium in Cloudy Planetary Atmospheres] Paper by R. E. Samueison quantifying the effects due to non-LTE in an atmosphere<br />
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Category:Thermodynamic systems<br />
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类别: 热力学系统<br />
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*[http://scienceworld.wolfram.com/physics/LocalThermodynamicEquilibrium.html Local Thermodynamic Equilibrium]<br />
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Category:Thermodynamics<br />
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分类: 热力学<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Thermodynamic equilibrium]]. Its edit history can be viewed at [[平衡热力学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%B9%B3%E8%A1%A1%E7%83%AD%E5%8A%9B%E5%AD%A6&diff=21696平衡热力学2021-02-09T07:49:16Z<p>Jxzhou:/* Fluctuations within an isolated system in its own internal thermodynamic equilibrium 孤立系统内部热力学平衡的涨落 */</p>
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<div>此词条暂由小竹凉翻译,翻译字数共5339,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{short description|State of thermodynamic system(s) where no net macroscopic flow of matter or energy occurs}}<br />
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'''Thermodynamic equilibrium''' is an [[axiomatic]] concept of [[thermodynamics]]. It is an internal [[State variables|state]] of a single [[thermodynamic system]], or a relation between several thermodynamic systems connected by more or less permeable or impermeable [[Thermodynamic system#Walls|walls]]. In thermodynamic equilibrium there are no net [[macroscopic]] [[Flow (mathematics)|flows]] of [[matter]] or of [[energy]], either within a system or between systems. <br />
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Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium there are no net macroscopic flows of matter or of energy, either within a system or between systems. <br />
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'''热力学平衡'''是'''<font color="#ff8000">热力学 Thermodynamics</font>'''的一个'''<font color="#ff8000">不言自明的 Axiomatic</font>'''概念。它是单个'''<font color="#ff8000">热力学系统 Thermodynamic System</font>'''的内部'''<font color="#ff8000">状态 State</font>''',或者是几个热力学系统之间通过或多或少的渗透或不渗透的'''<font color="#ff8000">壁 Wall</font>'''连接的关系。无论是在一个系统内还是在系统之间,在热力学平衡中不存在'''<font color="#ff8000">物质 Matter</font>'''或'''<font color="#ff8000">能量 Energy</font>'''的净'''<font color="#ff8000">宏观 Macroscopic</font>''' '''<font color="#ff8000">流动 Flow</font>'''。<br />
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In a system that is in its own state of internal thermodynamic equilibrium, no [[macroscopic]] change occurs. <br />
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In a system that is in its own state of internal thermodynamic equilibrium, no macroscopic change occurs. <br />
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在一个处于内部热力学平衡状态的系统中,不会发生'''<font color="#ff8000">宏观 Macroscopic</font>'''变化。<br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual [[Thermal equilibrium|thermal]], [[Mechanical equilibrium|mechanical]], [[Chemical equilibrium|chemical]], and [[Radiative equilibrium|radiative]] equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a [[thermodynamic operation]]. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a thermodynamic operation. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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相互热力学平衡的体系同时处于互相之间的'''<font color="#ff8000">热 Thermal</font>'''平衡、'''<font color="#ff8000">力学 Mechanical</font>'''平衡、'''<font color="#ff8000">化学 Chemical</font>'''平衡和'''<font color="#ff8000">辐射 Radiative</font>'''平衡。系统可以处于其中一种相互平衡状态,尽管其他状态未平衡。在热力学平衡中所有的平衡同时并且无限期地保持,直到被'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''打破。在一个宏观平衡中,微观交换是完全或几乎完全平衡的;这是对宏观平衡概念的物理解释。<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform [[temperature]]. Its [[Intensive and extensive properties|intensive properties]], other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform temperature. Its intensive properties, other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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一个处于内部热力学状态平衡的热力学系统具有空间均匀的'''<font color="#ff8000">温度 Temperature</font>'''。除了温度以外,它的'''<font color="#ff8000">强度性质 Intensive Properties</font>'''可以由于周围环境施加的不变的长程力场而导致空间不均匀性。<br />
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In systems that are at a state of [[non-equilibrium]] there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a '''meta-stable equilibrium'''.<br />
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In systems that are at a state of non-equilibrium there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a meta-stable equilibrium.<br />
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相比之下,处于'''<font color="#ff8000">非平衡状态 non-equilibrium</font>'''的系统中有物质或能量的净流动。如果这些变化可以在一个还没有发生的系统中被触发,那么这个系统就被称为处于一个'''亚稳定的平衡状态'''。<br />
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Though not a widely named a "law," it is an [[axiom]] of thermodynamics that there exist states of thermodynamic equilibrium. The [[second law of thermodynamics]] states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the [[entropy|entropies]] of the portions.<br />
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Though not a widely named a "law," it is an axiom of thermodynamics that there exist states of thermodynamic equilibrium. The second law of thermodynamics states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the entropies of the portions.<br />
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虽然不是一个广泛命名的“定律” ,但存在热力学平衡状态是一个热力学'''<font color="#ff8000">公理 Axiom</font>'''。'''<font color="#ff8000">热力学第二定律 second law of thermodynamics</font>'''指出,当一个物质体从一个平衡状态开始,在这个状态中,它的一部分被或多或少渗透或不渗透的分区保持在不同的状态,并且是孤立的,热力学操作移除分区或使分区更具渗透性,然后它会自发地达到自己内部热力学平衡的新状态,并伴随着部分'''<font color="#ff8000">熵 Entropy</font>'''的总和增加。<br />
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== Overview 概览==<br />
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{{Thermodynamics|cTopic=[[Thermodynamic system|Systems]]}}<br />
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Classical thermodynamics deals with states of [[dynamic equilibrium]]. The state of a system at thermodynamic equilibrium is the one for which some [[thermodynamic potential]] is minimized, or for which the [[entropy]] (''S'') is maximized, for specified conditions. One such potential is the [[Helmholtz free energy]] (''A''), for a system with surroundings at controlled constant temperature and volume:<br />
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Classical thermodynamics deals with states of dynamic equilibrium. The state of a system at thermodynamic equilibrium is the one for which some thermodynamic potential is minimized, or for which the entropy (S) is maximized, for specified conditions. One such potential is the Helmholtz free energy (A), for a system with surroundings at controlled constant temperature and volume:<br />
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经典热力学研究'''<font color="#ff8000">动态平衡 Dynamic Equilibrium</font>'''的状态。系统的热力学平衡状态是对于特定的条件,一些'''<font color="#ff8000">热力学势 Thermodynamic Potential</font>'''被最小化,或者'''<font color="#ff8000">熵 Entropy</font>'''(S)被最大化。对于一个周围环境温度和体积恒定的系统,其中一个这样的热力学势是'''<font color="#ff8000">亥姆霍兹自由能 Helmholtz Free Energy</font>'''(A):<br />
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:<math>A = U - TS</math><br />
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<math>A = U - TS</math><br />
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A = U-TS<br />
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Another potential, the [[Gibbs free energy]] (''G''), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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Another potential, the Gibbs free energy (G), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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在恒定温度和压力的系统中,另一个热力学势'''<font color="#ff8000">吉布斯自由能 Gibbs Free Energy</font>'''(G)在热力学平衡状态最小:<br />
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:<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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where ''T'' denotes the absolute thermodynamic temperature, ''P'' the pressure, ''S'' the entropy, ''V'' the volume, and ''U'' the internal energy of the system.<br />
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where T denotes the absolute thermodynamic temperature, P the pressure, S the entropy, V the volume, and U the internal energy of the system.<br />
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其中 T 表示热力学绝对温度,P 表示压强,S 表示熵,V 表示体积,U 表示体系的内能。<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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热力学平衡是一种独特的稳定定态,当系统长时间与周围环境相互作用时,它可以被接近或最终到达。上述势能是数学构造的热力学量,在特定的环境条件下最小化。<br />
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== Conditions 条件==<br />
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* For a completely isolated system, ''S'' is maximum at thermodynamic equilibrium. 对于一个完全孤立的系统,S在热力学平衡中取最大值。<br />
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* For a system with controlled constant temperature and volume, ''A'' is minimum at thermodynamic equilibrium. 对于一个恒定温度和体积的系统来说,A在热力学平衡中取最小值。<br />
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* For a system with controlled constant temperature and pressure, ''G'' is minimum at thermodynamic equilibrium. 对于一个恒温恒压的系统,G在热力学平衡中取最小值。<br />
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The various types of equilibriums are achieved as follows:<br />
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The various types of equilibriums are achieved as follows:<br />
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实现各种类型的平衡的方法如下:<br />
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*Two systems are in ''thermal equilibrium'' when their [[temperature]]s are the same. 当两个系统的'''<font color="#ff8000">温度 Temperature</font>'''相同时,它们就处于''热平衡状态''<br />
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*Two systems are in ''mechanical equilibrium'' when their [[pressure]]s are the same. 当两个体系的'''<font color="#ff8000">压力 Pressure</font>'''相同时,它们就处于''力学平衡''<br />
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*Two systems are in ''diffusive equilibrium'' when their [[chemical potential]]s are the same. 当两个题体系的'''<font color="#ff8000">化学势 Chemical Potential</font>'''相同时,它们就处于''扩散平衡''<br />
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*All [[forces]] are balanced and there is no significant external driving force.<br />
所有的'''<font color="#ff8000">力 Force</font>'''都是平衡的,没有明显的外部驱动力<br />
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==Relation of exchange equilibrium between systems 系统之间的交换均衡关系==<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability.<ref name="Nster_a">Münster, A. (1970), p. 49.</ref> When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability. When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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通常,热力学系统的周围环境也可以被看作是另一个热力学系统。在这种观点中,我们可以把系统及其周围环境看作是相互接触的两个系统,远程作用力也将它们联系在一起。系统的包围物是两个系统之间的接触面或边界。在热力学形式中,该表面被认为具有特定的渗透性质。例如,接触的表面可能被认为只能透热,使能量只能作为热传递。当远程力在时间上不发生变化,两个系统之间的热量传递减慢并最终永久停止时,这两个系统被称为热平衡; 这就是接触平衡的一个例子。其它类型的接触平衡可用其它类型的比渗透率来定义。当两个系统对于某一特定类型的渗透率处于接触平衡时,它们具有属于该特定类型渗透率的强变量的共同值。这种强度变量的例子有温度、压力、化学势。<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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接触平衡也可视为交换平衡。在接触平衡状态下,两系统之间某些量的传递速率存在零平衡。例如,对于只能透热的壁,内能作为热在两个系统之间的扩散速率是相等并反向的。两个系统之间的绝热壁只对作为功传递的能量有渗透作用; 在力学平衡,两个系统之间作为功的能量传递速率相等且相反。如果是一个简单的壁,那么通过它的体积转移率也是相等且相反的; 即它两边的压力是相等的。如果绝热壁比较复杂,有一种杠杆,有一个面积比,那么两个体系在交换平衡中的压力与体积交换比成反比,这使得转移率的零平衡作功。<br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<ref name="Planck 1914 40">[[Max Planck|Planck. M.]] (1914), p. 40.</ref><br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<br />
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辐射交换可以发生在两个不同的系统之间。当两个体系温度相同时,辐射交换平衡占优势。<br />
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==Thermodynamic state of internal equilibrium of a system 系统内部平衡的热力学状态==<br />
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A collection of matter may be entirely [[Isolated system|isolated]] from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium.<ref>Haase, R. (1971), p. 4.</ref><ref>Callen, H.B. (1960/1985), p. 26.</ref> (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics.<ref>{{Cite journal |doi = 10.1119/1.4914528|bibcode = 2015AmJPh..83..628M|title = Time and irreversibility in axiomatic thermodynamics|year = 2015|last1 = Marsland|first1 = Robert|last2 = Brown|first2 = Harvey R.|last3 = Valente|first3 = Giovanni|journal = American Journal of Physics|volume = 83|issue = 7|pages = 628–634}}</ref> One textbook<ref>[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963), p. 5.</ref> calls it the "zeroth law", remarking that the authors think this more befitting that title than its [[Zeroth law of thermodynamics|more customary definition]], which apparently was suggested by [[Ralph H. Fowler|Fowler]].)<br />
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A collection of matter may be entirely isolated from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium. (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics. One textbook calls it the "zeroth law", remarking that the authors think this more befitting that title than its more customary definition, which apparently was suggested by Fowler.)<br />
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物质的集合可能与其周围的环境完全'''<font color="#ff8000">孤立 Isolated</font>'''。如果它在无限长的时间内一直保持不受干扰,按照经典热力学假定,它处于一个没有发生任何变化,没有流动的状态,即内部平衡的热力学状态。(这种假设有时被称为“负第一”热力学定律,但并不常见。有教科书称之为“第零定律” ,作者'''<font color="#ff8000">福勒 Fowler</font>'''认为这个名称是'''<font color="#ff8000">更符合惯例的定义 More Customary Definition</font>'''。)<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a [[thermodynamic operation]] be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a thermodynamic operation be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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这种状态是所谓的经典热力学或平衡态热力学的主要关注点,因为它们是系统中被认为在这门学科中得到很好定义的唯一状态。一个与另一个系统处于接触平衡状态可以被一个'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''隔离,在隔离发生时,其内部不会发生任何变化。因此,一个与另一个系统处于接触平衡状态时也可以被视为处于其自身的内部热力学平衡状态。<br />
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==Multiple contact equilibrium 多点接触平衡==<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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热力学形式允许一个系统同时与其他多个系统接触,这些系统可能有也可能没有相互接触,且这些接触具有不同的渗透性。如果这些系统都与世界其他部分相互隔离,那么它们彼此之间就会达到各自的接触平衡。<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy.<ref name="Caratheodory">Carathéodory, C. (1909).</ref><ref>Prigogine, I. (1947), p. 48.</ref><ref>Landsberg, P. T. (1961), pp. 128–142.</ref><ref>Tisza, L. (1966), p. 108.</ref> Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy. Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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如果几个系统彼此之间没有绝热壁,但是它们与世界其他部分共同隔离,那么它们就会达到多重接触平衡状态,且有共同的温度,总的内能和熵。在众多强度量中,这是温度的一个独特性质。即使在远距离作用力存在的情况下,它也是有效的。(也就是说,没有“力”可以维持温度的差异。)举个例子,在热力学平衡的一个垂直的引力场系统中,顶部壁面的压力比底部壁面的压力小,但是各处的温度都是一样的。<br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural [[thermodynamic process]].<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), § 1.12.</ref> It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings.<ref>Levine, I.N. (1983), p. 40.</ref><ref>Lieb, E.H., Yngvason, J. (1999), pp. 17–18.</ref> The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of [[Second law of thermodynamics#Description#Kelvin statement|"inanimate" agency]]; a system in thermodynamic equilibrium is inanimate.<ref>[[William Thomson, 1st Baron Kelvin|Thomson, W.]] (1851).</ref><br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural thermodynamic process. It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings. The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of "inanimate" agency; a system in thermodynamic equilibrium is inanimate.<br />
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热力操作可能作为一个事件发生在周围环境的壁上,既不直接影响与周围环境联系的壁,也不直接影响其内部,且发生在一个明确的有限的时间内。例如,一个固定的绝热壁可以在环境中被放置或拆除。由于这种操作仅限于周围环境,系统可能会在一段时间内远离自身最初的内部状态---- 热力学平衡。根据热力学第二定律的说法,整体经历了变化并最终与周围环境达到了新的平衡。继Planck之后,这一连串的事件被称为自然'''<font color="#ff8000">热力学过程 Thermodynamic Process</font>'''。即使在这个过程中,当系统和周围环境都不处于明确的内部平衡状态时,存在着暂时偏离热力学平衡的现象,由于初始状态和最终状态都是热力学平衡的,这在平衡热力学中也是允许的。一个自然过程在其主要部分中以有限的速率进行,因此,它从根本上不同于虚构的准静态“过程”;即不在整个过程中无限缓慢地进行而且虚构地“可逆”。经典热力学允许,即使一个过程可能需要很长的时间才能达到热力学平衡,如果主要部分的过程是在一个有限的比率中,那么它被认为是自然的,并受制于热力学第二定律,即不可逆的。工程设计的机器、人工设备和操作是允许在周围环境中进行的。允许在环境中而不是在系统中进行此类操作和设备,是开尔文在他的一个热力学第二定律的陈述中提到'''<font color="#ff8000">无生命机构 Inanimate Agency</font>'''的原因; 在热力学平衡的系统是无生命的。<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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否则,热力操作可能会直接影响系统的壁。<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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通常可以很方便地假设周围的某些子系统比系统大得多,以至于这个过程只能影响周围子系统的强度变量,然后将这些子系统称为相关强度变量的储备库。<br />
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== Local and global equilibrium 局部和全局均衡==<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by [[intensive quantity|intensive]] parameters. As an example, [[temperature]] controls [[Heat equation|heat exchanges]]. ''Global thermodynamic equilibrium'' (GTE) means that those [[intensive quantity|intensive]] parameters are homogeneous throughout the whole system, while ''local thermodynamic equilibrium'' (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by intensive parameters. As an example, temperature controls heat exchanges. Global thermodynamic equilibrium (GTE) means that those intensive parameters are homogeneous throughout the whole system, while local thermodynamic equilibrium (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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区分全局性和局部性热力学平衡是很有用的。在热力学中,系统内部和系统与外部之间的交换是由'''<font color="#ff8000">强度 Intensive</font>'''参数控制的。例如,'''<font color="#ff8000">温度 Temperature</font>'''控制'''<font color="#ff8000">热交换 Heat Equation</font>'''。全局热力学平衡(GTE)意味着这些'''<font color="#ff8000">强度 Intensive</font>'''参数在整个系统中是均匀的,而局部热力学平衡(LTE)意味着这些强度参数在空间和时间上是变化的,但变化如此缓慢,以至于对于任何一点,人们都可以假设在该点的某个邻域存在热力学平衡。<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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如果对系统的描述要求强度参数的变化过大,那么这些强度参数的定义所依据的假设本身就会失效,系统将既不处于全局平衡,也不处于局部平衡。例如,粒子需要一定数量的碰撞来平衡其周围环境。如果在这些碰撞中移动的平均距离使它离开平衡邻域,它将永远不会平衡,也就不会有 LTE。根据定义,温度与平衡邻域的平均内部能量成正比。由于没有达到平衡邻域,温度的概念就不成立,温度也就变得无法定义。<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to [[massive]] particles. In a [[radiation|radiating]] gas, the [[photon]]s being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to massive particles. In a radiating gas, the photons being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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值得注意的是,这种局部平衡可能只适用于系统中的某个粒子子集。例如,LTE 通常只适用于'''<font color="#ff8000">大 Massive</font>'''质量粒子。在'''<font color="#ff8000">辐射 Radiation</font>'''气体中,被气体发射和吸收的'''<font color="#ff8000">光子 Photon</font>'''不需要彼此在一个热力学平衡内,或与气体中的大量粒子在一起,LTE 才能存在。在某些情况下,自由电子并不需要与大得多的原子或分子处于平衡状态,LTE 才能存在。<br />
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As an example, LTE will exist in a glass of water that contains a melting [[ice cube]]. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the [[Maxwell–Boltzmann distribution]] for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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As an example, LTE will exist in a glass of water that contains a melting ice cube. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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例如,LTE 将存在于一个装有正在融化的'''<font color="#ff8000">冰块 Ice Cube</font>'''的水杯中。玻璃杯内的温度可以在任何时候定义,但是离冰块近的地方要比离冰块远的地方冷。如果观察到位于给定点附近的分子的能量,它们将按照麦克斯韦-波兹曼分布在一定温度下的分布。如果观察到位于另一点附近的分子的能量,它们将按照'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''分布到另一个温度。<br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural [[transport phenomena]] may lead a system from local to global thermodynamic equilibrium. Going back to our example, the [[diffusion]] of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<ref>H.R. Griem, 2005</ref><br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural transport phenomena may lead a system from local to global thermodynamic equilibrium. Going back to our example, the diffusion of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<br />
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局部热力学平衡不需要局部或全局的平稳性。换句话说,每一个小区域不需要有一个恒定的温度。然而,它确实要求每个小的局部变化缓慢到足以维持其局部麦克斯韦-波尔兹曼速度分布。全局非平衡态只有通过系统与外界的交换才能保持稳定。例如,通过在水杯中不断添加细粉冰来补偿熔化,并持续排出融水,可以保持全局稳定的静态。自然'''<font color="#ff8000">输运现象 Transport Phenomena</font>'''会使一个局部热力学平衡系统逐渐达到全局的热力学平衡。回顾我们的例子,热量的扩散将导致我们的玻璃杯水流向全局热力学平衡,在这种状态下,玻璃杯的温度是完全均匀的。<br />
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==Reservations 保留意见==<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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学识渊博的笔者在热力学领域对热力学平衡描述时,经常对他们的描述附加条件或保留意见。有些笔者含蓄地保留了或多或少的空白,以待说明。<br />
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For example, one widely cited writer, [[Herbert Callen|H. B. Callen]] writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. ''Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!''"<ref>Callen, H.B. (1960/1985), p. 15.</ref><br />
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For example, one widely cited writer, H. B. Callen writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!"<br />
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例如,一位被广泛引用的作家'''<font color="#ff8000">H.B.卡伦 H.B.Callen</font>'''在这里写道: “实际上,很少有系统处于绝对和真正的平衡状态。”他提到了放射性过程,认为它们可能需要“宇宙时间才能完成,因此通常可以忽略”。他补充道: “在实践中,平衡的标准是循环的。在操作上,如果一个系统的性质一致地用热力学理论来描述,那么它就处于平衡状态! ”<br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<ref>Beattie, J.A., Oppenheim, I. (1979), p. 3.</ref><br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<br />
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J.A.贝蒂和 I.奥本海姆写道: “坚持对平衡定义的严格解释,将排除热力学应用于实际系统的所有状态。”<br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment",<ref>Callen, H.B. (1960/1985), p. 485.</ref> and cited by Adkins as having written a "classic text",<ref>Adkins, C.J. (1968/1983), p. ''xiii''.</ref> [[Brian Pippard|A.B. Pippard]] writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<ref>Pippard, A.B. (1957/1966), p. 6.</ref><br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment", and cited by Adkins as having written a "classic text", A.B. Pippard writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<br />
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Callen引用另一位作者的话说,他给出了“学术且严谨的论述” ,Adkins引用他的话说,他写了一本“经典著作”—— '''<font color="#ff8000">A.B.皮帕德 A.B.Pippard</font>'''在文中写道: “只要时间足够长,过冷水蒸汽最终会凝结,... ..。时间可能是漫长的,也许长达10年或者更长。就大多数目的而言,只要这种迅速的变化不是人为地刺激,这些系统就可以被视为处于平衡状态。”<br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster">Münster, A. (1970), p. 53.</ref><br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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另一位作者A.Münster,写道。他观察到热核反应发生的速度非常缓慢,以至于在热力学中可以忽略不计。他评论道: “‘绝对平衡’或‘所有可想象过程的平衡’的概念没有物理意义。”他说: “ ... 我们只能考虑特定过程和确定的实验条件下的平衡。”<br />
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According to [[László Tisza|L. Tisza]]: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<ref>Tisza, L. (1966), p. 119.</ref><br />
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According to L. Tisza: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<br />
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根据'''<font color="#ff8000">L.缇莎 L.Tisza</font>'''的说法: “ ... 在讨论接近绝对零度的现象时。经典理论的绝对预测变得特别模糊,因为在非平衡状态下发生冻结是非常普遍的。”<br />
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==Definitions 定义==<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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一个系统最普遍的热力学平衡是通过与周围环境的接触,允许所有化学物质和各种能量同时通过。热力学平衡中的系统可能以均匀加速度在空间中运动,但此时不能改变其形状或大小; 因此它是由空间中的刚性体积来定义的。它可能存在于外力场中,由远远大于系统本身的外部因素决定,因此系统内的事件不会对外力场产生相当大的影响。只有当外力场是均匀的,并且确定了它的均匀加速度,或者它处于一个非均匀力场中,但是由于表面的局部力,例如机械压力,使它保持静止时,这个系统才能处于热力学平衡。<br />
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Thermodynamic equilibrium is a [[primitive notion]] of the theory of thermodynamics. According to [[Philip M. Morse|P.M. Morse]]: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are ''not'' conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments."<ref>[[Philip M. Morse|Morse, P.M.]] (1969), p. 7.</ref> This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<ref>Bailyn, M. (1994), p. 20.</ref><br />
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Thermodynamic equilibrium is a primitive notion of the theory of thermodynamics. According to P.M. Morse: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are not conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments." This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<br />
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热力学平衡是热力学理论的一个'''<font color="#ff8000">基本概念 Primitive Notion</font>'''。'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''说: “应该强调的是,存在热力学状态这一事实,以及存在由平衡态唯一指定的热力学变量这一事实,并不是从某些哲学第一原理得出的逻辑结论。这些结论不可避免地来自两个多世纪的实验。”这意味着热力学平衡不能仅仅用热力学的其他理论概念来定义。M.Bailyn提出了一个基本的热力学定律理论,它定义并假设了热力学平衡的存在。<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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热力学平衡的教科书定义通常被仔细说明,并有些保留。<br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<ref>Münster, A. (1970), p. 52.</ref><br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<br />
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例如,A. Münster写道:“当一个孤立系统中没有以可测量的速率发生状态变化时,系统处于热力学平衡状态。”这里有两项保留:系统是孤立的;任何状态的变化都是不可测量的缓慢。他通过对在室温且没有催化剂的情况下混合氧和氢的说明,讨论了第二个条件。Münster指出,描述热力学平衡状态所需要的宏观变量比给定系统任何其他状态都少。这是部分,但不完全是,因为系统内和流过系统的所有流都是零。<br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in ''equilibrium''.<ref>Haase, R. (1971), pp. 3–4.</ref><br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in equilibrium.<br />
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R. Haase's的热力学演示并不从对热力学平衡的限制开始,因为他打算考虑非平衡态热力学。他考虑一个具有时间不变性质的任意系统。他通过切断除外力场以外的所有外部影响来测试它的热力学平衡。如果在绝缘之后,没有任何变化,他说,系统处于平衡状态。<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness".<ref>Callen, H.B. (1960/1985), p. 13.</ref> This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness". This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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在一个标题为“热力学平衡”的章节中,H.B. Callen在一个段落中定义了平衡状态.他指出,它们“是由系统内部的内在因素决定的”。它们是“终端状态” ,随着时间的推移,系统会以“冰川般缓慢”的速度朝着这个终端状态演化。这个说法并没有明确,对于热力学平衡系统必须是孤立的;;Callen也没有说明他所说的“内在因素”是什么意思。<br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<ref>Adkins, C.J. (1968/1983), p. ''7''.</ref><br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<br />
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另一位教科书作者,C.J.Adkins,明确允许热力学平衡在非孤立的系统中发生。然而,他的系统在物质转移方面是封闭的。他写道: “一般来说,热力学平衡的方法包括热和类似功的形式与周围环境的相互作用。”他将这种热力学平衡与只有通过热接触才能进行能量传递的热平衡相区别。<br />
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Another textbook author, [[J.R. Partington]], writes: "(i) ''An equilibrium state is one which is independent of time''." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..."<ref>Partington, J.R. (1949), p. 161.</ref> This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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Another textbook author, J.R. Partington, writes: "(i) An equilibrium state is one which is independent of time." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..." This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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另一位教科书作者'''<font color="#ff8000">J.R.帕廷顿 J.R.Partington</font>'''写道: “(i)平衡状态是独立于时间的状态。”但是,在提到“只是明显处于平衡状态”的系统时,他补充说: “这样的系统处于‘虚假平衡’状态。帕廷顿的陈述没有明确指出平衡是指一个孤立的系统。和Münster一样,Partington也指的是氧和氢的混合物。他补充说:“在一个真正的平衡状态,任何影响状态的外部条件的微小变化都会产生一个微小的状态变化... ... ”这个条件意味着热力学平衡必须在小的扰动下保持稳定; 这个要求对于热力学平衡的严格意义是必不可少的。<br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, ''thermodynamic—equilibrium.''"<ref>Crawford, F.H. (1963), p. 5.</ref><br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, thermodynamic—equilibrium."<br />
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在F.H.Crawford的一本学生教科书中,有一个标题为“热力学平衡”的章节。它区分了几种流动的驱动因素,然后说: “这些是孤立系统明显普遍趋向于完全机械、热、化学和电力状态的例子——或者简单地说,热力学平衡状态。”<br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in ''equilibrium''."<ref>Buchdahl, H.A. (1966), p. 8.</ref> Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being ''in equilibrium'' so long as experimental tests show that 'slow' transitions are in effect reversible."<ref>Buchdahl, H.A. (1966), p. 111.</ref> It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<ref>Adkins, C.J. (1968/1983), p. 8.</ref><br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in equilibrium." Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being in equilibrium so long as experimental tests show that 'slow' transitions are in effect reversible." It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<br />
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H.A. Buchdahl的一本关于经典热力学的专著考虑了热力学系统的平衡,而实际上并没有写热力学平衡一词。Buchdahl在提到封闭的物质交换系统时写道: “如果一个系统处于一个适当的静态状态,那么它将被称为处于平衡状态。”出于热力学描述的目的,Buchdahl的专著也讨论了非晶态玻璃。它说: “更准确地说,只要实验测试表明‘慢’跃迁实际上是可逆的,玻璃就可以被认为处于平衡状态。”通常来说不会将这一条件作为热力学平衡定义的一部分,而是假定相反的情况:如果热力学平衡中的一个物体受到足够慢的过程的影响,则该过程可被视为足够接近可逆,并且该物体在过程中足够接近热力学平衡。<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of ''contact equilibrium''. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by [[Constantin Carathéodory|C. Carathéodory]], and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster" /> Thermodynamic equilibrium for an open system means that, with respect to every relevant kind of selectively permeable wall, contact equilibrium exists when the respective intensive parameters of the system and surroundings are equal.<ref name="Nster_a" /> This definition does not consider the most general kind of thermodynamic equilibrium, which is through unselective contacts. This definition does not simply state that no current of matter or energy exists in the interior or at the boundaries; but it is compatible with the following definition, which does so state.<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of contact equilibrium. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by C. Carathéodory, and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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通过引入接触平衡的概念,A. Münster仔细地扩展了孤立系统热力学平衡的定义。这指定了在考虑非孤立系统的热力学平衡时允许的特定过程,并特别关心开放系统,这些开放系统可能从周围环境获得或丢失物质。感兴趣的系统和周围系统之间的接触平衡,通过一种特殊的壁与之接触,其余的连接系统是孤立的。这种特殊类型的壁也被'''<font color="#ff8000">C.喀喇西奥多里 C.Carathéodory</font>'''考虑过,其他作家也提到过。它们具有选择渗透性。它们可能只对机械功有渗透性,或者只对热有渗透性,或者只对某种特定的化学物质有渗透性。每个接触平衡定义了一个强度参数; 例如,只能透热的壁定义了一个经验温度。对于感兴趣的体系中每一种化学成分,都可以存在接触平衡。在接触平衡中,尽管有可能通过选择性渗透壁进行交换,但是感兴趣的系统是不变的,好像它处在孤立的热力学平衡。这个方案遵循的一般规则是: “ ... ... 我们只能考虑特定过程和特定实验条件下的平衡。”<br />
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[[Mark Zemansky|M. Zemansky]] also distinguishes mechanical, chemical, and thermal equilibrium. He then writes: "When the conditions for all three types of equilibrium are satisfied, the system is said to be in a state of thermodynamic equilibrium".<ref>[[Mark Zemansky|Zemansky, M.]] (1937/1968), p. 27.</ref><br />
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'''<font color="#ff8000">M.泽曼斯基 M.Zemansky</font>'''还区分了力学、化学和热平衡。他接着写道: “当这三种均衡的条件都满足时,系统就处于热力学平衡状态。”<br />
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P.M. Morse writes that thermodynamics is concerned with "states of thermodynamic equilibrium". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<br />
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[[Philip M. Morse|P.M. Morse]] writes that thermodynamics is concerned with "''states of thermodynamic equilibrium''". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<ref>[[Philip M. Morse|Morse, P.M.]] (1969), pp. 6, 37.</ref><br />
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'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''写道,热力学关注的是“热力学平衡状态”。在讨论物体与周围热源之间的热量传递时,他也使用了“热平衡”这个短语,尽管没有明确定义一个特殊的术语“热平衡”<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "full thermodynamic equilibrium state".<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "''full'' thermodynamic equilibrium state".<ref>Waldram, J.R. (1985), p. 5.</ref><br />
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J.R. Waldram写到了“一个明确的热力学状态”。他将一个系统定义为“当其观测量随时间停止变化时”的“热平衡”。但是在这个定义之下不久,他写到一块玻璃还没有达到“完全的热力学平衡状态”。<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, thermodynamic equilibrium is said to exist." He is not here considering the presence of an external force field.<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, ''thermodynamic equilibrium'' is said to exist." He is not here considering the presence of an external force field.<ref>Bailyn, M. (1994), p. 21.</ref><br />
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考虑到平衡状态,M.Bailyn写道: “每个强度变量都有自己的平衡类型。”然后他定义了热平衡、力学平衡和物质平衡。因此,他写道: “如果所有的强度变量都是一致的,那么热力学平衡就是存在的。”他在这里没有考虑外力场的存在。<br />
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J.G. Kirkwood and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of thermodynamic equilibrium if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<br />
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[[John Gamble Kirkwood|J.G. Kirkwood]] and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of ''thermodynamic equilibrium'' if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<ref>Kirkwood, J.G., Oppenheim, I. (1961), p. 2</ref><br />
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'''<font color="#ff8000">J.G.柯克伍德 J.G.Kirkwood</font>'''和 I.Oppenheim 将热力学平衡定义为: “一个系统处于热力学平衡状态,如果,在实验的时间内,(a)它强度特性与时间无关,(b)它的内部或与周围环境的边界处没有物质或能量流。”显然,他们没有把定义限制在孤立的或封闭的系统。它们不讨论“缓慢”发生变化的可能性,并且超出了分配给实验的时间范围。他们注意到,对于两个相接触的系统,存在一个强度性质的小子类,如果这个小子类的所有子类都相等,那么所有各自的强度性质都相等。只要满足其他一些条件,热力学平衡状态可以由这个子类定义。<br />
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==Characteristics of a state of internal thermodynamic equilibrium 内部热力学平衡状态的特征==<br />
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===Homogeneity in the absence of external forces 在没有外力的情况下的均匀性===<br />
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A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous.<ref name="Planck 1903 3"/> This means that the material in any small volume element of the system can be interchanged with the material of any other geometrically congruent volume element of the system, and the effect is to leave the system thermodynamically unchanged. In general, a strong external force field makes a system of a single phase in its own internal thermodynamic equilibrium inhomogeneous with respect to some [[Intensive and extensive properties|intensive variables]]. For example, a relatively dense component of a mixture can be concentrated by centrifugation.<br />
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在没有外力的情况下,由单一相组成的热力学系统,在其自身的内部热力学平衡中是均匀的。这意味着系统中任何小体积单元中的材料可以与系统中任何其他几何相等的体积单元中的材料互换,其效果是使系统在热力学上保持不变。一般来说,一个强外力场使得一个单相系统在其自身的内部热力学平衡中对于一些'''<font color="#ff8000">强度量 Intensive Variable</font>'''是不均匀的。例如,可以通过离心来浓缩混合物中相对密度较大的组分。<br />
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===Uniform temperature 均匀温度===<br />
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Such equilibrium inhomogeneity, induced by external forces, does not occur for the intensive variable [[temperature]]. According to [[Edward A. Guggenheim|E.A. Guggenheim]], "The most important conception of thermodynamics is temperature."<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), p.5.</ref> Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface."<ref name="Planck 1903 3">[[Max Planck|Planck, M.]] (1897/1927), p.3.</ref> As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.<br />
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这种由外力引起的平衡不均匀性,对于强度量'''<font color="#ff8000">温度 Temperature</font>'''不会发生。'''<font color="#ff8000">E.A.古根海姆 E.A. Guggenheim</font>'''认为,“热力学最重要的概念是温度。“Planck在介绍他的论文时,简要叙述了热、温度和热平衡,然后宣布: ”在下文中,我们将主要讨论任何形式的均匀、各向同性的物体,它们的物质具有相同的温度和密度,并受到到处垂直于表面的均匀压力的作用。和Carathéodory 一样,Planck将表面效应、外场和各向异性晶体排除在外。虽然Planck提到了温度,但并没有明确提到热力学平衡的概念。相比之下,Carathéodory关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ,虽然没有明确地使用短语‘热力学平衡’ ,也没有明确地假设存在一个温度来定义它。<br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform.<ref name="Planck 1914 40"/> This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers.<ref>Gibbs, J.W. (1876/1878), pp. 144-150.</ref><ref>[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966), pp. 127–130.</ref><ref>Münster, A. (1970), pp. 309–310.</ref><ref>Bailyn, M. (1994), pp. 254-256.</ref><ref>{{cite journal | last1 = Verkley | first1 = W.T.M. | last2 = Gerkema | first2 = T. | year = 2004 | title = On maximum entropy profiles | journal = J. Atmos. Sci. | volume = 61 | issue = 8| pages = 931–936 | doi=10.1175/1520-0469(2004)061<0931:omep>2.0.co;2| bibcode = 2004JAtS...61..931V | doi-access = free }}</ref><ref>{{cite journal | last1 = Akmaev | first1 = R.A. | year = 2008 | title = On the energetics of maximum-entropy temperature profiles | url = | journal = Q. J. R. Meteorol. Soc. | volume = 134 | issue = 630| pages = 187–197 | doi=10.1002/qj.209| bibcode = 2008QJRMS.134..187A }}</ref> Considerations of kinetic theory or statistical mechanics also support this statement.<ref>Maxwell, J.C. (1867).</ref><ref>Boltzmann, L. (1896/1964), p. 143.</ref><ref>Chapman, S., Cowling, T.G. (1939/1970), Section 4.14, pp. 75–78.</ref><ref>[[J. R. Partington|Partington, J.R.]] (1949), pp. 275–278.</ref><ref>{{cite journal | last1 = Coombes | first1 = C.A. | last2 = Laue | first2 = H. | year = 1985 | title = A paradox concerning the temperature distribution of a gas in a gravitational field | url = | journal = Am. J. Phys. | volume = 53 | issue = 3| pages = 272–273 | doi=10.1119/1.14138| bibcode = 1985AmJPh..53..272C }}</ref><ref>{{cite journal | last1 = Román | first1 = F.L. | last2 = White | first2 = J.A. | last3 = Velasco | first3 = S. | year = 1995 | title = Microcanonical single-particle distributions for an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 16 | issue = 2| pages = 83–90 | doi=10.1088/0143-0807/16/2/008| bibcode = 1995EJPh...16...83R }}</ref><ref>{{cite journal | last1 = Velasco | first1 = S. | last2 = Román | first2 = F.L. | last3 = White | first3 = J.A. | year = 1996 | title = On a paradox concerning the temperature distribution of an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 17 | issue = | pages = 43–44 | doi=10.1088/0143-0807/17/1/008}}</ref><br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform. This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers. Considerations of kinetic theory or statistical mechanics also support this statement.<br />
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热力学平衡系统内的温度在时间和空间上都是均匀的。在一个处于内部热力学平衡的系统中,不存在净的内部宏观流动。特别是,这意味着系统的所有局部都处于相互辐射交换平衡。这意味着系统的温度在空间上是均匀的。这在所有情况下都是如此,包括那些非均匀外力场。对于外部施加的引力场,这可以使用拉格郎日乘子法通过变分的计算在宏观热力学术语中证明。动力学理论或统计力学也支持这种说法。<br />
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In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium.<ref name="Fitts 43"/><br />
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为了使一个系统处于它自己的内部热力学平衡状态,它必须处于它自己的内部热平衡状态是必要不充分的; 一个系统在到达内部热平衡之前到达内部力学平衡是可能的。<br />
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===Number of real variables needed for specification 规范所需的实变量数目===<br />
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In his exposition of his scheme of closed system equilibrium thermodynamics, C. Carathéodory initially postulates that experiment reveals that a definite number of real variables define the states that are the points of the manifold of equilibria.<ref name="Caratheodory" /> In the words of Prigogine and Defay (1945): "It is a matter of experience that when we have specified a certain number of macroscopic properties of a system, then all the other properties are fixed."<ref>Prigogine, I., Defay, R. (1950/1954), p. 1.</ref><ref>Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005), p. 4.</ref> As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.<br />
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在他关于封闭系统平衡态热力学方案的论述中,C.Carathéodory 最初假定实验揭示了一定数量的实变量定义了作为平衡态流形点的状态。用 Prigogine 和 Defay (1945)的话说: “这是一个经验问题,当我们确定了一个系统一定数量的宏观属性时,那么所有其他属性都是固定的”。如上所述,A. Münster认为,定义热力学平衡所需的变量数量相对于给定孤立系统的任何状态来说都是最少的。如上所述,J.G. Kirkwood 和 I. Oppenheim 指出,热力学平衡状态可以由一个特殊子类的强度变量来定义,该子类中有一定数量的成员。<br />
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If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.<br />
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如果热力学平衡位于一个外力场中,那么通常只有温度在空间上是均匀的。如果外力场非零,温度以外的强度变量通常是不均匀的。在这种情况下,一般需要附加变量来描述空间非均匀性。<br />
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===Stability against small perturbations 对小扰动的稳定性===<br />
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As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.<br />
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如上所述,J.R. Partington 指出热力学平衡状态在小的瞬态扰动下是稳定的。如果没有这个条件,一般来说,研究热力学平衡系统的实验就会遇到严重的困难。<br />
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===Approach to thermodynamic equilibrium within an isolated system 孤立系统中的热力学平衡===<br />
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When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium. Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<br />
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When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium.<ref name="Fitts 43">Fitts, D.D. (1962), p. 43.</ref> Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<ref>Denbigh, K.G. (1951), p. 42.</ref><br />
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当一个物质体从不均匀的非平衡状态或化学非平衡状态开始,然后被孤立,它会自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如,在这种演化的许多情况下,内部力学平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是,在这种演化的许多情况下,热平衡的发展要比化学平衡快得多。<br />
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===Fluctuations within an isolated system in its own internal thermodynamic equilibrium 孤立系统内部热力学平衡的涨落===<br />
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In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
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在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
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To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics.<ref>Tschoegl, N.W. (2000). ''Fundamentals of Equilibrium and Steady-State Thermodynamics'', Elsevier, Amsterdam, {{ISBN|0-444-50426-5}}, p. 21.</ref> But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
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To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics. But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
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考虑孤立热力学系统中的涨落概念,一个方便的例子是由其内能、体积和质量组成等广延量表示的系统。根据定义,它们是不随时间变化的。根据定义,这些量与它们的共轭状态强度函数的时不变标称值相结合,包括逆温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广延量的值,不足以提供这些标称值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
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It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.<br />
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可以承认,在重复测量这些共轭强度状态函数时,发现它们的值随时间略有不同。这种可变性被认为是由于内部涨落。不同测量值平均到其标称值。<br />
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If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<ref>Buchdahl, H.A. (1966), p. 16.</ref><br />
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If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<br />
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如果系统真的像经典热力学所假定的那样是宏观的,那么系统的涨落很小以至于宏观上无法检测到。这就是所谓的热力学极限。实际上,物质的分子性质和动量转移的量子性质由于它们太小而看不见,已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中,平衡的涨落概念是不存在的。”<br />
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If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
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如果系统被重复细分,最终产生的系统足够小,可以表现出明显的涨落。这是一个介观层面的研究。涨落则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
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If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在涨落过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,并且需要量子统计力学。涨落可以变得相对占主导地位,测量问题变得重要。<br />
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The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
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"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有随时间变化趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的标称值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微涨落期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组标称值。除非已知属于平衡状态的标称值,否则根据单一的度量无法进行判断。<br />
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=== Thermal equilibrium ===<br />
热平衡<br />
{{Main|Thermal equilibrium}}<br />
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An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process."<ref>Eu, B.C. (2002), page 13.</ref> This illustrates the importance for thermodynamics of the concept of temperature.<br />
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热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
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A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<br />
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一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数。<br />
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[[Thermal equilibrium]] is achieved when two systems in [[thermal contact]] with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<ref>[[Raj Pathria|R. K. Pathria]], 1996</ref><br />
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当两个相互'''<font color="#ff8000">热接触 Thermal Contact</font>'''的系统不再有净能量交换时,就会产生'''<font color="#ff8000">热平衡 Thermal Equilibrium</font>'''。因此,如果两个系统处于热平衡,那么它们的温度是相同的<br />
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Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
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Thermal equilibrium occurs when a system's [[macroscopic]] thermal observables have ceased to change with time. For example, an [[ideal gas]] whose [[Distribution function (physics)|distribution function]] has stabilised to a specific [[Maxwell–Boltzmann distribution]] would be in thermal equilibrium. This outcome allows a single [[temperature]] and [[pressure]] to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<ref>de Groot, S.R., Mazur, P. (1962), p. 44.</ref><br />
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当一个系统的'''<font color="#ff8000">宏观 Macroscopic</font>'''热观测值不再随时间变化时,就会出现热平衡。例如,一种'''<font color="#ff8000">分布函数 Distribution Function</font>'''稳定到一个特定的'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''的'''<font color="#ff8000">理想气体 Ideal Gas</font>'''即处于热平衡状态。这个结果可以将单一的'''<font color="#ff8000">温度 Temperature</font>'''和'''<font color="#ff8000">压力 Pressure</font>'''归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
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Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle. It states that a non-equilibrium system evolves such as to maximize its entropy production.<br />
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定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
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==Non-equilibrium==<br />
非平衡<br />
{{Main|Non-equilibrium thermodynamics}}<br />
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Thermodynamic models <br />
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热力学模型<br />
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A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<ref>de Groot, S.R., Mazur, P. (1962), p. 43.</ref><br />
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一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数<br />
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Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
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Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle.<ref>{{cite book|last1=Ziegler|first1=H.|title=An Introduction to Thermomechanics.|date=1983|location=North Holland, Amsterdam.}}</ref><ref>{{cite journal|last1=Onsager|first1=Lars|title=Reciprocal Relations in Irreversible Processes|journal=Phys. Rev.|date=1931|volume=37|issue=4|doi=10.1103/PhysRev.37.405|bibcode=1931PhRv...37..405O|pages=405–426|doi-access=free}}</ref> It states that a non-equilibrium system evolves such as to maximize its entropy production.<ref>{{cite book|last1=Kleidon|first1=A.|last2=et.|first2=al.|title=Non-equilibrium Thermodynamics and the Production of Entropy.|date=2005|edition=Heidelberg: Springer.}}</ref><ref>{{cite journal|last1=Belkin|first1=Andrey|last2=et.|first2=al.|title=Self-Assembled Wiggling Nano-Structures and the Principle of Maximum Entropy Production|journal=Sci. Rep.|doi=10.1038/srep08323|bibcode=2015NatSR...5E8323B|pmc=4321171|pmid=25662746|volume=5|year=2015|page=8323}}</ref><br />
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定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
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Topics in control theory<br />
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控制理论主题<br />
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==See also ==<br />
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{{Portal|Chemistry}}<br />
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;Thermodynamic models 热力学模型<br />
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* [[Non-random two-liquid model]] (NRTL model) - Phase equilibrium calculations 非随机两液模型(NRTL 模型)-相平衡计算<br />
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* [[UNIQUAC]] model - Phase equilibrium calculations UNIQUAC 模型-相平衡计算<br />
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* [[Time crystal]] 时间晶体<br />
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{{colend}}<br />
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;Topics in control theory 控制理论主题<br />
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{{colbegin}}<br />
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* [[Steady state]] 稳态<br />
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* [[Transient state]] 瞬态<br />
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* [[Coefficient diagram method]] 系数图法<br />
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* [[Control reconfiguration]] 控制重构<br />
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* [[Cut-insertion theorem]] 切入定理<br />
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* [[Feedback]] 反馈<br />
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* [[H infinity]] H 无限<br />
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* [[Hankel singular value]] 汉克尔奇异值<br />
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* [[Krener's theorem]] 克雷纳定理<br />
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* [[Lead-lag compensator]] 超前滞后补偿器<br />
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* [[Minor loop feedback]] 小循环反馈<br />
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* [[Minor loop feedback|Multi-loop feedback]] 小循环反馈 | 多循环反馈<br />
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* [[Positive systems]] 正向系统<br />
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* [[Radial basis function]] 径向基底函数<br />
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Other related topics<br />
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其他相关话题<br />
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* [[Root locus]] 根轨迹<br />
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* [[Signal-flow graph]]s 信号流图<br />
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* [[Stable polynomial]] 稳定多项式<br />
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* [[State space representation]] 状态空间<br />
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* [[Underactuation]] 欠驱动<br />
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* [[Youla–Kucera parametrization]] 尤拉-库切拉参数化<br />
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* [[Markov chain approximation method]] 马尔可夫链近似法<br />
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{{colend}}<br />
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;Other related topics<br />
其他相关话题<br />
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{{colbegin}}<br />
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* [[Automation and remote control]] 自动化和远程控制<br />
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* [[Bond graph]] 键合图<br />
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* [[Control engineering]] 控制工程<br />
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* [[Control–feedback–abort loop]] 控制-反馈-中止循环<br />
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* [[Controller (control theory)]] 控制器(控制理论)<br />
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* [[Cybernetics]] 控制论<br />
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* [[Intelligent control]] 智能控制<br />
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* [[Mathematical system theory]] 数学系统论<br />
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* [[Negative feedback amplifier]] 负反馈放大器<br />
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* [[People in systems and control]] 系统和控制中的人<br />
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* [[Perceptual control theory]] 知觉控制理论<br />
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* [[Systems theory]] 系统论<br />
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* [[Time scale calculus]] 时间尺度演算<br />
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{{colend}}<br />
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<br />
====[https://swarma.org/?p=21322 什么是非平衡态热力学 | 集智百科]====<br />
非平衡态热力学 Non-equilibrium thermodynamics 是热力学的一个分支,研究某些不处于热力学平衡中的物理系统<br />
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==General references==<br />
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* Cesare Barbieri (2007) ''Fundamentals of Astronomy''. First Edition (QB43.3.B37 2006) CRC Press {{ISBN|0-7503-0886-9}}, {{ISBN|978-0-7503-0886-1}}<br />
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* Hans R. Griem (2005) ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}<br />
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* C. Michael Hogan, Leda C. Patmore and Harry Seidman (1973) ''Statistical Prediction of Dynamic Thermal Equilibrium Temperatures using Standard Meteorological Data Bases'', Second Edition (EPA-660/2-73-003 2006) United States Environmental Protection Agency Office of Research and Development, Washington, D.C. [http://library.wur.nl/WebQuery/catalog/lang/1851848]<br />
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* F. Mandl (1988) ''Statistical Physics'', Second Edition, John Wiley & Sons<br />
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==References==<br />
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{{Reflist|colwidth=35em}}<br />
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==Cited bibliography==<br />
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*Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', third edition, McGraw-Hill, London, {{ISBN|0-521-25445-0}}.<br />
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*Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, {{ISBN|0-88318-797-3}}.<br />
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*Beattie, J.A., Oppenheim, I. (1979). ''Principles of Thermodynamics'', Elsevier Scientific Publishing, Amsterdam, {{ISBN|0-444-41806-7}}.<br />
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*[[Ludwig Boltzmann|Boltzmann, L.]] (1896/1964). ''Lectures on Gas Theory'', translated by S.G. Brush, University of California Press, Berkeley.<br />
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*Buchdahl, H.A. (1966). ''The Concepts of Classical Thermodynamics'', Cambridge University Press, Cambridge UK.<br />
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*[[Herbert Callen|Callen, H.B.]] (1960/1985). ''Thermodynamics and an Introduction to Thermostatistics'', (1st edition 1960) 2nd edition 1985, Wiley, New York, {{ISBN|0-471-86256-8}}.<br />
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*[[Constantin Carathéodory|Carathéodory, C.]] (1909). [https://web.archive.org/web/20160304213645/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0067&DMDID=DMDLOG_0033&L=1 Untersuchungen über die Grundlagen der Thermodynamik], ''[[Mathematische Annalen]]'', '''67''': 355–386. A translation may be found [http://neo-classical-physics.info/uploads/3/0/6/5/3065888/caratheodory_-_thermodynamics.pdf here]. Also a mostly reliable [https://books.google.com/books?id=xwBRAAAAMAAJ&q=Investigation+into+the+foundations translation is to be found] at Kestin, J. (1976). ''The Second Law of Thermodynamics'', Dowden, Hutchinson & Ross, Stroudsburg PA.<br />
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*[[Sydney Chapman (mathematician)|Chapman, S.]], [[Thomas George Cowling|Cowling, T.G.]] (1939/1970). ''The Mathematical Theory of Non-uniform gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases'', third edition 1970, Cambridge University Press, London.<br />
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*Crawford, F.H. (1963). ''Heat, Thermodynamics, and Statistical Physics'', Rupert Hart-Davis, London, Harcourt, Brace & World, Inc.<br />
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*de Groot, S.R., Mazur, P. (1962). ''Non-equilibrium Thermodynamics'', North-Holland, Amsterdam. Reprinted (1984), Dover Publications Inc., New York, {{ISBN|0486647412}}.<br />
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*Denbigh, K.G. (1951). ''Thermodynamics of the Steady State'', Methuen, London.<br />
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*Eu, B.C. (2002). ''Generalized Thermodynamics. The Thermodynamics of Irreversible Processes and Generalized Hydrodynamics'', Kluwer Academic Publishers, Dordrecht, {{ISBN|1-4020-0788-4}}.<br />
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*Fitts, D.D. (1962). ''Nonequilibrium thermodynamics. A Phenomenological Theory of Irreversible Processes in Fluid Systems'', McGraw-Hill, New York.<br />
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*[[Josiah Willard Gibbs|Gibbs, J.W.]] (1876/1878). On the equilibrium of heterogeneous substances, ''Trans. Conn. Acad.'', '''3''': 108–248, 343–524, reprinted in ''The Collected Works of J. Willard Gibbs, Ph.D, LL. D.'', edited by W.R. Longley, R.G. Van Name, Longmans, Green & Co., New York, 1928, volume 1, pp.&nbsp;55–353.<br />
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*Griem, H.R. (2005). ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}.<br />
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*[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', fifth revised edition, North-Holland, Amsterdam.<br />
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*Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of ''Thermodynamics'', pages 1–97 of volume 1, ed. W. Jost, of ''Physical Chemistry. An Advanced Treatise'', ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081.<br />
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*[[John Gamble Kirkwood|Kirkwood, J.G.]], Oppenheim, I. (1961). ''Chemical Thermodynamics'', McGraw-Hill Book Company, New York.<br />
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*Landsberg, P.T. (1961). ''Thermodynamics with Quantum Statistical Illustrations'', Interscience, New York.<br />
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*{{cite journal |last1=Lieb |first1=E. H. |last2=Yngvason |first2=J. |year=1999 |title=The Physics and Mathematics of the Second Law of Thermodynamics |journal=Phys. Rep. |volume=310 |issue= 1|pages=1–96 |doi= 10.1016/S0370-1573(98)00082-9|arxiv = cond-mat/9708200 |bibcode = 1999PhR...310....1L |s2cid=119620408 }}<br />
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*Levine, I.N. (1983), ''Physical Chemistry'', second edition, McGraw-Hill, New York, {{ISBN|978-0072538625}}.<br />
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*{{cite journal | last1 = Maxwell | first1 = J.C. | authorlink = James Clerk Maxwell | year = 1867 | title = On the dynamical theory of gases | url = | journal = Phil. Trans. Roy. Soc. London | volume = 157 | issue = | pages = 49–88 }}<br />
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*[[Philip M. Morse|Morse, P.M.]] (1969). ''Thermal Physics'', second edition, W.A. Benjamin, Inc, New York.<br />
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*Münster, A. (1970). ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London.<br />
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*[[J.R. Partington|Partington, J.R.]] (1949). ''An Advanced Treatise on Physical Chemistry'', volume 1, ''Fundamental Principles. The Properties of Gases'', Longmans, Green and Co., London.<br />
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*[[Brian Pippard|Pippard, A.B.]] (1957/1966). ''The Elements of Classical Thermodynamics'', reprinted with corrections 1966, Cambridge University Press, London.<br />
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* [[Max Planck|Planck. M.]] (1914). [https://archive.org/details/theoryofheatradi00planrich ''The Theory of Heat Radiation''], a translation by Masius, M. of the second German edition, P. Blakiston's Son & Co., Philadelphia.<br />
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*[[Ilya Prigogine|Prigogine, I.]] (1947). ''Étude Thermodynamique des Phénomènes irréversibles'', Dunod, Paris, and Desoers, Liège.<br />
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*[[Ilya Prigogine|Prigogine, I.]], Defay, R. (1950/1954). ''Chemical Thermodynamics'', Longmans, Green & Co, London.<br />
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*Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005). ''Physical Chemistry'', fourth edition, Wiley, Hoboken NJ.<br />
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*[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966). ''Elements of Thermodynamics'', Addison-Wesley Publishing, Reading MA.<br />
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*{{cite journal|last=Thomson|first=W.|author-link=William Thomson, 1st Baron Kelvin|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Transactions of the Royal Society of Edinburgh|date=March 1851|volume=XX|issue=part II|pages=261–268; 289–298}} Also published in {{cite journal|last=Thomson|first=W.|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Phil. Mag. |date=December 1852 |volume=IV |series=4 |issue=22 |pages=8–21 |url=https://archive.org/details/londonedinburghp04maga |accessdate=25 June 2012}}<br />
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*[[László Tisza|Tisza, L.]] (1966). ''Generalized Thermodynamics'', M.I.T Press, Cambridge MA.<br />
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*[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963). ''Lectures in Statistical Mechanics'', American Mathematical Society, Providence RI.<br />
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*Waldram, J.R. (1985). ''The Theory of Thermodynamics'', Cambridge University Press, Cambridge UK, {{ISBN|0-521-24575-3}}.<br />
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*[[Mark Zemansky|Zemansky, M.]] (1937/1968). ''Heat and Thermodynamics. An Intermediate Textbook'', fifth edition 1967, McGraw–Hill Book Company, New York.<br />
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== External links ==<br />
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Category:Equilibrium chemistry<br />
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类别: 平衡化学<br />
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*[http://ads.harvard.edu/books/1989fsa..book/AbookC15.pdf Breakdown of Local Thermodynamic Equilibrium] George W. Collins, The Fundamentals of Stellar Astrophysics, Chapter 15<br />
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Category:Thermodynamic cycles<br />
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类别: 热力循环<br />
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*[http://spiff.rit.edu/classes/phys440/lectures/lte/lte.html Thermodynamic Equilibrium, Local and otherwise] lecture by Michael Richmond<br />
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Category:Thermodynamic processes<br />
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类别: 热力学过程<br />
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*[http://journals.ametsoc.org/doi/abs/10.1175/1520-0469%281970%29027%3C0711:NLTEIC%3E2.0.CO%3B2 Non-Local Thermodynamic Equilibrium in Cloudy Planetary Atmospheres] Paper by R. E. Samueison quantifying the effects due to non-LTE in an atmosphere<br />
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Category:Thermodynamic systems<br />
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类别: 热力学系统<br />
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*[http://scienceworld.wolfram.com/physics/LocalThermodynamicEquilibrium.html Local Thermodynamic Equilibrium]<br />
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Category:Thermodynamics<br />
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分类: 热力学<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Thermodynamic equilibrium]]. Its edit history can be viewed at [[平衡热力学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%B9%B3%E8%A1%A1%E7%83%AD%E5%8A%9B%E5%AD%A6&diff=21695平衡热力学2021-02-09T07:44:41Z<p>Jxzhou:/* Fluctuations within an isolated system in its own internal thermodynamic equilibrium 孤立系统内部热力学平衡的涨落 */</p>
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<div>此词条暂由小竹凉翻译,翻译字数共5339,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{short description|State of thermodynamic system(s) where no net macroscopic flow of matter or energy occurs}}<br />
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'''Thermodynamic equilibrium''' is an [[axiomatic]] concept of [[thermodynamics]]. It is an internal [[State variables|state]] of a single [[thermodynamic system]], or a relation between several thermodynamic systems connected by more or less permeable or impermeable [[Thermodynamic system#Walls|walls]]. In thermodynamic equilibrium there are no net [[macroscopic]] [[Flow (mathematics)|flows]] of [[matter]] or of [[energy]], either within a system or between systems. <br />
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Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium there are no net macroscopic flows of matter or of energy, either within a system or between systems. <br />
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'''热力学平衡'''是'''<font color="#ff8000">热力学 Thermodynamics</font>'''的一个'''<font color="#ff8000">不言自明的 Axiomatic</font>'''概念。它是单个'''<font color="#ff8000">热力学系统 Thermodynamic System</font>'''的内部'''<font color="#ff8000">状态 State</font>''',或者是几个热力学系统之间通过或多或少的渗透或不渗透的'''<font color="#ff8000">壁 Wall</font>'''连接的关系。无论是在一个系统内还是在系统之间,在热力学平衡中不存在'''<font color="#ff8000">物质 Matter</font>'''或'''<font color="#ff8000">能量 Energy</font>'''的净'''<font color="#ff8000">宏观 Macroscopic</font>''' '''<font color="#ff8000">流动 Flow</font>'''。<br />
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In a system that is in its own state of internal thermodynamic equilibrium, no [[macroscopic]] change occurs. <br />
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In a system that is in its own state of internal thermodynamic equilibrium, no macroscopic change occurs. <br />
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在一个处于内部热力学平衡状态的系统中,不会发生'''<font color="#ff8000">宏观 Macroscopic</font>'''变化。<br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual [[Thermal equilibrium|thermal]], [[Mechanical equilibrium|mechanical]], [[Chemical equilibrium|chemical]], and [[Radiative equilibrium|radiative]] equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a [[thermodynamic operation]]. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a thermodynamic operation. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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相互热力学平衡的体系同时处于互相之间的'''<font color="#ff8000">热 Thermal</font>'''平衡、'''<font color="#ff8000">力学 Mechanical</font>'''平衡、'''<font color="#ff8000">化学 Chemical</font>'''平衡和'''<font color="#ff8000">辐射 Radiative</font>'''平衡。系统可以处于其中一种相互平衡状态,尽管其他状态未平衡。在热力学平衡中所有的平衡同时并且无限期地保持,直到被'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''打破。在一个宏观平衡中,微观交换是完全或几乎完全平衡的;这是对宏观平衡概念的物理解释。<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform [[temperature]]. Its [[Intensive and extensive properties|intensive properties]], other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform temperature. Its intensive properties, other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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一个处于内部热力学状态平衡的热力学系统具有空间均匀的'''<font color="#ff8000">温度 Temperature</font>'''。除了温度以外,它的'''<font color="#ff8000">强度性质 Intensive Properties</font>'''可以由于周围环境施加的不变的长程力场而导致空间不均匀性。<br />
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In systems that are at a state of [[non-equilibrium]] there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a '''meta-stable equilibrium'''.<br />
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In systems that are at a state of non-equilibrium there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a meta-stable equilibrium.<br />
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相比之下,处于'''<font color="#ff8000">非平衡状态 non-equilibrium</font>'''的系统中有物质或能量的净流动。如果这些变化可以在一个还没有发生的系统中被触发,那么这个系统就被称为处于一个'''亚稳定的平衡状态'''。<br />
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Though not a widely named a "law," it is an [[axiom]] of thermodynamics that there exist states of thermodynamic equilibrium. The [[second law of thermodynamics]] states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the [[entropy|entropies]] of the portions.<br />
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Though not a widely named a "law," it is an axiom of thermodynamics that there exist states of thermodynamic equilibrium. The second law of thermodynamics states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the entropies of the portions.<br />
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虽然不是一个广泛命名的“定律” ,但存在热力学平衡状态是一个热力学'''<font color="#ff8000">公理 Axiom</font>'''。'''<font color="#ff8000">热力学第二定律 second law of thermodynamics</font>'''指出,当一个物质体从一个平衡状态开始,在这个状态中,它的一部分被或多或少渗透或不渗透的分区保持在不同的状态,并且是孤立的,热力学操作移除分区或使分区更具渗透性,然后它会自发地达到自己内部热力学平衡的新状态,并伴随着部分'''<font color="#ff8000">熵 Entropy</font>'''的总和增加。<br />
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== Overview 概览==<br />
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{{Thermodynamics|cTopic=[[Thermodynamic system|Systems]]}}<br />
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Classical thermodynamics deals with states of [[dynamic equilibrium]]. The state of a system at thermodynamic equilibrium is the one for which some [[thermodynamic potential]] is minimized, or for which the [[entropy]] (''S'') is maximized, for specified conditions. One such potential is the [[Helmholtz free energy]] (''A''), for a system with surroundings at controlled constant temperature and volume:<br />
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Classical thermodynamics deals with states of dynamic equilibrium. The state of a system at thermodynamic equilibrium is the one for which some thermodynamic potential is minimized, or for which the entropy (S) is maximized, for specified conditions. One such potential is the Helmholtz free energy (A), for a system with surroundings at controlled constant temperature and volume:<br />
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经典热力学研究'''<font color="#ff8000">动态平衡 Dynamic Equilibrium</font>'''的状态。系统的热力学平衡状态是对于特定的条件,一些'''<font color="#ff8000">热力学势 Thermodynamic Potential</font>'''被最小化,或者'''<font color="#ff8000">熵 Entropy</font>'''(S)被最大化。对于一个周围环境温度和体积恒定的系统,其中一个这样的热力学势是'''<font color="#ff8000">亥姆霍兹自由能 Helmholtz Free Energy</font>'''(A):<br />
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:<math>A = U - TS</math><br />
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<math>A = U - TS</math><br />
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A = U-TS<br />
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Another potential, the [[Gibbs free energy]] (''G''), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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Another potential, the Gibbs free energy (G), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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在恒定温度和压力的系统中,另一个热力学势'''<font color="#ff8000">吉布斯自由能 Gibbs Free Energy</font>'''(G)在热力学平衡状态最小:<br />
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:<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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where ''T'' denotes the absolute thermodynamic temperature, ''P'' the pressure, ''S'' the entropy, ''V'' the volume, and ''U'' the internal energy of the system.<br />
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where T denotes the absolute thermodynamic temperature, P the pressure, S the entropy, V the volume, and U the internal energy of the system.<br />
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其中 T 表示热力学绝对温度,P 表示压强,S 表示熵,V 表示体积,U 表示体系的内能。<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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热力学平衡是一种独特的稳定定态,当系统长时间与周围环境相互作用时,它可以被接近或最终到达。上述势能是数学构造的热力学量,在特定的环境条件下最小化。<br />
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== Conditions 条件==<br />
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* For a completely isolated system, ''S'' is maximum at thermodynamic equilibrium. 对于一个完全孤立的系统,S在热力学平衡中取最大值。<br />
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* For a system with controlled constant temperature and volume, ''A'' is minimum at thermodynamic equilibrium. 对于一个恒定温度和体积的系统来说,A在热力学平衡中取最小值。<br />
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* For a system with controlled constant temperature and pressure, ''G'' is minimum at thermodynamic equilibrium. 对于一个恒温恒压的系统,G在热力学平衡中取最小值。<br />
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The various types of equilibriums are achieved as follows:<br />
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The various types of equilibriums are achieved as follows:<br />
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实现各种类型的平衡的方法如下:<br />
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*Two systems are in ''thermal equilibrium'' when their [[temperature]]s are the same. 当两个系统的'''<font color="#ff8000">温度 Temperature</font>'''相同时,它们就处于''热平衡状态''<br />
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*Two systems are in ''mechanical equilibrium'' when their [[pressure]]s are the same. 当两个体系的'''<font color="#ff8000">压力 Pressure</font>'''相同时,它们就处于''力学平衡''<br />
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*Two systems are in ''diffusive equilibrium'' when their [[chemical potential]]s are the same. 当两个题体系的'''<font color="#ff8000">化学势 Chemical Potential</font>'''相同时,它们就处于''扩散平衡''<br />
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*All [[forces]] are balanced and there is no significant external driving force.<br />
所有的'''<font color="#ff8000">力 Force</font>'''都是平衡的,没有明显的外部驱动力<br />
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==Relation of exchange equilibrium between systems 系统之间的交换均衡关系==<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability.<ref name="Nster_a">Münster, A. (1970), p. 49.</ref> When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability. When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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通常,热力学系统的周围环境也可以被看作是另一个热力学系统。在这种观点中,我们可以把系统及其周围环境看作是相互接触的两个系统,远程作用力也将它们联系在一起。系统的包围物是两个系统之间的接触面或边界。在热力学形式中,该表面被认为具有特定的渗透性质。例如,接触的表面可能被认为只能透热,使能量只能作为热传递。当远程力在时间上不发生变化,两个系统之间的热量传递减慢并最终永久停止时,这两个系统被称为热平衡; 这就是接触平衡的一个例子。其它类型的接触平衡可用其它类型的比渗透率来定义。当两个系统对于某一特定类型的渗透率处于接触平衡时,它们具有属于该特定类型渗透率的强变量的共同值。这种强度变量的例子有温度、压力、化学势。<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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接触平衡也可视为交换平衡。在接触平衡状态下,两系统之间某些量的传递速率存在零平衡。例如,对于只能透热的壁,内能作为热在两个系统之间的扩散速率是相等并反向的。两个系统之间的绝热壁只对作为功传递的能量有渗透作用; 在力学平衡,两个系统之间作为功的能量传递速率相等且相反。如果是一个简单的壁,那么通过它的体积转移率也是相等且相反的; 即它两边的压力是相等的。如果绝热壁比较复杂,有一种杠杆,有一个面积比,那么两个体系在交换平衡中的压力与体积交换比成反比,这使得转移率的零平衡作功。<br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<ref name="Planck 1914 40">[[Max Planck|Planck. M.]] (1914), p. 40.</ref><br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<br />
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辐射交换可以发生在两个不同的系统之间。当两个体系温度相同时,辐射交换平衡占优势。<br />
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==Thermodynamic state of internal equilibrium of a system 系统内部平衡的热力学状态==<br />
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A collection of matter may be entirely [[Isolated system|isolated]] from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium.<ref>Haase, R. (1971), p. 4.</ref><ref>Callen, H.B. (1960/1985), p. 26.</ref> (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics.<ref>{{Cite journal |doi = 10.1119/1.4914528|bibcode = 2015AmJPh..83..628M|title = Time and irreversibility in axiomatic thermodynamics|year = 2015|last1 = Marsland|first1 = Robert|last2 = Brown|first2 = Harvey R.|last3 = Valente|first3 = Giovanni|journal = American Journal of Physics|volume = 83|issue = 7|pages = 628–634}}</ref> One textbook<ref>[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963), p. 5.</ref> calls it the "zeroth law", remarking that the authors think this more befitting that title than its [[Zeroth law of thermodynamics|more customary definition]], which apparently was suggested by [[Ralph H. Fowler|Fowler]].)<br />
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A collection of matter may be entirely isolated from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium. (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics. One textbook calls it the "zeroth law", remarking that the authors think this more befitting that title than its more customary definition, which apparently was suggested by Fowler.)<br />
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物质的集合可能与其周围的环境完全'''<font color="#ff8000">孤立 Isolated</font>'''。如果它在无限长的时间内一直保持不受干扰,按照经典热力学假定,它处于一个没有发生任何变化,没有流动的状态,即内部平衡的热力学状态。(这种假设有时被称为“负第一”热力学定律,但并不常见。有教科书称之为“第零定律” ,作者'''<font color="#ff8000">福勒 Fowler</font>'''认为这个名称是'''<font color="#ff8000">更符合惯例的定义 More Customary Definition</font>'''。)<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a [[thermodynamic operation]] be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a thermodynamic operation be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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这种状态是所谓的经典热力学或平衡态热力学的主要关注点,因为它们是系统中被认为在这门学科中得到很好定义的唯一状态。一个与另一个系统处于接触平衡状态可以被一个'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''隔离,在隔离发生时,其内部不会发生任何变化。因此,一个与另一个系统处于接触平衡状态时也可以被视为处于其自身的内部热力学平衡状态。<br />
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==Multiple contact equilibrium 多点接触平衡==<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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热力学形式允许一个系统同时与其他多个系统接触,这些系统可能有也可能没有相互接触,且这些接触具有不同的渗透性。如果这些系统都与世界其他部分相互隔离,那么它们彼此之间就会达到各自的接触平衡。<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy.<ref name="Caratheodory">Carathéodory, C. (1909).</ref><ref>Prigogine, I. (1947), p. 48.</ref><ref>Landsberg, P. T. (1961), pp. 128–142.</ref><ref>Tisza, L. (1966), p. 108.</ref> Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy. Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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如果几个系统彼此之间没有绝热壁,但是它们与世界其他部分共同隔离,那么它们就会达到多重接触平衡状态,且有共同的温度,总的内能和熵。在众多强度量中,这是温度的一个独特性质。即使在远距离作用力存在的情况下,它也是有效的。(也就是说,没有“力”可以维持温度的差异。)举个例子,在热力学平衡的一个垂直的引力场系统中,顶部壁面的压力比底部壁面的压力小,但是各处的温度都是一样的。<br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural [[thermodynamic process]].<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), § 1.12.</ref> It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings.<ref>Levine, I.N. (1983), p. 40.</ref><ref>Lieb, E.H., Yngvason, J. (1999), pp. 17–18.</ref> The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of [[Second law of thermodynamics#Description#Kelvin statement|"inanimate" agency]]; a system in thermodynamic equilibrium is inanimate.<ref>[[William Thomson, 1st Baron Kelvin|Thomson, W.]] (1851).</ref><br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural thermodynamic process. It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings. The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of "inanimate" agency; a system in thermodynamic equilibrium is inanimate.<br />
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热力操作可能作为一个事件发生在周围环境的壁上,既不直接影响与周围环境联系的壁,也不直接影响其内部,且发生在一个明确的有限的时间内。例如,一个固定的绝热壁可以在环境中被放置或拆除。由于这种操作仅限于周围环境,系统可能会在一段时间内远离自身最初的内部状态---- 热力学平衡。根据热力学第二定律的说法,整体经历了变化并最终与周围环境达到了新的平衡。继Planck之后,这一连串的事件被称为自然'''<font color="#ff8000">热力学过程 Thermodynamic Process</font>'''。即使在这个过程中,当系统和周围环境都不处于明确的内部平衡状态时,存在着暂时偏离热力学平衡的现象,由于初始状态和最终状态都是热力学平衡的,这在平衡热力学中也是允许的。一个自然过程在其主要部分中以有限的速率进行,因此,它从根本上不同于虚构的准静态“过程”;即不在整个过程中无限缓慢地进行而且虚构地“可逆”。经典热力学允许,即使一个过程可能需要很长的时间才能达到热力学平衡,如果主要部分的过程是在一个有限的比率中,那么它被认为是自然的,并受制于热力学第二定律,即不可逆的。工程设计的机器、人工设备和操作是允许在周围环境中进行的。允许在环境中而不是在系统中进行此类操作和设备,是开尔文在他的一个热力学第二定律的陈述中提到'''<font color="#ff8000">无生命机构 Inanimate Agency</font>'''的原因; 在热力学平衡的系统是无生命的。<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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否则,热力操作可能会直接影响系统的壁。<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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通常可以很方便地假设周围的某些子系统比系统大得多,以至于这个过程只能影响周围子系统的强度变量,然后将这些子系统称为相关强度变量的储备库。<br />
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== Local and global equilibrium 局部和全局均衡==<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by [[intensive quantity|intensive]] parameters. As an example, [[temperature]] controls [[Heat equation|heat exchanges]]. ''Global thermodynamic equilibrium'' (GTE) means that those [[intensive quantity|intensive]] parameters are homogeneous throughout the whole system, while ''local thermodynamic equilibrium'' (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by intensive parameters. As an example, temperature controls heat exchanges. Global thermodynamic equilibrium (GTE) means that those intensive parameters are homogeneous throughout the whole system, while local thermodynamic equilibrium (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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区分全局性和局部性热力学平衡是很有用的。在热力学中,系统内部和系统与外部之间的交换是由'''<font color="#ff8000">强度 Intensive</font>'''参数控制的。例如,'''<font color="#ff8000">温度 Temperature</font>'''控制'''<font color="#ff8000">热交换 Heat Equation</font>'''。全局热力学平衡(GTE)意味着这些'''<font color="#ff8000">强度 Intensive</font>'''参数在整个系统中是均匀的,而局部热力学平衡(LTE)意味着这些强度参数在空间和时间上是变化的,但变化如此缓慢,以至于对于任何一点,人们都可以假设在该点的某个邻域存在热力学平衡。<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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如果对系统的描述要求强度参数的变化过大,那么这些强度参数的定义所依据的假设本身就会失效,系统将既不处于全局平衡,也不处于局部平衡。例如,粒子需要一定数量的碰撞来平衡其周围环境。如果在这些碰撞中移动的平均距离使它离开平衡邻域,它将永远不会平衡,也就不会有 LTE。根据定义,温度与平衡邻域的平均内部能量成正比。由于没有达到平衡邻域,温度的概念就不成立,温度也就变得无法定义。<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to [[massive]] particles. In a [[radiation|radiating]] gas, the [[photon]]s being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to massive particles. In a radiating gas, the photons being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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值得注意的是,这种局部平衡可能只适用于系统中的某个粒子子集。例如,LTE 通常只适用于'''<font color="#ff8000">大 Massive</font>'''质量粒子。在'''<font color="#ff8000">辐射 Radiation</font>'''气体中,被气体发射和吸收的'''<font color="#ff8000">光子 Photon</font>'''不需要彼此在一个热力学平衡内,或与气体中的大量粒子在一起,LTE 才能存在。在某些情况下,自由电子并不需要与大得多的原子或分子处于平衡状态,LTE 才能存在。<br />
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As an example, LTE will exist in a glass of water that contains a melting [[ice cube]]. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the [[Maxwell–Boltzmann distribution]] for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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As an example, LTE will exist in a glass of water that contains a melting ice cube. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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例如,LTE 将存在于一个装有正在融化的'''<font color="#ff8000">冰块 Ice Cube</font>'''的水杯中。玻璃杯内的温度可以在任何时候定义,但是离冰块近的地方要比离冰块远的地方冷。如果观察到位于给定点附近的分子的能量,它们将按照麦克斯韦-波兹曼分布在一定温度下的分布。如果观察到位于另一点附近的分子的能量,它们将按照'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''分布到另一个温度。<br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural [[transport phenomena]] may lead a system from local to global thermodynamic equilibrium. Going back to our example, the [[diffusion]] of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<ref>H.R. Griem, 2005</ref><br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural transport phenomena may lead a system from local to global thermodynamic equilibrium. Going back to our example, the diffusion of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<br />
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局部热力学平衡不需要局部或全局的平稳性。换句话说,每一个小区域不需要有一个恒定的温度。然而,它确实要求每个小的局部变化缓慢到足以维持其局部麦克斯韦-波尔兹曼速度分布。全局非平衡态只有通过系统与外界的交换才能保持稳定。例如,通过在水杯中不断添加细粉冰来补偿熔化,并持续排出融水,可以保持全局稳定的静态。自然'''<font color="#ff8000">输运现象 Transport Phenomena</font>'''会使一个局部热力学平衡系统逐渐达到全局的热力学平衡。回顾我们的例子,热量的扩散将导致我们的玻璃杯水流向全局热力学平衡,在这种状态下,玻璃杯的温度是完全均匀的。<br />
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==Reservations 保留意见==<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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学识渊博的笔者在热力学领域对热力学平衡描述时,经常对他们的描述附加条件或保留意见。有些笔者含蓄地保留了或多或少的空白,以待说明。<br />
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For example, one widely cited writer, [[Herbert Callen|H. B. Callen]] writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. ''Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!''"<ref>Callen, H.B. (1960/1985), p. 15.</ref><br />
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For example, one widely cited writer, H. B. Callen writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!"<br />
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例如,一位被广泛引用的作家'''<font color="#ff8000">H.B.卡伦 H.B.Callen</font>'''在这里写道: “实际上,很少有系统处于绝对和真正的平衡状态。”他提到了放射性过程,认为它们可能需要“宇宙时间才能完成,因此通常可以忽略”。他补充道: “在实践中,平衡的标准是循环的。在操作上,如果一个系统的性质一致地用热力学理论来描述,那么它就处于平衡状态! ”<br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<ref>Beattie, J.A., Oppenheim, I. (1979), p. 3.</ref><br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<br />
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J.A.贝蒂和 I.奥本海姆写道: “坚持对平衡定义的严格解释,将排除热力学应用于实际系统的所有状态。”<br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment",<ref>Callen, H.B. (1960/1985), p. 485.</ref> and cited by Adkins as having written a "classic text",<ref>Adkins, C.J. (1968/1983), p. ''xiii''.</ref> [[Brian Pippard|A.B. Pippard]] writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<ref>Pippard, A.B. (1957/1966), p. 6.</ref><br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment", and cited by Adkins as having written a "classic text", A.B. Pippard writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<br />
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Callen引用另一位作者的话说,他给出了“学术且严谨的论述” ,Adkins引用他的话说,他写了一本“经典著作”—— '''<font color="#ff8000">A.B.皮帕德 A.B.Pippard</font>'''在文中写道: “只要时间足够长,过冷水蒸汽最终会凝结,... ..。时间可能是漫长的,也许长达10年或者更长。就大多数目的而言,只要这种迅速的变化不是人为地刺激,这些系统就可以被视为处于平衡状态。”<br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster">Münster, A. (1970), p. 53.</ref><br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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另一位作者A.Münster,写道。他观察到热核反应发生的速度非常缓慢,以至于在热力学中可以忽略不计。他评论道: “‘绝对平衡’或‘所有可想象过程的平衡’的概念没有物理意义。”他说: “ ... 我们只能考虑特定过程和确定的实验条件下的平衡。”<br />
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According to [[László Tisza|L. Tisza]]: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<ref>Tisza, L. (1966), p. 119.</ref><br />
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According to L. Tisza: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<br />
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根据'''<font color="#ff8000">L.缇莎 L.Tisza</font>'''的说法: “ ... 在讨论接近绝对零度的现象时。经典理论的绝对预测变得特别模糊,因为在非平衡状态下发生冻结是非常普遍的。”<br />
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==Definitions 定义==<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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一个系统最普遍的热力学平衡是通过与周围环境的接触,允许所有化学物质和各种能量同时通过。热力学平衡中的系统可能以均匀加速度在空间中运动,但此时不能改变其形状或大小; 因此它是由空间中的刚性体积来定义的。它可能存在于外力场中,由远远大于系统本身的外部因素决定,因此系统内的事件不会对外力场产生相当大的影响。只有当外力场是均匀的,并且确定了它的均匀加速度,或者它处于一个非均匀力场中,但是由于表面的局部力,例如机械压力,使它保持静止时,这个系统才能处于热力学平衡。<br />
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Thermodynamic equilibrium is a [[primitive notion]] of the theory of thermodynamics. According to [[Philip M. Morse|P.M. Morse]]: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are ''not'' conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments."<ref>[[Philip M. Morse|Morse, P.M.]] (1969), p. 7.</ref> This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<ref>Bailyn, M. (1994), p. 20.</ref><br />
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Thermodynamic equilibrium is a primitive notion of the theory of thermodynamics. According to P.M. Morse: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are not conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments." This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<br />
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热力学平衡是热力学理论的一个'''<font color="#ff8000">基本概念 Primitive Notion</font>'''。'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''说: “应该强调的是,存在热力学状态这一事实,以及存在由平衡态唯一指定的热力学变量这一事实,并不是从某些哲学第一原理得出的逻辑结论。这些结论不可避免地来自两个多世纪的实验。”这意味着热力学平衡不能仅仅用热力学的其他理论概念来定义。M.Bailyn提出了一个基本的热力学定律理论,它定义并假设了热力学平衡的存在。<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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热力学平衡的教科书定义通常被仔细说明,并有些保留。<br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<ref>Münster, A. (1970), p. 52.</ref><br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<br />
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例如,A. Münster写道:“当一个孤立系统中没有以可测量的速率发生状态变化时,系统处于热力学平衡状态。”这里有两项保留:系统是孤立的;任何状态的变化都是不可测量的缓慢。他通过对在室温且没有催化剂的情况下混合氧和氢的说明,讨论了第二个条件。Münster指出,描述热力学平衡状态所需要的宏观变量比给定系统任何其他状态都少。这是部分,但不完全是,因为系统内和流过系统的所有流都是零。<br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in ''equilibrium''.<ref>Haase, R. (1971), pp. 3–4.</ref><br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in equilibrium.<br />
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R. Haase's的热力学演示并不从对热力学平衡的限制开始,因为他打算考虑非平衡态热力学。他考虑一个具有时间不变性质的任意系统。他通过切断除外力场以外的所有外部影响来测试它的热力学平衡。如果在绝缘之后,没有任何变化,他说,系统处于平衡状态。<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness".<ref>Callen, H.B. (1960/1985), p. 13.</ref> This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness". This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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在一个标题为“热力学平衡”的章节中,H.B. Callen在一个段落中定义了平衡状态.他指出,它们“是由系统内部的内在因素决定的”。它们是“终端状态” ,随着时间的推移,系统会以“冰川般缓慢”的速度朝着这个终端状态演化。这个说法并没有明确,对于热力学平衡系统必须是孤立的;;Callen也没有说明他所说的“内在因素”是什么意思。<br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<ref>Adkins, C.J. (1968/1983), p. ''7''.</ref><br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<br />
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另一位教科书作者,C.J.Adkins,明确允许热力学平衡在非孤立的系统中发生。然而,他的系统在物质转移方面是封闭的。他写道: “一般来说,热力学平衡的方法包括热和类似功的形式与周围环境的相互作用。”他将这种热力学平衡与只有通过热接触才能进行能量传递的热平衡相区别。<br />
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Another textbook author, [[J.R. Partington]], writes: "(i) ''An equilibrium state is one which is independent of time''." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..."<ref>Partington, J.R. (1949), p. 161.</ref> This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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Another textbook author, J.R. Partington, writes: "(i) An equilibrium state is one which is independent of time." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..." This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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另一位教科书作者'''<font color="#ff8000">J.R.帕廷顿 J.R.Partington</font>'''写道: “(i)平衡状态是独立于时间的状态。”但是,在提到“只是明显处于平衡状态”的系统时,他补充说: “这样的系统处于‘虚假平衡’状态。帕廷顿的陈述没有明确指出平衡是指一个孤立的系统。和Münster一样,Partington也指的是氧和氢的混合物。他补充说:“在一个真正的平衡状态,任何影响状态的外部条件的微小变化都会产生一个微小的状态变化... ... ”这个条件意味着热力学平衡必须在小的扰动下保持稳定; 这个要求对于热力学平衡的严格意义是必不可少的。<br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, ''thermodynamic—equilibrium.''"<ref>Crawford, F.H. (1963), p. 5.</ref><br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, thermodynamic—equilibrium."<br />
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在F.H.Crawford的一本学生教科书中,有一个标题为“热力学平衡”的章节。它区分了几种流动的驱动因素,然后说: “这些是孤立系统明显普遍趋向于完全机械、热、化学和电力状态的例子——或者简单地说,热力学平衡状态。”<br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in ''equilibrium''."<ref>Buchdahl, H.A. (1966), p. 8.</ref> Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being ''in equilibrium'' so long as experimental tests show that 'slow' transitions are in effect reversible."<ref>Buchdahl, H.A. (1966), p. 111.</ref> It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<ref>Adkins, C.J. (1968/1983), p. 8.</ref><br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in equilibrium." Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being in equilibrium so long as experimental tests show that 'slow' transitions are in effect reversible." It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<br />
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H.A. Buchdahl的一本关于经典热力学的专著考虑了热力学系统的平衡,而实际上并没有写热力学平衡一词。Buchdahl在提到封闭的物质交换系统时写道: “如果一个系统处于一个适当的静态状态,那么它将被称为处于平衡状态。”出于热力学描述的目的,Buchdahl的专著也讨论了非晶态玻璃。它说: “更准确地说,只要实验测试表明‘慢’跃迁实际上是可逆的,玻璃就可以被认为处于平衡状态。”通常来说不会将这一条件作为热力学平衡定义的一部分,而是假定相反的情况:如果热力学平衡中的一个物体受到足够慢的过程的影响,则该过程可被视为足够接近可逆,并且该物体在过程中足够接近热力学平衡。<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of ''contact equilibrium''. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by [[Constantin Carathéodory|C. Carathéodory]], and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster" /> Thermodynamic equilibrium for an open system means that, with respect to every relevant kind of selectively permeable wall, contact equilibrium exists when the respective intensive parameters of the system and surroundings are equal.<ref name="Nster_a" /> This definition does not consider the most general kind of thermodynamic equilibrium, which is through unselective contacts. This definition does not simply state that no current of matter or energy exists in the interior or at the boundaries; but it is compatible with the following definition, which does so state.<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of contact equilibrium. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by C. Carathéodory, and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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通过引入接触平衡的概念,A. Münster仔细地扩展了孤立系统热力学平衡的定义。这指定了在考虑非孤立系统的热力学平衡时允许的特定过程,并特别关心开放系统,这些开放系统可能从周围环境获得或丢失物质。感兴趣的系统和周围系统之间的接触平衡,通过一种特殊的壁与之接触,其余的连接系统是孤立的。这种特殊类型的壁也被'''<font color="#ff8000">C.喀喇西奥多里 C.Carathéodory</font>'''考虑过,其他作家也提到过。它们具有选择渗透性。它们可能只对机械功有渗透性,或者只对热有渗透性,或者只对某种特定的化学物质有渗透性。每个接触平衡定义了一个强度参数; 例如,只能透热的壁定义了一个经验温度。对于感兴趣的体系中每一种化学成分,都可以存在接触平衡。在接触平衡中,尽管有可能通过选择性渗透壁进行交换,但是感兴趣的系统是不变的,好像它处在孤立的热力学平衡。这个方案遵循的一般规则是: “ ... ... 我们只能考虑特定过程和特定实验条件下的平衡。”<br />
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[[Mark Zemansky|M. Zemansky]] also distinguishes mechanical, chemical, and thermal equilibrium. He then writes: "When the conditions for all three types of equilibrium are satisfied, the system is said to be in a state of thermodynamic equilibrium".<ref>[[Mark Zemansky|Zemansky, M.]] (1937/1968), p. 27.</ref><br />
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'''<font color="#ff8000">M.泽曼斯基 M.Zemansky</font>'''还区分了力学、化学和热平衡。他接着写道: “当这三种均衡的条件都满足时,系统就处于热力学平衡状态。”<br />
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P.M. Morse writes that thermodynamics is concerned with "states of thermodynamic equilibrium". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<br />
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[[Philip M. Morse|P.M. Morse]] writes that thermodynamics is concerned with "''states of thermodynamic equilibrium''". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<ref>[[Philip M. Morse|Morse, P.M.]] (1969), pp. 6, 37.</ref><br />
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'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''写道,热力学关注的是“热力学平衡状态”。在讨论物体与周围热源之间的热量传递时,他也使用了“热平衡”这个短语,尽管没有明确定义一个特殊的术语“热平衡”<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "full thermodynamic equilibrium state".<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "''full'' thermodynamic equilibrium state".<ref>Waldram, J.R. (1985), p. 5.</ref><br />
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J.R. Waldram写到了“一个明确的热力学状态”。他将一个系统定义为“当其观测量随时间停止变化时”的“热平衡”。但是在这个定义之下不久,他写到一块玻璃还没有达到“完全的热力学平衡状态”。<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, thermodynamic equilibrium is said to exist." He is not here considering the presence of an external force field.<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, ''thermodynamic equilibrium'' is said to exist." He is not here considering the presence of an external force field.<ref>Bailyn, M. (1994), p. 21.</ref><br />
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考虑到平衡状态,M.Bailyn写道: “每个强度变量都有自己的平衡类型。”然后他定义了热平衡、力学平衡和物质平衡。因此,他写道: “如果所有的强度变量都是一致的,那么热力学平衡就是存在的。”他在这里没有考虑外力场的存在。<br />
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J.G. Kirkwood and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of thermodynamic equilibrium if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<br />
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[[John Gamble Kirkwood|J.G. Kirkwood]] and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of ''thermodynamic equilibrium'' if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<ref>Kirkwood, J.G., Oppenheim, I. (1961), p. 2</ref><br />
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'''<font color="#ff8000">J.G.柯克伍德 J.G.Kirkwood</font>'''和 I.Oppenheim 将热力学平衡定义为: “一个系统处于热力学平衡状态,如果,在实验的时间内,(a)它强度特性与时间无关,(b)它的内部或与周围环境的边界处没有物质或能量流。”显然,他们没有把定义限制在孤立的或封闭的系统。它们不讨论“缓慢”发生变化的可能性,并且超出了分配给实验的时间范围。他们注意到,对于两个相接触的系统,存在一个强度性质的小子类,如果这个小子类的所有子类都相等,那么所有各自的强度性质都相等。只要满足其他一些条件,热力学平衡状态可以由这个子类定义。<br />
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==Characteristics of a state of internal thermodynamic equilibrium 内部热力学平衡状态的特征==<br />
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===Homogeneity in the absence of external forces 在没有外力的情况下的均匀性===<br />
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A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous.<ref name="Planck 1903 3"/> This means that the material in any small volume element of the system can be interchanged with the material of any other geometrically congruent volume element of the system, and the effect is to leave the system thermodynamically unchanged. In general, a strong external force field makes a system of a single phase in its own internal thermodynamic equilibrium inhomogeneous with respect to some [[Intensive and extensive properties|intensive variables]]. For example, a relatively dense component of a mixture can be concentrated by centrifugation.<br />
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在没有外力的情况下,由单一相组成的热力学系统,在其自身的内部热力学平衡中是均匀的。这意味着系统中任何小体积单元中的材料可以与系统中任何其他几何相等的体积单元中的材料互换,其效果是使系统在热力学上保持不变。一般来说,一个强外力场使得一个单相系统在其自身的内部热力学平衡中对于一些'''<font color="#ff8000">强度量 Intensive Variable</font>'''是不均匀的。例如,可以通过离心来浓缩混合物中相对密度较大的组分。<br />
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===Uniform temperature 均匀温度===<br />
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Such equilibrium inhomogeneity, induced by external forces, does not occur for the intensive variable [[temperature]]. According to [[Edward A. Guggenheim|E.A. Guggenheim]], "The most important conception of thermodynamics is temperature."<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), p.5.</ref> Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface."<ref name="Planck 1903 3">[[Max Planck|Planck, M.]] (1897/1927), p.3.</ref> As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.<br />
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这种由外力引起的平衡不均匀性,对于强度量'''<font color="#ff8000">温度 Temperature</font>'''不会发生。'''<font color="#ff8000">E.A.古根海姆 E.A. Guggenheim</font>'''认为,“热力学最重要的概念是温度。“Planck在介绍他的论文时,简要叙述了热、温度和热平衡,然后宣布: ”在下文中,我们将主要讨论任何形式的均匀、各向同性的物体,它们的物质具有相同的温度和密度,并受到到处垂直于表面的均匀压力的作用。和Carathéodory 一样,Planck将表面效应、外场和各向异性晶体排除在外。虽然Planck提到了温度,但并没有明确提到热力学平衡的概念。相比之下,Carathéodory关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ,虽然没有明确地使用短语‘热力学平衡’ ,也没有明确地假设存在一个温度来定义它。<br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform.<ref name="Planck 1914 40"/> This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers.<ref>Gibbs, J.W. (1876/1878), pp. 144-150.</ref><ref>[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966), pp. 127–130.</ref><ref>Münster, A. (1970), pp. 309–310.</ref><ref>Bailyn, M. (1994), pp. 254-256.</ref><ref>{{cite journal | last1 = Verkley | first1 = W.T.M. | last2 = Gerkema | first2 = T. | year = 2004 | title = On maximum entropy profiles | journal = J. Atmos. Sci. | volume = 61 | issue = 8| pages = 931–936 | doi=10.1175/1520-0469(2004)061<0931:omep>2.0.co;2| bibcode = 2004JAtS...61..931V | doi-access = free }}</ref><ref>{{cite journal | last1 = Akmaev | first1 = R.A. | year = 2008 | title = On the energetics of maximum-entropy temperature profiles | url = | journal = Q. J. R. Meteorol. Soc. | volume = 134 | issue = 630| pages = 187–197 | doi=10.1002/qj.209| bibcode = 2008QJRMS.134..187A }}</ref> Considerations of kinetic theory or statistical mechanics also support this statement.<ref>Maxwell, J.C. (1867).</ref><ref>Boltzmann, L. (1896/1964), p. 143.</ref><ref>Chapman, S., Cowling, T.G. (1939/1970), Section 4.14, pp. 75–78.</ref><ref>[[J. R. Partington|Partington, J.R.]] (1949), pp. 275–278.</ref><ref>{{cite journal | last1 = Coombes | first1 = C.A. | last2 = Laue | first2 = H. | year = 1985 | title = A paradox concerning the temperature distribution of a gas in a gravitational field | url = | journal = Am. J. Phys. | volume = 53 | issue = 3| pages = 272–273 | doi=10.1119/1.14138| bibcode = 1985AmJPh..53..272C }}</ref><ref>{{cite journal | last1 = Román | first1 = F.L. | last2 = White | first2 = J.A. | last3 = Velasco | first3 = S. | year = 1995 | title = Microcanonical single-particle distributions for an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 16 | issue = 2| pages = 83–90 | doi=10.1088/0143-0807/16/2/008| bibcode = 1995EJPh...16...83R }}</ref><ref>{{cite journal | last1 = Velasco | first1 = S. | last2 = Román | first2 = F.L. | last3 = White | first3 = J.A. | year = 1996 | title = On a paradox concerning the temperature distribution of an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 17 | issue = | pages = 43–44 | doi=10.1088/0143-0807/17/1/008}}</ref><br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform. This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers. Considerations of kinetic theory or statistical mechanics also support this statement.<br />
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热力学平衡系统内的温度在时间和空间上都是均匀的。在一个处于内部热力学平衡的系统中,不存在净的内部宏观流动。特别是,这意味着系统的所有局部都处于相互辐射交换平衡。这意味着系统的温度在空间上是均匀的。这在所有情况下都是如此,包括那些非均匀外力场。对于外部施加的引力场,这可以使用拉格郎日乘子法通过变分的计算在宏观热力学术语中证明。动力学理论或统计力学也支持这种说法。<br />
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In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium.<ref name="Fitts 43"/><br />
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为了使一个系统处于它自己的内部热力学平衡状态,它必须处于它自己的内部热平衡状态是必要不充分的; 一个系统在到达内部热平衡之前到达内部力学平衡是可能的。<br />
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===Number of real variables needed for specification 规范所需的实变量数目===<br />
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In his exposition of his scheme of closed system equilibrium thermodynamics, C. Carathéodory initially postulates that experiment reveals that a definite number of real variables define the states that are the points of the manifold of equilibria.<ref name="Caratheodory" /> In the words of Prigogine and Defay (1945): "It is a matter of experience that when we have specified a certain number of macroscopic properties of a system, then all the other properties are fixed."<ref>Prigogine, I., Defay, R. (1950/1954), p. 1.</ref><ref>Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005), p. 4.</ref> As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.<br />
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在他关于封闭系统平衡态热力学方案的论述中,C.Carathéodory 最初假定实验揭示了一定数量的实变量定义了作为平衡态流形点的状态。用 Prigogine 和 Defay (1945)的话说: “这是一个经验问题,当我们确定了一个系统一定数量的宏观属性时,那么所有其他属性都是固定的”。如上所述,A. Münster认为,定义热力学平衡所需的变量数量相对于给定孤立系统的任何状态来说都是最少的。如上所述,J.G. Kirkwood 和 I. Oppenheim 指出,热力学平衡状态可以由一个特殊子类的强度变量来定义,该子类中有一定数量的成员。<br />
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If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.<br />
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如果热力学平衡位于一个外力场中,那么通常只有温度在空间上是均匀的。如果外力场非零,温度以外的强度变量通常是不均匀的。在这种情况下,一般需要附加变量来描述空间非均匀性。<br />
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===Stability against small perturbations 对小扰动的稳定性===<br />
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As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.<br />
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如上所述,J.R. Partington 指出热力学平衡状态在小的瞬态扰动下是稳定的。如果没有这个条件,一般来说,研究热力学平衡系统的实验就会遇到严重的困难。<br />
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===Approach to thermodynamic equilibrium within an isolated system 孤立系统中的热力学平衡===<br />
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When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium. Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<br />
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When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium.<ref name="Fitts 43">Fitts, D.D. (1962), p. 43.</ref> Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<ref>Denbigh, K.G. (1951), p. 42.</ref><br />
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当一个物质体从不均匀的非平衡状态或化学非平衡状态开始,然后被孤立,它会自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如,在这种演化的许多情况下,内部力学平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是,在这种演化的许多情况下,热平衡的发展要比化学平衡快得多。<br />
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===Fluctuations within an isolated system in its own internal thermodynamic equilibrium 孤立系统内部热力学平衡的涨落===<br />
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In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
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在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
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To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics.<ref>Tschoegl, N.W. (2000). ''Fundamentals of Equilibrium and Steady-State Thermodynamics'', Elsevier, Amsterdam, {{ISBN|0-444-50426-5}}, p. 21.</ref> But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
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To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics. But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
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考虑孤立热力学系统中的涨落概念,一个方便的例子是由其内能、体积和质量组成等广延量表示的系统。根据定义,它们是不随时间变化的。根据定义,这些量与它们的共轭状态强度函数的时不变标称值相结合,包括逆温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广延量的值,不足以提供这些标称值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
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It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.<br />
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可以承认,在重复测量这些共轭强度状态函数时,发现它们的值随时间略有不同。这种可变性被认为是由于内部涨落。不同测量值平均到其标称值。<br />
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If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<ref>Buchdahl, H.A. (1966), p. 16.</ref><br />
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If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<br />
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如果系统真的像经典热力学所假定的那样是宏观的,那么系统的涨落很小以至于宏观上无法检测到。这就是所谓的热力学极限。实际上,物质的分子性质和动量转移的量子性质由于它们太小而看不见,已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中,平衡的涨落概念是不存在的。”<br />
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If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
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如果系统被重复细分,最终产生的系统足够小,可以表现出明显的涨落。这是一个介观层面的研究。涨落则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
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If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在涨落过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,并且需要量子统计力学。涨落可以变得相对占主导地位,测量问题变得重要。<br />
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Thermal equilibrium is achieved when two systems in thermal contact with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<br />
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当两个相互热接触的系统不再有净能量交换时,就会产生热平衡。因此,如果两个系统处于热平衡,那么它们的温度是相同的。<br />
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The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
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"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有时间趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的标称值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微波动期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。非已知属于平衡状态的标称值,否则根据单一的度量无法进行判断。<br />
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Thermal equilibrium occurs when a system's macroscopic thermal observables have ceased to change with time. For example, an ideal gas whose distribution function has stabilised to a specific Maxwell–Boltzmann distribution would be in thermal equilibrium. This outcome allows a single temperature and pressure to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<br />
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当系统的宏观热观测值不再随着时间变化时,就会出现热平衡。例如,一种分布函数稳定到一个特定的麦克斯韦-波兹曼分布的理想气体即处于热平衡状态。这个结果可以将单一的温度和压力归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是很有可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
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=== Thermal equilibrium ===<br />
热平衡<br />
{{Main|Thermal equilibrium}}<br />
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An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process."<ref>Eu, B.C. (2002), page 13.</ref> This illustrates the importance for thermodynamics of the concept of temperature.<br />
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热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
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A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<br />
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一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数。<br />
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[[Thermal equilibrium]] is achieved when two systems in [[thermal contact]] with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<ref>[[Raj Pathria|R. K. Pathria]], 1996</ref><br />
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当两个相互'''<font color="#ff8000">热接触 Thermal Contact</font>'''的系统不再有净能量交换时,就会产生'''<font color="#ff8000">热平衡 Thermal Equilibrium</font>'''。因此,如果两个系统处于热平衡,那么它们的温度是相同的<br />
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Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
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Thermal equilibrium occurs when a system's [[macroscopic]] thermal observables have ceased to change with time. For example, an [[ideal gas]] whose [[Distribution function (physics)|distribution function]] has stabilised to a specific [[Maxwell–Boltzmann distribution]] would be in thermal equilibrium. This outcome allows a single [[temperature]] and [[pressure]] to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<ref>de Groot, S.R., Mazur, P. (1962), p. 44.</ref><br />
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当一个系统的'''<font color="#ff8000">宏观 Macroscopic</font>'''热观测值不再随时间变化时,就会出现热平衡。例如,一种'''<font color="#ff8000">分布函数 Distribution Function</font>'''稳定到一个特定的'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''的'''<font color="#ff8000">理想气体 Ideal Gas</font>'''即处于热平衡状态。这个结果可以将单一的'''<font color="#ff8000">温度 Temperature</font>'''和'''<font color="#ff8000">压力 Pressure</font>'''归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
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Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle. It states that a non-equilibrium system evolves such as to maximize its entropy production.<br />
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定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
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==Non-equilibrium==<br />
非平衡<br />
{{Main|Non-equilibrium thermodynamics}}<br />
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Thermodynamic models <br />
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热力学模型<br />
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A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<ref>de Groot, S.R., Mazur, P. (1962), p. 43.</ref><br />
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一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数<br />
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Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
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Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle.<ref>{{cite book|last1=Ziegler|first1=H.|title=An Introduction to Thermomechanics.|date=1983|location=North Holland, Amsterdam.}}</ref><ref>{{cite journal|last1=Onsager|first1=Lars|title=Reciprocal Relations in Irreversible Processes|journal=Phys. Rev.|date=1931|volume=37|issue=4|doi=10.1103/PhysRev.37.405|bibcode=1931PhRv...37..405O|pages=405–426|doi-access=free}}</ref> It states that a non-equilibrium system evolves such as to maximize its entropy production.<ref>{{cite book|last1=Kleidon|first1=A.|last2=et.|first2=al.|title=Non-equilibrium Thermodynamics and the Production of Entropy.|date=2005|edition=Heidelberg: Springer.}}</ref><ref>{{cite journal|last1=Belkin|first1=Andrey|last2=et.|first2=al.|title=Self-Assembled Wiggling Nano-Structures and the Principle of Maximum Entropy Production|journal=Sci. Rep.|doi=10.1038/srep08323|bibcode=2015NatSR...5E8323B|pmc=4321171|pmid=25662746|volume=5|year=2015|page=8323}}</ref><br />
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定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
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Topics in control theory<br />
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控制理论主题<br />
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==See also ==<br />
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{{Portal|Chemistry}}<br />
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;Thermodynamic models 热力学模型<br />
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{{colbegin}}<br />
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* [[Non-random two-liquid model]] (NRTL model) - Phase equilibrium calculations 非随机两液模型(NRTL 模型)-相平衡计算<br />
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* [[UNIQUAC]] model - Phase equilibrium calculations UNIQUAC 模型-相平衡计算<br />
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* [[Time crystal]] 时间晶体<br />
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{{colend}}<br />
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;Topics in control theory 控制理论主题<br />
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{{colbegin}}<br />
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* [[Steady state]] 稳态<br />
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* [[Transient state]] 瞬态<br />
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* [[Coefficient diagram method]] 系数图法<br />
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* [[Control reconfiguration]] 控制重构<br />
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* [[Cut-insertion theorem]] 切入定理<br />
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* [[Feedback]] 反馈<br />
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* [[H infinity]] H 无限<br />
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* [[Hankel singular value]] 汉克尔奇异值<br />
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* [[Krener's theorem]] 克雷纳定理<br />
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* [[Lead-lag compensator]] 超前滞后补偿器<br />
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* [[Minor loop feedback]] 小循环反馈<br />
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* [[Minor loop feedback|Multi-loop feedback]] 小循环反馈 | 多循环反馈<br />
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* [[Positive systems]] 正向系统<br />
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* [[Radial basis function]] 径向基底函数<br />
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Other related topics<br />
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其他相关话题<br />
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* [[Root locus]] 根轨迹<br />
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* [[Signal-flow graph]]s 信号流图<br />
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* [[Stable polynomial]] 稳定多项式<br />
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* [[State space representation]] 状态空间<br />
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* [[Underactuation]] 欠驱动<br />
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* [[Youla–Kucera parametrization]] 尤拉-库切拉参数化<br />
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* [[Markov chain approximation method]] 马尔可夫链近似法<br />
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{{colend}}<br />
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;Other related topics<br />
其他相关话题<br />
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{{colbegin}}<br />
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* [[Automation and remote control]] 自动化和远程控制<br />
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* [[Bond graph]] 键合图<br />
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* [[Control engineering]] 控制工程<br />
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* [[Control–feedback–abort loop]] 控制-反馈-中止循环<br />
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* [[Controller (control theory)]] 控制器(控制理论)<br />
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* [[Cybernetics]] 控制论<br />
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* [[Intelligent control]] 智能控制<br />
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* [[Mathematical system theory]] 数学系统论<br />
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* [[Negative feedback amplifier]] 负反馈放大器<br />
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* [[People in systems and control]] 系统和控制中的人<br />
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* [[Perceptual control theory]] 知觉控制理论<br />
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* [[Systems theory]] 系统论<br />
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* [[Time scale calculus]] 时间尺度演算<br />
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{{colend}}<br />
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<br />
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== 编者推荐 ==<br />
===集智文章推荐===<br />
<br />
====[https://swarma.org/?p=21322 什么是非平衡态热力学 | 集智百科]====<br />
非平衡态热力学 Non-equilibrium thermodynamics 是热力学的一个分支,研究某些不处于热力学平衡中的物理系统<br />
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==General references==<br />
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* Cesare Barbieri (2007) ''Fundamentals of Astronomy''. First Edition (QB43.3.B37 2006) CRC Press {{ISBN|0-7503-0886-9}}, {{ISBN|978-0-7503-0886-1}}<br />
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* Hans R. Griem (2005) ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}<br />
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* C. Michael Hogan, Leda C. Patmore and Harry Seidman (1973) ''Statistical Prediction of Dynamic Thermal Equilibrium Temperatures using Standard Meteorological Data Bases'', Second Edition (EPA-660/2-73-003 2006) United States Environmental Protection Agency Office of Research and Development, Washington, D.C. [http://library.wur.nl/WebQuery/catalog/lang/1851848]<br />
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* F. Mandl (1988) ''Statistical Physics'', Second Edition, John Wiley & Sons<br />
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==References==<br />
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{{Reflist|colwidth=35em}}<br />
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==Cited bibliography==<br />
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*Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', third edition, McGraw-Hill, London, {{ISBN|0-521-25445-0}}.<br />
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*Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, {{ISBN|0-88318-797-3}}.<br />
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*Beattie, J.A., Oppenheim, I. (1979). ''Principles of Thermodynamics'', Elsevier Scientific Publishing, Amsterdam, {{ISBN|0-444-41806-7}}.<br />
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*[[Ludwig Boltzmann|Boltzmann, L.]] (1896/1964). ''Lectures on Gas Theory'', translated by S.G. Brush, University of California Press, Berkeley.<br />
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*Buchdahl, H.A. (1966). ''The Concepts of Classical Thermodynamics'', Cambridge University Press, Cambridge UK.<br />
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*[[Herbert Callen|Callen, H.B.]] (1960/1985). ''Thermodynamics and an Introduction to Thermostatistics'', (1st edition 1960) 2nd edition 1985, Wiley, New York, {{ISBN|0-471-86256-8}}.<br />
<br />
*[[Constantin Carathéodory|Carathéodory, C.]] (1909). [https://web.archive.org/web/20160304213645/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0067&DMDID=DMDLOG_0033&L=1 Untersuchungen über die Grundlagen der Thermodynamik], ''[[Mathematische Annalen]]'', '''67''': 355–386. A translation may be found [http://neo-classical-physics.info/uploads/3/0/6/5/3065888/caratheodory_-_thermodynamics.pdf here]. Also a mostly reliable [https://books.google.com/books?id=xwBRAAAAMAAJ&q=Investigation+into+the+foundations translation is to be found] at Kestin, J. (1976). ''The Second Law of Thermodynamics'', Dowden, Hutchinson & Ross, Stroudsburg PA.<br />
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*[[Sydney Chapman (mathematician)|Chapman, S.]], [[Thomas George Cowling|Cowling, T.G.]] (1939/1970). ''The Mathematical Theory of Non-uniform gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases'', third edition 1970, Cambridge University Press, London.<br />
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*Crawford, F.H. (1963). ''Heat, Thermodynamics, and Statistical Physics'', Rupert Hart-Davis, London, Harcourt, Brace & World, Inc.<br />
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*de Groot, S.R., Mazur, P. (1962). ''Non-equilibrium Thermodynamics'', North-Holland, Amsterdam. Reprinted (1984), Dover Publications Inc., New York, {{ISBN|0486647412}}.<br />
<br />
*Denbigh, K.G. (1951). ''Thermodynamics of the Steady State'', Methuen, London.<br />
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*Eu, B.C. (2002). ''Generalized Thermodynamics. The Thermodynamics of Irreversible Processes and Generalized Hydrodynamics'', Kluwer Academic Publishers, Dordrecht, {{ISBN|1-4020-0788-4}}.<br />
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*Fitts, D.D. (1962). ''Nonequilibrium thermodynamics. A Phenomenological Theory of Irreversible Processes in Fluid Systems'', McGraw-Hill, New York.<br />
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*[[Josiah Willard Gibbs|Gibbs, J.W.]] (1876/1878). On the equilibrium of heterogeneous substances, ''Trans. Conn. Acad.'', '''3''': 108–248, 343–524, reprinted in ''The Collected Works of J. Willard Gibbs, Ph.D, LL. D.'', edited by W.R. Longley, R.G. Van Name, Longmans, Green & Co., New York, 1928, volume 1, pp.&nbsp;55–353.<br />
<br />
*Griem, H.R. (2005). ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}.<br />
<br />
*[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', fifth revised edition, North-Holland, Amsterdam.<br />
<br />
*Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of ''Thermodynamics'', pages 1–97 of volume 1, ed. W. Jost, of ''Physical Chemistry. An Advanced Treatise'', ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081.<br />
<br />
*[[John Gamble Kirkwood|Kirkwood, J.G.]], Oppenheim, I. (1961). ''Chemical Thermodynamics'', McGraw-Hill Book Company, New York.<br />
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*Landsberg, P.T. (1961). ''Thermodynamics with Quantum Statistical Illustrations'', Interscience, New York.<br />
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*{{cite journal |last1=Lieb |first1=E. H. |last2=Yngvason |first2=J. |year=1999 |title=The Physics and Mathematics of the Second Law of Thermodynamics |journal=Phys. Rep. |volume=310 |issue= 1|pages=1–96 |doi= 10.1016/S0370-1573(98)00082-9|arxiv = cond-mat/9708200 |bibcode = 1999PhR...310....1L |s2cid=119620408 }}<br />
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*Levine, I.N. (1983), ''Physical Chemistry'', second edition, McGraw-Hill, New York, {{ISBN|978-0072538625}}.<br />
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*{{cite journal | last1 = Maxwell | first1 = J.C. | authorlink = James Clerk Maxwell | year = 1867 | title = On the dynamical theory of gases | url = | journal = Phil. Trans. Roy. Soc. London | volume = 157 | issue = | pages = 49–88 }}<br />
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*[[Philip M. Morse|Morse, P.M.]] (1969). ''Thermal Physics'', second edition, W.A. Benjamin, Inc, New York.<br />
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*Münster, A. (1970). ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London.<br />
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*[[J.R. Partington|Partington, J.R.]] (1949). ''An Advanced Treatise on Physical Chemistry'', volume 1, ''Fundamental Principles. The Properties of Gases'', Longmans, Green and Co., London.<br />
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*[[Brian Pippard|Pippard, A.B.]] (1957/1966). ''The Elements of Classical Thermodynamics'', reprinted with corrections 1966, Cambridge University Press, London.<br />
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* [[Max Planck|Planck. M.]] (1914). [https://archive.org/details/theoryofheatradi00planrich ''The Theory of Heat Radiation''], a translation by Masius, M. of the second German edition, P. Blakiston's Son & Co., Philadelphia.<br />
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*[[Ilya Prigogine|Prigogine, I.]] (1947). ''Étude Thermodynamique des Phénomènes irréversibles'', Dunod, Paris, and Desoers, Liège.<br />
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*[[Ilya Prigogine|Prigogine, I.]], Defay, R. (1950/1954). ''Chemical Thermodynamics'', Longmans, Green & Co, London.<br />
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*Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005). ''Physical Chemistry'', fourth edition, Wiley, Hoboken NJ.<br />
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*[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966). ''Elements of Thermodynamics'', Addison-Wesley Publishing, Reading MA.<br />
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*{{cite journal|last=Thomson|first=W.|author-link=William Thomson, 1st Baron Kelvin|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Transactions of the Royal Society of Edinburgh|date=March 1851|volume=XX|issue=part II|pages=261–268; 289–298}} Also published in {{cite journal|last=Thomson|first=W.|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Phil. Mag. |date=December 1852 |volume=IV |series=4 |issue=22 |pages=8–21 |url=https://archive.org/details/londonedinburghp04maga |accessdate=25 June 2012}}<br />
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*[[László Tisza|Tisza, L.]] (1966). ''Generalized Thermodynamics'', M.I.T Press, Cambridge MA.<br />
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*[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963). ''Lectures in Statistical Mechanics'', American Mathematical Society, Providence RI.<br />
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*Waldram, J.R. (1985). ''The Theory of Thermodynamics'', Cambridge University Press, Cambridge UK, {{ISBN|0-521-24575-3}}.<br />
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*[[Mark Zemansky|Zemansky, M.]] (1937/1968). ''Heat and Thermodynamics. An Intermediate Textbook'', fifth edition 1967, McGraw–Hill Book Company, New York.<br />
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== External links ==<br />
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Category:Equilibrium chemistry<br />
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类别: 平衡化学<br />
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*[http://ads.harvard.edu/books/1989fsa..book/AbookC15.pdf Breakdown of Local Thermodynamic Equilibrium] George W. Collins, The Fundamentals of Stellar Astrophysics, Chapter 15<br />
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Category:Thermodynamic cycles<br />
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类别: 热力循环<br />
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*[http://spiff.rit.edu/classes/phys440/lectures/lte/lte.html Thermodynamic Equilibrium, Local and otherwise] lecture by Michael Richmond<br />
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Category:Thermodynamic processes<br />
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类别: 热力学过程<br />
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*[http://journals.ametsoc.org/doi/abs/10.1175/1520-0469%281970%29027%3C0711:NLTEIC%3E2.0.CO%3B2 Non-Local Thermodynamic Equilibrium in Cloudy Planetary Atmospheres] Paper by R. E. Samueison quantifying the effects due to non-LTE in an atmosphere<br />
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Category:Thermodynamic systems<br />
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类别: 热力学系统<br />
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*[http://scienceworld.wolfram.com/physics/LocalThermodynamicEquilibrium.html Local Thermodynamic Equilibrium]<br />
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Category:Thermodynamics<br />
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分类: 热力学<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Thermodynamic equilibrium]]. Its edit history can be viewed at [[平衡热力学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%B9%B3%E8%A1%A1%E7%83%AD%E5%8A%9B%E5%AD%A6&diff=21668平衡热力学2021-02-07T13:06:22Z<p>Jxzhou:/* Fluctuations within an isolated system in its own internal thermodynamic equilibrium 孤立系统内部热力学平衡的涨落 */</p>
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<div>此词条暂由小竹凉翻译,翻译字数共5339,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{short description|State of thermodynamic system(s) where no net macroscopic flow of matter or energy occurs}}<br />
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'''Thermodynamic equilibrium''' is an [[axiomatic]] concept of [[thermodynamics]]. It is an internal [[State variables|state]] of a single [[thermodynamic system]], or a relation between several thermodynamic systems connected by more or less permeable or impermeable [[Thermodynamic system#Walls|walls]]. In thermodynamic equilibrium there are no net [[macroscopic]] [[Flow (mathematics)|flows]] of [[matter]] or of [[energy]], either within a system or between systems. <br />
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Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium there are no net macroscopic flows of matter or of energy, either within a system or between systems. <br />
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'''热力学平衡'''是'''<font color="#ff8000">热力学 Thermodynamics</font>'''的一个'''<font color="#ff8000">不言自明的 Axiomatic</font>'''概念。它是单个'''<font color="#ff8000">热力学系统 Thermodynamic System</font>'''的内部'''<font color="#ff8000">状态 State</font>''',或者是几个热力学系统之间通过或多或少的渗透或不渗透的'''<font color="#ff8000">壁 Wall</font>'''连接的关系。无论是在一个系统内还是在系统之间,在热力学平衡中不存在'''<font color="#ff8000">物质 Matter</font>'''或'''<font color="#ff8000">能量 Energy</font>'''的净'''<font color="#ff8000">宏观 Macroscopic</font>''' '''<font color="#ff8000">流动 Flow</font>'''。<br />
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In a system that is in its own state of internal thermodynamic equilibrium, no [[macroscopic]] change occurs. <br />
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In a system that is in its own state of internal thermodynamic equilibrium, no macroscopic change occurs. <br />
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在一个处于内部热力学平衡状态的系统中,不会发生'''<font color="#ff8000">宏观 Macroscopic</font>'''变化。<br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual [[Thermal equilibrium|thermal]], [[Mechanical equilibrium|mechanical]], [[Chemical equilibrium|chemical]], and [[Radiative equilibrium|radiative]] equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a [[thermodynamic operation]]. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a thermodynamic operation. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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相互热力学平衡的体系同时处于互相之间的'''<font color="#ff8000">热 Thermal</font>'''平衡、'''<font color="#ff8000">力学 Mechanical</font>'''平衡、'''<font color="#ff8000">化学 Chemical</font>'''平衡和'''<font color="#ff8000">辐射 Radiative</font>'''平衡。系统可以处于其中一种相互平衡状态,尽管其他状态未平衡。在热力学平衡中所有的平衡同时并且无限期地保持,直到被'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''打破。在一个宏观平衡中,微观交换是完全或几乎完全平衡的;这是对宏观平衡概念的物理解释。<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform [[temperature]]. Its [[Intensive and extensive properties|intensive properties]], other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform temperature. Its intensive properties, other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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一个处于内部热力学状态平衡的热力学系统具有空间均匀的'''<font color="#ff8000">温度 Temperature</font>'''。除了温度以外,它的'''<font color="#ff8000">强度性质 Intensive Properties</font>'''可以由于周围环境施加的不变的长程力场而导致空间不均匀性。<br />
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In systems that are at a state of [[non-equilibrium]] there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a '''meta-stable equilibrium'''.<br />
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In systems that are at a state of non-equilibrium there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a meta-stable equilibrium.<br />
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相比之下,处于'''<font color="#ff8000">非平衡状态 non-equilibrium</font>'''的系统中有物质或能量的净流动。如果这些变化可以在一个还没有发生的系统中被触发,那么这个系统就被称为处于一个'''亚稳定的平衡状态'''。<br />
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Though not a widely named a "law," it is an [[axiom]] of thermodynamics that there exist states of thermodynamic equilibrium. The [[second law of thermodynamics]] states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the [[entropy|entropies]] of the portions.<br />
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Though not a widely named a "law," it is an axiom of thermodynamics that there exist states of thermodynamic equilibrium. The second law of thermodynamics states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the entropies of the portions.<br />
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虽然不是一个广泛命名的“定律” ,但存在热力学平衡状态是一个热力学'''<font color="#ff8000">公理 Axiom</font>'''。'''<font color="#ff8000">热力学第二定律 second law of thermodynamics</font>'''指出,当一个物质体从一个平衡状态开始,在这个状态中,它的一部分被或多或少渗透或不渗透的分区保持在不同的状态,并且是孤立的,热力学操作移除分区或使分区更具渗透性,然后它会自发地达到自己内部热力学平衡的新状态,并伴随着部分'''<font color="#ff8000">熵 Entropy</font>'''的总和增加。<br />
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== Overview 概览==<br />
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{{Thermodynamics|cTopic=[[Thermodynamic system|Systems]]}}<br />
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Classical thermodynamics deals with states of [[dynamic equilibrium]]. The state of a system at thermodynamic equilibrium is the one for which some [[thermodynamic potential]] is minimized, or for which the [[entropy]] (''S'') is maximized, for specified conditions. One such potential is the [[Helmholtz free energy]] (''A''), for a system with surroundings at controlled constant temperature and volume:<br />
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Classical thermodynamics deals with states of dynamic equilibrium. The state of a system at thermodynamic equilibrium is the one for which some thermodynamic potential is minimized, or for which the entropy (S) is maximized, for specified conditions. One such potential is the Helmholtz free energy (A), for a system with surroundings at controlled constant temperature and volume:<br />
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经典热力学研究'''<font color="#ff8000">动态平衡 Dynamic Equilibrium</font>'''的状态。系统的热力学平衡状态是对于特定的条件,一些'''<font color="#ff8000">热力学势 Thermodynamic Potential</font>'''被最小化,或者'''<font color="#ff8000">熵 Entropy</font>'''(S)被最大化。对于一个周围环境温度和体积恒定的系统,其中一个这样的热力学势是'''<font color="#ff8000">亥姆霍兹自由能 Helmholtz Free Energy</font>'''(A):<br />
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:<math>A = U - TS</math><br />
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<math>A = U - TS</math><br />
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A = U-TS<br />
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Another potential, the [[Gibbs free energy]] (''G''), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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Another potential, the Gibbs free energy (G), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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在恒定温度和压力的系统中,另一个热力学势'''<font color="#ff8000">吉布斯自由能 Gibbs Free Energy</font>'''(G)在热力学平衡状态最小:<br />
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:<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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where ''T'' denotes the absolute thermodynamic temperature, ''P'' the pressure, ''S'' the entropy, ''V'' the volume, and ''U'' the internal energy of the system.<br />
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where T denotes the absolute thermodynamic temperature, P the pressure, S the entropy, V the volume, and U the internal energy of the system.<br />
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其中 T 表示热力学绝对温度,P 表示压强,S 表示熵,V 表示体积,U 表示体系的内能。<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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热力学平衡是一种独特的稳定定态,当系统长时间与周围环境相互作用时,它可以被接近或最终到达。上述势能是数学构造的热力学量,在特定的环境条件下最小化。<br />
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== Conditions 条件==<br />
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* For a completely isolated system, ''S'' is maximum at thermodynamic equilibrium. 对于一个完全孤立的系统,S在热力学平衡中取最大值。<br />
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* For a system with controlled constant temperature and volume, ''A'' is minimum at thermodynamic equilibrium. 对于一个恒定温度和体积的系统来说,A在热力学平衡中取最小值。<br />
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* For a system with controlled constant temperature and pressure, ''G'' is minimum at thermodynamic equilibrium. 对于一个恒温恒压的系统,G在热力学平衡中取最小值。<br />
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The various types of equilibriums are achieved as follows:<br />
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The various types of equilibriums are achieved as follows:<br />
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实现各种类型的平衡的方法如下:<br />
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*Two systems are in ''thermal equilibrium'' when their [[temperature]]s are the same. 当两个系统的'''<font color="#ff8000">温度 Temperature</font>'''相同时,它们就处于''热平衡状态''<br />
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*Two systems are in ''mechanical equilibrium'' when their [[pressure]]s are the same. 当两个体系的'''<font color="#ff8000">压力 Pressure</font>'''相同时,它们就处于''力学平衡''<br />
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*Two systems are in ''diffusive equilibrium'' when their [[chemical potential]]s are the same. 当两个题体系的'''<font color="#ff8000">化学势 Chemical Potential</font>'''相同时,它们就处于''扩散平衡''<br />
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*All [[forces]] are balanced and there is no significant external driving force.<br />
所有的'''<font color="#ff8000">力 Force</font>'''都是平衡的,没有明显的外部驱动力<br />
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==Relation of exchange equilibrium between systems 系统之间的交换均衡关系==<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability.<ref name="Nster_a">Münster, A. (1970), p. 49.</ref> When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability. When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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通常,热力学系统的周围环境也可以被看作是另一个热力学系统。在这种观点中,我们可以把系统及其周围环境看作是相互接触的两个系统,远程作用力也将它们联系在一起。系统的包围物是两个系统之间的接触面或边界。在热力学形式中,该表面被认为具有特定的渗透性质。例如,接触的表面可能被认为只能透热,使能量只能作为热传递。当远程力在时间上不发生变化,两个系统之间的热量传递减慢并最终永久停止时,这两个系统被称为热平衡; 这就是接触平衡的一个例子。其它类型的接触平衡可用其它类型的比渗透率来定义。当两个系统对于某一特定类型的渗透率处于接触平衡时,它们具有属于该特定类型渗透率的强变量的共同值。这种强度变量的例子有温度、压力、化学势。<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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接触平衡也可视为交换平衡。在接触平衡状态下,两系统之间某些量的传递速率存在零平衡。例如,对于只能透热的壁,内能作为热在两个系统之间的扩散速率是相等并反向的。两个系统之间的绝热壁只对作为功传递的能量有渗透作用; 在力学平衡,两个系统之间作为功的能量传递速率相等且相反。如果是一个简单的壁,那么通过它的体积转移率也是相等且相反的; 即它两边的压力是相等的。如果绝热壁比较复杂,有一种杠杆,有一个面积比,那么两个体系在交换平衡中的压力与体积交换比成反比,这使得转移率的零平衡作功。<br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<ref name="Planck 1914 40">[[Max Planck|Planck. M.]] (1914), p. 40.</ref><br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<br />
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辐射交换可以发生在两个不同的系统之间。当两个体系温度相同时,辐射交换平衡占优势。<br />
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==Thermodynamic state of internal equilibrium of a system 系统内部平衡的热力学状态==<br />
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A collection of matter may be entirely [[Isolated system|isolated]] from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium.<ref>Haase, R. (1971), p. 4.</ref><ref>Callen, H.B. (1960/1985), p. 26.</ref> (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics.<ref>{{Cite journal |doi = 10.1119/1.4914528|bibcode = 2015AmJPh..83..628M|title = Time and irreversibility in axiomatic thermodynamics|year = 2015|last1 = Marsland|first1 = Robert|last2 = Brown|first2 = Harvey R.|last3 = Valente|first3 = Giovanni|journal = American Journal of Physics|volume = 83|issue = 7|pages = 628–634}}</ref> One textbook<ref>[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963), p. 5.</ref> calls it the "zeroth law", remarking that the authors think this more befitting that title than its [[Zeroth law of thermodynamics|more customary definition]], which apparently was suggested by [[Ralph H. Fowler|Fowler]].)<br />
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A collection of matter may be entirely isolated from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium. (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics. One textbook calls it the "zeroth law", remarking that the authors think this more befitting that title than its more customary definition, which apparently was suggested by Fowler.)<br />
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物质的集合可能与其周围的环境完全'''<font color="#ff8000">孤立 Isolated</font>'''。如果它在无限长的时间内一直保持不受干扰,按照经典热力学假定,它处于一个没有发生任何变化,没有流动的状态,即内部平衡的热力学状态。(这种假设有时被称为“负第一”热力学定律,但并不常见。有教科书称之为“第零定律” ,作者'''<font color="#ff8000">福勒 Fowler</font>'''认为这个名称是'''<font color="#ff8000">更符合惯例的定义 More Customary Definition</font>'''。)<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a [[thermodynamic operation]] be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a thermodynamic operation be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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这种状态是所谓的经典热力学或平衡态热力学的主要关注点,因为它们是系统中被认为在这门学科中得到很好定义的唯一状态。一个与另一个系统处于接触平衡状态可以被一个'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''隔离,在隔离发生时,其内部不会发生任何变化。因此,一个与另一个系统处于接触平衡状态时也可以被视为处于其自身的内部热力学平衡状态。<br />
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==Multiple contact equilibrium 多点接触平衡==<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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热力学形式允许一个系统同时与其他多个系统接触,这些系统可能有也可能没有相互接触,且这些接触具有不同的渗透性。如果这些系统都与世界其他部分相互隔离,那么它们彼此之间就会达到各自的接触平衡。<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy.<ref name="Caratheodory">Carathéodory, C. (1909).</ref><ref>Prigogine, I. (1947), p. 48.</ref><ref>Landsberg, P. T. (1961), pp. 128–142.</ref><ref>Tisza, L. (1966), p. 108.</ref> Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy. Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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如果几个系统彼此之间没有绝热壁,但是它们与世界其他部分共同隔离,那么它们就会达到多重接触平衡状态,且有共同的温度,总的内能和熵。在众多强度量中,这是温度的一个独特性质。即使在远距离作用力存在的情况下,它也是有效的。(也就是说,没有“力”可以维持温度的差异。)举个例子,在热力学平衡的一个垂直的引力场系统中,顶部壁面的压力比底部壁面的压力小,但是各处的温度都是一样的。<br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural [[thermodynamic process]].<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), § 1.12.</ref> It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings.<ref>Levine, I.N. (1983), p. 40.</ref><ref>Lieb, E.H., Yngvason, J. (1999), pp. 17–18.</ref> The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of [[Second law of thermodynamics#Description#Kelvin statement|"inanimate" agency]]; a system in thermodynamic equilibrium is inanimate.<ref>[[William Thomson, 1st Baron Kelvin|Thomson, W.]] (1851).</ref><br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural thermodynamic process. It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings. The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of "inanimate" agency; a system in thermodynamic equilibrium is inanimate.<br />
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热力操作可能作为一个事件发生在周围环境的壁上,既不直接影响与周围环境联系的壁,也不直接影响其内部,且发生在一个明确的有限的时间内。例如,一个固定的绝热壁可以在环境中被放置或拆除。由于这种操作仅限于周围环境,系统可能会在一段时间内远离自身最初的内部状态---- 热力学平衡。根据热力学第二定律的说法,整体经历了变化并最终与周围环境达到了新的平衡。继Planck之后,这一连串的事件被称为自然'''<font color="#ff8000">热力学过程 Thermodynamic Process</font>'''。即使在这个过程中,当系统和周围环境都不处于明确的内部平衡状态时,存在着暂时偏离热力学平衡的现象,由于初始状态和最终状态都是热力学平衡的,这在平衡热力学中也是允许的。一个自然过程在其主要部分中以有限的速率进行,因此,它从根本上不同于虚构的准静态“过程”;即不在整个过程中无限缓慢地进行而且虚构地“可逆”。经典热力学允许,即使一个过程可能需要很长的时间才能达到热力学平衡,如果主要部分的过程是在一个有限的比率中,那么它被认为是自然的,并受制于热力学第二定律,即不可逆的。工程设计的机器、人工设备和操作是允许在周围环境中进行的。允许在环境中而不是在系统中进行此类操作和设备,是开尔文在他的一个热力学第二定律的陈述中提到'''<font color="#ff8000">无生命机构 Inanimate Agency</font>'''的原因; 在热力学平衡的系统是无生命的。<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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否则,热力操作可能会直接影响系统的壁。<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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通常可以很方便地假设周围的某些子系统比系统大得多,以至于这个过程只能影响周围子系统的强度变量,然后将这些子系统称为相关强度变量的储备库。<br />
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== Local and global equilibrium 局部和全局均衡==<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by [[intensive quantity|intensive]] parameters. As an example, [[temperature]] controls [[Heat equation|heat exchanges]]. ''Global thermodynamic equilibrium'' (GTE) means that those [[intensive quantity|intensive]] parameters are homogeneous throughout the whole system, while ''local thermodynamic equilibrium'' (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by intensive parameters. As an example, temperature controls heat exchanges. Global thermodynamic equilibrium (GTE) means that those intensive parameters are homogeneous throughout the whole system, while local thermodynamic equilibrium (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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区分全局性和局部性热力学平衡是很有用的。在热力学中,系统内部和系统与外部之间的交换是由'''<font color="#ff8000">强度 Intensive</font>'''参数控制的。例如,'''<font color="#ff8000">温度 Temperature</font>'''控制'''<font color="#ff8000">热交换 Heat Equation</font>'''。全局热力学平衡(GTE)意味着这些'''<font color="#ff8000">强度 Intensive</font>'''参数在整个系统中是均匀的,而局部热力学平衡(LTE)意味着这些强度参数在空间和时间上是变化的,但变化如此缓慢,以至于对于任何一点,人们都可以假设在该点的某个邻域存在热力学平衡。<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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如果对系统的描述要求强度参数的变化过大,那么这些强度参数的定义所依据的假设本身就会失效,系统将既不处于全局平衡,也不处于局部平衡。例如,粒子需要一定数量的碰撞来平衡其周围环境。如果在这些碰撞中移动的平均距离使它离开平衡邻域,它将永远不会平衡,也就不会有 LTE。根据定义,温度与平衡邻域的平均内部能量成正比。由于没有达到平衡邻域,温度的概念就不成立,温度也就变得无法定义。<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to [[massive]] particles. In a [[radiation|radiating]] gas, the [[photon]]s being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to massive particles. In a radiating gas, the photons being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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值得注意的是,这种局部平衡可能只适用于系统中的某个粒子子集。例如,LTE 通常只适用于'''<font color="#ff8000">大 Massive</font>'''质量粒子。在'''<font color="#ff8000">辐射 Radiation</font>'''气体中,被气体发射和吸收的'''<font color="#ff8000">光子 Photon</font>'''不需要彼此在一个热力学平衡内,或与气体中的大量粒子在一起,LTE 才能存在。在某些情况下,自由电子并不需要与大得多的原子或分子处于平衡状态,LTE 才能存在。<br />
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As an example, LTE will exist in a glass of water that contains a melting [[ice cube]]. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the [[Maxwell–Boltzmann distribution]] for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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As an example, LTE will exist in a glass of water that contains a melting ice cube. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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例如,LTE 将存在于一个装有正在融化的'''<font color="#ff8000">冰块 Ice Cube</font>'''的水杯中。玻璃杯内的温度可以在任何时候定义,但是离冰块近的地方要比离冰块远的地方冷。如果观察到位于给定点附近的分子的能量,它们将按照麦克斯韦-波兹曼分布在一定温度下的分布。如果观察到位于另一点附近的分子的能量,它们将按照'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''分布到另一个温度。<br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural [[transport phenomena]] may lead a system from local to global thermodynamic equilibrium. Going back to our example, the [[diffusion]] of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<ref>H.R. Griem, 2005</ref><br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural transport phenomena may lead a system from local to global thermodynamic equilibrium. Going back to our example, the diffusion of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<br />
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局部热力学平衡不需要局部或全局的平稳性。换句话说,每一个小区域不需要有一个恒定的温度。然而,它确实要求每个小的局部变化缓慢到足以维持其局部麦克斯韦-波尔兹曼速度分布。全局非平衡态只有通过系统与外界的交换才能保持稳定。例如,通过在水杯中不断添加细粉冰来补偿熔化,并持续排出融水,可以保持全局稳定的静态。自然'''<font color="#ff8000">输运现象 Transport Phenomena</font>'''会使一个局部热力学平衡系统逐渐达到全局的热力学平衡。回顾我们的例子,热量的扩散将导致我们的玻璃杯水流向全局热力学平衡,在这种状态下,玻璃杯的温度是完全均匀的。<br />
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==Reservations 保留意见==<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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学识渊博的笔者在热力学领域对热力学平衡描述时,经常对他们的描述附加条件或保留意见。有些笔者含蓄地保留了或多或少的空白,以待说明。<br />
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For example, one widely cited writer, [[Herbert Callen|H. B. Callen]] writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. ''Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!''"<ref>Callen, H.B. (1960/1985), p. 15.</ref><br />
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For example, one widely cited writer, H. B. Callen writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!"<br />
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例如,一位被广泛引用的作家'''<font color="#ff8000">H.B.卡伦 H.B.Callen</font>'''在这里写道: “实际上,很少有系统处于绝对和真正的平衡状态。”他提到了放射性过程,认为它们可能需要“宇宙时间才能完成,因此通常可以忽略”。他补充道: “在实践中,平衡的标准是循环的。在操作上,如果一个系统的性质一致地用热力学理论来描述,那么它就处于平衡状态! ”<br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<ref>Beattie, J.A., Oppenheim, I. (1979), p. 3.</ref><br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<br />
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J.A.贝蒂和 I.奥本海姆写道: “坚持对平衡定义的严格解释,将排除热力学应用于实际系统的所有状态。”<br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment",<ref>Callen, H.B. (1960/1985), p. 485.</ref> and cited by Adkins as having written a "classic text",<ref>Adkins, C.J. (1968/1983), p. ''xiii''.</ref> [[Brian Pippard|A.B. Pippard]] writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<ref>Pippard, A.B. (1957/1966), p. 6.</ref><br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment", and cited by Adkins as having written a "classic text", A.B. Pippard writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<br />
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Callen引用另一位作者的话说,他给出了“学术且严谨的论述” ,Adkins引用他的话说,他写了一本“经典著作”—— '''<font color="#ff8000">A.B.皮帕德 A.B.Pippard</font>'''在文中写道: “只要时间足够长,过冷水蒸汽最终会凝结,... ..。时间可能是漫长的,也许长达10年或者更长。就大多数目的而言,只要这种迅速的变化不是人为地刺激,这些系统就可以被视为处于平衡状态。”<br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster">Münster, A. (1970), p. 53.</ref><br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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另一位作者A.Münster,写道。他观察到热核反应发生的速度非常缓慢,以至于在热力学中可以忽略不计。他评论道: “‘绝对平衡’或‘所有可想象过程的平衡’的概念没有物理意义。”他说: “ ... 我们只能考虑特定过程和确定的实验条件下的平衡。”<br />
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According to [[László Tisza|L. Tisza]]: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<ref>Tisza, L. (1966), p. 119.</ref><br />
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According to L. Tisza: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<br />
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根据'''<font color="#ff8000">L.缇莎 L.Tisza</font>'''的说法: “ ... 在讨论接近绝对零度的现象时。经典理论的绝对预测变得特别模糊,因为在非平衡状态下发生冻结是非常普遍的。”<br />
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==Definitions 定义==<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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一个系统最普遍的热力学平衡是通过与周围环境的接触,允许所有化学物质和各种能量同时通过。热力学平衡中的系统可能以均匀加速度在空间中运动,但此时不能改变其形状或大小; 因此它是由空间中的刚性体积来定义的。它可能存在于外力场中,由远远大于系统本身的外部因素决定,因此系统内的事件不会对外力场产生相当大的影响。只有当外力场是均匀的,并且确定了它的均匀加速度,或者它处于一个非均匀力场中,但是由于表面的局部力,例如机械压力,使它保持静止时,这个系统才能处于热力学平衡。<br />
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Thermodynamic equilibrium is a [[primitive notion]] of the theory of thermodynamics. According to [[Philip M. Morse|P.M. Morse]]: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are ''not'' conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments."<ref>[[Philip M. Morse|Morse, P.M.]] (1969), p. 7.</ref> This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<ref>Bailyn, M. (1994), p. 20.</ref><br />
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Thermodynamic equilibrium is a primitive notion of the theory of thermodynamics. According to P.M. Morse: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are not conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments." This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<br />
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热力学平衡是热力学理论的一个'''<font color="#ff8000">基本概念 Primitive Notion</font>'''。'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''说: “应该强调的是,存在热力学状态这一事实,以及存在由平衡态唯一指定的热力学变量这一事实,并不是从某些哲学第一原理得出的逻辑结论。这些结论不可避免地来自两个多世纪的实验。”这意味着热力学平衡不能仅仅用热力学的其他理论概念来定义。M.Bailyn提出了一个基本的热力学定律理论,它定义并假设了热力学平衡的存在。<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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热力学平衡的教科书定义通常被仔细说明,并有些保留。<br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<ref>Münster, A. (1970), p. 52.</ref><br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<br />
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例如,A. Münster写道:“当一个孤立系统中没有以可测量的速率发生状态变化时,系统处于热力学平衡状态。”这里有两项保留:系统是孤立的;任何状态的变化都是不可测量的缓慢。他通过对在室温且没有催化剂的情况下混合氧和氢的说明,讨论了第二个条件。Münster指出,描述热力学平衡状态所需要的宏观变量比给定系统任何其他状态都少。这是部分,但不完全是,因为系统内和流过系统的所有流都是零。<br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in ''equilibrium''.<ref>Haase, R. (1971), pp. 3–4.</ref><br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in equilibrium.<br />
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R. Haase's的热力学演示并不从对热力学平衡的限制开始,因为他打算考虑非平衡态热力学。他考虑一个具有时间不变性质的任意系统。他通过切断除外力场以外的所有外部影响来测试它的热力学平衡。如果在绝缘之后,没有任何变化,他说,系统处于平衡状态。<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness".<ref>Callen, H.B. (1960/1985), p. 13.</ref> This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness". This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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在一个标题为“热力学平衡”的章节中,H.B. Callen在一个段落中定义了平衡状态.他指出,它们“是由系统内部的内在因素决定的”。它们是“终端状态” ,随着时间的推移,系统会以“冰川般缓慢”的速度朝着这个终端状态演化。这个说法并没有明确,对于热力学平衡系统必须是孤立的;;Callen也没有说明他所说的“内在因素”是什么意思。<br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<ref>Adkins, C.J. (1968/1983), p. ''7''.</ref><br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<br />
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另一位教科书作者,C.J.Adkins,明确允许热力学平衡在非孤立的系统中发生。然而,他的系统在物质转移方面是封闭的。他写道: “一般来说,热力学平衡的方法包括热和类似功的形式与周围环境的相互作用。”他将这种热力学平衡与只有通过热接触才能进行能量传递的热平衡相区别。<br />
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Another textbook author, [[J.R. Partington]], writes: "(i) ''An equilibrium state is one which is independent of time''." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..."<ref>Partington, J.R. (1949), p. 161.</ref> This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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Another textbook author, J.R. Partington, writes: "(i) An equilibrium state is one which is independent of time." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..." This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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另一位教科书作者'''<font color="#ff8000">J.R.帕廷顿 J.R.Partington</font>'''写道: “(i)平衡状态是独立于时间的状态。”但是,在提到“只是明显处于平衡状态”的系统时,他补充说: “这样的系统处于‘虚假平衡’状态。帕廷顿的陈述没有明确指出平衡是指一个孤立的系统。和Münster一样,Partington也指的是氧和氢的混合物。他补充说:“在一个真正的平衡状态,任何影响状态的外部条件的微小变化都会产生一个微小的状态变化... ... ”这个条件意味着热力学平衡必须在小的扰动下保持稳定; 这个要求对于热力学平衡的严格意义是必不可少的。<br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, ''thermodynamic—equilibrium.''"<ref>Crawford, F.H. (1963), p. 5.</ref><br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, thermodynamic—equilibrium."<br />
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在F.H.Crawford的一本学生教科书中,有一个标题为“热力学平衡”的章节。它区分了几种流动的驱动因素,然后说: “这些是孤立系统明显普遍趋向于完全机械、热、化学和电力状态的例子——或者简单地说,热力学平衡状态。”<br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in ''equilibrium''."<ref>Buchdahl, H.A. (1966), p. 8.</ref> Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being ''in equilibrium'' so long as experimental tests show that 'slow' transitions are in effect reversible."<ref>Buchdahl, H.A. (1966), p. 111.</ref> It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<ref>Adkins, C.J. (1968/1983), p. 8.</ref><br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in equilibrium." Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being in equilibrium so long as experimental tests show that 'slow' transitions are in effect reversible." It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<br />
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H.A. Buchdahl的一本关于经典热力学的专著考虑了热力学系统的平衡,而实际上并没有写热力学平衡一词。Buchdahl在提到封闭的物质交换系统时写道: “如果一个系统处于一个适当的静态状态,那么它将被称为处于平衡状态。”出于热力学描述的目的,Buchdahl的专著也讨论了非晶态玻璃。它说: “更准确地说,只要实验测试表明‘慢’跃迁实际上是可逆的,玻璃就可以被认为处于平衡状态。”通常来说不会将这一条件作为热力学平衡定义的一部分,而是假定相反的情况:如果热力学平衡中的一个物体受到足够慢的过程的影响,则该过程可被视为足够接近可逆,并且该物体在过程中足够接近热力学平衡。<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of ''contact equilibrium''. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by [[Constantin Carathéodory|C. Carathéodory]], and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster" /> Thermodynamic equilibrium for an open system means that, with respect to every relevant kind of selectively permeable wall, contact equilibrium exists when the respective intensive parameters of the system and surroundings are equal.<ref name="Nster_a" /> This definition does not consider the most general kind of thermodynamic equilibrium, which is through unselective contacts. This definition does not simply state that no current of matter or energy exists in the interior or at the boundaries; but it is compatible with the following definition, which does so state.<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of contact equilibrium. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by C. Carathéodory, and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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通过引入接触平衡的概念,A. Münster仔细地扩展了孤立系统热力学平衡的定义。这指定了在考虑非孤立系统的热力学平衡时允许的特定过程,并特别关心开放系统,这些开放系统可能从周围环境获得或丢失物质。感兴趣的系统和周围系统之间的接触平衡,通过一种特殊的壁与之接触,其余的连接系统是孤立的。这种特殊类型的壁也被'''<font color="#ff8000">C.喀喇西奥多里 C.Carathéodory</font>'''考虑过,其他作家也提到过。它们具有选择渗透性。它们可能只对机械功有渗透性,或者只对热有渗透性,或者只对某种特定的化学物质有渗透性。每个接触平衡定义了一个强度参数; 例如,只能透热的壁定义了一个经验温度。对于感兴趣的体系中每一种化学成分,都可以存在接触平衡。在接触平衡中,尽管有可能通过选择性渗透壁进行交换,但是感兴趣的系统是不变的,好像它处在孤立的热力学平衡。这个方案遵循的一般规则是: “ ... ... 我们只能考虑特定过程和特定实验条件下的平衡。”<br />
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[[Mark Zemansky|M. Zemansky]] also distinguishes mechanical, chemical, and thermal equilibrium. He then writes: "When the conditions for all three types of equilibrium are satisfied, the system is said to be in a state of thermodynamic equilibrium".<ref>[[Mark Zemansky|Zemansky, M.]] (1937/1968), p. 27.</ref><br />
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'''<font color="#ff8000">M.泽曼斯基 M.Zemansky</font>'''还区分了力学、化学和热平衡。他接着写道: “当这三种均衡的条件都满足时,系统就处于热力学平衡状态。”<br />
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P.M. Morse writes that thermodynamics is concerned with "states of thermodynamic equilibrium". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<br />
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[[Philip M. Morse|P.M. Morse]] writes that thermodynamics is concerned with "''states of thermodynamic equilibrium''". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<ref>[[Philip M. Morse|Morse, P.M.]] (1969), pp. 6, 37.</ref><br />
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'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''写道,热力学关注的是“热力学平衡状态”。在讨论物体与周围热源之间的热量传递时,他也使用了“热平衡”这个短语,尽管没有明确定义一个特殊的术语“热平衡”<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "full thermodynamic equilibrium state".<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "''full'' thermodynamic equilibrium state".<ref>Waldram, J.R. (1985), p. 5.</ref><br />
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J.R. Waldram写到了“一个明确的热力学状态”。他将一个系统定义为“当其观测量随时间停止变化时”的“热平衡”。但是在这个定义之下不久,他写到一块玻璃还没有达到“完全的热力学平衡状态”。<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, thermodynamic equilibrium is said to exist." He is not here considering the presence of an external force field.<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, ''thermodynamic equilibrium'' is said to exist." He is not here considering the presence of an external force field.<ref>Bailyn, M. (1994), p. 21.</ref><br />
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考虑到平衡状态,M.Bailyn写道: “每个强度变量都有自己的平衡类型。”然后他定义了热平衡、力学平衡和物质平衡。因此,他写道: “如果所有的强度变量都是一致的,那么热力学平衡就是存在的。”他在这里没有考虑外力场的存在。<br />
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J.G. Kirkwood and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of thermodynamic equilibrium if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<br />
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[[John Gamble Kirkwood|J.G. Kirkwood]] and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of ''thermodynamic equilibrium'' if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<ref>Kirkwood, J.G., Oppenheim, I. (1961), p. 2</ref><br />
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'''<font color="#ff8000">J.G.柯克伍德 J.G.Kirkwood</font>'''和 I.Oppenheim 将热力学平衡定义为: “一个系统处于热力学平衡状态,如果,在实验的时间内,(a)它强度特性与时间无关,(b)它的内部或与周围环境的边界处没有物质或能量流。”显然,他们没有把定义限制在孤立的或封闭的系统。它们不讨论“缓慢”发生变化的可能性,并且超出了分配给实验的时间范围。他们注意到,对于两个相接触的系统,存在一个强度性质的小子类,如果这个小子类的所有子类都相等,那么所有各自的强度性质都相等。只要满足其他一些条件,热力学平衡状态可以由这个子类定义。<br />
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==Characteristics of a state of internal thermodynamic equilibrium 内部热力学平衡状态的特征==<br />
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===Homogeneity in the absence of external forces 在没有外力的情况下的均匀性===<br />
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A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous.<ref name="Planck 1903 3"/> This means that the material in any small volume element of the system can be interchanged with the material of any other geometrically congruent volume element of the system, and the effect is to leave the system thermodynamically unchanged. In general, a strong external force field makes a system of a single phase in its own internal thermodynamic equilibrium inhomogeneous with respect to some [[Intensive and extensive properties|intensive variables]]. For example, a relatively dense component of a mixture can be concentrated by centrifugation.<br />
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在没有外力的情况下,由单一相组成的热力学系统,在其自身的内部热力学平衡中是均匀的。这意味着系统中任何小体积单元中的材料可以与系统中任何其他几何相等的体积单元中的材料互换,其效果是使系统在热力学上保持不变。一般来说,一个强外力场使得一个单相系统在其自身的内部热力学平衡中对于一些'''<font color="#ff8000">强度量 Intensive Variable</font>'''是不均匀的。例如,可以通过离心来浓缩混合物中相对密度较大的组分。<br />
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===Uniform temperature 均匀温度===<br />
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Such equilibrium inhomogeneity, induced by external forces, does not occur for the intensive variable [[temperature]]. According to [[Edward A. Guggenheim|E.A. Guggenheim]], "The most important conception of thermodynamics is temperature."<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), p.5.</ref> Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface."<ref name="Planck 1903 3">[[Max Planck|Planck, M.]] (1897/1927), p.3.</ref> As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.<br />
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这种由外力引起的平衡不均匀性,对于强度量'''<font color="#ff8000">温度 Temperature</font>'''不会发生。'''<font color="#ff8000">E.A.古根海姆 E.A. Guggenheim</font>'''认为,“热力学最重要的概念是温度。“Planck在介绍他的论文时,简要叙述了热、温度和热平衡,然后宣布: ”在下文中,我们将主要讨论任何形式的均匀、各向同性的物体,它们的物质具有相同的温度和密度,并受到到处垂直于表面的均匀压力的作用。和Carathéodory 一样,Planck将表面效应、外场和各向异性晶体排除在外。虽然Planck提到了温度,但并没有明确提到热力学平衡的概念。相比之下,Carathéodory关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ,虽然没有明确地使用短语‘热力学平衡’ ,也没有明确地假设存在一个温度来定义它。<br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform.<ref name="Planck 1914 40"/> This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers.<ref>Gibbs, J.W. (1876/1878), pp. 144-150.</ref><ref>[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966), pp. 127–130.</ref><ref>Münster, A. (1970), pp. 309–310.</ref><ref>Bailyn, M. (1994), pp. 254-256.</ref><ref>{{cite journal | last1 = Verkley | first1 = W.T.M. | last2 = Gerkema | first2 = T. | year = 2004 | title = On maximum entropy profiles | journal = J. Atmos. Sci. | volume = 61 | issue = 8| pages = 931–936 | doi=10.1175/1520-0469(2004)061<0931:omep>2.0.co;2| bibcode = 2004JAtS...61..931V | doi-access = free }}</ref><ref>{{cite journal | last1 = Akmaev | first1 = R.A. | year = 2008 | title = On the energetics of maximum-entropy temperature profiles | url = | journal = Q. J. R. Meteorol. Soc. | volume = 134 | issue = 630| pages = 187–197 | doi=10.1002/qj.209| bibcode = 2008QJRMS.134..187A }}</ref> Considerations of kinetic theory or statistical mechanics also support this statement.<ref>Maxwell, J.C. (1867).</ref><ref>Boltzmann, L. (1896/1964), p. 143.</ref><ref>Chapman, S., Cowling, T.G. (1939/1970), Section 4.14, pp. 75–78.</ref><ref>[[J. R. Partington|Partington, J.R.]] (1949), pp. 275–278.</ref><ref>{{cite journal | last1 = Coombes | first1 = C.A. | last2 = Laue | first2 = H. | year = 1985 | title = A paradox concerning the temperature distribution of a gas in a gravitational field | url = | journal = Am. J. Phys. | volume = 53 | issue = 3| pages = 272–273 | doi=10.1119/1.14138| bibcode = 1985AmJPh..53..272C }}</ref><ref>{{cite journal | last1 = Román | first1 = F.L. | last2 = White | first2 = J.A. | last3 = Velasco | first3 = S. | year = 1995 | title = Microcanonical single-particle distributions for an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 16 | issue = 2| pages = 83–90 | doi=10.1088/0143-0807/16/2/008| bibcode = 1995EJPh...16...83R }}</ref><ref>{{cite journal | last1 = Velasco | first1 = S. | last2 = Román | first2 = F.L. | last3 = White | first3 = J.A. | year = 1996 | title = On a paradox concerning the temperature distribution of an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 17 | issue = | pages = 43–44 | doi=10.1088/0143-0807/17/1/008}}</ref><br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform. This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers. Considerations of kinetic theory or statistical mechanics also support this statement.<br />
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热力学平衡系统内的温度在时间和空间上都是均匀的。在一个处于内部热力学平衡的系统中,不存在净的内部宏观流动。特别是,这意味着系统的所有局部都处于相互辐射交换平衡。这意味着系统的温度在空间上是均匀的。这在所有情况下都是如此,包括那些非均匀外力场。对于外部施加的引力场,这可以使用拉格郎日乘子法通过变分的计算在宏观热力学术语中证明。动力学理论或统计力学也支持这种说法。<br />
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In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium.<ref name="Fitts 43"/><br />
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为了使一个系统处于它自己的内部热力学平衡状态,它必须处于它自己的内部热平衡状态是必要不充分的; 一个系统在到达内部热平衡之前到达内部力学平衡是可能的。<br />
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===Number of real variables needed for specification 规范所需的实变量数目===<br />
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In his exposition of his scheme of closed system equilibrium thermodynamics, C. Carathéodory initially postulates that experiment reveals that a definite number of real variables define the states that are the points of the manifold of equilibria.<ref name="Caratheodory" /> In the words of Prigogine and Defay (1945): "It is a matter of experience that when we have specified a certain number of macroscopic properties of a system, then all the other properties are fixed."<ref>Prigogine, I., Defay, R. (1950/1954), p. 1.</ref><ref>Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005), p. 4.</ref> As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.<br />
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在他关于封闭系统平衡态热力学方案的论述中,C.Carathéodory 最初假定实验揭示了一定数量的实变量定义了作为平衡态流形点的状态。用 Prigogine 和 Defay (1945)的话说: “这是一个经验问题,当我们确定了一个系统一定数量的宏观属性时,那么所有其他属性都是固定的”。如上所述,A. Münster认为,定义热力学平衡所需的变量数量相对于给定孤立系统的任何状态来说都是最少的。如上所述,J.G. Kirkwood 和 I. Oppenheim 指出,热力学平衡状态可以由一个特殊子类的强度变量来定义,该子类中有一定数量的成员。<br />
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If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.<br />
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如果热力学平衡位于一个外力场中,那么通常只有温度在空间上是均匀的。如果外力场非零,温度以外的强度变量通常是不均匀的。在这种情况下,一般需要附加变量来描述空间非均匀性。<br />
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===Stability against small perturbations 对小扰动的稳定性===<br />
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As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.<br />
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如上所述,J.R. Partington 指出热力学平衡状态在小的瞬态扰动下是稳定的。如果没有这个条件,一般来说,研究热力学平衡系统的实验就会遇到严重的困难。<br />
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===Approach to thermodynamic equilibrium within an isolated system 孤立系统中的热力学平衡===<br />
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When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium. Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<br />
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When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium.<ref name="Fitts 43">Fitts, D.D. (1962), p. 43.</ref> Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<ref>Denbigh, K.G. (1951), p. 42.</ref><br />
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当一个物质体从不均匀的非平衡状态或化学非平衡状态开始,然后被孤立,它会自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如,在这种演化的许多情况下,内部力学平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是,在这种演化的许多情况下,热平衡的发展要比化学平衡快得多。<br />
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===Fluctuations within an isolated system in its own internal thermodynamic equilibrium 孤立系统内部热力学平衡的涨落===<br />
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In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
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在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
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To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics.<ref>Tschoegl, N.W. (2000). ''Fundamentals of Equilibrium and Steady-State Thermodynamics'', Elsevier, Amsterdam, {{ISBN|0-444-50426-5}}, p. 21.</ref> But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
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To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics. But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
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考虑孤立热力学系统中的涨落概念,一个方便的例子是由其内能、体积和质量组成等广延量表示的系统。根据定义,它们是不随时间变化的。根据定义,这些量与它们的共轭状态强度函数的时不变标称值相结合,包括逆温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广延量的值,不足以提供这些标称值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
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It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.<br />
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可以承认,在重复测量这些共轭强度状态函数时,发现它们的值随时间略有不同。这种可变性被认为是由于内部涨落。不同测量值平均到其标称值。<br />
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If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<ref>Buchdahl, H.A. (1966), p. 16.</ref><br />
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If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<br />
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如果系统真的像经典热力学所假定的那样是宏观的,那么系统的涨落很小以至于宏观上无法检测到。这就是所谓的热力学极限。实际上,物质的分子性质和动量转移的量子性质由于它们太小而看不见,已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中,平衡的涨落概念是不存在的。”<br />
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If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
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如果系统被重复细分,最终产生的系统足够小,可以表现出明显的涨落。这是一个介观层面的研究。涨落则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
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If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在波动过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,即需要量子统计力学。波动可以变得相对占主导地位,测量问题变得重要。<br />
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Thermal equilibrium is achieved when two systems in thermal contact with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<br />
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当两个相互热接触的系统不再有净能量交换时,就会产生热平衡。因此,如果两个系统处于热平衡,那么它们的温度是相同的。<br />
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The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
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"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有时间趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的标称值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微波动期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。非已知属于平衡状态的标称值,否则根据单一的度量无法进行判断。<br />
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Thermal equilibrium occurs when a system's macroscopic thermal observables have ceased to change with time. For example, an ideal gas whose distribution function has stabilised to a specific Maxwell–Boltzmann distribution would be in thermal equilibrium. This outcome allows a single temperature and pressure to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<br />
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当系统的宏观热观测值不再随着时间变化时,就会出现热平衡。例如,一种分布函数稳定到一个特定的麦克斯韦-波兹曼分布的理想气体即处于热平衡状态。这个结果可以将单一的温度和压力归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是很有可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
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=== Thermal equilibrium ===<br />
热平衡<br />
{{Main|Thermal equilibrium}}<br />
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An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process."<ref>Eu, B.C. (2002), page 13.</ref> This illustrates the importance for thermodynamics of the concept of temperature.<br />
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热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
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A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<br />
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一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数。<br />
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[[Thermal equilibrium]] is achieved when two systems in [[thermal contact]] with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<ref>[[Raj Pathria|R. K. Pathria]], 1996</ref><br />
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当两个相互'''<font color="#ff8000">热接触 Thermal Contact</font>'''的系统不再有净能量交换时,就会产生'''<font color="#ff8000">热平衡 Thermal Equilibrium</font>'''。因此,如果两个系统处于热平衡,那么它们的温度是相同的<br />
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Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
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Thermal equilibrium occurs when a system's [[macroscopic]] thermal observables have ceased to change with time. For example, an [[ideal gas]] whose [[Distribution function (physics)|distribution function]] has stabilised to a specific [[Maxwell–Boltzmann distribution]] would be in thermal equilibrium. This outcome allows a single [[temperature]] and [[pressure]] to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<ref>de Groot, S.R., Mazur, P. (1962), p. 44.</ref><br />
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当一个系统的'''<font color="#ff8000">宏观 Macroscopic</font>'''热观测值不再随时间变化时,就会出现热平衡。例如,一种'''<font color="#ff8000">分布函数 Distribution Function</font>'''稳定到一个特定的'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''的'''<font color="#ff8000">理想气体 Ideal Gas</font>'''即处于热平衡状态。这个结果可以将单一的'''<font color="#ff8000">温度 Temperature</font>'''和'''<font color="#ff8000">压力 Pressure</font>'''归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
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Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle. It states that a non-equilibrium system evolves such as to maximize its entropy production.<br />
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定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
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==Non-equilibrium==<br />
非平衡<br />
{{Main|Non-equilibrium thermodynamics}}<br />
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Thermodynamic models <br />
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热力学模型<br />
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A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<ref>de Groot, S.R., Mazur, P. (1962), p. 43.</ref><br />
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一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数<br />
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Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
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Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle.<ref>{{cite book|last1=Ziegler|first1=H.|title=An Introduction to Thermomechanics.|date=1983|location=North Holland, Amsterdam.}}</ref><ref>{{cite journal|last1=Onsager|first1=Lars|title=Reciprocal Relations in Irreversible Processes|journal=Phys. Rev.|date=1931|volume=37|issue=4|doi=10.1103/PhysRev.37.405|bibcode=1931PhRv...37..405O|pages=405–426|doi-access=free}}</ref> It states that a non-equilibrium system evolves such as to maximize its entropy production.<ref>{{cite book|last1=Kleidon|first1=A.|last2=et.|first2=al.|title=Non-equilibrium Thermodynamics and the Production of Entropy.|date=2005|edition=Heidelberg: Springer.}}</ref><ref>{{cite journal|last1=Belkin|first1=Andrey|last2=et.|first2=al.|title=Self-Assembled Wiggling Nano-Structures and the Principle of Maximum Entropy Production|journal=Sci. Rep.|doi=10.1038/srep08323|bibcode=2015NatSR...5E8323B|pmc=4321171|pmid=25662746|volume=5|year=2015|page=8323}}</ref><br />
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定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
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Topics in control theory<br />
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控制理论主题<br />
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==See also ==<br />
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{{Portal|Chemistry}}<br />
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;Thermodynamic models 热力学模型<br />
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{{colbegin}}<br />
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* [[Non-random two-liquid model]] (NRTL model) - Phase equilibrium calculations 非随机两液模型(NRTL 模型)-相平衡计算<br />
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* [[UNIQUAC]] model - Phase equilibrium calculations UNIQUAC 模型-相平衡计算<br />
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* [[Time crystal]] 时间晶体<br />
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{{colend}}<br />
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;Topics in control theory 控制理论主题<br />
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{{colbegin}}<br />
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* [[Steady state]] 稳态<br />
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* [[Transient state]] 瞬态<br />
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* [[Coefficient diagram method]] 系数图法<br />
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* [[Control reconfiguration]] 控制重构<br />
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* [[Cut-insertion theorem]] 切入定理<br />
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* [[Feedback]] 反馈<br />
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* [[H infinity]] H 无限<br />
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* [[Hankel singular value]] 汉克尔奇异值<br />
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* [[Krener's theorem]] 克雷纳定理<br />
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* [[Lead-lag compensator]] 超前滞后补偿器<br />
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* [[Minor loop feedback]] 小循环反馈<br />
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* [[Minor loop feedback|Multi-loop feedback]] 小循环反馈 | 多循环反馈<br />
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* [[Positive systems]] 正向系统<br />
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* [[Radial basis function]] 径向基底函数<br />
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Other related topics<br />
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其他相关话题<br />
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* [[Root locus]] 根轨迹<br />
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* [[Signal-flow graph]]s 信号流图<br />
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* [[Stable polynomial]] 稳定多项式<br />
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* [[State space representation]] 状态空间<br />
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* [[Underactuation]] 欠驱动<br />
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* [[Youla–Kucera parametrization]] 尤拉-库切拉参数化<br />
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* [[Markov chain approximation method]] 马尔可夫链近似法<br />
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{{colend}}<br />
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;Other related topics<br />
其他相关话题<br />
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{{colbegin}}<br />
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* [[Automation and remote control]] 自动化和远程控制<br />
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* [[Bond graph]] 键合图<br />
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* [[Control engineering]] 控制工程<br />
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* [[Control–feedback–abort loop]] 控制-反馈-中止循环<br />
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* [[Controller (control theory)]] 控制器(控制理论)<br />
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* [[Cybernetics]] 控制论<br />
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* [[Intelligent control]] 智能控制<br />
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* [[Mathematical system theory]] 数学系统论<br />
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* [[Negative feedback amplifier]] 负反馈放大器<br />
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* [[People in systems and control]] 系统和控制中的人<br />
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* [[Perceptual control theory]] 知觉控制理论<br />
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* [[Systems theory]] 系统论<br />
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* [[Time scale calculus]] 时间尺度演算<br />
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{{colend}}<br />
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== 编者推荐 ==<br />
===集智文章推荐===<br />
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====[https://swarma.org/?p=21322 什么是非平衡态热力学 | 集智百科]====<br />
非平衡态热力学 Non-equilibrium thermodynamics 是热力学的一个分支,研究某些不处于热力学平衡中的物理系统<br />
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==General references==<br />
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* Cesare Barbieri (2007) ''Fundamentals of Astronomy''. First Edition (QB43.3.B37 2006) CRC Press {{ISBN|0-7503-0886-9}}, {{ISBN|978-0-7503-0886-1}}<br />
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* Hans R. Griem (2005) ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}<br />
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* C. Michael Hogan, Leda C. Patmore and Harry Seidman (1973) ''Statistical Prediction of Dynamic Thermal Equilibrium Temperatures using Standard Meteorological Data Bases'', Second Edition (EPA-660/2-73-003 2006) United States Environmental Protection Agency Office of Research and Development, Washington, D.C. [http://library.wur.nl/WebQuery/catalog/lang/1851848]<br />
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* F. Mandl (1988) ''Statistical Physics'', Second Edition, John Wiley & Sons<br />
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==References==<br />
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{{Reflist|colwidth=35em}}<br />
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==Cited bibliography==<br />
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*Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', third edition, McGraw-Hill, London, {{ISBN|0-521-25445-0}}.<br />
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*Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, {{ISBN|0-88318-797-3}}.<br />
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*Beattie, J.A., Oppenheim, I. (1979). ''Principles of Thermodynamics'', Elsevier Scientific Publishing, Amsterdam, {{ISBN|0-444-41806-7}}.<br />
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*[[Ludwig Boltzmann|Boltzmann, L.]] (1896/1964). ''Lectures on Gas Theory'', translated by S.G. Brush, University of California Press, Berkeley.<br />
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*Buchdahl, H.A. (1966). ''The Concepts of Classical Thermodynamics'', Cambridge University Press, Cambridge UK.<br />
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*[[Herbert Callen|Callen, H.B.]] (1960/1985). ''Thermodynamics and an Introduction to Thermostatistics'', (1st edition 1960) 2nd edition 1985, Wiley, New York, {{ISBN|0-471-86256-8}}.<br />
<br />
*[[Constantin Carathéodory|Carathéodory, C.]] (1909). [https://web.archive.org/web/20160304213645/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0067&DMDID=DMDLOG_0033&L=1 Untersuchungen über die Grundlagen der Thermodynamik], ''[[Mathematische Annalen]]'', '''67''': 355–386. A translation may be found [http://neo-classical-physics.info/uploads/3/0/6/5/3065888/caratheodory_-_thermodynamics.pdf here]. Also a mostly reliable [https://books.google.com/books?id=xwBRAAAAMAAJ&q=Investigation+into+the+foundations translation is to be found] at Kestin, J. (1976). ''The Second Law of Thermodynamics'', Dowden, Hutchinson & Ross, Stroudsburg PA.<br />
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*[[Sydney Chapman (mathematician)|Chapman, S.]], [[Thomas George Cowling|Cowling, T.G.]] (1939/1970). ''The Mathematical Theory of Non-uniform gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases'', third edition 1970, Cambridge University Press, London.<br />
<br />
*Crawford, F.H. (1963). ''Heat, Thermodynamics, and Statistical Physics'', Rupert Hart-Davis, London, Harcourt, Brace & World, Inc.<br />
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*de Groot, S.R., Mazur, P. (1962). ''Non-equilibrium Thermodynamics'', North-Holland, Amsterdam. Reprinted (1984), Dover Publications Inc., New York, {{ISBN|0486647412}}.<br />
<br />
*Denbigh, K.G. (1951). ''Thermodynamics of the Steady State'', Methuen, London.<br />
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*Eu, B.C. (2002). ''Generalized Thermodynamics. The Thermodynamics of Irreversible Processes and Generalized Hydrodynamics'', Kluwer Academic Publishers, Dordrecht, {{ISBN|1-4020-0788-4}}.<br />
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*Fitts, D.D. (1962). ''Nonequilibrium thermodynamics. A Phenomenological Theory of Irreversible Processes in Fluid Systems'', McGraw-Hill, New York.<br />
<br />
*[[Josiah Willard Gibbs|Gibbs, J.W.]] (1876/1878). On the equilibrium of heterogeneous substances, ''Trans. Conn. Acad.'', '''3''': 108–248, 343–524, reprinted in ''The Collected Works of J. Willard Gibbs, Ph.D, LL. D.'', edited by W.R. Longley, R.G. Van Name, Longmans, Green & Co., New York, 1928, volume 1, pp.&nbsp;55–353.<br />
<br />
*Griem, H.R. (2005). ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}.<br />
<br />
*[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', fifth revised edition, North-Holland, Amsterdam.<br />
<br />
*Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of ''Thermodynamics'', pages 1–97 of volume 1, ed. W. Jost, of ''Physical Chemistry. An Advanced Treatise'', ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081.<br />
<br />
*[[John Gamble Kirkwood|Kirkwood, J.G.]], Oppenheim, I. (1961). ''Chemical Thermodynamics'', McGraw-Hill Book Company, New York.<br />
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*Landsberg, P.T. (1961). ''Thermodynamics with Quantum Statistical Illustrations'', Interscience, New York.<br />
<br />
*{{cite journal |last1=Lieb |first1=E. H. |last2=Yngvason |first2=J. |year=1999 |title=The Physics and Mathematics of the Second Law of Thermodynamics |journal=Phys. Rep. |volume=310 |issue= 1|pages=1–96 |doi= 10.1016/S0370-1573(98)00082-9|arxiv = cond-mat/9708200 |bibcode = 1999PhR...310....1L |s2cid=119620408 }}<br />
<br />
*Levine, I.N. (1983), ''Physical Chemistry'', second edition, McGraw-Hill, New York, {{ISBN|978-0072538625}}.<br />
<br />
*{{cite journal | last1 = Maxwell | first1 = J.C. | authorlink = James Clerk Maxwell | year = 1867 | title = On the dynamical theory of gases | url = | journal = Phil. Trans. Roy. Soc. London | volume = 157 | issue = | pages = 49–88 }}<br />
<br />
*[[Philip M. Morse|Morse, P.M.]] (1969). ''Thermal Physics'', second edition, W.A. Benjamin, Inc, New York.<br />
<br />
*Münster, A. (1970). ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London.<br />
<br />
*[[J.R. Partington|Partington, J.R.]] (1949). ''An Advanced Treatise on Physical Chemistry'', volume 1, ''Fundamental Principles. The Properties of Gases'', Longmans, Green and Co., London.<br />
<br />
*[[Brian Pippard|Pippard, A.B.]] (1957/1966). ''The Elements of Classical Thermodynamics'', reprinted with corrections 1966, Cambridge University Press, London.<br />
<br />
* [[Max Planck|Planck. M.]] (1914). [https://archive.org/details/theoryofheatradi00planrich ''The Theory of Heat Radiation''], a translation by Masius, M. of the second German edition, P. Blakiston's Son & Co., Philadelphia.<br />
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*[[Ilya Prigogine|Prigogine, I.]] (1947). ''Étude Thermodynamique des Phénomènes irréversibles'', Dunod, Paris, and Desoers, Liège.<br />
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*[[Ilya Prigogine|Prigogine, I.]], Defay, R. (1950/1954). ''Chemical Thermodynamics'', Longmans, Green & Co, London.<br />
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*Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005). ''Physical Chemistry'', fourth edition, Wiley, Hoboken NJ.<br />
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*[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966). ''Elements of Thermodynamics'', Addison-Wesley Publishing, Reading MA.<br />
<br />
*{{cite journal|last=Thomson|first=W.|author-link=William Thomson, 1st Baron Kelvin|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Transactions of the Royal Society of Edinburgh|date=March 1851|volume=XX|issue=part II|pages=261–268; 289–298}} Also published in {{cite journal|last=Thomson|first=W.|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Phil. Mag. |date=December 1852 |volume=IV |series=4 |issue=22 |pages=8–21 |url=https://archive.org/details/londonedinburghp04maga |accessdate=25 June 2012}}<br />
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*[[László Tisza|Tisza, L.]] (1966). ''Generalized Thermodynamics'', M.I.T Press, Cambridge MA.<br />
<br />
*[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963). ''Lectures in Statistical Mechanics'', American Mathematical Society, Providence RI.<br />
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*Waldram, J.R. (1985). ''The Theory of Thermodynamics'', Cambridge University Press, Cambridge UK, {{ISBN|0-521-24575-3}}.<br />
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*[[Mark Zemansky|Zemansky, M.]] (1937/1968). ''Heat and Thermodynamics. An Intermediate Textbook'', fifth edition 1967, McGraw–Hill Book Company, New York.<br />
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== External links ==<br />
<br />
Category:Equilibrium chemistry<br />
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类别: 平衡化学<br />
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*[http://ads.harvard.edu/books/1989fsa..book/AbookC15.pdf Breakdown of Local Thermodynamic Equilibrium] George W. Collins, The Fundamentals of Stellar Astrophysics, Chapter 15<br />
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Category:Thermodynamic cycles<br />
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类别: 热力循环<br />
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*[http://spiff.rit.edu/classes/phys440/lectures/lte/lte.html Thermodynamic Equilibrium, Local and otherwise] lecture by Michael Richmond<br />
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Category:Thermodynamic processes<br />
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类别: 热力学过程<br />
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*[http://journals.ametsoc.org/doi/abs/10.1175/1520-0469%281970%29027%3C0711:NLTEIC%3E2.0.CO%3B2 Non-Local Thermodynamic Equilibrium in Cloudy Planetary Atmospheres] Paper by R. E. Samueison quantifying the effects due to non-LTE in an atmosphere<br />
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Category:Thermodynamic systems<br />
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类别: 热力学系统<br />
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*[http://scienceworld.wolfram.com/physics/LocalThermodynamicEquilibrium.html Local Thermodynamic Equilibrium]<br />
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Category:Thermodynamics<br />
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分类: 热力学<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Thermodynamic equilibrium]]. Its edit history can be viewed at [[平衡热力学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%B9%B3%E8%A1%A1%E7%83%AD%E5%8A%9B%E5%AD%A6&diff=21667平衡热力学2021-02-07T12:53:15Z<p>Jxzhou:/* Fluctuations within an isolated system in its own internal thermodynamic equilibrium 孤立系统内部热力学平衡的 */</p>
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<div>此词条暂由小竹凉翻译,翻译字数共5339,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{short description|State of thermodynamic system(s) where no net macroscopic flow of matter or energy occurs}}<br />
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'''Thermodynamic equilibrium''' is an [[axiomatic]] concept of [[thermodynamics]]. It is an internal [[State variables|state]] of a single [[thermodynamic system]], or a relation between several thermodynamic systems connected by more or less permeable or impermeable [[Thermodynamic system#Walls|walls]]. In thermodynamic equilibrium there are no net [[macroscopic]] [[Flow (mathematics)|flows]] of [[matter]] or of [[energy]], either within a system or between systems. <br />
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Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium there are no net macroscopic flows of matter or of energy, either within a system or between systems. <br />
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'''热力学平衡'''是'''<font color="#ff8000">热力学 Thermodynamics</font>'''的一个'''<font color="#ff8000">不言自明的 Axiomatic</font>'''概念。它是单个'''<font color="#ff8000">热力学系统 Thermodynamic System</font>'''的内部'''<font color="#ff8000">状态 State</font>''',或者是几个热力学系统之间通过或多或少的渗透或不渗透的'''<font color="#ff8000">壁 Wall</font>'''连接的关系。无论是在一个系统内还是在系统之间,在热力学平衡中不存在'''<font color="#ff8000">物质 Matter</font>'''或'''<font color="#ff8000">能量 Energy</font>'''的净'''<font color="#ff8000">宏观 Macroscopic</font>''' '''<font color="#ff8000">流动 Flow</font>'''。<br />
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In a system that is in its own state of internal thermodynamic equilibrium, no [[macroscopic]] change occurs. <br />
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In a system that is in its own state of internal thermodynamic equilibrium, no macroscopic change occurs. <br />
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在一个处于内部热力学平衡状态的系统中,不会发生'''<font color="#ff8000">宏观 Macroscopic</font>'''变化。<br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual [[Thermal equilibrium|thermal]], [[Mechanical equilibrium|mechanical]], [[Chemical equilibrium|chemical]], and [[Radiative equilibrium|radiative]] equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a [[thermodynamic operation]]. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a thermodynamic operation. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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相互热力学平衡的体系同时处于互相之间的'''<font color="#ff8000">热 Thermal</font>'''平衡、'''<font color="#ff8000">力学 Mechanical</font>'''平衡、'''<font color="#ff8000">化学 Chemical</font>'''平衡和'''<font color="#ff8000">辐射 Radiative</font>'''平衡。系统可以处于其中一种相互平衡状态,尽管其他状态未平衡。在热力学平衡中所有的平衡同时并且无限期地保持,直到被'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''打破。在一个宏观平衡中,微观交换是完全或几乎完全平衡的;这是对宏观平衡概念的物理解释。<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform [[temperature]]. Its [[Intensive and extensive properties|intensive properties]], other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform temperature. Its intensive properties, other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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一个处于内部热力学状态平衡的热力学系统具有空间均匀的'''<font color="#ff8000">温度 Temperature</font>'''。除了温度以外,它的'''<font color="#ff8000">强度性质 Intensive Properties</font>'''可以由于周围环境施加的不变的长程力场而导致空间不均匀性。<br />
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In systems that are at a state of [[non-equilibrium]] there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a '''meta-stable equilibrium'''.<br />
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In systems that are at a state of non-equilibrium there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a meta-stable equilibrium.<br />
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相比之下,处于'''<font color="#ff8000">非平衡状态 non-equilibrium</font>'''的系统中有物质或能量的净流动。如果这些变化可以在一个还没有发生的系统中被触发,那么这个系统就被称为处于一个'''亚稳定的平衡状态'''。<br />
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Though not a widely named a "law," it is an [[axiom]] of thermodynamics that there exist states of thermodynamic equilibrium. The [[second law of thermodynamics]] states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the [[entropy|entropies]] of the portions.<br />
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Though not a widely named a "law," it is an axiom of thermodynamics that there exist states of thermodynamic equilibrium. The second law of thermodynamics states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the entropies of the portions.<br />
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虽然不是一个广泛命名的“定律” ,但存在热力学平衡状态是一个热力学'''<font color="#ff8000">公理 Axiom</font>'''。'''<font color="#ff8000">热力学第二定律 second law of thermodynamics</font>'''指出,当一个物质体从一个平衡状态开始,在这个状态中,它的一部分被或多或少渗透或不渗透的分区保持在不同的状态,并且是孤立的,热力学操作移除分区或使分区更具渗透性,然后它会自发地达到自己内部热力学平衡的新状态,并伴随着部分'''<font color="#ff8000">熵 Entropy</font>'''的总和增加。<br />
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== Overview 概览==<br />
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{{Thermodynamics|cTopic=[[Thermodynamic system|Systems]]}}<br />
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Classical thermodynamics deals with states of [[dynamic equilibrium]]. The state of a system at thermodynamic equilibrium is the one for which some [[thermodynamic potential]] is minimized, or for which the [[entropy]] (''S'') is maximized, for specified conditions. One such potential is the [[Helmholtz free energy]] (''A''), for a system with surroundings at controlled constant temperature and volume:<br />
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Classical thermodynamics deals with states of dynamic equilibrium. The state of a system at thermodynamic equilibrium is the one for which some thermodynamic potential is minimized, or for which the entropy (S) is maximized, for specified conditions. One such potential is the Helmholtz free energy (A), for a system with surroundings at controlled constant temperature and volume:<br />
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经典热力学研究'''<font color="#ff8000">动态平衡 Dynamic Equilibrium</font>'''的状态。系统的热力学平衡状态是对于特定的条件,一些'''<font color="#ff8000">热力学势 Thermodynamic Potential</font>'''被最小化,或者'''<font color="#ff8000">熵 Entropy</font>'''(S)被最大化。对于一个周围环境温度和体积恒定的系统,其中一个这样的热力学势是'''<font color="#ff8000">亥姆霍兹自由能 Helmholtz Free Energy</font>'''(A):<br />
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:<math>A = U - TS</math><br />
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<math>A = U - TS</math><br />
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A = U-TS<br />
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Another potential, the [[Gibbs free energy]] (''G''), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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Another potential, the Gibbs free energy (G), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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在恒定温度和压力的系统中,另一个热力学势'''<font color="#ff8000">吉布斯自由能 Gibbs Free Energy</font>'''(G)在热力学平衡状态最小:<br />
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:<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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where ''T'' denotes the absolute thermodynamic temperature, ''P'' the pressure, ''S'' the entropy, ''V'' the volume, and ''U'' the internal energy of the system.<br />
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where T denotes the absolute thermodynamic temperature, P the pressure, S the entropy, V the volume, and U the internal energy of the system.<br />
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其中 T 表示热力学绝对温度,P 表示压强,S 表示熵,V 表示体积,U 表示体系的内能。<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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热力学平衡是一种独特的稳定定态,当系统长时间与周围环境相互作用时,它可以被接近或最终到达。上述势能是数学构造的热力学量,在特定的环境条件下最小化。<br />
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== Conditions 条件==<br />
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* For a completely isolated system, ''S'' is maximum at thermodynamic equilibrium. 对于一个完全孤立的系统,S在热力学平衡中取最大值。<br />
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* For a system with controlled constant temperature and volume, ''A'' is minimum at thermodynamic equilibrium. 对于一个恒定温度和体积的系统来说,A在热力学平衡中取最小值。<br />
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* For a system with controlled constant temperature and pressure, ''G'' is minimum at thermodynamic equilibrium. 对于一个恒温恒压的系统,G在热力学平衡中取最小值。<br />
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The various types of equilibriums are achieved as follows:<br />
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The various types of equilibriums are achieved as follows:<br />
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实现各种类型的平衡的方法如下:<br />
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*Two systems are in ''thermal equilibrium'' when their [[temperature]]s are the same. 当两个系统的'''<font color="#ff8000">温度 Temperature</font>'''相同时,它们就处于''热平衡状态''<br />
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*Two systems are in ''mechanical equilibrium'' when their [[pressure]]s are the same. 当两个体系的'''<font color="#ff8000">压力 Pressure</font>'''相同时,它们就处于''力学平衡''<br />
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*Two systems are in ''diffusive equilibrium'' when their [[chemical potential]]s are the same. 当两个题体系的'''<font color="#ff8000">化学势 Chemical Potential</font>'''相同时,它们就处于''扩散平衡''<br />
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*All [[forces]] are balanced and there is no significant external driving force.<br />
所有的'''<font color="#ff8000">力 Force</font>'''都是平衡的,没有明显的外部驱动力<br />
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==Relation of exchange equilibrium between systems 系统之间的交换均衡关系==<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability.<ref name="Nster_a">Münster, A. (1970), p. 49.</ref> When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability. When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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通常,热力学系统的周围环境也可以被看作是另一个热力学系统。在这种观点中,我们可以把系统及其周围环境看作是相互接触的两个系统,远程作用力也将它们联系在一起。系统的包围物是两个系统之间的接触面或边界。在热力学形式中,该表面被认为具有特定的渗透性质。例如,接触的表面可能被认为只能透热,使能量只能作为热传递。当远程力在时间上不发生变化,两个系统之间的热量传递减慢并最终永久停止时,这两个系统被称为热平衡; 这就是接触平衡的一个例子。其它类型的接触平衡可用其它类型的比渗透率来定义。当两个系统对于某一特定类型的渗透率处于接触平衡时,它们具有属于该特定类型渗透率的强变量的共同值。这种强度变量的例子有温度、压力、化学势。<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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接触平衡也可视为交换平衡。在接触平衡状态下,两系统之间某些量的传递速率存在零平衡。例如,对于只能透热的壁,内能作为热在两个系统之间的扩散速率是相等并反向的。两个系统之间的绝热壁只对作为功传递的能量有渗透作用; 在力学平衡,两个系统之间作为功的能量传递速率相等且相反。如果是一个简单的壁,那么通过它的体积转移率也是相等且相反的; 即它两边的压力是相等的。如果绝热壁比较复杂,有一种杠杆,有一个面积比,那么两个体系在交换平衡中的压力与体积交换比成反比,这使得转移率的零平衡作功。<br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<ref name="Planck 1914 40">[[Max Planck|Planck. M.]] (1914), p. 40.</ref><br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<br />
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辐射交换可以发生在两个不同的系统之间。当两个体系温度相同时,辐射交换平衡占优势。<br />
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==Thermodynamic state of internal equilibrium of a system 系统内部平衡的热力学状态==<br />
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A collection of matter may be entirely [[Isolated system|isolated]] from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium.<ref>Haase, R. (1971), p. 4.</ref><ref>Callen, H.B. (1960/1985), p. 26.</ref> (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics.<ref>{{Cite journal |doi = 10.1119/1.4914528|bibcode = 2015AmJPh..83..628M|title = Time and irreversibility in axiomatic thermodynamics|year = 2015|last1 = Marsland|first1 = Robert|last2 = Brown|first2 = Harvey R.|last3 = Valente|first3 = Giovanni|journal = American Journal of Physics|volume = 83|issue = 7|pages = 628–634}}</ref> One textbook<ref>[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963), p. 5.</ref> calls it the "zeroth law", remarking that the authors think this more befitting that title than its [[Zeroth law of thermodynamics|more customary definition]], which apparently was suggested by [[Ralph H. Fowler|Fowler]].)<br />
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A collection of matter may be entirely isolated from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium. (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics. One textbook calls it the "zeroth law", remarking that the authors think this more befitting that title than its more customary definition, which apparently was suggested by Fowler.)<br />
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物质的集合可能与其周围的环境完全'''<font color="#ff8000">孤立 Isolated</font>'''。如果它在无限长的时间内一直保持不受干扰,按照经典热力学假定,它处于一个没有发生任何变化,没有流动的状态,即内部平衡的热力学状态。(这种假设有时被称为“负第一”热力学定律,但并不常见。有教科书称之为“第零定律” ,作者'''<font color="#ff8000">福勒 Fowler</font>'''认为这个名称是'''<font color="#ff8000">更符合惯例的定义 More Customary Definition</font>'''。)<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a [[thermodynamic operation]] be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a thermodynamic operation be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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这种状态是所谓的经典热力学或平衡态热力学的主要关注点,因为它们是系统中被认为在这门学科中得到很好定义的唯一状态。一个与另一个系统处于接触平衡状态可以被一个'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''隔离,在隔离发生时,其内部不会发生任何变化。因此,一个与另一个系统处于接触平衡状态时也可以被视为处于其自身的内部热力学平衡状态。<br />
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==Multiple contact equilibrium 多点接触平衡==<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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热力学形式允许一个系统同时与其他多个系统接触,这些系统可能有也可能没有相互接触,且这些接触具有不同的渗透性。如果这些系统都与世界其他部分相互隔离,那么它们彼此之间就会达到各自的接触平衡。<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy.<ref name="Caratheodory">Carathéodory, C. (1909).</ref><ref>Prigogine, I. (1947), p. 48.</ref><ref>Landsberg, P. T. (1961), pp. 128–142.</ref><ref>Tisza, L. (1966), p. 108.</ref> Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy. Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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如果几个系统彼此之间没有绝热壁,但是它们与世界其他部分共同隔离,那么它们就会达到多重接触平衡状态,且有共同的温度,总的内能和熵。在众多强度量中,这是温度的一个独特性质。即使在远距离作用力存在的情况下,它也是有效的。(也就是说,没有“力”可以维持温度的差异。)举个例子,在热力学平衡的一个垂直的引力场系统中,顶部壁面的压力比底部壁面的压力小,但是各处的温度都是一样的。<br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural [[thermodynamic process]].<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), § 1.12.</ref> It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings.<ref>Levine, I.N. (1983), p. 40.</ref><ref>Lieb, E.H., Yngvason, J. (1999), pp. 17–18.</ref> The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of [[Second law of thermodynamics#Description#Kelvin statement|"inanimate" agency]]; a system in thermodynamic equilibrium is inanimate.<ref>[[William Thomson, 1st Baron Kelvin|Thomson, W.]] (1851).</ref><br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural thermodynamic process. It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings. The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of "inanimate" agency; a system in thermodynamic equilibrium is inanimate.<br />
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热力操作可能作为一个事件发生在周围环境的壁上,既不直接影响与周围环境联系的壁,也不直接影响其内部,且发生在一个明确的有限的时间内。例如,一个固定的绝热壁可以在环境中被放置或拆除。由于这种操作仅限于周围环境,系统可能会在一段时间内远离自身最初的内部状态---- 热力学平衡。根据热力学第二定律的说法,整体经历了变化并最终与周围环境达到了新的平衡。继Planck之后,这一连串的事件被称为自然'''<font color="#ff8000">热力学过程 Thermodynamic Process</font>'''。即使在这个过程中,当系统和周围环境都不处于明确的内部平衡状态时,存在着暂时偏离热力学平衡的现象,由于初始状态和最终状态都是热力学平衡的,这在平衡热力学中也是允许的。一个自然过程在其主要部分中以有限的速率进行,因此,它从根本上不同于虚构的准静态“过程”;即不在整个过程中无限缓慢地进行而且虚构地“可逆”。经典热力学允许,即使一个过程可能需要很长的时间才能达到热力学平衡,如果主要部分的过程是在一个有限的比率中,那么它被认为是自然的,并受制于热力学第二定律,即不可逆的。工程设计的机器、人工设备和操作是允许在周围环境中进行的。允许在环境中而不是在系统中进行此类操作和设备,是开尔文在他的一个热力学第二定律的陈述中提到'''<font color="#ff8000">无生命机构 Inanimate Agency</font>'''的原因; 在热力学平衡的系统是无生命的。<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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否则,热力操作可能会直接影响系统的壁。<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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通常可以很方便地假设周围的某些子系统比系统大得多,以至于这个过程只能影响周围子系统的强度变量,然后将这些子系统称为相关强度变量的储备库。<br />
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== Local and global equilibrium 局部和全局均衡==<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by [[intensive quantity|intensive]] parameters. As an example, [[temperature]] controls [[Heat equation|heat exchanges]]. ''Global thermodynamic equilibrium'' (GTE) means that those [[intensive quantity|intensive]] parameters are homogeneous throughout the whole system, while ''local thermodynamic equilibrium'' (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by intensive parameters. As an example, temperature controls heat exchanges. Global thermodynamic equilibrium (GTE) means that those intensive parameters are homogeneous throughout the whole system, while local thermodynamic equilibrium (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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区分全局性和局部性热力学平衡是很有用的。在热力学中,系统内部和系统与外部之间的交换是由'''<font color="#ff8000">强度 Intensive</font>'''参数控制的。例如,'''<font color="#ff8000">温度 Temperature</font>'''控制'''<font color="#ff8000">热交换 Heat Equation</font>'''。全局热力学平衡(GTE)意味着这些'''<font color="#ff8000">强度 Intensive</font>'''参数在整个系统中是均匀的,而局部热力学平衡(LTE)意味着这些强度参数在空间和时间上是变化的,但变化如此缓慢,以至于对于任何一点,人们都可以假设在该点的某个邻域存在热力学平衡。<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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如果对系统的描述要求强度参数的变化过大,那么这些强度参数的定义所依据的假设本身就会失效,系统将既不处于全局平衡,也不处于局部平衡。例如,粒子需要一定数量的碰撞来平衡其周围环境。如果在这些碰撞中移动的平均距离使它离开平衡邻域,它将永远不会平衡,也就不会有 LTE。根据定义,温度与平衡邻域的平均内部能量成正比。由于没有达到平衡邻域,温度的概念就不成立,温度也就变得无法定义。<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to [[massive]] particles. In a [[radiation|radiating]] gas, the [[photon]]s being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to massive particles. In a radiating gas, the photons being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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值得注意的是,这种局部平衡可能只适用于系统中的某个粒子子集。例如,LTE 通常只适用于'''<font color="#ff8000">大 Massive</font>'''质量粒子。在'''<font color="#ff8000">辐射 Radiation</font>'''气体中,被气体发射和吸收的'''<font color="#ff8000">光子 Photon</font>'''不需要彼此在一个热力学平衡内,或与气体中的大量粒子在一起,LTE 才能存在。在某些情况下,自由电子并不需要与大得多的原子或分子处于平衡状态,LTE 才能存在。<br />
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As an example, LTE will exist in a glass of water that contains a melting [[ice cube]]. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the [[Maxwell–Boltzmann distribution]] for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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As an example, LTE will exist in a glass of water that contains a melting ice cube. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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例如,LTE 将存在于一个装有正在融化的'''<font color="#ff8000">冰块 Ice Cube</font>'''的水杯中。玻璃杯内的温度可以在任何时候定义,但是离冰块近的地方要比离冰块远的地方冷。如果观察到位于给定点附近的分子的能量,它们将按照麦克斯韦-波兹曼分布在一定温度下的分布。如果观察到位于另一点附近的分子的能量,它们将按照'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''分布到另一个温度。<br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural [[transport phenomena]] may lead a system from local to global thermodynamic equilibrium. Going back to our example, the [[diffusion]] of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<ref>H.R. Griem, 2005</ref><br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural transport phenomena may lead a system from local to global thermodynamic equilibrium. Going back to our example, the diffusion of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<br />
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局部热力学平衡不需要局部或全局的平稳性。换句话说,每一个小区域不需要有一个恒定的温度。然而,它确实要求每个小的局部变化缓慢到足以维持其局部麦克斯韦-波尔兹曼速度分布。全局非平衡态只有通过系统与外界的交换才能保持稳定。例如,通过在水杯中不断添加细粉冰来补偿熔化,并持续排出融水,可以保持全局稳定的静态。自然'''<font color="#ff8000">输运现象 Transport Phenomena</font>'''会使一个局部热力学平衡系统逐渐达到全局的热力学平衡。回顾我们的例子,热量的扩散将导致我们的玻璃杯水流向全局热力学平衡,在这种状态下,玻璃杯的温度是完全均匀的。<br />
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==Reservations 保留意见==<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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学识渊博的笔者在热力学领域对热力学平衡描述时,经常对他们的描述附加条件或保留意见。有些笔者含蓄地保留了或多或少的空白,以待说明。<br />
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For example, one widely cited writer, [[Herbert Callen|H. B. Callen]] writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. ''Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!''"<ref>Callen, H.B. (1960/1985), p. 15.</ref><br />
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For example, one widely cited writer, H. B. Callen writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!"<br />
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例如,一位被广泛引用的作家'''<font color="#ff8000">H.B.卡伦 H.B.Callen</font>'''在这里写道: “实际上,很少有系统处于绝对和真正的平衡状态。”他提到了放射性过程,认为它们可能需要“宇宙时间才能完成,因此通常可以忽略”。他补充道: “在实践中,平衡的标准是循环的。在操作上,如果一个系统的性质一致地用热力学理论来描述,那么它就处于平衡状态! ”<br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<ref>Beattie, J.A., Oppenheim, I. (1979), p. 3.</ref><br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<br />
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J.A.贝蒂和 I.奥本海姆写道: “坚持对平衡定义的严格解释,将排除热力学应用于实际系统的所有状态。”<br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment",<ref>Callen, H.B. (1960/1985), p. 485.</ref> and cited by Adkins as having written a "classic text",<ref>Adkins, C.J. (1968/1983), p. ''xiii''.</ref> [[Brian Pippard|A.B. Pippard]] writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<ref>Pippard, A.B. (1957/1966), p. 6.</ref><br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment", and cited by Adkins as having written a "classic text", A.B. Pippard writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<br />
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Callen引用另一位作者的话说,他给出了“学术且严谨的论述” ,Adkins引用他的话说,他写了一本“经典著作”—— '''<font color="#ff8000">A.B.皮帕德 A.B.Pippard</font>'''在文中写道: “只要时间足够长,过冷水蒸汽最终会凝结,... ..。时间可能是漫长的,也许长达10年或者更长。就大多数目的而言,只要这种迅速的变化不是人为地刺激,这些系统就可以被视为处于平衡状态。”<br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster">Münster, A. (1970), p. 53.</ref><br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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另一位作者A.Münster,写道。他观察到热核反应发生的速度非常缓慢,以至于在热力学中可以忽略不计。他评论道: “‘绝对平衡’或‘所有可想象过程的平衡’的概念没有物理意义。”他说: “ ... 我们只能考虑特定过程和确定的实验条件下的平衡。”<br />
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According to [[László Tisza|L. Tisza]]: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<ref>Tisza, L. (1966), p. 119.</ref><br />
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According to L. Tisza: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<br />
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根据'''<font color="#ff8000">L.缇莎 L.Tisza</font>'''的说法: “ ... 在讨论接近绝对零度的现象时。经典理论的绝对预测变得特别模糊,因为在非平衡状态下发生冻结是非常普遍的。”<br />
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==Definitions 定义==<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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一个系统最普遍的热力学平衡是通过与周围环境的接触,允许所有化学物质和各种能量同时通过。热力学平衡中的系统可能以均匀加速度在空间中运动,但此时不能改变其形状或大小; 因此它是由空间中的刚性体积来定义的。它可能存在于外力场中,由远远大于系统本身的外部因素决定,因此系统内的事件不会对外力场产生相当大的影响。只有当外力场是均匀的,并且确定了它的均匀加速度,或者它处于一个非均匀力场中,但是由于表面的局部力,例如机械压力,使它保持静止时,这个系统才能处于热力学平衡。<br />
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Thermodynamic equilibrium is a [[primitive notion]] of the theory of thermodynamics. According to [[Philip M. Morse|P.M. Morse]]: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are ''not'' conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments."<ref>[[Philip M. Morse|Morse, P.M.]] (1969), p. 7.</ref> This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<ref>Bailyn, M. (1994), p. 20.</ref><br />
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Thermodynamic equilibrium is a primitive notion of the theory of thermodynamics. According to P.M. Morse: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are not conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments." This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<br />
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热力学平衡是热力学理论的一个'''<font color="#ff8000">基本概念 Primitive Notion</font>'''。'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''说: “应该强调的是,存在热力学状态这一事实,以及存在由平衡态唯一指定的热力学变量这一事实,并不是从某些哲学第一原理得出的逻辑结论。这些结论不可避免地来自两个多世纪的实验。”这意味着热力学平衡不能仅仅用热力学的其他理论概念来定义。M.Bailyn提出了一个基本的热力学定律理论,它定义并假设了热力学平衡的存在。<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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热力学平衡的教科书定义通常被仔细说明,并有些保留。<br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<ref>Münster, A. (1970), p. 52.</ref><br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<br />
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例如,A. Münster写道:“当一个孤立系统中没有以可测量的速率发生状态变化时,系统处于热力学平衡状态。”这里有两项保留:系统是孤立的;任何状态的变化都是不可测量的缓慢。他通过对在室温且没有催化剂的情况下混合氧和氢的说明,讨论了第二个条件。Münster指出,描述热力学平衡状态所需要的宏观变量比给定系统任何其他状态都少。这是部分,但不完全是,因为系统内和流过系统的所有流都是零。<br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in ''equilibrium''.<ref>Haase, R. (1971), pp. 3–4.</ref><br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in equilibrium.<br />
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R. Haase's的热力学演示并不从对热力学平衡的限制开始,因为他打算考虑非平衡态热力学。他考虑一个具有时间不变性质的任意系统。他通过切断除外力场以外的所有外部影响来测试它的热力学平衡。如果在绝缘之后,没有任何变化,他说,系统处于平衡状态。<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness".<ref>Callen, H.B. (1960/1985), p. 13.</ref> This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness". This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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在一个标题为“热力学平衡”的章节中,H.B. Callen在一个段落中定义了平衡状态.他指出,它们“是由系统内部的内在因素决定的”。它们是“终端状态” ,随着时间的推移,系统会以“冰川般缓慢”的速度朝着这个终端状态演化。这个说法并没有明确,对于热力学平衡系统必须是孤立的;;Callen也没有说明他所说的“内在因素”是什么意思。<br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<ref>Adkins, C.J. (1968/1983), p. ''7''.</ref><br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<br />
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另一位教科书作者,C.J.Adkins,明确允许热力学平衡在非孤立的系统中发生。然而,他的系统在物质转移方面是封闭的。他写道: “一般来说,热力学平衡的方法包括热和类似功的形式与周围环境的相互作用。”他将这种热力学平衡与只有通过热接触才能进行能量传递的热平衡相区别。<br />
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Another textbook author, [[J.R. Partington]], writes: "(i) ''An equilibrium state is one which is independent of time''." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..."<ref>Partington, J.R. (1949), p. 161.</ref> This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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Another textbook author, J.R. Partington, writes: "(i) An equilibrium state is one which is independent of time." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..." This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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另一位教科书作者'''<font color="#ff8000">J.R.帕廷顿 J.R.Partington</font>'''写道: “(i)平衡状态是独立于时间的状态。”但是,在提到“只是明显处于平衡状态”的系统时,他补充说: “这样的系统处于‘虚假平衡’状态。帕廷顿的陈述没有明确指出平衡是指一个孤立的系统。和Münster一样,Partington也指的是氧和氢的混合物。他补充说:“在一个真正的平衡状态,任何影响状态的外部条件的微小变化都会产生一个微小的状态变化... ... ”这个条件意味着热力学平衡必须在小的扰动下保持稳定; 这个要求对于热力学平衡的严格意义是必不可少的。<br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, ''thermodynamic—equilibrium.''"<ref>Crawford, F.H. (1963), p. 5.</ref><br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, thermodynamic—equilibrium."<br />
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在F.H.Crawford的一本学生教科书中,有一个标题为“热力学平衡”的章节。它区分了几种流动的驱动因素,然后说: “这些是孤立系统明显普遍趋向于完全机械、热、化学和电力状态的例子——或者简单地说,热力学平衡状态。”<br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in ''equilibrium''."<ref>Buchdahl, H.A. (1966), p. 8.</ref> Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being ''in equilibrium'' so long as experimental tests show that 'slow' transitions are in effect reversible."<ref>Buchdahl, H.A. (1966), p. 111.</ref> It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<ref>Adkins, C.J. (1968/1983), p. 8.</ref><br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in equilibrium." Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being in equilibrium so long as experimental tests show that 'slow' transitions are in effect reversible." It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<br />
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H.A. Buchdahl的一本关于经典热力学的专著考虑了热力学系统的平衡,而实际上并没有写热力学平衡一词。Buchdahl在提到封闭的物质交换系统时写道: “如果一个系统处于一个适当的静态状态,那么它将被称为处于平衡状态。”出于热力学描述的目的,Buchdahl的专著也讨论了非晶态玻璃。它说: “更准确地说,只要实验测试表明‘慢’跃迁实际上是可逆的,玻璃就可以被认为处于平衡状态。”通常来说不会将这一条件作为热力学平衡定义的一部分,而是假定相反的情况:如果热力学平衡中的一个物体受到足够慢的过程的影响,则该过程可被视为足够接近可逆,并且该物体在过程中足够接近热力学平衡。<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of ''contact equilibrium''. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by [[Constantin Carathéodory|C. Carathéodory]], and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster" /> Thermodynamic equilibrium for an open system means that, with respect to every relevant kind of selectively permeable wall, contact equilibrium exists when the respective intensive parameters of the system and surroundings are equal.<ref name="Nster_a" /> This definition does not consider the most general kind of thermodynamic equilibrium, which is through unselective contacts. This definition does not simply state that no current of matter or energy exists in the interior or at the boundaries; but it is compatible with the following definition, which does so state.<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of contact equilibrium. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by C. Carathéodory, and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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通过引入接触平衡的概念,A. Münster仔细地扩展了孤立系统热力学平衡的定义。这指定了在考虑非孤立系统的热力学平衡时允许的特定过程,并特别关心开放系统,这些开放系统可能从周围环境获得或丢失物质。感兴趣的系统和周围系统之间的接触平衡,通过一种特殊的壁与之接触,其余的连接系统是孤立的。这种特殊类型的壁也被'''<font color="#ff8000">C.喀喇西奥多里 C.Carathéodory</font>'''考虑过,其他作家也提到过。它们具有选择渗透性。它们可能只对机械功有渗透性,或者只对热有渗透性,或者只对某种特定的化学物质有渗透性。每个接触平衡定义了一个强度参数; 例如,只能透热的壁定义了一个经验温度。对于感兴趣的体系中每一种化学成分,都可以存在接触平衡。在接触平衡中,尽管有可能通过选择性渗透壁进行交换,但是感兴趣的系统是不变的,好像它处在孤立的热力学平衡。这个方案遵循的一般规则是: “ ... ... 我们只能考虑特定过程和特定实验条件下的平衡。”<br />
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[[Mark Zemansky|M. Zemansky]] also distinguishes mechanical, chemical, and thermal equilibrium. He then writes: "When the conditions for all three types of equilibrium are satisfied, the system is said to be in a state of thermodynamic equilibrium".<ref>[[Mark Zemansky|Zemansky, M.]] (1937/1968), p. 27.</ref><br />
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'''<font color="#ff8000">M.泽曼斯基 M.Zemansky</font>'''还区分了力学、化学和热平衡。他接着写道: “当这三种均衡的条件都满足时,系统就处于热力学平衡状态。”<br />
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P.M. Morse writes that thermodynamics is concerned with "states of thermodynamic equilibrium". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<br />
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[[Philip M. Morse|P.M. Morse]] writes that thermodynamics is concerned with "''states of thermodynamic equilibrium''". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<ref>[[Philip M. Morse|Morse, P.M.]] (1969), pp. 6, 37.</ref><br />
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'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''写道,热力学关注的是“热力学平衡状态”。在讨论物体与周围热源之间的热量传递时,他也使用了“热平衡”这个短语,尽管没有明确定义一个特殊的术语“热平衡”<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "full thermodynamic equilibrium state".<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "''full'' thermodynamic equilibrium state".<ref>Waldram, J.R. (1985), p. 5.</ref><br />
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J.R. Waldram写到了“一个明确的热力学状态”。他将一个系统定义为“当其观测量随时间停止变化时”的“热平衡”。但是在这个定义之下不久,他写到一块玻璃还没有达到“完全的热力学平衡状态”。<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, thermodynamic equilibrium is said to exist." He is not here considering the presence of an external force field.<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, ''thermodynamic equilibrium'' is said to exist." He is not here considering the presence of an external force field.<ref>Bailyn, M. (1994), p. 21.</ref><br />
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考虑到平衡状态,M.Bailyn写道: “每个强度变量都有自己的平衡类型。”然后他定义了热平衡、力学平衡和物质平衡。因此,他写道: “如果所有的强度变量都是一致的,那么热力学平衡就是存在的。”他在这里没有考虑外力场的存在。<br />
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J.G. Kirkwood and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of thermodynamic equilibrium if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<br />
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[[John Gamble Kirkwood|J.G. Kirkwood]] and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of ''thermodynamic equilibrium'' if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<ref>Kirkwood, J.G., Oppenheim, I. (1961), p. 2</ref><br />
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'''<font color="#ff8000">J.G.柯克伍德 J.G.Kirkwood</font>'''和 I.Oppenheim 将热力学平衡定义为: “一个系统处于热力学平衡状态,如果,在实验的时间内,(a)它强度特性与时间无关,(b)它的内部或与周围环境的边界处没有物质或能量流。”显然,他们没有把定义限制在孤立的或封闭的系统。它们不讨论“缓慢”发生变化的可能性,并且超出了分配给实验的时间范围。他们注意到,对于两个相接触的系统,存在一个强度性质的小子类,如果这个小子类的所有子类都相等,那么所有各自的强度性质都相等。只要满足其他一些条件,热力学平衡状态可以由这个子类定义。<br />
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==Characteristics of a state of internal thermodynamic equilibrium 内部热力学平衡状态的特征==<br />
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===Homogeneity in the absence of external forces 在没有外力的情况下的均匀性===<br />
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A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous.<ref name="Planck 1903 3"/> This means that the material in any small volume element of the system can be interchanged with the material of any other geometrically congruent volume element of the system, and the effect is to leave the system thermodynamically unchanged. In general, a strong external force field makes a system of a single phase in its own internal thermodynamic equilibrium inhomogeneous with respect to some [[Intensive and extensive properties|intensive variables]]. For example, a relatively dense component of a mixture can be concentrated by centrifugation.<br />
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在没有外力的情况下,由单一相组成的热力学系统,在其自身的内部热力学平衡中是均匀的。这意味着系统中任何小体积单元中的材料可以与系统中任何其他几何相等的体积单元中的材料互换,其效果是使系统在热力学上保持不变。一般来说,一个强外力场使得一个单相系统在其自身的内部热力学平衡中对于一些'''<font color="#ff8000">强度量 Intensive Variable</font>'''是不均匀的。例如,可以通过离心来浓缩混合物中相对密度较大的组分。<br />
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===Uniform temperature 均匀温度===<br />
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Such equilibrium inhomogeneity, induced by external forces, does not occur for the intensive variable [[temperature]]. According to [[Edward A. Guggenheim|E.A. Guggenheim]], "The most important conception of thermodynamics is temperature."<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), p.5.</ref> Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface."<ref name="Planck 1903 3">[[Max Planck|Planck, M.]] (1897/1927), p.3.</ref> As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.<br />
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这种由外力引起的平衡不均匀性,对于强度量'''<font color="#ff8000">温度 Temperature</font>'''不会发生。'''<font color="#ff8000">E.A.古根海姆 E.A. Guggenheim</font>'''认为,“热力学最重要的概念是温度。“Planck在介绍他的论文时,简要叙述了热、温度和热平衡,然后宣布: ”在下文中,我们将主要讨论任何形式的均匀、各向同性的物体,它们的物质具有相同的温度和密度,并受到到处垂直于表面的均匀压力的作用。和Carathéodory 一样,Planck将表面效应、外场和各向异性晶体排除在外。虽然Planck提到了温度,但并没有明确提到热力学平衡的概念。相比之下,Carathéodory关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ,虽然没有明确地使用短语‘热力学平衡’ ,也没有明确地假设存在一个温度来定义它。<br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform.<ref name="Planck 1914 40"/> This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers.<ref>Gibbs, J.W. (1876/1878), pp. 144-150.</ref><ref>[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966), pp. 127–130.</ref><ref>Münster, A. (1970), pp. 309–310.</ref><ref>Bailyn, M. (1994), pp. 254-256.</ref><ref>{{cite journal | last1 = Verkley | first1 = W.T.M. | last2 = Gerkema | first2 = T. | year = 2004 | title = On maximum entropy profiles | journal = J. Atmos. Sci. | volume = 61 | issue = 8| pages = 931–936 | doi=10.1175/1520-0469(2004)061<0931:omep>2.0.co;2| bibcode = 2004JAtS...61..931V | doi-access = free }}</ref><ref>{{cite journal | last1 = Akmaev | first1 = R.A. | year = 2008 | title = On the energetics of maximum-entropy temperature profiles | url = | journal = Q. J. R. Meteorol. Soc. | volume = 134 | issue = 630| pages = 187–197 | doi=10.1002/qj.209| bibcode = 2008QJRMS.134..187A }}</ref> Considerations of kinetic theory or statistical mechanics also support this statement.<ref>Maxwell, J.C. (1867).</ref><ref>Boltzmann, L. (1896/1964), p. 143.</ref><ref>Chapman, S., Cowling, T.G. (1939/1970), Section 4.14, pp. 75–78.</ref><ref>[[J. R. Partington|Partington, J.R.]] (1949), pp. 275–278.</ref><ref>{{cite journal | last1 = Coombes | first1 = C.A. | last2 = Laue | first2 = H. | year = 1985 | title = A paradox concerning the temperature distribution of a gas in a gravitational field | url = | journal = Am. J. Phys. | volume = 53 | issue = 3| pages = 272–273 | doi=10.1119/1.14138| bibcode = 1985AmJPh..53..272C }}</ref><ref>{{cite journal | last1 = Román | first1 = F.L. | last2 = White | first2 = J.A. | last3 = Velasco | first3 = S. | year = 1995 | title = Microcanonical single-particle distributions for an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 16 | issue = 2| pages = 83–90 | doi=10.1088/0143-0807/16/2/008| bibcode = 1995EJPh...16...83R }}</ref><ref>{{cite journal | last1 = Velasco | first1 = S. | last2 = Román | first2 = F.L. | last3 = White | first3 = J.A. | year = 1996 | title = On a paradox concerning the temperature distribution of an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 17 | issue = | pages = 43–44 | doi=10.1088/0143-0807/17/1/008}}</ref><br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform. This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers. Considerations of kinetic theory or statistical mechanics also support this statement.<br />
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热力学平衡系统内的温度在时间和空间上都是均匀的。在一个处于内部热力学平衡的系统中,不存在净的内部宏观流动。特别是,这意味着系统的所有局部都处于相互辐射交换平衡。这意味着系统的温度在空间上是均匀的。这在所有情况下都是如此,包括那些非均匀外力场。对于外部施加的引力场,这可以使用拉格郎日乘子法通过变分的计算在宏观热力学术语中证明。动力学理论或统计力学也支持这种说法。<br />
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In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium.<ref name="Fitts 43"/><br />
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为了使一个系统处于它自己的内部热力学平衡状态,它必须处于它自己的内部热平衡状态是必要不充分的; 一个系统在到达内部热平衡之前到达内部力学平衡是可能的。<br />
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===Number of real variables needed for specification 规范所需的实变量数目===<br />
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In his exposition of his scheme of closed system equilibrium thermodynamics, C. Carathéodory initially postulates that experiment reveals that a definite number of real variables define the states that are the points of the manifold of equilibria.<ref name="Caratheodory" /> In the words of Prigogine and Defay (1945): "It is a matter of experience that when we have specified a certain number of macroscopic properties of a system, then all the other properties are fixed."<ref>Prigogine, I., Defay, R. (1950/1954), p. 1.</ref><ref>Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005), p. 4.</ref> As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.<br />
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在他关于封闭系统平衡态热力学方案的论述中,C.Carathéodory 最初假定实验揭示了一定数量的实变量定义了作为平衡态流形点的状态。用 Prigogine 和 Defay (1945)的话说: “这是一个经验问题,当我们确定了一个系统一定数量的宏观属性时,那么所有其他属性都是固定的”。如上所述,A. Münster认为,定义热力学平衡所需的变量数量相对于给定孤立系统的任何状态来说都是最少的。如上所述,J.G. Kirkwood 和 I. Oppenheim 指出,热力学平衡状态可以由一个特殊子类的强度变量来定义,该子类中有一定数量的成员。<br />
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If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.<br />
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如果热力学平衡位于一个外力场中,那么通常只有温度在空间上是均匀的。如果外力场非零,温度以外的强度变量通常是不均匀的。在这种情况下,一般需要附加变量来描述空间非均匀性。<br />
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===Stability against small perturbations 对小扰动的稳定性===<br />
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As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.<br />
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如上所述,J.R. Partington 指出热力学平衡状态在小的瞬态扰动下是稳定的。如果没有这个条件,一般来说,研究热力学平衡系统的实验就会遇到严重的困难。<br />
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===Approach to thermodynamic equilibrium within an isolated system 孤立系统中的热力学平衡===<br />
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When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium. Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<br />
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When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium.<ref name="Fitts 43">Fitts, D.D. (1962), p. 43.</ref> Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<ref>Denbigh, K.G. (1951), p. 42.</ref><br />
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当一个物质体从不均匀的非平衡状态或化学非平衡状态开始,然后被孤立,它会自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如,在这种演化的许多情况下,内部力学平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是,在这种演化的许多情况下,热平衡的发展要比化学平衡快得多。<br />
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===Fluctuations within an isolated system in its own internal thermodynamic equilibrium 孤立系统内部热力学平衡的涨落===<br />
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In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
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在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
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To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics.<ref>Tschoegl, N.W. (2000). ''Fundamentals of Equilibrium and Steady-State Thermodynamics'', Elsevier, Amsterdam, {{ISBN|0-444-50426-5}}, p. 21.</ref> But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
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To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics. But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
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考虑孤立热力学系统中的涨落概念,一个方便的例子是由其内能、体积和质量组成等广延量表示的系统。根据定义,它们是不随时间变化的。根据定义,这些量与它们的共轭状态强度函数的时不变标称值相结合,包括逆温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广延量的值,不足以提供这些标称值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
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It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.<br />
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可以承认,在重复测量这些共轭强度状态函数时,发现它们的值随时间略有不同。这种可变性被认为是由于内部涨落。不同测量值平均到其标称值。<br />
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If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<ref>Buchdahl, H.A. (1966), p. 16.</ref><br />
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If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<br />
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如果系统真的像经典热力学所假定的那样是宏观的,那么系统的涨落很小以至于宏观上无法检测到。这就是所谓的热力学极限。实际上,物质的分子性质和动量转移的量子性质由于它们太小而看不见,已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中,平衡的涨落概念是不存在的。”<br />
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If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
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如果系统被重复细分,最终产生的系统足够小,可以表现出明显的涨落。这是一个介观层面的研究。涨落则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
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An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process." This illustrates the importance for thermodynamics of the concept of temperature.<br />
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热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
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If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在波动过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,即需要量子统计力学。波动可以变得相对占主导地位,测量问题变得重要。<br />
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Thermal equilibrium is achieved when two systems in thermal contact with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<br />
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当两个相互热接触的系统不再有净能量交换时,就会产生热平衡。因此,如果两个系统处于热平衡,那么它们的温度是相同的。<br />
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The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
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"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有时间趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的标称值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微波动期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。非已知属于平衡状态的标称值,否则根据单一的度量无法进行判断。<br />
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Thermal equilibrium occurs when a system's macroscopic thermal observables have ceased to change with time. For example, an ideal gas whose distribution function has stabilised to a specific Maxwell–Boltzmann distribution would be in thermal equilibrium. This outcome allows a single temperature and pressure to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<br />
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当系统的宏观热观测值不再随着时间变化时,就会出现热平衡。例如,一种分布函数稳定到一个特定的麦克斯韦-波兹曼分布的理想气体即处于热平衡状态。这个结果可以将单一的温度和压力归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是很有可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
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=== Thermal equilibrium ===<br />
热平衡<br />
{{Main|Thermal equilibrium}}<br />
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An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process."<ref>Eu, B.C. (2002), page 13.</ref> This illustrates the importance for thermodynamics of the concept of temperature.<br />
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热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
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A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<br />
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一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数。<br />
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[[Thermal equilibrium]] is achieved when two systems in [[thermal contact]] with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<ref>[[Raj Pathria|R. K. Pathria]], 1996</ref><br />
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当两个相互'''<font color="#ff8000">热接触 Thermal Contact</font>'''的系统不再有净能量交换时,就会产生'''<font color="#ff8000">热平衡 Thermal Equilibrium</font>'''。因此,如果两个系统处于热平衡,那么它们的温度是相同的<br />
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Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
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Thermal equilibrium occurs when a system's [[macroscopic]] thermal observables have ceased to change with time. For example, an [[ideal gas]] whose [[Distribution function (physics)|distribution function]] has stabilised to a specific [[Maxwell–Boltzmann distribution]] would be in thermal equilibrium. This outcome allows a single [[temperature]] and [[pressure]] to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<ref>de Groot, S.R., Mazur, P. (1962), p. 44.</ref><br />
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当一个系统的'''<font color="#ff8000">宏观 Macroscopic</font>'''热观测值不再随时间变化时,就会出现热平衡。例如,一种'''<font color="#ff8000">分布函数 Distribution Function</font>'''稳定到一个特定的'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''的'''<font color="#ff8000">理想气体 Ideal Gas</font>'''即处于热平衡状态。这个结果可以将单一的'''<font color="#ff8000">温度 Temperature</font>'''和'''<font color="#ff8000">压力 Pressure</font>'''归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
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Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle. It states that a non-equilibrium system evolves such as to maximize its entropy production.<br />
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定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
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==Non-equilibrium==<br />
非平衡<br />
{{Main|Non-equilibrium thermodynamics}}<br />
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Thermodynamic models <br />
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热力学模型<br />
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A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<ref>de Groot, S.R., Mazur, P. (1962), p. 43.</ref><br />
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一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数<br />
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Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
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Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle.<ref>{{cite book|last1=Ziegler|first1=H.|title=An Introduction to Thermomechanics.|date=1983|location=North Holland, Amsterdam.}}</ref><ref>{{cite journal|last1=Onsager|first1=Lars|title=Reciprocal Relations in Irreversible Processes|journal=Phys. Rev.|date=1931|volume=37|issue=4|doi=10.1103/PhysRev.37.405|bibcode=1931PhRv...37..405O|pages=405–426|doi-access=free}}</ref> It states that a non-equilibrium system evolves such as to maximize its entropy production.<ref>{{cite book|last1=Kleidon|first1=A.|last2=et.|first2=al.|title=Non-equilibrium Thermodynamics and the Production of Entropy.|date=2005|edition=Heidelberg: Springer.}}</ref><ref>{{cite journal|last1=Belkin|first1=Andrey|last2=et.|first2=al.|title=Self-Assembled Wiggling Nano-Structures and the Principle of Maximum Entropy Production|journal=Sci. Rep.|doi=10.1038/srep08323|bibcode=2015NatSR...5E8323B|pmc=4321171|pmid=25662746|volume=5|year=2015|page=8323}}</ref><br />
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定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
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Topics in control theory<br />
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控制理论主题<br />
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==See also ==<br />
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{{Portal|Chemistry}}<br />
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;Thermodynamic models 热力学模型<br />
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{{colbegin}}<br />
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* [[Non-random two-liquid model]] (NRTL model) - Phase equilibrium calculations 非随机两液模型(NRTL 模型)-相平衡计算<br />
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* [[UNIQUAC]] model - Phase equilibrium calculations UNIQUAC 模型-相平衡计算<br />
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* [[Time crystal]] 时间晶体<br />
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{{colend}}<br />
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;Topics in control theory 控制理论主题<br />
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{{colbegin}}<br />
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* [[Steady state]] 稳态<br />
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* [[Transient state]] 瞬态<br />
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* [[Coefficient diagram method]] 系数图法<br />
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* [[Control reconfiguration]] 控制重构<br />
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* [[Cut-insertion theorem]] 切入定理<br />
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* [[Feedback]] 反馈<br />
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* [[H infinity]] H 无限<br />
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* [[Hankel singular value]] 汉克尔奇异值<br />
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* [[Krener's theorem]] 克雷纳定理<br />
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* [[Lead-lag compensator]] 超前滞后补偿器<br />
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* [[Minor loop feedback]] 小循环反馈<br />
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* [[Minor loop feedback|Multi-loop feedback]] 小循环反馈 | 多循环反馈<br />
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* [[Positive systems]] 正向系统<br />
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* [[Radial basis function]] 径向基底函数<br />
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Other related topics<br />
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其他相关话题<br />
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* [[Root locus]] 根轨迹<br />
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* [[Signal-flow graph]]s 信号流图<br />
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* [[Stable polynomial]] 稳定多项式<br />
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* [[State space representation]] 状态空间<br />
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* [[Underactuation]] 欠驱动<br />
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* [[Youla–Kucera parametrization]] 尤拉-库切拉参数化<br />
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* [[Markov chain approximation method]] 马尔可夫链近似法<br />
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{{colend}}<br />
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;Other related topics<br />
其他相关话题<br />
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{{colbegin}}<br />
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* [[Automation and remote control]] 自动化和远程控制<br />
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* [[Bond graph]] 键合图<br />
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* [[Control engineering]] 控制工程<br />
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* [[Control–feedback–abort loop]] 控制-反馈-中止循环<br />
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* [[Controller (control theory)]] 控制器(控制理论)<br />
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* [[Cybernetics]] 控制论<br />
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* [[Intelligent control]] 智能控制<br />
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* [[Mathematical system theory]] 数学系统论<br />
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* [[Negative feedback amplifier]] 负反馈放大器<br />
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* [[People in systems and control]] 系统和控制中的人<br />
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* [[Perceptual control theory]] 知觉控制理论<br />
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* [[Systems theory]] 系统论<br />
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* [[Time scale calculus]] 时间尺度演算<br />
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{{colend}}<br />
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== 编者推荐 ==<br />
===集智文章推荐===<br />
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====[https://swarma.org/?p=21322 什么是非平衡态热力学 | 集智百科]====<br />
非平衡态热力学 Non-equilibrium thermodynamics 是热力学的一个分支,研究某些不处于热力学平衡中的物理系统<br />
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==General references==<br />
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* Cesare Barbieri (2007) ''Fundamentals of Astronomy''. First Edition (QB43.3.B37 2006) CRC Press {{ISBN|0-7503-0886-9}}, {{ISBN|978-0-7503-0886-1}}<br />
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* Hans R. Griem (2005) ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}<br />
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* C. Michael Hogan, Leda C. Patmore and Harry Seidman (1973) ''Statistical Prediction of Dynamic Thermal Equilibrium Temperatures using Standard Meteorological Data Bases'', Second Edition (EPA-660/2-73-003 2006) United States Environmental Protection Agency Office of Research and Development, Washington, D.C. [http://library.wur.nl/WebQuery/catalog/lang/1851848]<br />
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* F. Mandl (1988) ''Statistical Physics'', Second Edition, John Wiley & Sons<br />
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==References==<br />
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{{Reflist|colwidth=35em}}<br />
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==Cited bibliography==<br />
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*Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', third edition, McGraw-Hill, London, {{ISBN|0-521-25445-0}}.<br />
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*Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, {{ISBN|0-88318-797-3}}.<br />
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*Beattie, J.A., Oppenheim, I. (1979). ''Principles of Thermodynamics'', Elsevier Scientific Publishing, Amsterdam, {{ISBN|0-444-41806-7}}.<br />
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*[[Ludwig Boltzmann|Boltzmann, L.]] (1896/1964). ''Lectures on Gas Theory'', translated by S.G. Brush, University of California Press, Berkeley.<br />
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*Buchdahl, H.A. (1966). ''The Concepts of Classical Thermodynamics'', Cambridge University Press, Cambridge UK.<br />
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*[[Herbert Callen|Callen, H.B.]] (1960/1985). ''Thermodynamics and an Introduction to Thermostatistics'', (1st edition 1960) 2nd edition 1985, Wiley, New York, {{ISBN|0-471-86256-8}}.<br />
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*[[Constantin Carathéodory|Carathéodory, C.]] (1909). [https://web.archive.org/web/20160304213645/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0067&DMDID=DMDLOG_0033&L=1 Untersuchungen über die Grundlagen der Thermodynamik], ''[[Mathematische Annalen]]'', '''67''': 355–386. A translation may be found [http://neo-classical-physics.info/uploads/3/0/6/5/3065888/caratheodory_-_thermodynamics.pdf here]. Also a mostly reliable [https://books.google.com/books?id=xwBRAAAAMAAJ&q=Investigation+into+the+foundations translation is to be found] at Kestin, J. (1976). ''The Second Law of Thermodynamics'', Dowden, Hutchinson & Ross, Stroudsburg PA.<br />
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*[[Sydney Chapman (mathematician)|Chapman, S.]], [[Thomas George Cowling|Cowling, T.G.]] (1939/1970). ''The Mathematical Theory of Non-uniform gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases'', third edition 1970, Cambridge University Press, London.<br />
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*Crawford, F.H. (1963). ''Heat, Thermodynamics, and Statistical Physics'', Rupert Hart-Davis, London, Harcourt, Brace & World, Inc.<br />
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*de Groot, S.R., Mazur, P. (1962). ''Non-equilibrium Thermodynamics'', North-Holland, Amsterdam. Reprinted (1984), Dover Publications Inc., New York, {{ISBN|0486647412}}.<br />
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*Denbigh, K.G. (1951). ''Thermodynamics of the Steady State'', Methuen, London.<br />
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*Eu, B.C. (2002). ''Generalized Thermodynamics. The Thermodynamics of Irreversible Processes and Generalized Hydrodynamics'', Kluwer Academic Publishers, Dordrecht, {{ISBN|1-4020-0788-4}}.<br />
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*Fitts, D.D. (1962). ''Nonequilibrium thermodynamics. A Phenomenological Theory of Irreversible Processes in Fluid Systems'', McGraw-Hill, New York.<br />
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*[[Josiah Willard Gibbs|Gibbs, J.W.]] (1876/1878). On the equilibrium of heterogeneous substances, ''Trans. Conn. Acad.'', '''3''': 108–248, 343–524, reprinted in ''The Collected Works of J. Willard Gibbs, Ph.D, LL. D.'', edited by W.R. Longley, R.G. Van Name, Longmans, Green & Co., New York, 1928, volume 1, pp.&nbsp;55–353.<br />
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*Griem, H.R. (2005). ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}.<br />
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*[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', fifth revised edition, North-Holland, Amsterdam.<br />
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*Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of ''Thermodynamics'', pages 1–97 of volume 1, ed. W. Jost, of ''Physical Chemistry. An Advanced Treatise'', ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081.<br />
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*[[John Gamble Kirkwood|Kirkwood, J.G.]], Oppenheim, I. (1961). ''Chemical Thermodynamics'', McGraw-Hill Book Company, New York.<br />
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*Landsberg, P.T. (1961). ''Thermodynamics with Quantum Statistical Illustrations'', Interscience, New York.<br />
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*{{cite journal |last1=Lieb |first1=E. H. |last2=Yngvason |first2=J. |year=1999 |title=The Physics and Mathematics of the Second Law of Thermodynamics |journal=Phys. Rep. |volume=310 |issue= 1|pages=1–96 |doi= 10.1016/S0370-1573(98)00082-9|arxiv = cond-mat/9708200 |bibcode = 1999PhR...310....1L |s2cid=119620408 }}<br />
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*Levine, I.N. (1983), ''Physical Chemistry'', second edition, McGraw-Hill, New York, {{ISBN|978-0072538625}}.<br />
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*{{cite journal | last1 = Maxwell | first1 = J.C. | authorlink = James Clerk Maxwell | year = 1867 | title = On the dynamical theory of gases | url = | journal = Phil. Trans. Roy. Soc. London | volume = 157 | issue = | pages = 49–88 }}<br />
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*[[Philip M. Morse|Morse, P.M.]] (1969). ''Thermal Physics'', second edition, W.A. Benjamin, Inc, New York.<br />
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*Münster, A. (1970). ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London.<br />
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*[[J.R. Partington|Partington, J.R.]] (1949). ''An Advanced Treatise on Physical Chemistry'', volume 1, ''Fundamental Principles. The Properties of Gases'', Longmans, Green and Co., London.<br />
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*[[Brian Pippard|Pippard, A.B.]] (1957/1966). ''The Elements of Classical Thermodynamics'', reprinted with corrections 1966, Cambridge University Press, London.<br />
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* [[Max Planck|Planck. M.]] (1914). [https://archive.org/details/theoryofheatradi00planrich ''The Theory of Heat Radiation''], a translation by Masius, M. of the second German edition, P. Blakiston's Son & Co., Philadelphia.<br />
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*[[Ilya Prigogine|Prigogine, I.]] (1947). ''Étude Thermodynamique des Phénomènes irréversibles'', Dunod, Paris, and Desoers, Liège.<br />
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*[[Ilya Prigogine|Prigogine, I.]], Defay, R. (1950/1954). ''Chemical Thermodynamics'', Longmans, Green & Co, London.<br />
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*Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005). ''Physical Chemistry'', fourth edition, Wiley, Hoboken NJ.<br />
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*[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966). ''Elements of Thermodynamics'', Addison-Wesley Publishing, Reading MA.<br />
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*{{cite journal|last=Thomson|first=W.|author-link=William Thomson, 1st Baron Kelvin|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Transactions of the Royal Society of Edinburgh|date=March 1851|volume=XX|issue=part II|pages=261–268; 289–298}} Also published in {{cite journal|last=Thomson|first=W.|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Phil. Mag. |date=December 1852 |volume=IV |series=4 |issue=22 |pages=8–21 |url=https://archive.org/details/londonedinburghp04maga |accessdate=25 June 2012}}<br />
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*[[László Tisza|Tisza, L.]] (1966). ''Generalized Thermodynamics'', M.I.T Press, Cambridge MA.<br />
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*[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963). ''Lectures in Statistical Mechanics'', American Mathematical Society, Providence RI.<br />
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*Waldram, J.R. (1985). ''The Theory of Thermodynamics'', Cambridge University Press, Cambridge UK, {{ISBN|0-521-24575-3}}.<br />
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*[[Mark Zemansky|Zemansky, M.]] (1937/1968). ''Heat and Thermodynamics. An Intermediate Textbook'', fifth edition 1967, McGraw–Hill Book Company, New York.<br />
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== External links ==<br />
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Category:Equilibrium chemistry<br />
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类别: 平衡化学<br />
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*[http://ads.harvard.edu/books/1989fsa..book/AbookC15.pdf Breakdown of Local Thermodynamic Equilibrium] George W. Collins, The Fundamentals of Stellar Astrophysics, Chapter 15<br />
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Category:Thermodynamic cycles<br />
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类别: 热力循环<br />
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*[http://spiff.rit.edu/classes/phys440/lectures/lte/lte.html Thermodynamic Equilibrium, Local and otherwise] lecture by Michael Richmond<br />
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Category:Thermodynamic processes<br />
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类别: 热力学过程<br />
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*[http://journals.ametsoc.org/doi/abs/10.1175/1520-0469%281970%29027%3C0711:NLTEIC%3E2.0.CO%3B2 Non-Local Thermodynamic Equilibrium in Cloudy Planetary Atmospheres] Paper by R. E. Samueison quantifying the effects due to non-LTE in an atmosphere<br />
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Category:Thermodynamic systems<br />
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类别: 热力学系统<br />
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*[http://scienceworld.wolfram.com/physics/LocalThermodynamicEquilibrium.html Local Thermodynamic Equilibrium]<br />
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Category:Thermodynamics<br />
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分类: 热力学<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Thermodynamic equilibrium]]. Its edit history can be viewed at [[平衡热力学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%B9%B3%E8%A1%A1%E7%83%AD%E5%8A%9B%E5%AD%A6&diff=21611平衡热力学2021-02-06T08:05:42Z<p>Jxzhou:/* Fluctuations within an isolated system in its own internal thermodynamic equilibrium */</p>
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<div>此词条暂由小竹凉翻译,翻译字数共5339,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{short description|State of thermodynamic system(s) where no net macroscopic flow of matter or energy occurs}}<br />
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'''Thermodynamic equilibrium''' is an [[axiomatic]] concept of [[thermodynamics]]. It is an internal [[State variables|state]] of a single [[thermodynamic system]], or a relation between several thermodynamic systems connected by more or less permeable or impermeable [[Thermodynamic system#Walls|walls]]. In thermodynamic equilibrium there are no net [[macroscopic]] [[Flow (mathematics)|flows]] of [[matter]] or of [[energy]], either within a system or between systems. <br />
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Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium there are no net macroscopic flows of matter or of energy, either within a system or between systems. <br />
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'''热力学平衡'''是'''<font color="#ff8000">热力学 Thermodynamics</font>'''的一个'''<font color="#ff8000">不言自明的 Axiomatic</font>'''概念。它是单个'''<font color="#ff8000">热力学系统 Thermodynamic System</font>'''的内部'''<font color="#ff8000">状态 State</font>''',或者是几个热力学系统之间通过或多或少的渗透或不渗透的'''<font color="#ff8000">壁 Wall</font>'''连接的关系。无论是在一个系统内还是在系统之间,在热力学平衡中不存在'''<font color="#ff8000">物质 Matter</font>'''或'''<font color="#ff8000">能量 Energy</font>'''的净'''<font color="#ff8000">宏观 Macroscopic</font>''' '''<font color="#ff8000">流动 Flow</font>'''。<br />
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In a system that is in its own state of internal thermodynamic equilibrium, no [[macroscopic]] change occurs. <br />
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In a system that is in its own state of internal thermodynamic equilibrium, no macroscopic change occurs. <br />
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在一个处于内部热力学平衡状态的系统中,不会发生'''<font color="#ff8000">宏观 Macroscopic</font>'''变化。<br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual [[Thermal equilibrium|thermal]], [[Mechanical equilibrium|mechanical]], [[Chemical equilibrium|chemical]], and [[Radiative equilibrium|radiative]] equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a [[thermodynamic operation]]. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a thermodynamic operation. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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相互热力学平衡的体系同时处于互相之间的'''<font color="#ff8000">热 Thermal</font>'''平衡、'''<font color="#ff8000">力学 Mechanical</font>'''平衡、'''<font color="#ff8000">化学 Chemical</font>'''平衡和'''<font color="#ff8000">辐射 Radiative</font>'''平衡。系统可以处于其中一种相互平衡状态,尽管其他状态未平衡。在热力学平衡中所有的平衡同时并且无限期地保持,直到被'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''打破。在一个宏观平衡中,微观交换是完全或几乎完全平衡的;这是对宏观平衡概念的物理解释。<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform [[temperature]]. Its [[Intensive and extensive properties|intensive properties]], other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform temperature. Its intensive properties, other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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一个处于内部热力学状态平衡的热力学系统具有空间均匀的'''<font color="#ff8000">温度 Temperature</font>'''。除了温度以外,它的'''<font color="#ff8000">强度性质 Intensive Properties</font>'''可以由于周围环境施加的不变的长程力场而导致空间不均匀性。<br />
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In systems that are at a state of [[non-equilibrium]] there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a '''meta-stable equilibrium'''.<br />
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In systems that are at a state of non-equilibrium there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a meta-stable equilibrium.<br />
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相比之下,处于'''<font color="#ff8000">非平衡状态 non-equilibrium</font>'''的系统中有物质或能量的净流动。如果这些变化可以在一个还没有发生的系统中被触发,那么这个系统就被称为处于一个'''亚稳定的平衡状态'''。<br />
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Though not a widely named a "law," it is an [[axiom]] of thermodynamics that there exist states of thermodynamic equilibrium. The [[second law of thermodynamics]] states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the [[entropy|entropies]] of the portions.<br />
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Though not a widely named a "law," it is an axiom of thermodynamics that there exist states of thermodynamic equilibrium. The second law of thermodynamics states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the entropies of the portions.<br />
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虽然不是一个广泛命名的“定律” ,但存在热力学平衡状态是一个热力学'''<font color="#ff8000">公理 Axiom</font>'''。'''<font color="#ff8000">热力学第二定律 second law of thermodynamics</font>'''指出,当一个物质体从一个平衡状态开始,在这个状态中,它的一部分被或多或少渗透或不渗透的分区保持在不同的状态,并且是孤立的,热力学操作移除分区或使分区更具渗透性,然后它会自发地达到自己内部热力学平衡的新状态,并伴随着部分'''<font color="#ff8000">熵 Entropy</font>'''的总和增加。<br />
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== Overview 概览==<br />
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{{Thermodynamics|cTopic=[[Thermodynamic system|Systems]]}}<br />
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Classical thermodynamics deals with states of [[dynamic equilibrium]]. The state of a system at thermodynamic equilibrium is the one for which some [[thermodynamic potential]] is minimized, or for which the [[entropy]] (''S'') is maximized, for specified conditions. One such potential is the [[Helmholtz free energy]] (''A''), for a system with surroundings at controlled constant temperature and volume:<br />
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Classical thermodynamics deals with states of dynamic equilibrium. The state of a system at thermodynamic equilibrium is the one for which some thermodynamic potential is minimized, or for which the entropy (S) is maximized, for specified conditions. One such potential is the Helmholtz free energy (A), for a system with surroundings at controlled constant temperature and volume:<br />
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经典热力学研究'''<font color="#ff8000">动态平衡 Dynamic Equilibrium</font>'''的状态。系统的热力学平衡状态是对于特定的条件,一些'''<font color="#ff8000">热力学势 Thermodynamic Potential</font>'''被最小化,或者'''<font color="#ff8000">熵 Entropy</font>'''(S)被最大化。对于一个周围环境温度和体积恒定的系统,其中一个这样的热力学势是'''<font color="#ff8000">亥姆霍兹自由能 Helmholtz Free Energy</font>'''(A):<br />
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:<math>A = U - TS</math><br />
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<math>A = U - TS</math><br />
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A = U-TS<br />
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Another potential, the [[Gibbs free energy]] (''G''), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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Another potential, the Gibbs free energy (G), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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在恒定温度和压力的系统中,另一个热力学势'''<font color="#ff8000">吉布斯自由能 Gibbs Free Energy</font>'''(G)在热力学平衡状态最小:<br />
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:<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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where ''T'' denotes the absolute thermodynamic temperature, ''P'' the pressure, ''S'' the entropy, ''V'' the volume, and ''U'' the internal energy of the system.<br />
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where T denotes the absolute thermodynamic temperature, P the pressure, S the entropy, V the volume, and U the internal energy of the system.<br />
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其中 T 表示热力学绝对温度,P 表示压强,S 表示熵,V 表示体积,U 表示体系的内能。<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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热力学平衡是一种独特的稳定定态,当系统长时间与周围环境相互作用时,它可以被接近或最终到达。上述势能是数学构造的热力学量,在特定的环境条件下最小化。<br />
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== Conditions 条件==<br />
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* For a completely isolated system, ''S'' is maximum at thermodynamic equilibrium. 对于一个完全孤立的系统,S在热力学平衡中取最大值。<br />
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* For a system with controlled constant temperature and volume, ''A'' is minimum at thermodynamic equilibrium. 对于一个恒定温度和体积的系统来说,A在热力学平衡中取最小值。<br />
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* For a system with controlled constant temperature and pressure, ''G'' is minimum at thermodynamic equilibrium. 对于一个恒温恒压的系统,G在热力学平衡中取最小值。<br />
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The various types of equilibriums are achieved as follows:<br />
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The various types of equilibriums are achieved as follows:<br />
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实现各种类型的平衡的方法如下:<br />
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*Two systems are in ''thermal equilibrium'' when their [[temperature]]s are the same. 当两个系统的'''<font color="#ff8000">温度 Temperature</font>'''相同时,它们就处于''热平衡状态''<br />
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*Two systems are in ''mechanical equilibrium'' when their [[pressure]]s are the same. 当两个体系的'''<font color="#ff8000">压力 Pressure</font>'''相同时,它们就处于''力学平衡''<br />
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*Two systems are in ''diffusive equilibrium'' when their [[chemical potential]]s are the same. 当两个题体系的'''<font color="#ff8000">化学势 Chemical Potential</font>'''相同时,它们就处于''扩散平衡''<br />
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*All [[forces]] are balanced and there is no significant external driving force.<br />
所有的'''<font color="#ff8000">力 Force</font>'''都是平衡的,没有明显的外部驱动力<br />
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==Relation of exchange equilibrium between systems 系统之间的交换均衡关系==<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability.<ref name="Nster_a">Münster, A. (1970), p. 49.</ref> When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability. When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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通常,热力学系统的周围环境也可以被看作是另一个热力学系统。在这种观点中,我们可以把系统及其周围环境看作是相互接触的两个系统,远程作用力也将它们联系在一起。系统的包围物是两个系统之间的接触面或边界。在热力学形式中,该表面被认为具有特定的渗透性质。例如,接触的表面可能被认为只能透热,使能量只能作为热传递。当远程力在时间上不发生变化,两个系统之间的热量传递减慢并最终永久停止时,这两个系统被称为热平衡; 这就是接触平衡的一个例子。其它类型的接触平衡可用其它类型的比渗透率来定义。当两个系统对于某一特定类型的渗透率处于接触平衡时,它们具有属于该特定类型渗透率的强变量的共同值。这种强度变量的例子有温度、压力、化学势。<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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接触平衡也可视为交换平衡。在接触平衡状态下,两系统之间某些量的传递速率存在零平衡。例如,对于只能透热的壁,内能作为热在两个系统之间的扩散速率是相等并反向的。两个系统之间的绝热壁只对作为功传递的能量有渗透作用; 在力学平衡,两个系统之间作为功的能量传递速率相等且相反。如果是一个简单的壁,那么通过它的体积转移率也是相等且相反的; 即它两边的压力是相等的。如果绝热壁比较复杂,有一种杠杆,有一个面积比,那么两个体系在交换平衡中的压力与体积交换比成反比,这使得转移率的零平衡作功。<br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<ref name="Planck 1914 40">[[Max Planck|Planck. M.]] (1914), p. 40.</ref><br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<br />
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辐射交换可以发生在两个不同的系统之间。当两个体系温度相同时,辐射交换平衡占优势。<br />
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==Thermodynamic state of internal equilibrium of a system 系统内部平衡的热力学状态==<br />
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A collection of matter may be entirely [[Isolated system|isolated]] from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium.<ref>Haase, R. (1971), p. 4.</ref><ref>Callen, H.B. (1960/1985), p. 26.</ref> (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics.<ref>{{Cite journal |doi = 10.1119/1.4914528|bibcode = 2015AmJPh..83..628M|title = Time and irreversibility in axiomatic thermodynamics|year = 2015|last1 = Marsland|first1 = Robert|last2 = Brown|first2 = Harvey R.|last3 = Valente|first3 = Giovanni|journal = American Journal of Physics|volume = 83|issue = 7|pages = 628–634}}</ref> One textbook<ref>[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963), p. 5.</ref> calls it the "zeroth law", remarking that the authors think this more befitting that title than its [[Zeroth law of thermodynamics|more customary definition]], which apparently was suggested by [[Ralph H. Fowler|Fowler]].)<br />
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A collection of matter may be entirely isolated from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium. (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics. One textbook calls it the "zeroth law", remarking that the authors think this more befitting that title than its more customary definition, which apparently was suggested by Fowler.)<br />
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物质的集合可能与其周围的环境完全'''<font color="#ff8000">孤立 Isolated</font>'''。如果它在无限长的时间内一直保持不受干扰,按照经典热力学假定,它处于一个没有发生任何变化,没有流动的状态,即内部平衡的热力学状态。(这种假设有时被称为“负第一”热力学定律,但并不常见。有教科书称之为“第零定律” ,作者'''<font color="#ff8000">福勒 Fowler</font>'''认为这个名称是'''<font color="#ff8000">更符合惯例的定义 More Customary Definition</font>'''。)<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a [[thermodynamic operation]] be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a thermodynamic operation be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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这种状态是所谓的经典热力学或平衡态热力学的主要关注点,因为它们是系统中被认为在这门学科中得到很好定义的唯一状态。一个与另一个系统处于接触平衡状态可以被一个'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''隔离,在隔离发生时,其内部不会发生任何变化。因此,一个与另一个系统处于接触平衡状态时也可以被视为处于其自身的内部热力学平衡状态。<br />
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==Multiple contact equilibrium 多点接触平衡==<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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热力学形式允许一个系统同时与其他多个系统接触,这些系统可能有也可能没有相互接触,且这些接触具有不同的渗透性。如果这些系统都与世界其他部分相互隔离,那么它们彼此之间就会达到各自的接触平衡。<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy.<ref name="Caratheodory">Carathéodory, C. (1909).</ref><ref>Prigogine, I. (1947), p. 48.</ref><ref>Landsberg, P. T. (1961), pp. 128–142.</ref><ref>Tisza, L. (1966), p. 108.</ref> Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy. Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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如果几个系统彼此之间没有绝热壁,但是它们与世界其他部分共同隔离,那么它们就会达到多重接触平衡状态,且有共同的温度,总的内能和熵。在众多强度量中,这是温度的一个独特性质。即使在远距离作用力存在的情况下,它也是有效的。(也就是说,没有“力”可以维持温度的差异。)举个例子,在热力学平衡的一个垂直的引力场系统中,顶部壁面的压力比底部壁面的压力小,但是各处的温度都是一样的。<br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural [[thermodynamic process]].<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), § 1.12.</ref> It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings.<ref>Levine, I.N. (1983), p. 40.</ref><ref>Lieb, E.H., Yngvason, J. (1999), pp. 17–18.</ref> The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of [[Second law of thermodynamics#Description#Kelvin statement|"inanimate" agency]]; a system in thermodynamic equilibrium is inanimate.<ref>[[William Thomson, 1st Baron Kelvin|Thomson, W.]] (1851).</ref><br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural thermodynamic process. It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings. The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of "inanimate" agency; a system in thermodynamic equilibrium is inanimate.<br />
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热力操作可能作为一个事件发生在周围环境的壁上,既不直接影响与周围环境联系的壁,也不直接影响其内部,且发生在一个明确的有限的时间内。例如,一个固定的绝热壁可以在环境中被放置或拆除。由于这种操作仅限于周围环境,系统可能会在一段时间内远离自身最初的内部状态---- 热力学平衡。根据热力学第二定律的说法,整体经历了变化并最终与周围环境达到了新的平衡。继Planck之后,这一连串的事件被称为自然'''<font color="#ff8000">热力学过程 Thermodynamic Process</font>'''。即使在这个过程中,当系统和周围环境都不处于明确的内部平衡状态时,存在着暂时偏离热力学平衡的现象,由于初始状态和最终状态都是热力学平衡的,这在平衡热力学中也是允许的。一个自然过程在其主要部分中以有限的速率进行,因此,它从根本上不同于虚构的准静态“过程”;即不在整个过程中无限缓慢地进行而且虚构地“可逆”。经典热力学允许,即使一个过程可能需要很长的时间才能达到热力学平衡,如果主要部分的过程是在一个有限的比率中,那么它被认为是自然的,并受制于热力学第二定律,即不可逆的。工程设计的机器、人工设备和操作是允许在周围环境中进行的。允许在环境中而不是在系统中进行此类操作和设备,是开尔文在他的一个热力学第二定律的陈述中提到'''<font color="#ff8000">无生命机构 Inanimate Agency</font>'''的原因; 在热力学平衡的系统是无生命的。<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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否则,热力操作可能会直接影响系统的壁。<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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通常可以很方便地假设周围的某些子系统比系统大得多,以至于这个过程只能影响周围子系统的强度变量,然后将这些子系统称为相关强度变量的储备库。<br />
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== Local and global equilibrium 局部和全局均衡==<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by [[intensive quantity|intensive]] parameters. As an example, [[temperature]] controls [[Heat equation|heat exchanges]]. ''Global thermodynamic equilibrium'' (GTE) means that those [[intensive quantity|intensive]] parameters are homogeneous throughout the whole system, while ''local thermodynamic equilibrium'' (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by intensive parameters. As an example, temperature controls heat exchanges. Global thermodynamic equilibrium (GTE) means that those intensive parameters are homogeneous throughout the whole system, while local thermodynamic equilibrium (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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区分全局性和局部性热力学平衡是很有用的。在热力学中,系统内部和系统与外部之间的交换是由'''<font color="#ff8000">强度 Intensive</font>'''参数控制的。例如,'''<font color="#ff8000">温度 Temperature</font>'''控制'''<font color="#ff8000">热交换 Heat Equation</font>'''。全局热力学平衡(GTE)意味着这些'''<font color="#ff8000">强度 Intensive</font>'''参数在整个系统中是均匀的,而局部热力学平衡(LTE)意味着这些强度参数在空间和时间上是变化的,但变化如此缓慢,以至于对于任何一点,人们都可以假设在该点的某个邻域存在热力学平衡。<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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如果对系统的描述要求强度参数的变化过大,那么这些强度参数的定义所依据的假设本身就会失效,系统将既不处于全局平衡,也不处于局部平衡。例如,粒子需要一定数量的碰撞来平衡其周围环境。如果在这些碰撞中移动的平均距离使它离开平衡邻域,它将永远不会平衡,也就不会有 LTE。根据定义,温度与平衡邻域的平均内部能量成正比。由于没有达到平衡邻域,温度的概念就不成立,温度也就变得无法定义。<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to [[massive]] particles. In a [[radiation|radiating]] gas, the [[photon]]s being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to massive particles. In a radiating gas, the photons being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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值得注意的是,这种局部平衡可能只适用于系统中的某个粒子子集。例如,LTE 通常只适用于'''<font color="#ff8000">大 Massive</font>'''质量粒子。在'''<font color="#ff8000">辐射 Radiation</font>'''气体中,被气体发射和吸收的'''<font color="#ff8000">光子 Photon</font>'''不需要彼此在一个热力学平衡内,或与气体中的大量粒子在一起,LTE 才能存在。在某些情况下,自由电子并不需要与大得多的原子或分子处于平衡状态,LTE 才能存在。<br />
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As an example, LTE will exist in a glass of water that contains a melting [[ice cube]]. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the [[Maxwell–Boltzmann distribution]] for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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As an example, LTE will exist in a glass of water that contains a melting ice cube. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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例如,LTE 将存在于一个装有正在融化的'''<font color="#ff8000">冰块 Ice Cube</font>'''的水杯中。玻璃杯内的温度可以在任何时候定义,但是离冰块近的地方要比离冰块远的地方冷。如果观察到位于给定点附近的分子的能量,它们将按照麦克斯韦-波兹曼分布在一定温度下的分布。如果观察到位于另一点附近的分子的能量,它们将按照'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''分布到另一个温度。<br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural [[transport phenomena]] may lead a system from local to global thermodynamic equilibrium. Going back to our example, the [[diffusion]] of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<ref>H.R. Griem, 2005</ref><br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural transport phenomena may lead a system from local to global thermodynamic equilibrium. Going back to our example, the diffusion of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<br />
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局部热力学平衡不需要局部或全局的平稳性。换句话说,每一个小区域不需要有一个恒定的温度。然而,它确实要求每个小的局部变化缓慢到足以维持其局部麦克斯韦-波尔兹曼速度分布。全局非平衡态只有通过系统与外界的交换才能保持稳定。例如,通过在水杯中不断添加细粉冰来补偿熔化,并持续排出融水,可以保持全局稳定的静态。自然'''<font color="#ff8000">输运现象 Transport Phenomena</font>'''会使一个局部热力学平衡系统逐渐达到全局的热力学平衡。回顾我们的例子,热量的扩散将导致我们的玻璃杯水流向全局热力学平衡,在这种状态下,玻璃杯的温度是完全均匀的。<br />
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==Reservations 保留意见==<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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学识渊博的笔者在热力学领域对热力学平衡描述时,经常对他们的描述附加条件或保留意见。有些笔者含蓄地保留了或多或少的空白,以待说明。<br />
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For example, one widely cited writer, [[Herbert Callen|H. B. Callen]] writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. ''Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!''"<ref>Callen, H.B. (1960/1985), p. 15.</ref><br />
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For example, one widely cited writer, H. B. Callen writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!"<br />
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例如,一位被广泛引用的作家'''<font color="#ff8000">H.B.卡伦 H.B.Callen</font>'''在这里写道: “实际上,很少有系统处于绝对和真正的平衡状态。”他提到了放射性过程,认为它们可能需要“宇宙时间才能完成,因此通常可以忽略”。他补充道: “在实践中,平衡的标准是循环的。在操作上,如果一个系统的性质一致地用热力学理论来描述,那么它就处于平衡状态! ”<br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<ref>Beattie, J.A., Oppenheim, I. (1979), p. 3.</ref><br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<br />
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J.A.贝蒂和 I.奥本海姆写道: “坚持对平衡定义的严格解释,将排除热力学应用于实际系统的所有状态。”<br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment",<ref>Callen, H.B. (1960/1985), p. 485.</ref> and cited by Adkins as having written a "classic text",<ref>Adkins, C.J. (1968/1983), p. ''xiii''.</ref> [[Brian Pippard|A.B. Pippard]] writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<ref>Pippard, A.B. (1957/1966), p. 6.</ref><br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment", and cited by Adkins as having written a "classic text", A.B. Pippard writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<br />
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Callen引用另一位作者的话说,他给出了“学术且严谨的论述” ,Adkins引用他的话说,他写了一本“经典著作”—— '''<font color="#ff8000">A.B.皮帕德 A.B.Pippard</font>'''在文中写道: “只要时间足够长,过冷水蒸汽最终会凝结,... ..。时间可能是漫长的,也许长达10年或者更长。就大多数目的而言,只要这种迅速的变化不是人为地刺激,这些系统就可以被视为处于平衡状态。”<br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster">Münster, A. (1970), p. 53.</ref><br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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另一位作者A.Münster,写道。他观察到热核反应发生的速度非常缓慢,以至于在热力学中可以忽略不计。他评论道: “‘绝对平衡’或‘所有可想象过程的平衡’的概念没有物理意义。”他说: “ ... 我们只能考虑特定过程和确定的实验条件下的平衡。”<br />
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According to [[László Tisza|L. Tisza]]: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<ref>Tisza, L. (1966), p. 119.</ref><br />
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According to L. Tisza: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<br />
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根据'''<font color="#ff8000">L.缇莎 L.Tisza</font>'''的说法: “ ... 在讨论接近绝对零度的现象时。经典理论的绝对预测变得特别模糊,因为在非平衡状态下发生冻结是非常普遍的。”<br />
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==Definitions 定义==<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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一个系统最普遍的热力学平衡是通过与周围环境的接触,允许所有化学物质和各种能量同时通过。热力学平衡中的系统可能以均匀加速度在空间中运动,但此时不能改变其形状或大小; 因此它是由空间中的刚性体积来定义的。它可能存在于外力场中,由远远大于系统本身的外部因素决定,因此系统内的事件不会对外力场产生相当大的影响。只有当外力场是均匀的,并且确定了它的均匀加速度,或者它处于一个非均匀力场中,但是由于表面的局部力,例如机械压力,使它保持静止时,这个系统才能处于热力学平衡。<br />
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Thermodynamic equilibrium is a [[primitive notion]] of the theory of thermodynamics. According to [[Philip M. Morse|P.M. Morse]]: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are ''not'' conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments."<ref>[[Philip M. Morse|Morse, P.M.]] (1969), p. 7.</ref> This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<ref>Bailyn, M. (1994), p. 20.</ref><br />
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Thermodynamic equilibrium is a primitive notion of the theory of thermodynamics. According to P.M. Morse: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are not conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments." This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<br />
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热力学平衡是热力学理论的一个'''<font color="#ff8000">基本概念 Primitive Notion</font>'''。'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''说: “应该强调的是,存在热力学状态这一事实,以及存在由平衡态唯一指定的热力学变量这一事实,并不是从某些哲学第一原理得出的逻辑结论。这些结论不可避免地来自两个多世纪的实验。”这意味着热力学平衡不能仅仅用热力学的其他理论概念来定义。M.Bailyn提出了一个基本的热力学定律理论,它定义并假设了热力学平衡的存在。<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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热力学平衡的教科书定义通常被仔细说明,并有些保留。<br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<ref>Münster, A. (1970), p. 52.</ref><br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<br />
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例如,A. Münster写道:“当一个孤立系统中没有以可测量的速率发生状态变化时,系统处于热力学平衡状态。”这里有两项保留:系统是孤立的;任何状态的变化都是不可测量的缓慢。他通过对在室温且没有催化剂的情况下混合氧和氢的说明,讨论了第二个条件。Münster指出,描述热力学平衡状态所需要的宏观变量比给定系统任何其他状态都少。这是部分,但不完全是,因为系统内和流过系统的所有流都是零。<br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in ''equilibrium''.<ref>Haase, R. (1971), pp. 3–4.</ref><br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in equilibrium.<br />
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R. Haase's的热力学演示并不从对热力学平衡的限制开始,因为他打算考虑非平衡态热力学。他考虑一个具有时间不变性质的任意系统。他通过切断除外力场以外的所有外部影响来测试它的热力学平衡。如果在绝缘之后,没有任何变化,他说,系统处于平衡状态。<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness".<ref>Callen, H.B. (1960/1985), p. 13.</ref> This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness". This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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在一个标题为“热力学平衡”的章节中,H.B. Callen在一个段落中定义了平衡状态.他指出,它们“是由系统内部的内在因素决定的”。它们是“终端状态” ,随着时间的推移,系统会以“冰川般缓慢”的速度朝着这个终端状态演化。这个说法并没有明确,对于热力学平衡系统必须是孤立的;;Callen也没有说明他所说的“内在因素”是什么意思。<br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<ref>Adkins, C.J. (1968/1983), p. ''7''.</ref><br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<br />
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另一位教科书作者,C.J.Adkins,明确允许热力学平衡在非孤立的系统中发生。然而,他的系统在物质转移方面是封闭的。他写道: “一般来说,热力学平衡的方法包括热和类似功的形式与周围环境的相互作用。”他将这种热力学平衡与只有通过热接触才能进行能量传递的热平衡相区别。<br />
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Another textbook author, [[J.R. Partington]], writes: "(i) ''An equilibrium state is one which is independent of time''." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..."<ref>Partington, J.R. (1949), p. 161.</ref> This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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Another textbook author, J.R. Partington, writes: "(i) An equilibrium state is one which is independent of time." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..." This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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另一位教科书作者'''<font color="#ff8000">J.R.帕廷顿 J.R.Partington</font>'''写道: “(i)平衡状态是独立于时间的状态。”但是,在提到“只是明显处于平衡状态”的系统时,他补充说: “这样的系统处于‘虚假平衡’状态。帕廷顿的陈述没有明确指出平衡是指一个孤立的系统。和Münster一样,Partington也指的是氧和氢的混合物。他补充说:“在一个真正的平衡状态,任何影响状态的外部条件的微小变化都会产生一个微小的状态变化... ... ”这个条件意味着热力学平衡必须在小的扰动下保持稳定; 这个要求对于热力学平衡的严格意义是必不可少的。<br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, ''thermodynamic—equilibrium.''"<ref>Crawford, F.H. (1963), p. 5.</ref><br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, thermodynamic—equilibrium."<br />
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在F.H.Crawford的一本学生教科书中,有一个标题为“热力学平衡”的章节。它区分了几种流动的驱动因素,然后说: “这些是孤立系统明显普遍趋向于完全机械、热、化学和电力状态的例子——或者简单地说,热力学平衡状态。”<br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in ''equilibrium''."<ref>Buchdahl, H.A. (1966), p. 8.</ref> Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being ''in equilibrium'' so long as experimental tests show that 'slow' transitions are in effect reversible."<ref>Buchdahl, H.A. (1966), p. 111.</ref> It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<ref>Adkins, C.J. (1968/1983), p. 8.</ref><br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in equilibrium." Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being in equilibrium so long as experimental tests show that 'slow' transitions are in effect reversible." It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<br />
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H.A. Buchdahl的一本关于经典热力学的专著考虑了热力学系统的平衡,而实际上并没有写热力学平衡一词。Buchdahl在提到封闭的物质交换系统时写道: “如果一个系统处于一个适当的静态状态,那么它将被称为处于平衡状态。”出于热力学描述的目的,Buchdahl的专著也讨论了非晶态玻璃。它说: “更准确地说,只要实验测试表明‘慢’跃迁实际上是可逆的,玻璃就可以被认为处于平衡状态。”通常来说不会将这一条件作为热力学平衡定义的一部分,而是假定相反的情况:如果热力学平衡中的一个物体受到足够慢的过程的影响,则该过程可被视为足够接近可逆,并且该物体在过程中足够接近热力学平衡。<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of ''contact equilibrium''. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by [[Constantin Carathéodory|C. Carathéodory]], and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster" /> Thermodynamic equilibrium for an open system means that, with respect to every relevant kind of selectively permeable wall, contact equilibrium exists when the respective intensive parameters of the system and surroundings are equal.<ref name="Nster_a" /> This definition does not consider the most general kind of thermodynamic equilibrium, which is through unselective contacts. This definition does not simply state that no current of matter or energy exists in the interior or at the boundaries; but it is compatible with the following definition, which does so state.<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of contact equilibrium. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by C. Carathéodory, and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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通过引入接触平衡的概念,A. Münster仔细地扩展了孤立系统热力学平衡的定义。这指定了在考虑非孤立系统的热力学平衡时允许的特定过程,并特别关心开放系统,这些开放系统可能从周围环境获得或丢失物质。感兴趣的系统和周围系统之间的接触平衡,通过一种特殊的壁与之接触,其余的连接系统是孤立的。这种特殊类型的壁也被'''<font color="#ff8000">C.喀喇西奥多里 C.Carathéodory</font>'''考虑过,其他作家也提到过。它们具有选择渗透性。它们可能只对机械功有渗透性,或者只对热有渗透性,或者只对某种特定的化学物质有渗透性。每个接触平衡定义了一个强度参数; 例如,只能透热的壁定义了一个经验温度。对于感兴趣的体系中每一种化学成分,都可以存在接触平衡。在接触平衡中,尽管有可能通过选择性渗透壁进行交换,但是感兴趣的系统是不变的,好像它处在孤立的热力学平衡。这个方案遵循的一般规则是: “ ... ... 我们只能考虑特定过程和特定实验条件下的平衡。”<br />
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[[Mark Zemansky|M. Zemansky]] also distinguishes mechanical, chemical, and thermal equilibrium. He then writes: "When the conditions for all three types of equilibrium are satisfied, the system is said to be in a state of thermodynamic equilibrium".<ref>[[Mark Zemansky|Zemansky, M.]] (1937/1968), p. 27.</ref><br />
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'''<font color="#ff8000">M.泽曼斯基 M.Zemansky</font>'''还区分了力学、化学和热平衡。他接着写道: “当这三种均衡的条件都满足时,系统就处于热力学平衡状态。”<br />
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P.M. Morse writes that thermodynamics is concerned with "states of thermodynamic equilibrium". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<br />
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[[Philip M. Morse|P.M. Morse]] writes that thermodynamics is concerned with "''states of thermodynamic equilibrium''". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<ref>[[Philip M. Morse|Morse, P.M.]] (1969), pp. 6, 37.</ref><br />
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'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''写道,热力学关注的是“热力学平衡状态”。在讨论物体与周围热源之间的热量传递时,他也使用了“热平衡”这个短语,尽管没有明确定义一个特殊的术语“热平衡”<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "full thermodynamic equilibrium state".<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "''full'' thermodynamic equilibrium state".<ref>Waldram, J.R. (1985), p. 5.</ref><br />
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J.R. Waldram写到了“一个明确的热力学状态”。他将一个系统定义为“当其观测量随时间停止变化时”的“热平衡”。但是在这个定义之下不久,他写到一块玻璃还没有达到“完全的热力学平衡状态”。<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, thermodynamic equilibrium is said to exist." He is not here considering the presence of an external force field.<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, ''thermodynamic equilibrium'' is said to exist." He is not here considering the presence of an external force field.<ref>Bailyn, M. (1994), p. 21.</ref><br />
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考虑到平衡状态,M.Bailyn写道: “每个强度变量都有自己的平衡类型。”然后他定义了热平衡、力学平衡和物质平衡。因此,他写道: “如果所有的强度变量都是一致的,那么热力学平衡就是存在的。”他在这里没有考虑外力场的存在。<br />
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J.G. Kirkwood and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of thermodynamic equilibrium if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<br />
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[[John Gamble Kirkwood|J.G. Kirkwood]] and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of ''thermodynamic equilibrium'' if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<ref>Kirkwood, J.G., Oppenheim, I. (1961), p. 2</ref><br />
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'''<font color="#ff8000">J.G.柯克伍德 J.G.Kirkwood</font>'''和 I.Oppenheim 将热力学平衡定义为: “一个系统处于热力学平衡状态,如果,在实验的时间内,(a)它强度特性与时间无关,(b)它的内部或与周围环境的边界处没有物质或能量流。”显然,他们没有把定义限制在孤立的或封闭的系统。它们不讨论“缓慢”发生变化的可能性,并且超出了分配给实验的时间范围。他们注意到,对于两个相接触的系统,存在一个强度性质的小子类,如果这个小子类的所有子类都相等,那么所有各自的强度性质都相等。只要满足其他一些条件,热力学平衡状态可以由这个子类定义。<br />
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==Characteristics of a state of internal thermodynamic equilibrium 内部热力学平衡状态的特征==<br />
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===Homogeneity in the absence of external forces 在没有外力的情况下的均匀性===<br />
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A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous.<ref name="Planck 1903 3"/> This means that the material in any small volume element of the system can be interchanged with the material of any other geometrically congruent volume element of the system, and the effect is to leave the system thermodynamically unchanged. In general, a strong external force field makes a system of a single phase in its own internal thermodynamic equilibrium inhomogeneous with respect to some [[Intensive and extensive properties|intensive variables]]. For example, a relatively dense component of a mixture can be concentrated by centrifugation.<br />
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在没有外力的情况下,由单一相组成的热力学系统,在其自身的内部热力学平衡中是均匀的。这意味着系统中任何小体积单元中的材料可以与系统中任何其他几何相等的体积单元中的材料互换,其效果是使系统在热力学上保持不变。一般来说,一个强外力场使得一个单相系统在其自身的内部热力学平衡中对于一些'''<font color="#ff8000">强度量 Intensive Variable</font>'''是不均匀的。例如,可以通过离心来浓缩混合物中相对密度较大的组分。<br />
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===Uniform temperature 均匀温度===<br />
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Such equilibrium inhomogeneity, induced by external forces, does not occur for the intensive variable [[temperature]]. According to [[Edward A. Guggenheim|E.A. Guggenheim]], "The most important conception of thermodynamics is temperature."<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), p.5.</ref> Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface."<ref name="Planck 1903 3">[[Max Planck|Planck, M.]] (1897/1927), p.3.</ref> As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.<br />
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这种由外力引起的平衡不均匀性,对于强度量'''<font color="#ff8000">温度 Temperature</font>'''不会发生。'''<font color="#ff8000">E.A.古根海姆 E.A. Guggenheim</font>'''认为,“热力学最重要的概念是温度。“Planck在介绍他的论文时,简要叙述了热、温度和热平衡,然后宣布: ”在下文中,我们将主要讨论任何形式的均匀、各向同性的物体,它们的物质具有相同的温度和密度,并受到到处垂直于表面的均匀压力的作用。和Carathéodory 一样,Planck将表面效应、外场和各向异性晶体排除在外。虽然Planck提到了温度,但并没有明确提到热力学平衡的概念。相比之下,Carathéodory关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ,虽然没有明确地使用短语‘热力学平衡’ ,也没有明确地假设存在一个温度来定义它。<br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform.<ref name="Planck 1914 40"/> This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers.<ref>Gibbs, J.W. (1876/1878), pp. 144-150.</ref><ref>[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966), pp. 127–130.</ref><ref>Münster, A. (1970), pp. 309–310.</ref><ref>Bailyn, M. (1994), pp. 254-256.</ref><ref>{{cite journal | last1 = Verkley | first1 = W.T.M. | last2 = Gerkema | first2 = T. | year = 2004 | title = On maximum entropy profiles | journal = J. Atmos. Sci. | volume = 61 | issue = 8| pages = 931–936 | doi=10.1175/1520-0469(2004)061<0931:omep>2.0.co;2| bibcode = 2004JAtS...61..931V | doi-access = free }}</ref><ref>{{cite journal | last1 = Akmaev | first1 = R.A. | year = 2008 | title = On the energetics of maximum-entropy temperature profiles | url = | journal = Q. J. R. Meteorol. Soc. | volume = 134 | issue = 630| pages = 187–197 | doi=10.1002/qj.209| bibcode = 2008QJRMS.134..187A }}</ref> Considerations of kinetic theory or statistical mechanics also support this statement.<ref>Maxwell, J.C. (1867).</ref><ref>Boltzmann, L. (1896/1964), p. 143.</ref><ref>Chapman, S., Cowling, T.G. (1939/1970), Section 4.14, pp. 75–78.</ref><ref>[[J. R. Partington|Partington, J.R.]] (1949), pp. 275–278.</ref><ref>{{cite journal | last1 = Coombes | first1 = C.A. | last2 = Laue | first2 = H. | year = 1985 | title = A paradox concerning the temperature distribution of a gas in a gravitational field | url = | journal = Am. J. Phys. | volume = 53 | issue = 3| pages = 272–273 | doi=10.1119/1.14138| bibcode = 1985AmJPh..53..272C }}</ref><ref>{{cite journal | last1 = Román | first1 = F.L. | last2 = White | first2 = J.A. | last3 = Velasco | first3 = S. | year = 1995 | title = Microcanonical single-particle distributions for an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 16 | issue = 2| pages = 83–90 | doi=10.1088/0143-0807/16/2/008| bibcode = 1995EJPh...16...83R }}</ref><ref>{{cite journal | last1 = Velasco | first1 = S. | last2 = Román | first2 = F.L. | last3 = White | first3 = J.A. | year = 1996 | title = On a paradox concerning the temperature distribution of an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 17 | issue = | pages = 43–44 | doi=10.1088/0143-0807/17/1/008}}</ref><br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform. This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers. Considerations of kinetic theory or statistical mechanics also support this statement.<br />
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热力学平衡系统内的温度在时间和空间上都是均匀的。在一个处于内部热力学平衡的系统中,不存在净的内部宏观流动。特别是,这意味着系统的所有局部都处于相互辐射交换平衡。这意味着系统的温度在空间上是均匀的。这在所有情况下都是如此,包括那些非均匀外力场。对于外部施加的引力场,这可以使用拉格郎日乘子法通过变分的计算在宏观热力学术语中证明。动力学理论或统计力学也支持这种说法。<br />
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In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium.<ref name="Fitts 43"/><br />
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为了使一个系统处于它自己的内部热力学平衡状态,它必须处于它自己的内部热平衡状态是必要不充分的; 一个系统在到达内部热平衡之前到达内部力学平衡是可能的。<br />
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===Number of real variables needed for specification 规范所需的实变量数目===<br />
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In his exposition of his scheme of closed system equilibrium thermodynamics, C. Carathéodory initially postulates that experiment reveals that a definite number of real variables define the states that are the points of the manifold of equilibria.<ref name="Caratheodory" /> In the words of Prigogine and Defay (1945): "It is a matter of experience that when we have specified a certain number of macroscopic properties of a system, then all the other properties are fixed."<ref>Prigogine, I., Defay, R. (1950/1954), p. 1.</ref><ref>Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005), p. 4.</ref> As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.<br />
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在他关于封闭系统平衡态热力学方案的论述中,C.Carathéodory 最初假定实验揭示了一定数量的实变量定义了作为平衡态流形点的状态。用 Prigogine 和 Defay (1945)的话说: “这是一个经验问题,当我们确定了一个系统一定数量的宏观属性时,那么所有其他属性都是固定的”。如上所述,A. Münster认为,定义热力学平衡所需的变量数量相对于给定孤立系统的任何状态来说都是最少的。如上所述,J.G. Kirkwood 和 I. Oppenheim 指出,热力学平衡状态可以由一个特殊子类的强度变量来定义,该子类中有一定数量的成员。<br />
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If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.<br />
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如果热力学平衡位于一个外力场中,那么通常只有温度在空间上是均匀的。如果外力场非零,温度以外的强度变量通常是不均匀的。在这种情况下,一般需要附加变量来描述空间非均匀性。<br />
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===Stability against small perturbations 对小扰动的稳定性===<br />
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As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.<br />
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如上所述,J.R. Partington 指出热力学平衡状态在小的瞬态扰动下是稳定的。如果没有这个条件,一般来说,研究热力学平衡系统的实验就会遇到严重的困难。<br />
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===Approach to thermodynamic equilibrium within an isolated system 孤立系统中的热力学平衡===<br />
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When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium. Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<br />
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When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium.<ref name="Fitts 43">Fitts, D.D. (1962), p. 43.</ref> Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<ref>Denbigh, K.G. (1951), p. 42.</ref><br />
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当一个物质体从不均匀的非平衡状态或化学非平衡状态开始,然后被孤立,它会自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如,在这种演化的许多情况下,内部力学平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是,在这种演化的许多情况下,热平衡的发展要比化学平衡快得多。<br />
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===Fluctuations within an isolated system in its own internal thermodynamic equilibrium 孤立系统内部热力学平衡的===<br />
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If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
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如果系统被重复细分,最终产生的系统足够小,可以表现出明显的波动。这是一个介观层面的研究。波动则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
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In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
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在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
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In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
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在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
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If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
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如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在波动过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,即需要量子统计力学。波动可以变得相对占主导地位,测量问题变得重要。<br />
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To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics.<ref>Tschoegl, N.W. (2000). ''Fundamentals of Equilibrium and Steady-State Thermodynamics'', Elsevier, Amsterdam, {{ISBN|0-444-50426-5}}, p. 21.</ref> But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
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考虑孤立热力学系统中的波动概念,一个方便的例子是由其众多的状态变量,内能、体积和质量组成指定的系统。根据定义,它们是时不变的。根据定义,它们与它们的共轭状态密集函数的时不变名义值相结合,反向温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广泛的状态变量的值,不足以提供这些名义值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
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To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics. But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
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考虑孤立热力学系统中的波动概念,一个方便的例子是由其广泛的状态变量、内能、体积和质量组成指定的系统。根据定义,它们是时不变的。根据定义,它们与它们的共轭状态密集函数的时不变名义值相结合,反向温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广泛的状态变量的值,不足以提供这些名义值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
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The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
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"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有时间趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的标称值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微波动期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。非已知属于平衡状态的标称值,否则根据单一的度量无法进行判断。<br />
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It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.<br />
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可以承认,在重复测量这些共轭强度函数时,发现它们的值随时间略有不同。这种可变性被认为是由于内部波动。不同测量值平均到其名义值。<br />
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If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<ref>Buchdahl, H.A. (1966), p. 16.</ref><br />
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If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<br />
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如果这个系统真的像经典热力学所假定的那样是宏观的,那么这个系统的波动太小了,宏观上无法检测到。这就是所谓的热力学极限。实际上,物质的分子性质和动量转移的量子性质由于它们太小而看不见,已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中,平衡的波动概念是没有位置的。”<br />
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If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
<br />
如果系统被重复细分,最终产生的系统足够小,可以表现出明显的波动。这是一个介观层面的研究。波动则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
<br />
An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process." This illustrates the importance for thermodynamics of the concept of temperature.<br />
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热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
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If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在波动过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,即需要量子统计力学。波动可以变得相对占主导地位,测量问题变得重要。<br />
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Thermal equilibrium is achieved when two systems in thermal contact with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<br />
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当两个相互热接触的系统不再有净能量交换时,就会产生热平衡。因此,如果两个系统处于热平衡,那么它们的温度是相同的。<br />
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The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
<br />
"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有时间趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的标称值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微波动期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。非已知属于平衡状态的标称值,否则根据单一的度量无法进行判断。<br />
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Thermal equilibrium occurs when a system's macroscopic thermal observables have ceased to change with time. For example, an ideal gas whose distribution function has stabilised to a specific Maxwell–Boltzmann distribution would be in thermal equilibrium. This outcome allows a single temperature and pressure to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<br />
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当系统的宏观热观测值不再随着时间变化时,就会出现热平衡。例如,一种分布函数稳定到一个特定的麦克斯韦-波兹曼分布的理想气体即处于热平衡状态。这个结果可以将单一的温度和压力归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是很有可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
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=== Thermal equilibrium ===<br />
热平衡<br />
{{Main|Thermal equilibrium}}<br />
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An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process."<ref>Eu, B.C. (2002), page 13.</ref> This illustrates the importance for thermodynamics of the concept of temperature.<br />
<br />
热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
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A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<br />
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一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数。<br />
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[[Thermal equilibrium]] is achieved when two systems in [[thermal contact]] with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<ref>[[Raj Pathria|R. K. Pathria]], 1996</ref><br />
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当两个相互'''<font color="#ff8000">热接触 Thermal Contact</font>'''的系统不再有净能量交换时,就会产生'''<font color="#ff8000">热平衡 Thermal Equilibrium</font>'''。因此,如果两个系统处于热平衡,那么它们的温度是相同的<br />
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Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
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Thermal equilibrium occurs when a system's [[macroscopic]] thermal observables have ceased to change with time. For example, an [[ideal gas]] whose [[Distribution function (physics)|distribution function]] has stabilised to a specific [[Maxwell–Boltzmann distribution]] would be in thermal equilibrium. This outcome allows a single [[temperature]] and [[pressure]] to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<ref>de Groot, S.R., Mazur, P. (1962), p. 44.</ref><br />
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当一个系统的'''<font color="#ff8000">宏观 Macroscopic</font>'''热观测值不再随时间变化时,就会出现热平衡。例如,一种'''<font color="#ff8000">分布函数 Distribution Function</font>'''稳定到一个特定的'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''的'''<font color="#ff8000">理想气体 Ideal Gas</font>'''即处于热平衡状态。这个结果可以将单一的'''<font color="#ff8000">温度 Temperature</font>'''和'''<font color="#ff8000">压力 Pressure</font>'''归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
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Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle. It states that a non-equilibrium system evolves such as to maximize its entropy production.<br />
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定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
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==Non-equilibrium==<br />
非平衡<br />
{{Main|Non-equilibrium thermodynamics}}<br />
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Thermodynamic models <br />
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热力学模型<br />
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A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<ref>de Groot, S.R., Mazur, P. (1962), p. 43.</ref><br />
<br />
一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数<br />
<br />
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
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Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle.<ref>{{cite book|last1=Ziegler|first1=H.|title=An Introduction to Thermomechanics.|date=1983|location=North Holland, Amsterdam.}}</ref><ref>{{cite journal|last1=Onsager|first1=Lars|title=Reciprocal Relations in Irreversible Processes|journal=Phys. Rev.|date=1931|volume=37|issue=4|doi=10.1103/PhysRev.37.405|bibcode=1931PhRv...37..405O|pages=405–426|doi-access=free}}</ref> It states that a non-equilibrium system evolves such as to maximize its entropy production.<ref>{{cite book|last1=Kleidon|first1=A.|last2=et.|first2=al.|title=Non-equilibrium Thermodynamics and the Production of Entropy.|date=2005|edition=Heidelberg: Springer.}}</ref><ref>{{cite journal|last1=Belkin|first1=Andrey|last2=et.|first2=al.|title=Self-Assembled Wiggling Nano-Structures and the Principle of Maximum Entropy Production|journal=Sci. Rep.|doi=10.1038/srep08323|bibcode=2015NatSR...5E8323B|pmc=4321171|pmid=25662746|volume=5|year=2015|page=8323}}</ref><br />
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定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
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Topics in control theory<br />
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控制理论主题<br />
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==See also ==<br />
<br />
{{Portal|Chemistry}}<br />
<br />
;Thermodynamic models 热力学模型<br />
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{{colbegin}}<br />
<br />
* [[Non-random two-liquid model]] (NRTL model) - Phase equilibrium calculations 非随机两液模型(NRTL 模型)-相平衡计算<br />
<br />
* [[UNIQUAC]] model - Phase equilibrium calculations UNIQUAC 模型-相平衡计算<br />
<br />
* [[Time crystal]] 时间晶体<br />
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{{colend}}<br />
<br />
;Topics in control theory 控制理论主题<br />
<br />
{{colbegin}}<br />
<br />
* [[Steady state]] 稳态<br />
<br />
* [[Transient state]] 瞬态<br />
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* [[Coefficient diagram method]] 系数图法<br />
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* [[Control reconfiguration]] 控制重构<br />
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* [[Cut-insertion theorem]] 切入定理<br />
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* [[Feedback]] 反馈<br />
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* [[H infinity]] H 无限<br />
<br />
* [[Hankel singular value]] 汉克尔奇异值<br />
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* [[Krener's theorem]] 克雷纳定理<br />
<br />
* [[Lead-lag compensator]] 超前滞后补偿器<br />
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* [[Minor loop feedback]] 小循环反馈<br />
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* [[Minor loop feedback|Multi-loop feedback]] 小循环反馈 | 多循环反馈<br />
<br />
* [[Positive systems]] 正向系统<br />
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* [[Radial basis function]] 径向基底函数<br />
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Other related topics<br />
<br />
其他相关话题<br />
<br />
* [[Root locus]] 根轨迹<br />
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* [[Signal-flow graph]]s 信号流图<br />
<br />
* [[Stable polynomial]] 稳定多项式<br />
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* [[State space representation]] 状态空间<br />
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* [[Underactuation]] 欠驱动<br />
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* [[Youla–Kucera parametrization]] 尤拉-库切拉参数化<br />
<br />
* [[Markov chain approximation method]] 马尔可夫链近似法<br />
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{{colend}}<br />
<br />
;Other related topics<br />
其他相关话题<br />
<br />
{{colbegin}}<br />
<br />
* [[Automation and remote control]] 自动化和远程控制<br />
<br />
* [[Bond graph]] 键合图<br />
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* [[Control engineering]] 控制工程<br />
<br />
* [[Control–feedback–abort loop]] 控制-反馈-中止循环<br />
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* [[Controller (control theory)]] 控制器(控制理论)<br />
<br />
* [[Cybernetics]] 控制论<br />
<br />
* [[Intelligent control]] 智能控制<br />
<br />
* [[Mathematical system theory]] 数学系统论<br />
<br />
* [[Negative feedback amplifier]] 负反馈放大器<br />
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* [[People in systems and control]] 系统和控制中的人<br />
<br />
* [[Perceptual control theory]] 知觉控制理论<br />
<br />
* [[Systems theory]] 系统论<br />
<br />
* [[Time scale calculus]] 时间尺度演算<br />
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{{colend}}<br />
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<br />
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== 编者推荐 ==<br />
===集智文章推荐===<br />
<br />
====[https://swarma.org/?p=21322 什么是非平衡态热力学 | 集智百科]====<br />
非平衡态热力学 Non-equilibrium thermodynamics 是热力学的一个分支,研究某些不处于热力学平衡中的物理系统<br />
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<br />
<br />
<br />
==General references==<br />
<br />
* Cesare Barbieri (2007) ''Fundamentals of Astronomy''. First Edition (QB43.3.B37 2006) CRC Press {{ISBN|0-7503-0886-9}}, {{ISBN|978-0-7503-0886-1}}<br />
<br />
* Hans R. Griem (2005) ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}<br />
<br />
* C. Michael Hogan, Leda C. Patmore and Harry Seidman (1973) ''Statistical Prediction of Dynamic Thermal Equilibrium Temperatures using Standard Meteorological Data Bases'', Second Edition (EPA-660/2-73-003 2006) United States Environmental Protection Agency Office of Research and Development, Washington, D.C. [http://library.wur.nl/WebQuery/catalog/lang/1851848]<br />
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* F. Mandl (1988) ''Statistical Physics'', Second Edition, John Wiley & Sons<br />
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==References==<br />
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{{Reflist|colwidth=35em}}<br />
<br />
<br />
<br />
==Cited bibliography==<br />
<br />
<br />
<br />
*Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', third edition, McGraw-Hill, London, {{ISBN|0-521-25445-0}}.<br />
<br />
*Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, {{ISBN|0-88318-797-3}}.<br />
<br />
*Beattie, J.A., Oppenheim, I. (1979). ''Principles of Thermodynamics'', Elsevier Scientific Publishing, Amsterdam, {{ISBN|0-444-41806-7}}.<br />
<br />
*[[Ludwig Boltzmann|Boltzmann, L.]] (1896/1964). ''Lectures on Gas Theory'', translated by S.G. Brush, University of California Press, Berkeley.<br />
<br />
*Buchdahl, H.A. (1966). ''The Concepts of Classical Thermodynamics'', Cambridge University Press, Cambridge UK.<br />
<br />
*[[Herbert Callen|Callen, H.B.]] (1960/1985). ''Thermodynamics and an Introduction to Thermostatistics'', (1st edition 1960) 2nd edition 1985, Wiley, New York, {{ISBN|0-471-86256-8}}.<br />
<br />
*[[Constantin Carathéodory|Carathéodory, C.]] (1909). [https://web.archive.org/web/20160304213645/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0067&DMDID=DMDLOG_0033&L=1 Untersuchungen über die Grundlagen der Thermodynamik], ''[[Mathematische Annalen]]'', '''67''': 355–386. A translation may be found [http://neo-classical-physics.info/uploads/3/0/6/5/3065888/caratheodory_-_thermodynamics.pdf here]. Also a mostly reliable [https://books.google.com/books?id=xwBRAAAAMAAJ&q=Investigation+into+the+foundations translation is to be found] at Kestin, J. (1976). ''The Second Law of Thermodynamics'', Dowden, Hutchinson & Ross, Stroudsburg PA.<br />
<br />
*[[Sydney Chapman (mathematician)|Chapman, S.]], [[Thomas George Cowling|Cowling, T.G.]] (1939/1970). ''The Mathematical Theory of Non-uniform gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases'', third edition 1970, Cambridge University Press, London.<br />
<br />
*Crawford, F.H. (1963). ''Heat, Thermodynamics, and Statistical Physics'', Rupert Hart-Davis, London, Harcourt, Brace & World, Inc.<br />
<br />
*de Groot, S.R., Mazur, P. (1962). ''Non-equilibrium Thermodynamics'', North-Holland, Amsterdam. Reprinted (1984), Dover Publications Inc., New York, {{ISBN|0486647412}}.<br />
<br />
*Denbigh, K.G. (1951). ''Thermodynamics of the Steady State'', Methuen, London.<br />
<br />
*Eu, B.C. (2002). ''Generalized Thermodynamics. The Thermodynamics of Irreversible Processes and Generalized Hydrodynamics'', Kluwer Academic Publishers, Dordrecht, {{ISBN|1-4020-0788-4}}.<br />
<br />
*Fitts, D.D. (1962). ''Nonequilibrium thermodynamics. A Phenomenological Theory of Irreversible Processes in Fluid Systems'', McGraw-Hill, New York.<br />
<br />
*[[Josiah Willard Gibbs|Gibbs, J.W.]] (1876/1878). On the equilibrium of heterogeneous substances, ''Trans. Conn. Acad.'', '''3''': 108–248, 343–524, reprinted in ''The Collected Works of J. Willard Gibbs, Ph.D, LL. D.'', edited by W.R. Longley, R.G. Van Name, Longmans, Green & Co., New York, 1928, volume 1, pp.&nbsp;55–353.<br />
<br />
*Griem, H.R. (2005). ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}.<br />
<br />
*[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', fifth revised edition, North-Holland, Amsterdam.<br />
<br />
*Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of ''Thermodynamics'', pages 1–97 of volume 1, ed. W. Jost, of ''Physical Chemistry. An Advanced Treatise'', ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081.<br />
<br />
*[[John Gamble Kirkwood|Kirkwood, J.G.]], Oppenheim, I. (1961). ''Chemical Thermodynamics'', McGraw-Hill Book Company, New York.<br />
<br />
*Landsberg, P.T. (1961). ''Thermodynamics with Quantum Statistical Illustrations'', Interscience, New York.<br />
<br />
*{{cite journal |last1=Lieb |first1=E. H. |last2=Yngvason |first2=J. |year=1999 |title=The Physics and Mathematics of the Second Law of Thermodynamics |journal=Phys. Rep. |volume=310 |issue= 1|pages=1–96 |doi= 10.1016/S0370-1573(98)00082-9|arxiv = cond-mat/9708200 |bibcode = 1999PhR...310....1L |s2cid=119620408 }}<br />
<br />
*Levine, I.N. (1983), ''Physical Chemistry'', second edition, McGraw-Hill, New York, {{ISBN|978-0072538625}}.<br />
<br />
*{{cite journal | last1 = Maxwell | first1 = J.C. | authorlink = James Clerk Maxwell | year = 1867 | title = On the dynamical theory of gases | url = | journal = Phil. Trans. Roy. Soc. London | volume = 157 | issue = | pages = 49–88 }}<br />
<br />
*[[Philip M. Morse|Morse, P.M.]] (1969). ''Thermal Physics'', second edition, W.A. Benjamin, Inc, New York.<br />
<br />
*Münster, A. (1970). ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London.<br />
<br />
*[[J.R. Partington|Partington, J.R.]] (1949). ''An Advanced Treatise on Physical Chemistry'', volume 1, ''Fundamental Principles. The Properties of Gases'', Longmans, Green and Co., London.<br />
<br />
*[[Brian Pippard|Pippard, A.B.]] (1957/1966). ''The Elements of Classical Thermodynamics'', reprinted with corrections 1966, Cambridge University Press, London.<br />
<br />
* [[Max Planck|Planck. M.]] (1914). [https://archive.org/details/theoryofheatradi00planrich ''The Theory of Heat Radiation''], a translation by Masius, M. of the second German edition, P. Blakiston's Son & Co., Philadelphia.<br />
<br />
*[[Ilya Prigogine|Prigogine, I.]] (1947). ''Étude Thermodynamique des Phénomènes irréversibles'', Dunod, Paris, and Desoers, Liège.<br />
<br />
*[[Ilya Prigogine|Prigogine, I.]], Defay, R. (1950/1954). ''Chemical Thermodynamics'', Longmans, Green & Co, London.<br />
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*Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005). ''Physical Chemistry'', fourth edition, Wiley, Hoboken NJ.<br />
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*[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966). ''Elements of Thermodynamics'', Addison-Wesley Publishing, Reading MA.<br />
<br />
*{{cite journal|last=Thomson|first=W.|author-link=William Thomson, 1st Baron Kelvin|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Transactions of the Royal Society of Edinburgh|date=March 1851|volume=XX|issue=part II|pages=261–268; 289–298}} Also published in {{cite journal|last=Thomson|first=W.|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Phil. Mag. |date=December 1852 |volume=IV |series=4 |issue=22 |pages=8–21 |url=https://archive.org/details/londonedinburghp04maga |accessdate=25 June 2012}}<br />
<br />
*[[László Tisza|Tisza, L.]] (1966). ''Generalized Thermodynamics'', M.I.T Press, Cambridge MA.<br />
<br />
*[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963). ''Lectures in Statistical Mechanics'', American Mathematical Society, Providence RI.<br />
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*Waldram, J.R. (1985). ''The Theory of Thermodynamics'', Cambridge University Press, Cambridge UK, {{ISBN|0-521-24575-3}}.<br />
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*[[Mark Zemansky|Zemansky, M.]] (1937/1968). ''Heat and Thermodynamics. An Intermediate Textbook'', fifth edition 1967, McGraw–Hill Book Company, New York.<br />
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== External links ==<br />
<br />
Category:Equilibrium chemistry<br />
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类别: 平衡化学<br />
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*[http://ads.harvard.edu/books/1989fsa..book/AbookC15.pdf Breakdown of Local Thermodynamic Equilibrium] George W. Collins, The Fundamentals of Stellar Astrophysics, Chapter 15<br />
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Category:Thermodynamic cycles<br />
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类别: 热力循环<br />
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*[http://spiff.rit.edu/classes/phys440/lectures/lte/lte.html Thermodynamic Equilibrium, Local and otherwise] lecture by Michael Richmond<br />
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Category:Thermodynamic processes<br />
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类别: 热力学过程<br />
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*[http://journals.ametsoc.org/doi/abs/10.1175/1520-0469%281970%29027%3C0711:NLTEIC%3E2.0.CO%3B2 Non-Local Thermodynamic Equilibrium in Cloudy Planetary Atmospheres] Paper by R. E. Samueison quantifying the effects due to non-LTE in an atmosphere<br />
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Category:Thermodynamic systems<br />
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类别: 热力学系统<br />
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*[http://scienceworld.wolfram.com/physics/LocalThermodynamicEquilibrium.html Local Thermodynamic Equilibrium]<br />
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Category:Thermodynamics<br />
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分类: 热力学<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Thermodynamic equilibrium]]. Its edit history can be viewed at [[平衡热力学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%B9%B3%E8%A1%A1%E7%83%AD%E5%8A%9B%E5%AD%A6&diff=21509平衡热力学2021-02-03T09:58:41Z<p>Jxzhou:/* Characteristics of a state of internal thermodynamic equilibrium 内部热力学平衡状态的特征 */</p>
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<div>此词条暂由小竹凉翻译,翻译字数共5339,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{short description|State of thermodynamic system(s) where no net macroscopic flow of matter or energy occurs}}<br />
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'''Thermodynamic equilibrium''' is an [[axiomatic]] concept of [[thermodynamics]]. It is an internal [[State variables|state]] of a single [[thermodynamic system]], or a relation between several thermodynamic systems connected by more or less permeable or impermeable [[Thermodynamic system#Walls|walls]]. In thermodynamic equilibrium there are no net [[macroscopic]] [[Flow (mathematics)|flows]] of [[matter]] or of [[energy]], either within a system or between systems. <br />
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Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium there are no net macroscopic flows of matter or of energy, either within a system or between systems. <br />
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'''热力学平衡'''是'''<font color="#ff8000">热力学 Thermodynamics</font>'''的一个'''<font color="#ff8000">不言自明的 Axiomatic</font>'''概念。它是单个'''<font color="#ff8000">热力学系统 Thermodynamic System</font>'''的内部'''<font color="#ff8000">状态 State</font>''',或者是几个热力学系统之间通过或多或少的渗透或不渗透的'''<font color="#ff8000">壁 Wall</font>'''连接的关系。无论是在一个系统内还是在系统之间,在热力学平衡中不存在'''<font color="#ff8000">物质 Matter</font>'''或'''<font color="#ff8000">能量 Energy</font>'''的净'''<font color="#ff8000">宏观 Macroscopic</font>''' '''<font color="#ff8000">流动 Flow</font>'''。<br />
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In a system that is in its own state of internal thermodynamic equilibrium, no [[macroscopic]] change occurs. <br />
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In a system that is in its own state of internal thermodynamic equilibrium, no macroscopic change occurs. <br />
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在一个处于内部热力学平衡状态的系统中,不会发生'''<font color="#ff8000">宏观 Macroscopic</font>'''变化。<br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual [[Thermal equilibrium|thermal]], [[Mechanical equilibrium|mechanical]], [[Chemical equilibrium|chemical]], and [[Radiative equilibrium|radiative]] equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a [[thermodynamic operation]]. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a thermodynamic operation. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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相互热力学平衡的体系同时处于互相之间的'''<font color="#ff8000">热 Thermal</font>'''平衡、'''<font color="#ff8000">力学 Mechanical</font>'''平衡、'''<font color="#ff8000">化学 Chemical</font>'''平衡和'''<font color="#ff8000">辐射 Radiative</font>'''平衡。系统可以处于其中一种相互平衡状态,尽管其他状态未平衡。在热力学平衡中所有的平衡同时并且无限期地保持,直到被'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''打破。在一个宏观平衡中,微观交换是完全或几乎完全平衡的;这是对宏观平衡概念的物理解释。<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform [[temperature]]. Its [[Intensive and extensive properties|intensive properties]], other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform temperature. Its intensive properties, other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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一个处于内部热力学状态平衡的热力学系统具有空间均匀的'''<font color="#ff8000">温度 Temperature</font>'''。除了温度以外,它的'''<font color="#ff8000">强度性质 Intensive Properties</font>'''可以由于周围环境施加的不变的长程力场而导致空间不均匀性。<br />
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In systems that are at a state of [[non-equilibrium]] there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a '''meta-stable equilibrium'''.<br />
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In systems that are at a state of non-equilibrium there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a meta-stable equilibrium.<br />
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相比之下,处于'''<font color="#ff8000">非平衡状态 non-equilibrium</font>'''的系统中有物质或能量的净流动。如果这些变化可以在一个还没有发生的系统中被触发,那么这个系统就被称为处于一个'''亚稳定的平衡状态'''。<br />
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Though not a widely named a "law," it is an [[axiom]] of thermodynamics that there exist states of thermodynamic equilibrium. The [[second law of thermodynamics]] states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the [[entropy|entropies]] of the portions.<br />
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Though not a widely named a "law," it is an axiom of thermodynamics that there exist states of thermodynamic equilibrium. The second law of thermodynamics states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the entropies of the portions.<br />
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虽然不是一个广泛命名的“定律” ,但存在热力学平衡状态是一个热力学'''<font color="#ff8000">公理 Axiom</font>'''。'''<font color="#ff8000">热力学第二定律 second law of thermodynamics</font>'''指出,当一个物质体从一个平衡状态开始,在这个状态中,它的一部分被或多或少渗透或不渗透的分区保持在不同的状态,并且是孤立的,热力学操作移除分区或使分区更具渗透性,然后它会自发地达到自己内部热力学平衡的新状态,并伴随着部分'''<font color="#ff8000">熵 Entropy</font>'''的总和增加。<br />
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== Overview 概览==<br />
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{{Thermodynamics|cTopic=[[Thermodynamic system|Systems]]}}<br />
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Classical thermodynamics deals with states of [[dynamic equilibrium]]. The state of a system at thermodynamic equilibrium is the one for which some [[thermodynamic potential]] is minimized, or for which the [[entropy]] (''S'') is maximized, for specified conditions. One such potential is the [[Helmholtz free energy]] (''A''), for a system with surroundings at controlled constant temperature and volume:<br />
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Classical thermodynamics deals with states of dynamic equilibrium. The state of a system at thermodynamic equilibrium is the one for which some thermodynamic potential is minimized, or for which the entropy (S) is maximized, for specified conditions. One such potential is the Helmholtz free energy (A), for a system with surroundings at controlled constant temperature and volume:<br />
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经典热力学研究'''<font color="#ff8000">动态平衡 Dynamic Equilibrium</font>'''的状态。系统的热力学平衡状态是对于特定的条件,一些'''<font color="#ff8000">热力学势 Thermodynamic Potential</font>'''被最小化,或者'''<font color="#ff8000">熵 Entropy</font>'''(S)被最大化。对于一个周围环境温度和体积恒定的系统,其中一个这样的热力学势是'''<font color="#ff8000">亥姆霍兹自由能 Helmholtz Free Energy</font>'''(A):<br />
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:<math>A = U - TS</math><br />
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<math>A = U - TS</math><br />
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A = U-TS<br />
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Another potential, the [[Gibbs free energy]] (''G''), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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Another potential, the Gibbs free energy (G), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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在恒定温度和压力的系统中,另一个热力学势'''<font color="#ff8000">吉布斯自由能 Gibbs Free Energy</font>'''(G)在热力学平衡状态最小:<br />
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:<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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where ''T'' denotes the absolute thermodynamic temperature, ''P'' the pressure, ''S'' the entropy, ''V'' the volume, and ''U'' the internal energy of the system.<br />
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where T denotes the absolute thermodynamic temperature, P the pressure, S the entropy, V the volume, and U the internal energy of the system.<br />
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其中 T 表示热力学绝对温度,P 表示压强,S 表示熵,V 表示体积,U 表示体系的内能。<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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热力学平衡是一种独特的稳定定态,当系统长时间与周围环境相互作用时,它可以被接近或最终到达。上述势能是数学构造的热力学量,在特定的环境条件下最小化。<br />
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== Conditions 条件==<br />
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* For a completely isolated system, ''S'' is maximum at thermodynamic equilibrium. 对于一个完全孤立的系统,S在热力学平衡中取最大值。<br />
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* For a system with controlled constant temperature and volume, ''A'' is minimum at thermodynamic equilibrium. 对于一个恒定温度和体积的系统来说,A在热力学平衡中取最小值。<br />
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* For a system with controlled constant temperature and pressure, ''G'' is minimum at thermodynamic equilibrium. 对于一个恒温恒压的系统,G在热力学平衡中取最小值。<br />
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The various types of equilibriums are achieved as follows:<br />
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The various types of equilibriums are achieved as follows:<br />
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实现各种类型的平衡的方法如下:<br />
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*Two systems are in ''thermal equilibrium'' when their [[temperature]]s are the same. 当两个系统的'''<font color="#ff8000">温度 Temperature</font>'''相同时,它们就处于''热平衡状态''<br />
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*Two systems are in ''mechanical equilibrium'' when their [[pressure]]s are the same. 当两个体系的'''<font color="#ff8000">压力 Pressure</font>'''相同时,它们就处于''力学平衡''<br />
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*Two systems are in ''diffusive equilibrium'' when their [[chemical potential]]s are the same. 当两个题体系的'''<font color="#ff8000">化学势 Chemical Potential</font>'''相同时,它们就处于''扩散平衡''<br />
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*All [[forces]] are balanced and there is no significant external driving force.<br />
所有的'''<font color="#ff8000">力 Force</font>'''都是平衡的,没有明显的外部驱动力<br />
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==Relation of exchange equilibrium between systems 系统之间的交换均衡关系==<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability.<ref name="Nster_a">Münster, A. (1970), p. 49.</ref> When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability. When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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通常,热力学系统的周围环境也可以被看作是另一个热力学系统。在这种观点中,我们可以把系统及其周围环境看作是相互接触的两个系统,远程作用力也将它们联系在一起。系统的包围物是两个系统之间的接触面或边界。在热力学形式中,该表面被认为具有特定的渗透性质。例如,接触的表面可能被认为只能透热,使能量只能作为热传递。当远程力在时间上不发生变化,两个系统之间的热量传递减慢并最终永久停止时,这两个系统被称为热平衡; 这就是接触平衡的一个例子。其它类型的接触平衡可用其它类型的比渗透率来定义。当两个系统对于某一特定类型的渗透率处于接触平衡时,它们具有属于该特定类型渗透率的强变量的共同值。这种强度变量的例子有温度、压力、化学势。<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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接触平衡也可视为交换平衡。在接触平衡状态下,两系统之间某些量的传递速率存在零平衡。例如,对于只能透热的壁,内能作为热在两个系统之间的扩散速率是相等并反向的。两个系统之间的绝热壁只对作为功传递的能量有渗透作用; 在力学平衡,两个系统之间作为功的能量传递速率相等且相反。如果是一个简单的壁,那么通过它的体积转移率也是相等且相反的; 即它两边的压力是相等的。如果绝热壁比较复杂,有一种杠杆,有一个面积比,那么两个体系在交换平衡中的压力与体积交换比成反比,这使得转移率的零平衡作功。<br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<ref name="Planck 1914 40">[[Max Planck|Planck. M.]] (1914), p. 40.</ref><br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<br />
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辐射交换可以发生在两个不同的系统之间。当两个体系温度相同时,辐射交换平衡占优势。<br />
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==Thermodynamic state of internal equilibrium of a system 系统内部平衡的热力学状态==<br />
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A collection of matter may be entirely [[Isolated system|isolated]] from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium.<ref>Haase, R. (1971), p. 4.</ref><ref>Callen, H.B. (1960/1985), p. 26.</ref> (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics.<ref>{{Cite journal |doi = 10.1119/1.4914528|bibcode = 2015AmJPh..83..628M|title = Time and irreversibility in axiomatic thermodynamics|year = 2015|last1 = Marsland|first1 = Robert|last2 = Brown|first2 = Harvey R.|last3 = Valente|first3 = Giovanni|journal = American Journal of Physics|volume = 83|issue = 7|pages = 628–634}}</ref> One textbook<ref>[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963), p. 5.</ref> calls it the "zeroth law", remarking that the authors think this more befitting that title than its [[Zeroth law of thermodynamics|more customary definition]], which apparently was suggested by [[Ralph H. Fowler|Fowler]].)<br />
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A collection of matter may be entirely isolated from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium. (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics. One textbook calls it the "zeroth law", remarking that the authors think this more befitting that title than its more customary definition, which apparently was suggested by Fowler.)<br />
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物质的集合可能与其周围的环境完全'''<font color="#ff8000">孤立 Isolated</font>'''。如果它在无限长的时间内一直保持不受干扰,按照经典热力学假定,它处于一个没有发生任何变化,没有流动的状态,即内部平衡的热力学状态。(这种假设有时被称为“负第一”热力学定律,但并不常见。有教科书称之为“第零定律” ,作者'''<font color="#ff8000">福勒 Fowler</font>'''认为这个名称是'''<font color="#ff8000">更符合惯例的定义 More Customary Definition</font>'''。)<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a [[thermodynamic operation]] be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a thermodynamic operation be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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这种状态是所谓的经典热力学或平衡态热力学的主要关注点,因为它们是系统中被认为在这门学科中得到很好定义的唯一状态。一个与另一个系统处于接触平衡状态可以被一个'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''隔离,在隔离发生时,其内部不会发生任何变化。因此,一个与另一个系统处于接触平衡状态时也可以被视为处于其自身的内部热力学平衡状态。<br />
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==Multiple contact equilibrium 多点接触平衡==<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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热力学形式允许一个系统同时与其他多个系统接触,这些系统可能有也可能没有相互接触,且这些接触具有不同的渗透性。如果这些系统都与世界其他部分相互隔离,那么它们彼此之间就会达到各自的接触平衡。<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy.<ref name="Caratheodory">Carathéodory, C. (1909).</ref><ref>Prigogine, I. (1947), p. 48.</ref><ref>Landsberg, P. T. (1961), pp. 128–142.</ref><ref>Tisza, L. (1966), p. 108.</ref> Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy. Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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如果几个系统彼此之间没有绝热壁,但是它们与世界其他部分共同隔离,那么它们就会达到多重接触平衡状态,且有共同的温度,总的内能和熵。在众多强度量中,这是温度的一个独特性质。即使在远距离作用力存在的情况下,它也是有效的。(也就是说,没有“力”可以维持温度的差异。)举个例子,在热力学平衡的一个垂直的引力场系统中,顶部壁面的压力比底部壁面的压力小,但是各处的温度都是一样的。<br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural [[thermodynamic process]].<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), § 1.12.</ref> It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings.<ref>Levine, I.N. (1983), p. 40.</ref><ref>Lieb, E.H., Yngvason, J. (1999), pp. 17–18.</ref> The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of [[Second law of thermodynamics#Description#Kelvin statement|"inanimate" agency]]; a system in thermodynamic equilibrium is inanimate.<ref>[[William Thomson, 1st Baron Kelvin|Thomson, W.]] (1851).</ref><br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural thermodynamic process. It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings. The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of "inanimate" agency; a system in thermodynamic equilibrium is inanimate.<br />
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热力操作可能作为一个事件发生在周围环境的壁上,既不直接影响与周围环境联系的壁,也不直接影响其内部,且发生在一个明确的有限的时间内。例如,一个固定的绝热壁可以在环境中被放置或拆除。由于这种操作仅限于周围环境,系统可能会在一段时间内远离自身最初的内部状态---- 热力学平衡。根据热力学第二定律的说法,整体经历了变化并最终与周围环境达到了新的平衡。继Planck之后,这一连串的事件被称为自然'''<font color="#ff8000">热力学过程 Thermodynamic Process</font>'''。即使在这个过程中,当系统和周围环境都不处于明确的内部平衡状态时,存在着暂时偏离热力学平衡的现象,由于初始状态和最终状态都是热力学平衡的,这在平衡热力学中也是允许的。一个自然过程在其主要部分中以有限的速率进行,因此,它从根本上不同于虚构的准静态“过程”;即不在整个过程中无限缓慢地进行而且虚构地“可逆”。经典热力学允许,即使一个过程可能需要很长的时间才能达到热力学平衡,如果主要部分的过程是在一个有限的比率中,那么它被认为是自然的,并受制于热力学第二定律,即不可逆的。工程设计的机器、人工设备和操作是允许在周围环境中进行的。允许在环境中而不是在系统中进行此类操作和设备,是开尔文在他的一个热力学第二定律的陈述中提到'''<font color="#ff8000">无生命机构 Inanimate Agency</font>'''的原因; 在热力学平衡的系统是无生命的。<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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否则,热力操作可能会直接影响系统的壁。<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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通常可以很方便地假设周围的某些子系统比系统大得多,以至于这个过程只能影响周围子系统的强度变量,然后将这些子系统称为相关强度变量的储备库。<br />
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== Local and global equilibrium 局部和全局均衡==<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by [[intensive quantity|intensive]] parameters. As an example, [[temperature]] controls [[Heat equation|heat exchanges]]. ''Global thermodynamic equilibrium'' (GTE) means that those [[intensive quantity|intensive]] parameters are homogeneous throughout the whole system, while ''local thermodynamic equilibrium'' (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by intensive parameters. As an example, temperature controls heat exchanges. Global thermodynamic equilibrium (GTE) means that those intensive parameters are homogeneous throughout the whole system, while local thermodynamic equilibrium (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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区分全局性和局部性热力学平衡是很有用的。在热力学中,系统内部和系统与外部之间的交换是由'''<font color="#ff8000">强度 Intensive</font>'''参数控制的。例如,'''<font color="#ff8000">温度 Temperature</font>'''控制'''<font color="#ff8000">热交换 Heat Equation</font>'''。全局热力学平衡(GTE)意味着这些'''<font color="#ff8000">强度 Intensive</font>'''参数在整个系统中是均匀的,而局部热力学平衡(LTE)意味着这些强度参数在空间和时间上是变化的,但变化如此缓慢,以至于对于任何一点,人们都可以假设在该点的某个邻域存在热力学平衡。<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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如果对系统的描述要求强度参数的变化过大,那么这些强度参数的定义所依据的假设本身就会失效,系统将既不处于全局平衡,也不处于局部平衡。例如,粒子需要一定数量的碰撞来平衡其周围环境。如果在这些碰撞中移动的平均距离使它离开平衡邻域,它将永远不会平衡,也就不会有 LTE。根据定义,温度与平衡邻域的平均内部能量成正比。由于没有达到平衡邻域,温度的概念就不成立,温度也就变得无法定义。<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to [[massive]] particles. In a [[radiation|radiating]] gas, the [[photon]]s being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to massive particles. In a radiating gas, the photons being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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值得注意的是,这种局部平衡可能只适用于系统中的某个粒子子集。例如,LTE 通常只适用于'''<font color="#ff8000">大 Massive</font>'''质量粒子。在'''<font color="#ff8000">辐射 Radiation</font>'''气体中,被气体发射和吸收的'''<font color="#ff8000">光子 Photon</font>'''不需要彼此在一个热力学平衡内,或与气体中的大量粒子在一起,LTE 才能存在。在某些情况下,自由电子并不需要与大得多的原子或分子处于平衡状态,LTE 才能存在。<br />
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As an example, LTE will exist in a glass of water that contains a melting [[ice cube]]. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the [[Maxwell–Boltzmann distribution]] for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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As an example, LTE will exist in a glass of water that contains a melting ice cube. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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例如,LTE 将存在于一个装有正在融化的'''<font color="#ff8000">冰块 Ice Cube</font>'''的水杯中。玻璃杯内的温度可以在任何时候定义,但是离冰块近的地方要比离冰块远的地方冷。如果观察到位于给定点附近的分子的能量,它们将按照麦克斯韦-波兹曼分布在一定温度下的分布。如果观察到位于另一点附近的分子的能量,它们将按照'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''分布到另一个温度。<br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural [[transport phenomena]] may lead a system from local to global thermodynamic equilibrium. Going back to our example, the [[diffusion]] of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<ref>H.R. Griem, 2005</ref><br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural transport phenomena may lead a system from local to global thermodynamic equilibrium. Going back to our example, the diffusion of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<br />
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局部热力学平衡不需要局部或全局的平稳性。换句话说,每一个小区域不需要有一个恒定的温度。然而,它确实要求每个小的局部变化缓慢到足以维持其局部麦克斯韦-波尔兹曼速度分布。全局非平衡态只有通过系统与外界的交换才能保持稳定。例如,通过在水杯中不断添加细粉冰来补偿熔化,并持续排出融水,可以保持全局稳定的静态。自然'''<font color="#ff8000">输运现象 Transport Phenomena</font>'''会使一个局部热力学平衡系统逐渐达到全局的热力学平衡。回顾我们的例子,热量的扩散将导致我们的玻璃杯水流向全局热力学平衡,在这种状态下,玻璃杯的温度是完全均匀的。<br />
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==Reservations 保留意见==<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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学识渊博的笔者在热力学领域对热力学平衡描述时,经常对他们的描述附加条件或保留意见。有些笔者含蓄地保留了或多或少的空白,以待说明。<br />
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For example, one widely cited writer, [[Herbert Callen|H. B. Callen]] writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. ''Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!''"<ref>Callen, H.B. (1960/1985), p. 15.</ref><br />
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For example, one widely cited writer, H. B. Callen writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!"<br />
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例如,一位被广泛引用的作家'''<font color="#ff8000">H.B.卡伦 H.B.Callen</font>'''在这里写道: “实际上,很少有系统处于绝对和真正的平衡状态。”他提到了放射性过程,认为它们可能需要“宇宙时间才能完成,因此通常可以忽略”。他补充道: “在实践中,平衡的标准是循环的。在操作上,如果一个系统的性质一致地用热力学理论来描述,那么它就处于平衡状态! ”<br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<ref>Beattie, J.A., Oppenheim, I. (1979), p. 3.</ref><br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<br />
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J.A.贝蒂和 I.奥本海姆写道: “坚持对平衡定义的严格解释,将排除热力学应用于实际系统的所有状态。”<br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment",<ref>Callen, H.B. (1960/1985), p. 485.</ref> and cited by Adkins as having written a "classic text",<ref>Adkins, C.J. (1968/1983), p. ''xiii''.</ref> [[Brian Pippard|A.B. Pippard]] writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<ref>Pippard, A.B. (1957/1966), p. 6.</ref><br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment", and cited by Adkins as having written a "classic text", A.B. Pippard writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<br />
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Callen引用另一位作者的话说,他给出了“学术且严谨的论述” ,Adkins引用他的话说,他写了一本“经典著作”—— '''<font color="#ff8000">A.B.皮帕德 A.B.Pippard</font>'''在文中写道: “只要时间足够长,过冷水蒸汽最终会凝结,... ..。时间可能是漫长的,也许长达10年或者更长。就大多数目的而言,只要这种迅速的变化不是人为地刺激,这些系统就可以被视为处于平衡状态。”<br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster">Münster, A. (1970), p. 53.</ref><br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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另一位作者A.Münster,写道。他观察到热核反应发生的速度非常缓慢,以至于在热力学中可以忽略不计。他评论道: “‘绝对平衡’或‘所有可想象过程的平衡’的概念没有物理意义。”他说: “ ... 我们只能考虑特定过程和确定的实验条件下的平衡。”<br />
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According to [[László Tisza|L. Tisza]]: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<ref>Tisza, L. (1966), p. 119.</ref><br />
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According to L. Tisza: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<br />
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根据'''<font color="#ff8000">L.缇莎 L.Tisza</font>'''的说法: “ ... 在讨论接近绝对零度的现象时。经典理论的绝对预测变得特别模糊,因为在非平衡状态下发生冻结是非常普遍的。”<br />
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==Definitions 定义==<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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一个系统最普遍的热力学平衡是通过与周围环境的接触,允许所有化学物质和各种能量同时通过。热力学平衡中的系统可能以均匀加速度在空间中运动,但此时不能改变其形状或大小; 因此它是由空间中的刚性体积来定义的。它可能存在于外力场中,由远远大于系统本身的外部因素决定,因此系统内的事件不会对外力场产生相当大的影响。只有当外力场是均匀的,并且确定了它的均匀加速度,或者它处于一个非均匀力场中,但是由于表面的局部力,例如机械压力,使它保持静止时,这个系统才能处于热力学平衡。<br />
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Thermodynamic equilibrium is a [[primitive notion]] of the theory of thermodynamics. According to [[Philip M. Morse|P.M. Morse]]: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are ''not'' conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments."<ref>[[Philip M. Morse|Morse, P.M.]] (1969), p. 7.</ref> This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<ref>Bailyn, M. (1994), p. 20.</ref><br />
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Thermodynamic equilibrium is a primitive notion of the theory of thermodynamics. According to P.M. Morse: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are not conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments." This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<br />
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热力学平衡是热力学理论的一个'''<font color="#ff8000">基本概念 Primitive Notion</font>'''。'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''说: “应该强调的是,存在热力学状态这一事实,以及存在由平衡态唯一指定的热力学变量这一事实,并不是从某些哲学第一原理得出的逻辑结论。这些结论不可避免地来自两个多世纪的实验。”这意味着热力学平衡不能仅仅用热力学的其他理论概念来定义。M.Bailyn提出了一个基本的热力学定律理论,它定义并假设了热力学平衡的存在。<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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热力学平衡的教科书定义通常被仔细说明,并有些保留。<br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<ref>Münster, A. (1970), p. 52.</ref><br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<br />
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例如,A. Münster写道:“当一个孤立系统中没有以可测量的速率发生状态变化时,系统处于热力学平衡状态。”这里有两项保留:系统是孤立的;任何状态的变化都是不可测量的缓慢。他通过对在室温且没有催化剂的情况下混合氧和氢的说明,讨论了第二个条件。Münster指出,描述热力学平衡状态所需要的宏观变量比给定系统任何其他状态都少。这是部分,但不完全是,因为系统内和流过系统的所有流都是零。<br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in ''equilibrium''.<ref>Haase, R. (1971), pp. 3–4.</ref><br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in equilibrium.<br />
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R. Haase's的热力学演示并不从对热力学平衡的限制开始,因为他打算考虑非平衡态热力学。他考虑一个具有时间不变性质的任意系统。他通过切断除外力场以外的所有外部影响来测试它的热力学平衡。如果在绝缘之后,没有任何变化,他说,系统处于平衡状态。<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness".<ref>Callen, H.B. (1960/1985), p. 13.</ref> This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness". This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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在一个标题为“热力学平衡”的章节中,H.B. Callen在一个段落中定义了平衡状态.他指出,它们“是由系统内部的内在因素决定的”。它们是“终端状态” ,随着时间的推移,系统会以“冰川般缓慢”的速度朝着这个终端状态演化。这个说法并没有明确,对于热力学平衡系统必须是孤立的;;Callen也没有说明他所说的“内在因素”是什么意思。<br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<ref>Adkins, C.J. (1968/1983), p. ''7''.</ref><br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<br />
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另一位教科书作者,C.J.Adkins,明确允许热力学平衡在非孤立的系统中发生。然而,他的系统在物质转移方面是封闭的。他写道: “一般来说,热力学平衡的方法包括热和类似功的形式与周围环境的相互作用。”他将这种热力学平衡与只有通过热接触才能进行能量传递的热平衡相区别。<br />
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Another textbook author, [[J.R. Partington]], writes: "(i) ''An equilibrium state is one which is independent of time''." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..."<ref>Partington, J.R. (1949), p. 161.</ref> This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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Another textbook author, J.R. Partington, writes: "(i) An equilibrium state is one which is independent of time." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..." This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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另一位教科书作者'''<font color="#ff8000">J.R.帕廷顿 J.R.Partington</font>'''写道: “(i)平衡状态是独立于时间的状态。”但是,在提到“只是明显处于平衡状态”的系统时,他补充说: “这样的系统处于‘虚假平衡’状态。帕廷顿的陈述没有明确指出平衡是指一个孤立的系统。和Münster一样,Partington也指的是氧和氢的混合物。他补充说:“在一个真正的平衡状态,任何影响状态的外部条件的微小变化都会产生一个微小的状态变化... ... ”这个条件意味着热力学平衡必须在小的扰动下保持稳定; 这个要求对于热力学平衡的严格意义是必不可少的。<br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, ''thermodynamic—equilibrium.''"<ref>Crawford, F.H. (1963), p. 5.</ref><br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, thermodynamic—equilibrium."<br />
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在F.H.Crawford的一本学生教科书中,有一个标题为“热力学平衡”的章节。它区分了几种流动的驱动因素,然后说: “这些是孤立系统明显普遍趋向于完全机械、热、化学和电力状态的例子——或者简单地说,热力学平衡状态。”<br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in ''equilibrium''."<ref>Buchdahl, H.A. (1966), p. 8.</ref> Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being ''in equilibrium'' so long as experimental tests show that 'slow' transitions are in effect reversible."<ref>Buchdahl, H.A. (1966), p. 111.</ref> It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<ref>Adkins, C.J. (1968/1983), p. 8.</ref><br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in equilibrium." Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being in equilibrium so long as experimental tests show that 'slow' transitions are in effect reversible." It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<br />
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H.A. Buchdahl的一本关于经典热力学的专著考虑了热力学系统的平衡,而实际上并没有写热力学平衡一词。Buchdahl在提到封闭的物质交换系统时写道: “如果一个系统处于一个适当的静态状态,那么它将被称为处于平衡状态。”出于热力学描述的目的,Buchdahl的专著也讨论了非晶态玻璃。它说: “更准确地说,只要实验测试表明‘慢’跃迁实际上是可逆的,玻璃就可以被认为处于平衡状态。”通常来说不会将这一条件作为热力学平衡定义的一部分,而是假定相反的情况:如果热力学平衡中的一个物体受到足够慢的过程的影响,则该过程可被视为足够接近可逆,并且该物体在过程中足够接近热力学平衡。<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of ''contact equilibrium''. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by [[Constantin Carathéodory|C. Carathéodory]], and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster" /> Thermodynamic equilibrium for an open system means that, with respect to every relevant kind of selectively permeable wall, contact equilibrium exists when the respective intensive parameters of the system and surroundings are equal.<ref name="Nster_a" /> This definition does not consider the most general kind of thermodynamic equilibrium, which is through unselective contacts. This definition does not simply state that no current of matter or energy exists in the interior or at the boundaries; but it is compatible with the following definition, which does so state.<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of contact equilibrium. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by C. Carathéodory, and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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通过引入接触平衡的概念,A. Münster仔细地扩展了孤立系统热力学平衡的定义。这指定了在考虑非孤立系统的热力学平衡时允许的特定过程,并特别关心开放系统,这些开放系统可能从周围环境获得或丢失物质。感兴趣的系统和周围系统之间的接触平衡,通过一种特殊的壁与之接触,其余的连接系统是孤立的。这种特殊类型的壁也被'''<font color="#ff8000">C.喀喇西奥多里 C.Carathéodory</font>'''考虑过,其他作家也提到过。它们具有选择渗透性。它们可能只对机械功有渗透性,或者只对热有渗透性,或者只对某种特定的化学物质有渗透性。每个接触平衡定义了一个强度参数; 例如,只能透热的壁定义了一个经验温度。对于感兴趣的体系中每一种化学成分,都可以存在接触平衡。在接触平衡中,尽管有可能通过选择性渗透壁进行交换,但是感兴趣的系统是不变的,好像它处在孤立的热力学平衡。这个方案遵循的一般规则是: “ ... ... 我们只能考虑特定过程和特定实验条件下的平衡。”<br />
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[[Mark Zemansky|M. Zemansky]] also distinguishes mechanical, chemical, and thermal equilibrium. He then writes: "When the conditions for all three types of equilibrium are satisfied, the system is said to be in a state of thermodynamic equilibrium".<ref>[[Mark Zemansky|Zemansky, M.]] (1937/1968), p. 27.</ref><br />
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'''<font color="#ff8000">M.泽曼斯基 M.Zemansky</font>'''还区分了力学、化学和热平衡。他接着写道: “当这三种均衡的条件都满足时,系统就处于热力学平衡状态。”<br />
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P.M. Morse writes that thermodynamics is concerned with "states of thermodynamic equilibrium". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<br />
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[[Philip M. Morse|P.M. Morse]] writes that thermodynamics is concerned with "''states of thermodynamic equilibrium''". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<ref>[[Philip M. Morse|Morse, P.M.]] (1969), pp. 6, 37.</ref><br />
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'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''写道,热力学关注的是“热力学平衡状态”。在讨论物体与周围热源之间的热量传递时,他也使用了“热平衡”这个短语,尽管没有明确定义一个特殊的术语“热平衡”<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "full thermodynamic equilibrium state".<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "''full'' thermodynamic equilibrium state".<ref>Waldram, J.R. (1985), p. 5.</ref><br />
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J.R. Waldram写到了“一个明确的热力学状态”。他将一个系统定义为“当其观测量随时间停止变化时”的“热平衡”。但是在这个定义之下不久,他写到一块玻璃还没有达到“完全的热力学平衡状态”。<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, thermodynamic equilibrium is said to exist." He is not here considering the presence of an external force field.<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, ''thermodynamic equilibrium'' is said to exist." He is not here considering the presence of an external force field.<ref>Bailyn, M. (1994), p. 21.</ref><br />
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考虑到平衡状态,M.Bailyn写道: “每个强度变量都有自己的平衡类型。”然后他定义了热平衡、力学平衡和物质平衡。因此,他写道: “如果所有的强度变量都是一致的,那么热力学平衡就是存在的。”他在这里没有考虑外力场的存在。<br />
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J.G. Kirkwood and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of thermodynamic equilibrium if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<br />
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[[John Gamble Kirkwood|J.G. Kirkwood]] and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of ''thermodynamic equilibrium'' if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<ref>Kirkwood, J.G., Oppenheim, I. (1961), p. 2</ref><br />
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'''<font color="#ff8000">J.G.柯克伍德 J.G.Kirkwood</font>'''和 I.Oppenheim 将热力学平衡定义为: “一个系统处于热力学平衡状态,如果,在实验的时间内,(a)它强度特性与时间无关,(b)它的内部或与周围环境的边界处没有物质或能量流。”显然,他们没有把定义限制在孤立的或封闭的系统。它们不讨论“缓慢”发生变化的可能性,并且超出了分配给实验的时间范围。他们注意到,对于两个相接触的系统,存在一个强度性质的小子类,如果这个小子类的所有子类都相等,那么所有各自的强度性质都相等。只要满足其他一些条件,热力学平衡状态可以由这个子类定义。<br />
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==Characteristics of a state of internal thermodynamic equilibrium 内部热力学平衡状态的特征==<br />
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===Homogeneity in the absence of external forces 在没有外力的情况下的均匀性===<br />
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A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous.<ref name="Planck 1903 3"/> This means that the material in any small volume element of the system can be interchanged with the material of any other geometrically congruent volume element of the system, and the effect is to leave the system thermodynamically unchanged. In general, a strong external force field makes a system of a single phase in its own internal thermodynamic equilibrium inhomogeneous with respect to some [[Intensive and extensive properties|intensive variables]]. For example, a relatively dense component of a mixture can be concentrated by centrifugation.<br />
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在没有外力的情况下,由单一相组成的热力学系统,在其自身的内部热力学平衡中是均匀的。这意味着系统中任何小体积单元中的材料可以与系统中任何其他几何相等的体积单元中的材料互换,其效果是使系统在热力学上保持不变。一般来说,一个强外力场使得一个单相系统在其自身的内部热力学平衡中对于一些'''<font color="#ff8000">强度量 Intensive Variable</font>'''是不均匀的。例如,可以通过离心来浓缩混合物中相对密度较大的组分。<br />
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===Uniform temperature 均匀温度===<br />
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Such equilibrium inhomogeneity, induced by external forces, does not occur for the intensive variable [[temperature]]. According to [[Edward A. Guggenheim|E.A. Guggenheim]], "The most important conception of thermodynamics is temperature."<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), p.5.</ref> Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface."<ref name="Planck 1903 3">[[Max Planck|Planck, M.]] (1897/1927), p.3.</ref> As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.<br />
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这种由外力引起的平衡不均匀性,对于强度量'''<font color="#ff8000">温度 Temperature</font>'''不会发生。'''<font color="#ff8000">E.A.古根海姆 E.A. Guggenheim</font>'''认为,“热力学最重要的概念是温度。“Planck在介绍他的论文时,简要叙述了热、温度和热平衡,然后宣布: ”在下文中,我们将主要讨论任何形式的均匀、各向同性的物体,它们的物质具有相同的温度和密度,并受到到处垂直于表面的均匀压力的作用。和Carathéodory 一样,Planck将表面效应、外场和各向异性晶体排除在外。虽然Planck提到了温度,但并没有明确提到热力学平衡的概念。相比之下,Carathéodory关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ,虽然没有明确地使用短语‘热力学平衡’ ,也没有明确地假设存在一个温度来定义它。<br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform.<ref name="Planck 1914 40"/> This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers.<ref>Gibbs, J.W. (1876/1878), pp. 144-150.</ref><ref>[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966), pp. 127–130.</ref><ref>Münster, A. (1970), pp. 309–310.</ref><ref>Bailyn, M. (1994), pp. 254-256.</ref><ref>{{cite journal | last1 = Verkley | first1 = W.T.M. | last2 = Gerkema | first2 = T. | year = 2004 | title = On maximum entropy profiles | journal = J. Atmos. Sci. | volume = 61 | issue = 8| pages = 931–936 | doi=10.1175/1520-0469(2004)061<0931:omep>2.0.co;2| bibcode = 2004JAtS...61..931V | doi-access = free }}</ref><ref>{{cite journal | last1 = Akmaev | first1 = R.A. | year = 2008 | title = On the energetics of maximum-entropy temperature profiles | url = | journal = Q. J. R. Meteorol. Soc. | volume = 134 | issue = 630| pages = 187–197 | doi=10.1002/qj.209| bibcode = 2008QJRMS.134..187A }}</ref> Considerations of kinetic theory or statistical mechanics also support this statement.<ref>Maxwell, J.C. (1867).</ref><ref>Boltzmann, L. (1896/1964), p. 143.</ref><ref>Chapman, S., Cowling, T.G. (1939/1970), Section 4.14, pp. 75–78.</ref><ref>[[J. R. Partington|Partington, J.R.]] (1949), pp. 275–278.</ref><ref>{{cite journal | last1 = Coombes | first1 = C.A. | last2 = Laue | first2 = H. | year = 1985 | title = A paradox concerning the temperature distribution of a gas in a gravitational field | url = | journal = Am. J. Phys. | volume = 53 | issue = 3| pages = 272–273 | doi=10.1119/1.14138| bibcode = 1985AmJPh..53..272C }}</ref><ref>{{cite journal | last1 = Román | first1 = F.L. | last2 = White | first2 = J.A. | last3 = Velasco | first3 = S. | year = 1995 | title = Microcanonical single-particle distributions for an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 16 | issue = 2| pages = 83–90 | doi=10.1088/0143-0807/16/2/008| bibcode = 1995EJPh...16...83R }}</ref><ref>{{cite journal | last1 = Velasco | first1 = S. | last2 = Román | first2 = F.L. | last3 = White | first3 = J.A. | year = 1996 | title = On a paradox concerning the temperature distribution of an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 17 | issue = | pages = 43–44 | doi=10.1088/0143-0807/17/1/008}}</ref><br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform. This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers. Considerations of kinetic theory or statistical mechanics also support this statement.<br />
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热力学平衡系统内的温度在时间和空间上都是均匀的。在一个处于内部热力学平衡的系统中,不存在净的内部宏观流动。特别是,这意味着系统的所有局部都处于相互辐射交换平衡。这意味着系统的温度在空间上是均匀的。这在所有情况下都是如此,包括那些非均匀外力场。对于外部施加的引力场,这可以使用拉格郎日乘子法通过变分的计算在宏观热力学术语中证明。动力学理论或统计力学也支持这种说法。<br />
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In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium.<ref name="Fitts 43"/><br />
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为了使一个系统处于它自己的内部热力学平衡状态,它必须处于它自己的内部热平衡状态是必要不充分的; 一个系统在到达内部热平衡之前到达内部力学平衡是可能的。<br />
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===Number of real variables needed for specification 规范所需的实变量数目===<br />
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In his exposition of his scheme of closed system equilibrium thermodynamics, C. Carathéodory initially postulates that experiment reveals that a definite number of real variables define the states that are the points of the manifold of equilibria.<ref name="Caratheodory" /> In the words of Prigogine and Defay (1945): "It is a matter of experience that when we have specified a certain number of macroscopic properties of a system, then all the other properties are fixed."<ref>Prigogine, I., Defay, R. (1950/1954), p. 1.</ref><ref>Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005), p. 4.</ref> As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.<br />
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在他关于封闭系统平衡态热力学方案的论述中,C.Carathéodory 最初假定实验揭示了一定数量的实变量定义了作为平衡态流形点的状态。用 Prigogine 和 Defay (1945)的话说: “这是一个经验问题,当我们确定了一个系统一定数量的宏观属性时,那么所有其他属性都是固定的”。如上所述,A. Münster认为,定义热力学平衡所需的变量数量相对于给定孤立系统的任何状态来说都是最少的。如上所述,J.G. Kirkwood 和 I. Oppenheim 指出,热力学平衡状态可以由一个特殊子类的强度变量来定义,该子类中有一定数量的成员。<br />
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If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.<br />
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如果热力学平衡位于一个外力场中,那么通常只有温度在空间上是均匀的。如果外力场非零,温度以外的强度变量通常是不均匀的。在这种情况下,一般需要附加变量来描述空间非均匀性。<br />
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===Stability against small perturbations 对小扰动的稳定性===<br />
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As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.<br />
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如上所述,J.R. Partington 指出热力学平衡状态在小的瞬态扰动下是稳定的。如果没有这个条件,一般来说,研究热力学平衡系统的实验就会遇到严重的困难。<br />
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===Approach to thermodynamic equilibrium within an isolated system 孤立系统中的热力学平衡===<br />
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When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium. Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<br />
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When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium.<ref name="Fitts 43">Fitts, D.D. (1962), p. 43.</ref> Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<ref>Denbigh, K.G. (1951), p. 42.</ref><br />
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当一个物质体从不均匀的非平衡状态或化学非平衡状态开始,然后被孤立,它会自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如,在这种演化的许多情况下,内部力学平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是,在这种演化的许多情况下,热平衡的发展要比化学平衡快得多。<br />
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===Fluctuations within an isolated system in its own internal thermodynamic equilibrium===<br />
孤立系统内部热力学平衡的波动<br />
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If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
<br />
如果系统被重复细分,最终产生的系统足够小,可以表现出明显的波动。这是一个介观层面的研究。波动则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
<br />
In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
<br />
在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
<br />
In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
<br />
在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
<br />
If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
<br />
如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在波动过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,即需要量子统计力学。波动可以变得相对占主导地位,测量问题变得重要。<br />
<br />
To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics.<ref>Tschoegl, N.W. (2000). ''Fundamentals of Equilibrium and Steady-State Thermodynamics'', Elsevier, Amsterdam, {{ISBN|0-444-50426-5}}, p. 21.</ref> But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
<br />
考虑孤立热力学系统中的波动概念,一个方便的例子是由其众多的状态变量,内能、体积和质量组成指定的系统。根据定义,它们是时不变的。根据定义,它们与它们的共轭状态密集函数的时不变名义值相结合,反向温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广泛的状态变量的值,不足以提供这些名义值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
<br />
To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics. But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
<br />
考虑孤立热力学系统中的波动概念,一个方便的例子是由其广泛的状态变量、内能、体积和质量组成指定的系统。根据定义,它们是时不变的。根据定义,它们与它们的共轭状态密集函数的时不变名义值相结合,反向温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广泛的状态变量的值,不足以提供这些名义值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
<br />
<br />
The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
<br />
"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有时间趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的标称值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微波动期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。非已知属于平衡状态的标称值,否则根据单一的度量无法进行判断。<br />
<br />
It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.<br />
<br />
可以承认,在重复测量这些共轭强度函数时,发现它们的值随时间略有不同。这种可变性被认为是由于内部波动。不同测量值平均到其名义值。<br />
<br />
<br />
<br />
If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<ref>Buchdahl, H.A. (1966), p. 16.</ref><br />
<br />
If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<br />
<br />
如果这个系统真的像经典热力学所假定的那样是宏观的,那么这个系统的波动太小了,宏观上无法检测到。这就是所谓的热力学极限。实际上,物质的分子性质和动量转移的量子性质由于它们太小而看不见,已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中,平衡的波动概念是没有位置的。”<br />
<br />
If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
<br />
如果系统被重复细分,最终产生的系统足够小,可以表现出明显的波动。这是一个介观层面的研究。波动则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
<br />
An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process." This illustrates the importance for thermodynamics of the concept of temperature.<br />
<br />
热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
<br />
<br />
<br />
If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在波动过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,即需要量子统计力学。波动可以变得相对占主导地位,测量问题变得重要。<br />
<br />
Thermal equilibrium is achieved when two systems in thermal contact with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<br />
<br />
当两个相互热接触的系统不再有净能量交换时,就会产生热平衡。因此,如果两个系统处于热平衡,那么它们的温度是相同的。<br />
<br />
<br />
<br />
The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
<br />
"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有时间趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的标称值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微波动期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。非已知属于平衡状态的标称值,否则根据单一的度量无法进行判断。<br />
<br />
Thermal equilibrium occurs when a system's macroscopic thermal observables have ceased to change with time. For example, an ideal gas whose distribution function has stabilised to a specific Maxwell–Boltzmann distribution would be in thermal equilibrium. This outcome allows a single temperature and pressure to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<br />
<br />
当系统的宏观热观测值不再随着时间变化时,就会出现热平衡。例如,一种分布函数稳定到一个特定的麦克斯韦-波兹曼分布的理想气体即处于热平衡状态。这个结果可以将单一的温度和压力归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是很有可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
<br />
=== Thermal equilibrium ===<br />
热平衡<br />
{{Main|Thermal equilibrium}}<br />
<br />
<br />
<br />
An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process."<ref>Eu, B.C. (2002), page 13.</ref> This illustrates the importance for thermodynamics of the concept of temperature.<br />
<br />
热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
<br />
A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<br />
<br />
一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数。<br />
<br />
<br />
<br />
[[Thermal equilibrium]] is achieved when two systems in [[thermal contact]] with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<ref>[[Raj Pathria|R. K. Pathria]], 1996</ref><br />
<br />
当两个相互'''<font color="#ff8000">热接触 Thermal Contact</font>'''的系统不再有净能量交换时,就会产生'''<font color="#ff8000">热平衡 Thermal Equilibrium</font>'''。因此,如果两个系统处于热平衡,那么它们的温度是相同的<br />
<br />
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
<br />
非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
<br />
<br />
<br />
Thermal equilibrium occurs when a system's [[macroscopic]] thermal observables have ceased to change with time. For example, an [[ideal gas]] whose [[Distribution function (physics)|distribution function]] has stabilised to a specific [[Maxwell–Boltzmann distribution]] would be in thermal equilibrium. This outcome allows a single [[temperature]] and [[pressure]] to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<ref>de Groot, S.R., Mazur, P. (1962), p. 44.</ref><br />
<br />
当一个系统的'''<font color="#ff8000">宏观 Macroscopic</font>'''热观测值不再随时间变化时,就会出现热平衡。例如,一种'''<font color="#ff8000">分布函数 Distribution Function</font>'''稳定到一个特定的'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''的'''<font color="#ff8000">理想气体 Ideal Gas</font>'''即处于热平衡状态。这个结果可以将单一的'''<font color="#ff8000">温度 Temperature</font>'''和'''<font color="#ff8000">压力 Pressure</font>'''归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
<br />
Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle. It states that a non-equilibrium system evolves such as to maximize its entropy production.<br />
<br />
定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
<br />
==Non-equilibrium==<br />
非平衡<br />
{{Main|Non-equilibrium thermodynamics}}<br />
<br />
<br />
<br />
Thermodynamic models <br />
<br />
热力学模型<br />
<br />
A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<ref>de Groot, S.R., Mazur, P. (1962), p. 43.</ref><br />
<br />
一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数<br />
<br />
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
<br />
非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
<br />
<br />
Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle.<ref>{{cite book|last1=Ziegler|first1=H.|title=An Introduction to Thermomechanics.|date=1983|location=North Holland, Amsterdam.}}</ref><ref>{{cite journal|last1=Onsager|first1=Lars|title=Reciprocal Relations in Irreversible Processes|journal=Phys. Rev.|date=1931|volume=37|issue=4|doi=10.1103/PhysRev.37.405|bibcode=1931PhRv...37..405O|pages=405–426|doi-access=free}}</ref> It states that a non-equilibrium system evolves such as to maximize its entropy production.<ref>{{cite book|last1=Kleidon|first1=A.|last2=et.|first2=al.|title=Non-equilibrium Thermodynamics and the Production of Entropy.|date=2005|edition=Heidelberg: Springer.}}</ref><ref>{{cite journal|last1=Belkin|first1=Andrey|last2=et.|first2=al.|title=Self-Assembled Wiggling Nano-Structures and the Principle of Maximum Entropy Production|journal=Sci. Rep.|doi=10.1038/srep08323|bibcode=2015NatSR...5E8323B|pmc=4321171|pmid=25662746|volume=5|year=2015|page=8323}}</ref><br />
<br />
定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
<br />
Topics in control theory<br />
<br />
控制理论主题<br />
<br />
==See also ==<br />
<br />
{{Portal|Chemistry}}<br />
<br />
;Thermodynamic models 热力学模型<br />
<br />
{{colbegin}}<br />
<br />
* [[Non-random two-liquid model]] (NRTL model) - Phase equilibrium calculations 非随机两液模型(NRTL 模型)-相平衡计算<br />
<br />
* [[UNIQUAC]] model - Phase equilibrium calculations UNIQUAC 模型-相平衡计算<br />
<br />
* [[Time crystal]] 时间晶体<br />
<br />
{{colend}}<br />
<br />
;Topics in control theory 控制理论主题<br />
<br />
{{colbegin}}<br />
<br />
* [[Steady state]] 稳态<br />
<br />
* [[Transient state]] 瞬态<br />
<br />
* [[Coefficient diagram method]] 系数图法<br />
<br />
* [[Control reconfiguration]] 控制重构<br />
<br />
* [[Cut-insertion theorem]] 切入定理<br />
<br />
* [[Feedback]] 反馈<br />
<br />
* [[H infinity]] H 无限<br />
<br />
* [[Hankel singular value]] 汉克尔奇异值<br />
<br />
* [[Krener's theorem]] 克雷纳定理<br />
<br />
* [[Lead-lag compensator]] 超前滞后补偿器<br />
<br />
* [[Minor loop feedback]] 小循环反馈<br />
<br />
* [[Minor loop feedback|Multi-loop feedback]] 小循环反馈 | 多循环反馈<br />
<br />
* [[Positive systems]] 正向系统<br />
<br />
* [[Radial basis function]] 径向基底函数<br />
<br />
Other related topics<br />
<br />
其他相关话题<br />
<br />
* [[Root locus]] 根轨迹<br />
<br />
* [[Signal-flow graph]]s 信号流图<br />
<br />
* [[Stable polynomial]] 稳定多项式<br />
<br />
* [[State space representation]] 状态空间<br />
<br />
* [[Underactuation]] 欠驱动<br />
<br />
* [[Youla–Kucera parametrization]] 尤拉-库切拉参数化<br />
<br />
* [[Markov chain approximation method]] 马尔可夫链近似法<br />
<br />
{{colend}}<br />
<br />
;Other related topics<br />
其他相关话题<br />
<br />
{{colbegin}}<br />
<br />
* [[Automation and remote control]] 自动化和远程控制<br />
<br />
* [[Bond graph]] 键合图<br />
<br />
* [[Control engineering]] 控制工程<br />
<br />
* [[Control–feedback–abort loop]] 控制-反馈-中止循环<br />
<br />
* [[Controller (control theory)]] 控制器(控制理论)<br />
<br />
* [[Cybernetics]] 控制论<br />
<br />
* [[Intelligent control]] 智能控制<br />
<br />
* [[Mathematical system theory]] 数学系统论<br />
<br />
* [[Negative feedback amplifier]] 负反馈放大器<br />
<br />
* [[People in systems and control]] 系统和控制中的人<br />
<br />
* [[Perceptual control theory]] 知觉控制理论<br />
<br />
* [[Systems theory]] 系统论<br />
<br />
* [[Time scale calculus]] 时间尺度演算<br />
<br />
{{colend}}<br />
<br />
<br />
<br />
== 编者推荐 ==<br />
===集智文章推荐===<br />
<br />
====[https://swarma.org/?p=21322 什么是非平衡态热力学 | 集智百科]====<br />
非平衡态热力学 Non-equilibrium thermodynamics 是热力学的一个分支,研究某些不处于热力学平衡中的物理系统<br />
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<br />
<br />
<br />
==General references==<br />
<br />
* Cesare Barbieri (2007) ''Fundamentals of Astronomy''. First Edition (QB43.3.B37 2006) CRC Press {{ISBN|0-7503-0886-9}}, {{ISBN|978-0-7503-0886-1}}<br />
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* Hans R. Griem (2005) ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}<br />
<br />
* C. Michael Hogan, Leda C. Patmore and Harry Seidman (1973) ''Statistical Prediction of Dynamic Thermal Equilibrium Temperatures using Standard Meteorological Data Bases'', Second Edition (EPA-660/2-73-003 2006) United States Environmental Protection Agency Office of Research and Development, Washington, D.C. [http://library.wur.nl/WebQuery/catalog/lang/1851848]<br />
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* F. Mandl (1988) ''Statistical Physics'', Second Edition, John Wiley & Sons<br />
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<br />
==References==<br />
<br />
{{Reflist|colwidth=35em}}<br />
<br />
<br />
<br />
==Cited bibliography==<br />
<br />
<br />
<br />
*Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', third edition, McGraw-Hill, London, {{ISBN|0-521-25445-0}}.<br />
<br />
*Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, {{ISBN|0-88318-797-3}}.<br />
<br />
*Beattie, J.A., Oppenheim, I. (1979). ''Principles of Thermodynamics'', Elsevier Scientific Publishing, Amsterdam, {{ISBN|0-444-41806-7}}.<br />
<br />
*[[Ludwig Boltzmann|Boltzmann, L.]] (1896/1964). ''Lectures on Gas Theory'', translated by S.G. Brush, University of California Press, Berkeley.<br />
<br />
*Buchdahl, H.A. (1966). ''The Concepts of Classical Thermodynamics'', Cambridge University Press, Cambridge UK.<br />
<br />
*[[Herbert Callen|Callen, H.B.]] (1960/1985). ''Thermodynamics and an Introduction to Thermostatistics'', (1st edition 1960) 2nd edition 1985, Wiley, New York, {{ISBN|0-471-86256-8}}.<br />
<br />
*[[Constantin Carathéodory|Carathéodory, C.]] (1909). [https://web.archive.org/web/20160304213645/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0067&DMDID=DMDLOG_0033&L=1 Untersuchungen über die Grundlagen der Thermodynamik], ''[[Mathematische Annalen]]'', '''67''': 355–386. A translation may be found [http://neo-classical-physics.info/uploads/3/0/6/5/3065888/caratheodory_-_thermodynamics.pdf here]. Also a mostly reliable [https://books.google.com/books?id=xwBRAAAAMAAJ&q=Investigation+into+the+foundations translation is to be found] at Kestin, J. (1976). ''The Second Law of Thermodynamics'', Dowden, Hutchinson & Ross, Stroudsburg PA.<br />
<br />
*[[Sydney Chapman (mathematician)|Chapman, S.]], [[Thomas George Cowling|Cowling, T.G.]] (1939/1970). ''The Mathematical Theory of Non-uniform gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases'', third edition 1970, Cambridge University Press, London.<br />
<br />
*Crawford, F.H. (1963). ''Heat, Thermodynamics, and Statistical Physics'', Rupert Hart-Davis, London, Harcourt, Brace & World, Inc.<br />
<br />
*de Groot, S.R., Mazur, P. (1962). ''Non-equilibrium Thermodynamics'', North-Holland, Amsterdam. Reprinted (1984), Dover Publications Inc., New York, {{ISBN|0486647412}}.<br />
<br />
*Denbigh, K.G. (1951). ''Thermodynamics of the Steady State'', Methuen, London.<br />
<br />
*Eu, B.C. (2002). ''Generalized Thermodynamics. The Thermodynamics of Irreversible Processes and Generalized Hydrodynamics'', Kluwer Academic Publishers, Dordrecht, {{ISBN|1-4020-0788-4}}.<br />
<br />
*Fitts, D.D. (1962). ''Nonequilibrium thermodynamics. A Phenomenological Theory of Irreversible Processes in Fluid Systems'', McGraw-Hill, New York.<br />
<br />
*[[Josiah Willard Gibbs|Gibbs, J.W.]] (1876/1878). On the equilibrium of heterogeneous substances, ''Trans. Conn. Acad.'', '''3''': 108–248, 343–524, reprinted in ''The Collected Works of J. Willard Gibbs, Ph.D, LL. D.'', edited by W.R. Longley, R.G. Van Name, Longmans, Green & Co., New York, 1928, volume 1, pp.&nbsp;55–353.<br />
<br />
*Griem, H.R. (2005). ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}.<br />
<br />
*[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', fifth revised edition, North-Holland, Amsterdam.<br />
<br />
*Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of ''Thermodynamics'', pages 1–97 of volume 1, ed. W. Jost, of ''Physical Chemistry. An Advanced Treatise'', ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081.<br />
<br />
*[[John Gamble Kirkwood|Kirkwood, J.G.]], Oppenheim, I. (1961). ''Chemical Thermodynamics'', McGraw-Hill Book Company, New York.<br />
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*Landsberg, P.T. (1961). ''Thermodynamics with Quantum Statistical Illustrations'', Interscience, New York.<br />
<br />
*{{cite journal |last1=Lieb |first1=E. H. |last2=Yngvason |first2=J. |year=1999 |title=The Physics and Mathematics of the Second Law of Thermodynamics |journal=Phys. Rep. |volume=310 |issue= 1|pages=1–96 |doi= 10.1016/S0370-1573(98)00082-9|arxiv = cond-mat/9708200 |bibcode = 1999PhR...310....1L |s2cid=119620408 }}<br />
<br />
*Levine, I.N. (1983), ''Physical Chemistry'', second edition, McGraw-Hill, New York, {{ISBN|978-0072538625}}.<br />
<br />
*{{cite journal | last1 = Maxwell | first1 = J.C. | authorlink = James Clerk Maxwell | year = 1867 | title = On the dynamical theory of gases | url = | journal = Phil. Trans. Roy. Soc. London | volume = 157 | issue = | pages = 49–88 }}<br />
<br />
*[[Philip M. Morse|Morse, P.M.]] (1969). ''Thermal Physics'', second edition, W.A. Benjamin, Inc, New York.<br />
<br />
*Münster, A. (1970). ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London.<br />
<br />
*[[J.R. Partington|Partington, J.R.]] (1949). ''An Advanced Treatise on Physical Chemistry'', volume 1, ''Fundamental Principles. The Properties of Gases'', Longmans, Green and Co., London.<br />
<br />
*[[Brian Pippard|Pippard, A.B.]] (1957/1966). ''The Elements of Classical Thermodynamics'', reprinted with corrections 1966, Cambridge University Press, London.<br />
<br />
* [[Max Planck|Planck. M.]] (1914). [https://archive.org/details/theoryofheatradi00planrich ''The Theory of Heat Radiation''], a translation by Masius, M. of the second German edition, P. Blakiston's Son & Co., Philadelphia.<br />
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*[[Ilya Prigogine|Prigogine, I.]] (1947). ''Étude Thermodynamique des Phénomènes irréversibles'', Dunod, Paris, and Desoers, Liège.<br />
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*[[Ilya Prigogine|Prigogine, I.]], Defay, R. (1950/1954). ''Chemical Thermodynamics'', Longmans, Green & Co, London.<br />
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*Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005). ''Physical Chemistry'', fourth edition, Wiley, Hoboken NJ.<br />
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*[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966). ''Elements of Thermodynamics'', Addison-Wesley Publishing, Reading MA.<br />
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*{{cite journal|last=Thomson|first=W.|author-link=William Thomson, 1st Baron Kelvin|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Transactions of the Royal Society of Edinburgh|date=March 1851|volume=XX|issue=part II|pages=261–268; 289–298}} Also published in {{cite journal|last=Thomson|first=W.|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Phil. Mag. |date=December 1852 |volume=IV |series=4 |issue=22 |pages=8–21 |url=https://archive.org/details/londonedinburghp04maga |accessdate=25 June 2012}}<br />
<br />
*[[László Tisza|Tisza, L.]] (1966). ''Generalized Thermodynamics'', M.I.T Press, Cambridge MA.<br />
<br />
*[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963). ''Lectures in Statistical Mechanics'', American Mathematical Society, Providence RI.<br />
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*Waldram, J.R. (1985). ''The Theory of Thermodynamics'', Cambridge University Press, Cambridge UK, {{ISBN|0-521-24575-3}}.<br />
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*[[Mark Zemansky|Zemansky, M.]] (1937/1968). ''Heat and Thermodynamics. An Intermediate Textbook'', fifth edition 1967, McGraw–Hill Book Company, New York.<br />
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== External links ==<br />
<br />
Category:Equilibrium chemistry<br />
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类别: 平衡化学<br />
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*[http://ads.harvard.edu/books/1989fsa..book/AbookC15.pdf Breakdown of Local Thermodynamic Equilibrium] George W. Collins, The Fundamentals of Stellar Astrophysics, Chapter 15<br />
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Category:Thermodynamic cycles<br />
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类别: 热力循环<br />
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*[http://spiff.rit.edu/classes/phys440/lectures/lte/lte.html Thermodynamic Equilibrium, Local and otherwise] lecture by Michael Richmond<br />
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Category:Thermodynamic processes<br />
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类别: 热力学过程<br />
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*[http://journals.ametsoc.org/doi/abs/10.1175/1520-0469%281970%29027%3C0711:NLTEIC%3E2.0.CO%3B2 Non-Local Thermodynamic Equilibrium in Cloudy Planetary Atmospheres] Paper by R. E. Samueison quantifying the effects due to non-LTE in an atmosphere<br />
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Category:Thermodynamic systems<br />
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类别: 热力学系统<br />
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*[http://scienceworld.wolfram.com/physics/LocalThermodynamicEquilibrium.html Local Thermodynamic Equilibrium]<br />
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Category:Thermodynamics<br />
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分类: 热力学<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Thermodynamic equilibrium]]. Its edit history can be viewed at [[平衡热力学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%B9%B3%E8%A1%A1%E7%83%AD%E5%8A%9B%E5%AD%A6&diff=21489平衡热力学2021-02-01T07:12:03Z<p>Jxzhou:/* Characteristics of a state of internal thermodynamic equilibrium 内部热力学平衡状态的特征 */</p>
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<div>此词条暂由小竹凉翻译,翻译字数共5339,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{short description|State of thermodynamic system(s) where no net macroscopic flow of matter or energy occurs}}<br />
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'''Thermodynamic equilibrium''' is an [[axiomatic]] concept of [[thermodynamics]]. It is an internal [[State variables|state]] of a single [[thermodynamic system]], or a relation between several thermodynamic systems connected by more or less permeable or impermeable [[Thermodynamic system#Walls|walls]]. In thermodynamic equilibrium there are no net [[macroscopic]] [[Flow (mathematics)|flows]] of [[matter]] or of [[energy]], either within a system or between systems. <br />
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Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium there are no net macroscopic flows of matter or of energy, either within a system or between systems. <br />
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'''热力学平衡'''是'''<font color="#ff8000">热力学 Thermodynamics</font>'''的一个'''<font color="#ff8000">不言自明的 Axiomatic</font>'''概念。它是单个'''<font color="#ff8000">热力学系统 Thermodynamic System</font>'''的内部'''<font color="#ff8000">状态 State</font>''',或者是几个热力学系统之间通过或多或少的渗透或不渗透的'''<font color="#ff8000">壁 Wall</font>'''连接的关系。无论是在一个系统内还是在系统之间,在热力学平衡中不存在'''<font color="#ff8000">物质 Matter</font>'''或'''<font color="#ff8000">能量 Energy</font>'''的净'''<font color="#ff8000">宏观 Macroscopic</font>''' '''<font color="#ff8000">流动 Flow</font>'''。<br />
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In a system that is in its own state of internal thermodynamic equilibrium, no [[macroscopic]] change occurs. <br />
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In a system that is in its own state of internal thermodynamic equilibrium, no macroscopic change occurs. <br />
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在一个处于内部热力学平衡状态的系统中,不会发生'''<font color="#ff8000">宏观 Macroscopic</font>'''变化。<br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual [[Thermal equilibrium|thermal]], [[Mechanical equilibrium|mechanical]], [[Chemical equilibrium|chemical]], and [[Radiative equilibrium|radiative]] equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a [[thermodynamic operation]]. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a thermodynamic operation. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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相互热力学平衡的体系同时处于互相之间的'''<font color="#ff8000">热 Thermal</font>'''平衡、'''<font color="#ff8000">力学 Mechanical</font>'''平衡、'''<font color="#ff8000">化学 Chemical</font>'''平衡和'''<font color="#ff8000">辐射 Radiative</font>'''平衡。系统可以处于其中一种相互平衡状态,尽管其他状态未平衡。在热力学平衡中所有的平衡同时并且无限期地保持,直到被'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''打破。在一个宏观平衡中,微观交换是完全或几乎完全平衡的;这是对宏观平衡概念的物理解释。<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform [[temperature]]. Its [[Intensive and extensive properties|intensive properties]], other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform temperature. Its intensive properties, other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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一个处于内部热力学状态平衡的热力学系统具有空间均匀的'''<font color="#ff8000">温度 Temperature</font>'''。除了温度以外,它的'''<font color="#ff8000">强度性质 Intensive Properties</font>'''可以由于周围环境施加的不变的长程力场而导致空间不均匀性。<br />
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In systems that are at a state of [[non-equilibrium]] there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a '''meta-stable equilibrium'''.<br />
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In systems that are at a state of non-equilibrium there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a meta-stable equilibrium.<br />
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相比之下,处于'''<font color="#ff8000">非平衡状态 non-equilibrium</font>'''的系统中有物质或能量的净流动。如果这些变化可以在一个还没有发生的系统中被触发,那么这个系统就被称为处于一个'''亚稳定的平衡状态'''。<br />
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Though not a widely named a "law," it is an [[axiom]] of thermodynamics that there exist states of thermodynamic equilibrium. The [[second law of thermodynamics]] states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the [[entropy|entropies]] of the portions.<br />
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Though not a widely named a "law," it is an axiom of thermodynamics that there exist states of thermodynamic equilibrium. The second law of thermodynamics states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the entropies of the portions.<br />
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虽然不是一个广泛命名的“定律” ,但存在热力学平衡状态是一个热力学'''<font color="#ff8000">公理 Axiom</font>'''。'''<font color="#ff8000">热力学第二定律 second law of thermodynamics</font>'''指出,当一个物质体从一个平衡状态开始,在这个状态中,它的一部分被或多或少渗透或不渗透的分区保持在不同的状态,并且是孤立的,热力学操作移除分区或使分区更具渗透性,然后它会自发地达到自己内部热力学平衡的新状态,并伴随着部分'''<font color="#ff8000">熵 Entropy</font>'''的总和增加。<br />
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== Overview 概览==<br />
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{{Thermodynamics|cTopic=[[Thermodynamic system|Systems]]}}<br />
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Classical thermodynamics deals with states of [[dynamic equilibrium]]. The state of a system at thermodynamic equilibrium is the one for which some [[thermodynamic potential]] is minimized, or for which the [[entropy]] (''S'') is maximized, for specified conditions. One such potential is the [[Helmholtz free energy]] (''A''), for a system with surroundings at controlled constant temperature and volume:<br />
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Classical thermodynamics deals with states of dynamic equilibrium. The state of a system at thermodynamic equilibrium is the one for which some thermodynamic potential is minimized, or for which the entropy (S) is maximized, for specified conditions. One such potential is the Helmholtz free energy (A), for a system with surroundings at controlled constant temperature and volume:<br />
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经典热力学研究'''<font color="#ff8000">动态平衡 Dynamic Equilibrium</font>'''的状态。系统的热力学平衡状态是对于特定的条件,一些'''<font color="#ff8000">热力学势 Thermodynamic Potential</font>'''被最小化,或者'''<font color="#ff8000">熵 Entropy</font>'''(S)被最大化。对于一个周围环境温度和体积恒定的系统,其中一个这样的热力学势是'''<font color="#ff8000">亥姆霍兹自由能 Helmholtz Free Energy</font>'''(A):<br />
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:<math>A = U - TS</math><br />
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<math>A = U - TS</math><br />
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A = U-TS<br />
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Another potential, the [[Gibbs free energy]] (''G''), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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Another potential, the Gibbs free energy (G), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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在恒定温度和压力的系统中,另一个热力学势'''<font color="#ff8000">吉布斯自由能 Gibbs Free Energy</font>'''(G)在热力学平衡状态最小:<br />
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:<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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where ''T'' denotes the absolute thermodynamic temperature, ''P'' the pressure, ''S'' the entropy, ''V'' the volume, and ''U'' the internal energy of the system.<br />
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where T denotes the absolute thermodynamic temperature, P the pressure, S the entropy, V the volume, and U the internal energy of the system.<br />
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其中 T 表示热力学绝对温度,P 表示压强,S 表示熵,V 表示体积,U 表示体系的内能。<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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热力学平衡是一种独特的稳定定态,当系统长时间与周围环境相互作用时,它可以被接近或最终到达。上述势能是数学构造的热力学量,在特定的环境条件下最小化。<br />
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== Conditions 条件==<br />
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* For a completely isolated system, ''S'' is maximum at thermodynamic equilibrium. 对于一个完全孤立的系统,S在热力学平衡中取最大值。<br />
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* For a system with controlled constant temperature and volume, ''A'' is minimum at thermodynamic equilibrium. 对于一个恒定温度和体积的系统来说,A在热力学平衡中取最小值。<br />
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* For a system with controlled constant temperature and pressure, ''G'' is minimum at thermodynamic equilibrium. 对于一个恒温恒压的系统,G在热力学平衡中取最小值。<br />
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The various types of equilibriums are achieved as follows:<br />
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The various types of equilibriums are achieved as follows:<br />
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实现各种类型的平衡的方法如下:<br />
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*Two systems are in ''thermal equilibrium'' when their [[temperature]]s are the same. 当两个系统的'''<font color="#ff8000">温度 Temperature</font>'''相同时,它们就处于''热平衡状态''<br />
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*Two systems are in ''mechanical equilibrium'' when their [[pressure]]s are the same. 当两个体系的'''<font color="#ff8000">压力 Pressure</font>'''相同时,它们就处于''力学平衡''<br />
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*Two systems are in ''diffusive equilibrium'' when their [[chemical potential]]s are the same. 当两个题体系的'''<font color="#ff8000">化学势 Chemical Potential</font>'''相同时,它们就处于''扩散平衡''<br />
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*All [[forces]] are balanced and there is no significant external driving force.<br />
所有的'''<font color="#ff8000">力 Force</font>'''都是平衡的,没有明显的外部驱动力<br />
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==Relation of exchange equilibrium between systems 系统之间的交换均衡关系==<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability.<ref name="Nster_a">Münster, A. (1970), p. 49.</ref> When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability. When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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通常,热力学系统的周围环境也可以被看作是另一个热力学系统。在这种观点中,我们可以把系统及其周围环境看作是相互接触的两个系统,远程作用力也将它们联系在一起。系统的包围物是两个系统之间的接触面或边界。在热力学形式中,该表面被认为具有特定的渗透性质。例如,接触的表面可能被认为只能透热,使能量只能作为热传递。当远程力在时间上不发生变化,两个系统之间的热量传递减慢并最终永久停止时,这两个系统被称为热平衡; 这就是接触平衡的一个例子。其它类型的接触平衡可用其它类型的比渗透率来定义。当两个系统对于某一特定类型的渗透率处于接触平衡时,它们具有属于该特定类型渗透率的强变量的共同值。这种强度变量的例子有温度、压力、化学势。<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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接触平衡也可视为交换平衡。在接触平衡状态下,两系统之间某些量的传递速率存在零平衡。例如,对于只能透热的壁,内能作为热在两个系统之间的扩散速率是相等并反向的。两个系统之间的绝热壁只对作为功传递的能量有渗透作用; 在力学平衡,两个系统之间作为功的能量传递速率相等且相反。如果是一个简单的壁,那么通过它的体积转移率也是相等且相反的; 即它两边的压力是相等的。如果绝热壁比较复杂,有一种杠杆,有一个面积比,那么两个体系在交换平衡中的压力与体积交换比成反比,这使得转移率的零平衡作功。<br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<ref name="Planck 1914 40">[[Max Planck|Planck. M.]] (1914), p. 40.</ref><br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<br />
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辐射交换可以发生在两个不同的系统之间。当两个体系温度相同时,辐射交换平衡占优势。<br />
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==Thermodynamic state of internal equilibrium of a system 系统内部平衡的热力学状态==<br />
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A collection of matter may be entirely [[Isolated system|isolated]] from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium.<ref>Haase, R. (1971), p. 4.</ref><ref>Callen, H.B. (1960/1985), p. 26.</ref> (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics.<ref>{{Cite journal |doi = 10.1119/1.4914528|bibcode = 2015AmJPh..83..628M|title = Time and irreversibility in axiomatic thermodynamics|year = 2015|last1 = Marsland|first1 = Robert|last2 = Brown|first2 = Harvey R.|last3 = Valente|first3 = Giovanni|journal = American Journal of Physics|volume = 83|issue = 7|pages = 628–634}}</ref> One textbook<ref>[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963), p. 5.</ref> calls it the "zeroth law", remarking that the authors think this more befitting that title than its [[Zeroth law of thermodynamics|more customary definition]], which apparently was suggested by [[Ralph H. Fowler|Fowler]].)<br />
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A collection of matter may be entirely isolated from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium. (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics. One textbook calls it the "zeroth law", remarking that the authors think this more befitting that title than its more customary definition, which apparently was suggested by Fowler.)<br />
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物质的集合可能与其周围的环境完全'''<font color="#ff8000">孤立 Isolated</font>'''。如果它在无限长的时间内一直保持不受干扰,按照经典热力学假定,它处于一个没有发生任何变化,没有流动的状态,即内部平衡的热力学状态。(这种假设有时被称为“负第一”热力学定律,但并不常见。有教科书称之为“第零定律” ,作者'''<font color="#ff8000">福勒 Fowler</font>'''认为这个名称是'''<font color="#ff8000">更符合惯例的定义 More Customary Definition</font>'''。)<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a [[thermodynamic operation]] be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a thermodynamic operation be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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这种状态是所谓的经典热力学或平衡态热力学的主要关注点,因为它们是系统中被认为在这门学科中得到很好定义的唯一状态。一个与另一个系统处于接触平衡状态可以被一个'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''隔离,在隔离发生时,其内部不会发生任何变化。因此,一个与另一个系统处于接触平衡状态时也可以被视为处于其自身的内部热力学平衡状态。<br />
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==Multiple contact equilibrium 多点接触平衡==<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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热力学形式允许一个系统同时与其他多个系统接触,这些系统可能有也可能没有相互接触,且这些接触具有不同的渗透性。如果这些系统都与世界其他部分相互隔离,那么它们彼此之间就会达到各自的接触平衡。<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy.<ref name="Caratheodory">Carathéodory, C. (1909).</ref><ref>Prigogine, I. (1947), p. 48.</ref><ref>Landsberg, P. T. (1961), pp. 128–142.</ref><ref>Tisza, L. (1966), p. 108.</ref> Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy. Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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如果几个系统彼此之间没有绝热壁,但是它们与世界其他部分共同隔离,那么它们就会达到多重接触平衡状态,且有共同的温度,总的内能和熵。在众多强度量中,这是温度的一个独特性质。即使在远距离作用力存在的情况下,它也是有效的。(也就是说,没有“力”可以维持温度的差异。)举个例子,在热力学平衡的一个垂直的引力场系统中,顶部壁面的压力比底部壁面的压力小,但是各处的温度都是一样的。<br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural [[thermodynamic process]].<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), § 1.12.</ref> It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings.<ref>Levine, I.N. (1983), p. 40.</ref><ref>Lieb, E.H., Yngvason, J. (1999), pp. 17–18.</ref> The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of [[Second law of thermodynamics#Description#Kelvin statement|"inanimate" agency]]; a system in thermodynamic equilibrium is inanimate.<ref>[[William Thomson, 1st Baron Kelvin|Thomson, W.]] (1851).</ref><br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural thermodynamic process. It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings. The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of "inanimate" agency; a system in thermodynamic equilibrium is inanimate.<br />
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热力操作可能作为一个事件发生在周围环境的壁上,既不直接影响与周围环境联系的壁,也不直接影响其内部,且发生在一个明确的有限的时间内。例如,一个固定的绝热壁可以在环境中被放置或拆除。由于这种操作仅限于周围环境,系统可能会在一段时间内远离自身最初的内部状态---- 热力学平衡。根据热力学第二定律的说法,整体经历了变化并最终与周围环境达到了新的平衡。继Planck之后,这一连串的事件被称为自然'''<font color="#ff8000">热力学过程 Thermodynamic Process</font>'''。即使在这个过程中,当系统和周围环境都不处于明确的内部平衡状态时,存在着暂时偏离热力学平衡的现象,由于初始状态和最终状态都是热力学平衡的,这在平衡热力学中也是允许的。一个自然过程在其主要部分中以有限的速率进行,因此,它从根本上不同于虚构的准静态“过程”;即不在整个过程中无限缓慢地进行而且虚构地“可逆”。经典热力学允许,即使一个过程可能需要很长的时间才能达到热力学平衡,如果主要部分的过程是在一个有限的比率中,那么它被认为是自然的,并受制于热力学第二定律,即不可逆的。工程设计的机器、人工设备和操作是允许在周围环境中进行的。允许在环境中而不是在系统中进行此类操作和设备,是开尔文在他的一个热力学第二定律的陈述中提到'''<font color="#ff8000">无生命机构 Inanimate Agency</font>'''的原因; 在热力学平衡的系统是无生命的。<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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否则,热力操作可能会直接影响系统的壁。<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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通常可以很方便地假设周围的某些子系统比系统大得多,以至于这个过程只能影响周围子系统的强度变量,然后将这些子系统称为相关强度变量的储备库。<br />
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== Local and global equilibrium 局部和全局均衡==<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by [[intensive quantity|intensive]] parameters. As an example, [[temperature]] controls [[Heat equation|heat exchanges]]. ''Global thermodynamic equilibrium'' (GTE) means that those [[intensive quantity|intensive]] parameters are homogeneous throughout the whole system, while ''local thermodynamic equilibrium'' (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by intensive parameters. As an example, temperature controls heat exchanges. Global thermodynamic equilibrium (GTE) means that those intensive parameters are homogeneous throughout the whole system, while local thermodynamic equilibrium (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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区分全局性和局部性热力学平衡是很有用的。在热力学中,系统内部和系统与外部之间的交换是由'''<font color="#ff8000">强度 Intensive</font>'''参数控制的。例如,'''<font color="#ff8000">温度 Temperature</font>'''控制'''<font color="#ff8000">热交换 Heat Equation</font>'''。全局热力学平衡(GTE)意味着这些'''<font color="#ff8000">强度 Intensive</font>'''参数在整个系统中是均匀的,而局部热力学平衡(LTE)意味着这些强度参数在空间和时间上是变化的,但变化如此缓慢,以至于对于任何一点,人们都可以假设在该点的某个邻域存在热力学平衡。<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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如果对系统的描述要求强度参数的变化过大,那么这些强度参数的定义所依据的假设本身就会失效,系统将既不处于全局平衡,也不处于局部平衡。例如,粒子需要一定数量的碰撞来平衡其周围环境。如果在这些碰撞中移动的平均距离使它离开平衡邻域,它将永远不会平衡,也就不会有 LTE。根据定义,温度与平衡邻域的平均内部能量成正比。由于没有达到平衡邻域,温度的概念就不成立,温度也就变得无法定义。<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to [[massive]] particles. In a [[radiation|radiating]] gas, the [[photon]]s being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to massive particles. In a radiating gas, the photons being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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值得注意的是,这种局部平衡可能只适用于系统中的某个粒子子集。例如,LTE 通常只适用于'''<font color="#ff8000">大 Massive</font>'''质量粒子。在'''<font color="#ff8000">辐射 Radiation</font>'''气体中,被气体发射和吸收的'''<font color="#ff8000">光子 Photon</font>'''不需要彼此在一个热力学平衡内,或与气体中的大量粒子在一起,LTE 才能存在。在某些情况下,自由电子并不需要与大得多的原子或分子处于平衡状态,LTE 才能存在。<br />
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As an example, LTE will exist in a glass of water that contains a melting [[ice cube]]. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the [[Maxwell–Boltzmann distribution]] for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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As an example, LTE will exist in a glass of water that contains a melting ice cube. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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例如,LTE 将存在于一个装有正在融化的'''<font color="#ff8000">冰块 Ice Cube</font>'''的水杯中。玻璃杯内的温度可以在任何时候定义,但是离冰块近的地方要比离冰块远的地方冷。如果观察到位于给定点附近的分子的能量,它们将按照麦克斯韦-波兹曼分布在一定温度下的分布。如果观察到位于另一点附近的分子的能量,它们将按照'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''分布到另一个温度。<br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural [[transport phenomena]] may lead a system from local to global thermodynamic equilibrium. Going back to our example, the [[diffusion]] of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<ref>H.R. Griem, 2005</ref><br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural transport phenomena may lead a system from local to global thermodynamic equilibrium. Going back to our example, the diffusion of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<br />
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局部热力学平衡不需要局部或全局的平稳性。换句话说,每一个小区域不需要有一个恒定的温度。然而,它确实要求每个小的局部变化缓慢到足以维持其局部麦克斯韦-波尔兹曼速度分布。全局非平衡态只有通过系统与外界的交换才能保持稳定。例如,通过在水杯中不断添加细粉冰来补偿熔化,并持续排出融水,可以保持全局稳定的静态。自然'''<font color="#ff8000">输运现象 Transport Phenomena</font>'''会使一个局部热力学平衡系统逐渐达到全局的热力学平衡。回顾我们的例子,热量的扩散将导致我们的玻璃杯水流向全局热力学平衡,在这种状态下,玻璃杯的温度是完全均匀的。<br />
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==Reservations 保留意见==<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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学识渊博的笔者在热力学领域对热力学平衡描述时,经常对他们的描述附加条件或保留意见。有些笔者含蓄地保留了或多或少的空白,以待说明。<br />
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For example, one widely cited writer, [[Herbert Callen|H. B. Callen]] writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. ''Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!''"<ref>Callen, H.B. (1960/1985), p. 15.</ref><br />
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For example, one widely cited writer, H. B. Callen writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!"<br />
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例如,一位被广泛引用的作家'''<font color="#ff8000">H.B.卡伦 H.B.Callen</font>'''在这里写道: “实际上,很少有系统处于绝对和真正的平衡状态。”他提到了放射性过程,认为它们可能需要“宇宙时间才能完成,因此通常可以忽略”。他补充道: “在实践中,平衡的标准是循环的。在操作上,如果一个系统的性质一致地用热力学理论来描述,那么它就处于平衡状态! ”<br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<ref>Beattie, J.A., Oppenheim, I. (1979), p. 3.</ref><br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<br />
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J.A.贝蒂和 I.奥本海姆写道: “坚持对平衡定义的严格解释,将排除热力学应用于实际系统的所有状态。”<br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment",<ref>Callen, H.B. (1960/1985), p. 485.</ref> and cited by Adkins as having written a "classic text",<ref>Adkins, C.J. (1968/1983), p. ''xiii''.</ref> [[Brian Pippard|A.B. Pippard]] writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<ref>Pippard, A.B. (1957/1966), p. 6.</ref><br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment", and cited by Adkins as having written a "classic text", A.B. Pippard writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<br />
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Callen引用另一位作者的话说,他给出了“学术且严谨的论述” ,Adkins引用他的话说,他写了一本“经典著作”—— '''<font color="#ff8000">A.B.皮帕德 A.B.Pippard</font>'''在文中写道: “只要时间足够长,过冷水蒸汽最终会凝结,... ..。时间可能是漫长的,也许长达10年或者更长。就大多数目的而言,只要这种迅速的变化不是人为地刺激,这些系统就可以被视为处于平衡状态。”<br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster">Münster, A. (1970), p. 53.</ref><br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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另一位作者A.Münster,写道。他观察到热核反应发生的速度非常缓慢,以至于在热力学中可以忽略不计。他评论道: “‘绝对平衡’或‘所有可想象过程的平衡’的概念没有物理意义。”他说: “ ... 我们只能考虑特定过程和确定的实验条件下的平衡。”<br />
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According to [[László Tisza|L. Tisza]]: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<ref>Tisza, L. (1966), p. 119.</ref><br />
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According to L. Tisza: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<br />
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根据'''<font color="#ff8000">L.缇莎 L.Tisza</font>'''的说法: “ ... 在讨论接近绝对零度的现象时。经典理论的绝对预测变得特别模糊,因为在非平衡状态下发生冻结是非常普遍的。”<br />
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==Definitions 定义==<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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一个系统最普遍的热力学平衡是通过与周围环境的接触,允许所有化学物质和各种能量同时通过。热力学平衡中的系统可能以均匀加速度在空间中运动,但此时不能改变其形状或大小; 因此它是由空间中的刚性体积来定义的。它可能存在于外力场中,由远远大于系统本身的外部因素决定,因此系统内的事件不会对外力场产生相当大的影响。只有当外力场是均匀的,并且确定了它的均匀加速度,或者它处于一个非均匀力场中,但是由于表面的局部力,例如机械压力,使它保持静止时,这个系统才能处于热力学平衡。<br />
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Thermodynamic equilibrium is a [[primitive notion]] of the theory of thermodynamics. According to [[Philip M. Morse|P.M. Morse]]: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are ''not'' conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments."<ref>[[Philip M. Morse|Morse, P.M.]] (1969), p. 7.</ref> This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<ref>Bailyn, M. (1994), p. 20.</ref><br />
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Thermodynamic equilibrium is a primitive notion of the theory of thermodynamics. According to P.M. Morse: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are not conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments." This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<br />
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热力学平衡是热力学理论的一个'''<font color="#ff8000">基本概念 Primitive Notion</font>'''。'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''说: “应该强调的是,存在热力学状态这一事实,以及存在由平衡态唯一指定的热力学变量这一事实,并不是从某些哲学第一原理得出的逻辑结论。这些结论不可避免地来自两个多世纪的实验。”这意味着热力学平衡不能仅仅用热力学的其他理论概念来定义。M.Bailyn提出了一个基本的热力学定律理论,它定义并假设了热力学平衡的存在。<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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热力学平衡的教科书定义通常被仔细说明,并有些保留。<br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<ref>Münster, A. (1970), p. 52.</ref><br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<br />
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例如,A. Münster写道:“当一个孤立系统中没有以可测量的速率发生状态变化时,系统处于热力学平衡状态。”这里有两项保留:系统是孤立的;任何状态的变化都是不可测量的缓慢。他通过对在室温且没有催化剂的情况下混合氧和氢的说明,讨论了第二个条件。Münster指出,描述热力学平衡状态所需要的宏观变量比给定系统任何其他状态都少。这是部分,但不完全是,因为系统内和流过系统的所有流都是零。<br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in ''equilibrium''.<ref>Haase, R. (1971), pp. 3–4.</ref><br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in equilibrium.<br />
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R. Haase's的热力学演示并不从对热力学平衡的限制开始,因为他打算考虑非平衡态热力学。他考虑一个具有时间不变性质的任意系统。他通过切断除外力场以外的所有外部影响来测试它的热力学平衡。如果在绝缘之后,没有任何变化,他说,系统处于平衡状态。<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness".<ref>Callen, H.B. (1960/1985), p. 13.</ref> This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness". This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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在一个标题为“热力学平衡”的章节中,H.B. Callen在一个段落中定义了平衡状态.他指出,它们“是由系统内部的内在因素决定的”。它们是“终端状态” ,随着时间的推移,系统会以“冰川般缓慢”的速度朝着这个终端状态演化。这个说法并没有明确,对于热力学平衡系统必须是孤立的;;Callen也没有说明他所说的“内在因素”是什么意思。<br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<ref>Adkins, C.J. (1968/1983), p. ''7''.</ref><br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<br />
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另一位教科书作者,C.J.Adkins,明确允许热力学平衡在非孤立的系统中发生。然而,他的系统在物质转移方面是封闭的。他写道: “一般来说,热力学平衡的方法包括热和类似功的形式与周围环境的相互作用。”他将这种热力学平衡与只有通过热接触才能进行能量传递的热平衡相区别。<br />
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Another textbook author, [[J.R. Partington]], writes: "(i) ''An equilibrium state is one which is independent of time''." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..."<ref>Partington, J.R. (1949), p. 161.</ref> This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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Another textbook author, J.R. Partington, writes: "(i) An equilibrium state is one which is independent of time." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..." This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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另一位教科书作者'''<font color="#ff8000">J.R.帕廷顿 J.R.Partington</font>'''写道: “(i)平衡状态是独立于时间的状态。”但是,在提到“只是明显处于平衡状态”的系统时,他补充说: “这样的系统处于‘虚假平衡’状态。帕廷顿的陈述没有明确指出平衡是指一个孤立的系统。和Münster一样,Partington也指的是氧和氢的混合物。他补充说:“在一个真正的平衡状态,任何影响状态的外部条件的微小变化都会产生一个微小的状态变化... ... ”这个条件意味着热力学平衡必须在小的扰动下保持稳定; 这个要求对于热力学平衡的严格意义是必不可少的。<br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, ''thermodynamic—equilibrium.''"<ref>Crawford, F.H. (1963), p. 5.</ref><br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, thermodynamic—equilibrium."<br />
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在F.H.Crawford的一本学生教科书中,有一个标题为“热力学平衡”的章节。它区分了几种流动的驱动因素,然后说: “这些是孤立系统明显普遍趋向于完全机械、热、化学和电力状态的例子——或者简单地说,热力学平衡状态。”<br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in ''equilibrium''."<ref>Buchdahl, H.A. (1966), p. 8.</ref> Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being ''in equilibrium'' so long as experimental tests show that 'slow' transitions are in effect reversible."<ref>Buchdahl, H.A. (1966), p. 111.</ref> It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<ref>Adkins, C.J. (1968/1983), p. 8.</ref><br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in equilibrium." Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being in equilibrium so long as experimental tests show that 'slow' transitions are in effect reversible." It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<br />
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H.A. Buchdahl的一本关于经典热力学的专著考虑了热力学系统的平衡,而实际上并没有写热力学平衡一词。Buchdahl在提到封闭的物质交换系统时写道: “如果一个系统处于一个适当的静态状态,那么它将被称为处于平衡状态。”出于热力学描述的目的,Buchdahl的专著也讨论了非晶态玻璃。它说: “更准确地说,只要实验测试表明‘慢’跃迁实际上是可逆的,玻璃就可以被认为处于平衡状态。”通常来说不会将这一条件作为热力学平衡定义的一部分,而是假定相反的情况:如果热力学平衡中的一个物体受到足够慢的过程的影响,则该过程可被视为足够接近可逆,并且该物体在过程中足够接近热力学平衡。<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of ''contact equilibrium''. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by [[Constantin Carathéodory|C. Carathéodory]], and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster" /> Thermodynamic equilibrium for an open system means that, with respect to every relevant kind of selectively permeable wall, contact equilibrium exists when the respective intensive parameters of the system and surroundings are equal.<ref name="Nster_a" /> This definition does not consider the most general kind of thermodynamic equilibrium, which is through unselective contacts. This definition does not simply state that no current of matter or energy exists in the interior or at the boundaries; but it is compatible with the following definition, which does so state.<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of contact equilibrium. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by C. Carathéodory, and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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通过引入接触平衡的概念,A. Münster仔细地扩展了孤立系统热力学平衡的定义。这指定了在考虑非孤立系统的热力学平衡时允许的特定过程,并特别关心开放系统,这些开放系统可能从周围环境获得或丢失物质。感兴趣的系统和周围系统之间的接触平衡,通过一种特殊的壁与之接触,其余的连接系统是孤立的。这种特殊类型的壁也被'''<font color="#ff8000">C.喀喇西奥多里 C.Carathéodory</font>'''考虑过,其他作家也提到过。它们具有选择渗透性。它们可能只对机械功有渗透性,或者只对热有渗透性,或者只对某种特定的化学物质有渗透性。每个接触平衡定义了一个强度参数; 例如,只能透热的壁定义了一个经验温度。对于感兴趣的体系中每一种化学成分,都可以存在接触平衡。在接触平衡中,尽管有可能通过选择性渗透壁进行交换,但是感兴趣的系统是不变的,好像它处在孤立的热力学平衡。这个方案遵循的一般规则是: “ ... ... 我们只能考虑特定过程和特定实验条件下的平衡。”<br />
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[[Mark Zemansky|M. Zemansky]] also distinguishes mechanical, chemical, and thermal equilibrium. He then writes: "When the conditions for all three types of equilibrium are satisfied, the system is said to be in a state of thermodynamic equilibrium".<ref>[[Mark Zemansky|Zemansky, M.]] (1937/1968), p. 27.</ref><br />
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'''<font color="#ff8000">M.泽曼斯基 M.Zemansky</font>'''还区分了力学、化学和热平衡。他接着写道: “当这三种均衡的条件都满足时,系统就处于热力学平衡状态。”<br />
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P.M. Morse writes that thermodynamics is concerned with "states of thermodynamic equilibrium". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<br />
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[[Philip M. Morse|P.M. Morse]] writes that thermodynamics is concerned with "''states of thermodynamic equilibrium''". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<ref>[[Philip M. Morse|Morse, P.M.]] (1969), pp. 6, 37.</ref><br />
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'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''写道,热力学关注的是“热力学平衡状态”。在讨论物体与周围热源之间的热量传递时,他也使用了“热平衡”这个短语,尽管没有明确定义一个特殊的术语“热平衡”<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "full thermodynamic equilibrium state".<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "''full'' thermodynamic equilibrium state".<ref>Waldram, J.R. (1985), p. 5.</ref><br />
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J.R. Waldram写到了“一个明确的热力学状态”。他将一个系统定义为“当其观测量随时间停止变化时”的“热平衡”。但是在这个定义之下不久,他写到一块玻璃还没有达到“完全的热力学平衡状态”。<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, thermodynamic equilibrium is said to exist." He is not here considering the presence of an external force field.<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, ''thermodynamic equilibrium'' is said to exist." He is not here considering the presence of an external force field.<ref>Bailyn, M. (1994), p. 21.</ref><br />
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考虑到平衡状态,M.Bailyn写道: “每个强度变量都有自己的平衡类型。”然后他定义了热平衡、力学平衡和物质平衡。因此,他写道: “如果所有的强度变量都是一致的,那么热力学平衡就是存在的。”他在这里没有考虑外力场的存在。<br />
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J.G. Kirkwood and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of thermodynamic equilibrium if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<br />
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[[John Gamble Kirkwood|J.G. Kirkwood]] and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of ''thermodynamic equilibrium'' if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<ref>Kirkwood, J.G., Oppenheim, I. (1961), p. 2</ref><br />
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'''<font color="#ff8000">J.G.柯克伍德 J.G.Kirkwood</font>'''和 I.Oppenheim 将热力学平衡定义为: “一个系统处于热力学平衡状态,如果,在实验的时间内,(a)它强度特性与时间无关,(b)它的内部或与周围环境的边界处没有物质或能量流。”显然,他们没有把定义限制在孤立的或封闭的系统。它们不讨论“缓慢”发生变化的可能性,并且超出了分配给实验的时间范围。他们注意到,对于两个相接触的系统,存在一个强度性质的小子类,如果这个小子类的所有子类都相等,那么所有各自的强度性质都相等。只要满足其他一些条件,热力学平衡状态可以由这个子类定义。<br />
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==Characteristics of a state of internal thermodynamic equilibrium 内部热力学平衡状态的特征==<br />
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===Homogeneity in the absence of external forces 在没有外力的情况下的均匀性===<br />
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A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous.<ref name="Planck 1903 3"/> This means that the material in any small volume element of the system can be interchanged with the material of any other geometrically congruent volume element of the system, and the effect is to leave the system thermodynamically unchanged. In general, a strong external force field makes a system of a single phase in its own internal thermodynamic equilibrium inhomogeneous with respect to some [[Intensive and extensive properties|intensive variables]]. For example, a relatively dense component of a mixture can be concentrated by centrifugation.<br />
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在没有外力的情况下,由单一相组成的热力学系统,在其自身的内部热力学平衡中是均匀的。这意味着系统中任何小体积单元中的材料可以与系统中任何其他几何相等的体积单元中的材料互换,其效果是使系统在热力学上保持不变。一般来说,一个强外力场使得一个单相系统在其自身的内部热力学平衡中对于一些'''<font color="#ff8000">强度量 Intensive Variable</font>'''是不均匀的。例如,可以通过离心来浓缩混合物中相对密度较大的组分。<br />
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===Uniform temperature 均匀温度===<br />
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Such equilibrium inhomogeneity, induced by external forces, does not occur for the intensive variable [[temperature]]. According to [[Edward A. Guggenheim|E.A. Guggenheim]], "The most important conception of thermodynamics is temperature."<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), p.5.</ref> Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface."<ref name="Planck 1903 3">[[Max Planck|Planck, M.]] (1897/1927), p.3.</ref> As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.<br />
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这种由外力引起的平衡不均匀性,对于强度量'''<font color="#ff8000">温度 Temperature</font>'''不会发生。'''<font color="#ff8000">E.A.古根海姆 E.A. Guggenheim</font>'''认为,“热力学最重要的概念是温度。“Planck在介绍他的论文时,简要叙述了热、温度和热平衡,然后宣布: ”在下文中,我们将主要讨论任何形式的均匀、各向同性的物体,它们的物质具有相同的温度和密度,并受到到处垂直于表面的均匀压力的作用。和Carathéodory 一样,Planck将表面效应、外场和各向异性晶体排除在外。虽然Planck提到了温度,但并没有明确提到热力学平衡的概念。相比之下,Carathéodory关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ,虽然没有明确地使用短语‘热力学平衡’ ,也没有明确地假设存在一个温度来定义它。<br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform.<ref name="Planck 1914 40"/> This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers.<ref>Gibbs, J.W. (1876/1878), pp. 144-150.</ref><ref>[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966), pp. 127–130.</ref><ref>Münster, A. (1970), pp. 309–310.</ref><ref>Bailyn, M. (1994), pp. 254-256.</ref><ref>{{cite journal | last1 = Verkley | first1 = W.T.M. | last2 = Gerkema | first2 = T. | year = 2004 | title = On maximum entropy profiles | journal = J. Atmos. Sci. | volume = 61 | issue = 8| pages = 931–936 | doi=10.1175/1520-0469(2004)061<0931:omep>2.0.co;2| bibcode = 2004JAtS...61..931V | doi-access = free }}</ref><ref>{{cite journal | last1 = Akmaev | first1 = R.A. | year = 2008 | title = On the energetics of maximum-entropy temperature profiles | url = | journal = Q. J. R. Meteorol. Soc. | volume = 134 | issue = 630| pages = 187–197 | doi=10.1002/qj.209| bibcode = 2008QJRMS.134..187A }}</ref> Considerations of kinetic theory or statistical mechanics also support this statement.<ref>Maxwell, J.C. (1867).</ref><ref>Boltzmann, L. (1896/1964), p. 143.</ref><ref>Chapman, S., Cowling, T.G. (1939/1970), Section 4.14, pp. 75–78.</ref><ref>[[J. R. Partington|Partington, J.R.]] (1949), pp. 275–278.</ref><ref>{{cite journal | last1 = Coombes | first1 = C.A. | last2 = Laue | first2 = H. | year = 1985 | title = A paradox concerning the temperature distribution of a gas in a gravitational field | url = | journal = Am. J. Phys. | volume = 53 | issue = 3| pages = 272–273 | doi=10.1119/1.14138| bibcode = 1985AmJPh..53..272C }}</ref><ref>{{cite journal | last1 = Román | first1 = F.L. | last2 = White | first2 = J.A. | last3 = Velasco | first3 = S. | year = 1995 | title = Microcanonical single-particle distributions for an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 16 | issue = 2| pages = 83–90 | doi=10.1088/0143-0807/16/2/008| bibcode = 1995EJPh...16...83R }}</ref><ref>{{cite journal | last1 = Velasco | first1 = S. | last2 = Román | first2 = F.L. | last3 = White | first3 = J.A. | year = 1996 | title = On a paradox concerning the temperature distribution of an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 17 | issue = | pages = 43–44 | doi=10.1088/0143-0807/17/1/008}}</ref><br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform. This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers. Considerations of kinetic theory or statistical mechanics also support this statement.<br />
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热力学平衡系统内的温度在时间和空间上都是均匀的。在一个处于内部热力学平衡的系统中,不存在净的内部宏观流动。特别是,这意味着系统的所有局部都处于相互辐射交换平衡。这意味着系统的温度在空间上是均匀的。这在所有情况下都是如此,包括那些非均匀外力场。对于外部施加的引力场,这可以使用拉格郎日乘子法通过变分的计算在宏观热力学术语中证明。动力学理论或统计力学也支持这种说法。<br />
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In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium.<ref name="Fitts 43"/><br />
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为了使一个系统处于它自己的内部热力学平衡状态,它必须处于它自己的内部热平衡状态是必要不充分的; 一个系统在到达内部热平衡之前到达内部力学平衡是可能的。<br />
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===Number of real variables needed for specification===<br />
规范所需的实变量数目<br />
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In his exposition of his scheme of closed system equilibrium thermodynamics, C. Carathéodory initially postulates that experiment reveals that a definite number of real variables define the states that are the points of the manifold of equilibria.<ref name="Caratheodory" /> In the words of Prigogine and Defay (1945): "It is a matter of experience that when we have specified a certain number of macroscopic properties of a system, then all the other properties are fixed."<ref>Prigogine, I., Defay, R. (1950/1954), p. 1.</ref><ref>Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005), p. 4.</ref> As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.<br />
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在他关于封闭系统平衡态热力学方案的论述中,C.Carathéodory 最初假定实验揭示了一定数量的实变量定义了作为平衡态流形点的状态。用 Prigogine 和 Defay (1945)的话说: “这是一个经验问题,当我们确定了一个系统一定数量的宏观属性时,那么所有其他属性都是固定的。如上所述,A. Münster认为,定义热力学平衡所需的变量数量对于给定孤立系统的任何状态来说都是最少的。如上所述,J.G. Kirkwood 和 I. Oppenheim 指出,热力学平衡状态可以由一个特殊子类的强度变量来定义,该子类中有一定数量的成员。<br />
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When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium. Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<br />
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当一个物质体从不均匀的非平衡状态或化学非平衡状态开始,然后被孤立,它自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如,在这种演变的许多情况下,内部机械平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是,在这种演变的许多情况下,热平衡的发展要比化学平衡快得多。<br />
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If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.<br />
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如果热力学平衡位于一个外力场中,那么通常只有温度在空间上是均匀的。如果外力场非零,温度以外的强度变量通常是不均匀的。在这种情况下,一般需要附加变量来描述空间非均匀性。<br />
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===Stability against small perturbations===<br />
对小扰动的稳定性<br />
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In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
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在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
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As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.<br />
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如上所述,J.R. Partington 指出热力学平衡状态在小的瞬态扰动下是稳定的。如果没有这个条件,一般来说,研究热力学平衡系统的实验就会遇到严重的困难。<br />
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To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics. But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
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考虑孤立热力学系统中的波动概念,一个方便的例子是由其广泛的状态变量、内能、体积和质量组成指定的系统。根据定义,它们是时不变的。根据定义,它们与它们的共轭状态密集函数的时不变名义值相结合,反向温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广泛的状态变量的值,不足以提供这些名义值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
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===Approach to thermodynamic equilibrium within an isolated system===<br />
孤立系统中的热力学平衡<br />
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It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.<br />
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可以承认,在重复测量这些共轭强度函数时,发现它们的值随时间略有不同。这种可变性被认为是由于内部波动。不同测量值平均到其名义值。<br />
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When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium.<ref name="Fitts 43">Fitts, D.D. (1962), p. 43.</ref> Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<ref>Denbigh, K.G. (1951), p. 42.</ref><br />
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当一个物质体从不均匀的非平衡状态或化学非平衡状态开始,然后被孤立,它自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如,在这种演变的许多情况下,内部机械平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是,在这种演变的许多情况下,热平衡的发展要比化学平衡快得多。<br />
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If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<br />
<br />
如果这个系统真的像经典热力学所假定的那样是宏观的,那么这个系统的波动太小了,宏观上无法检测到。这就是所谓的热力学极限。实际上,物质的分子性质和动量转移的量子性质由于它们太小而看不见,已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中,平衡的波动概念是没有位置的。”<br />
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===Fluctuations within an isolated system in its own internal thermodynamic equilibrium===<br />
孤立系统内部热力学平衡的波动<br />
<br />
<br />
If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
<br />
如果系统被重复细分,最终产生的系统足够小,可以表现出明显的波动。这是一个介观层面的研究。波动则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
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In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
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在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
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If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
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如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在波动过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,即需要量子统计力学。波动可以变得相对占主导地位,测量问题变得重要。<br />
<br />
To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics.<ref>Tschoegl, N.W. (2000). ''Fundamentals of Equilibrium and Steady-State Thermodynamics'', Elsevier, Amsterdam, {{ISBN|0-444-50426-5}}, p. 21.</ref> But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
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考虑孤立热力学系统中的波动概念,一个方便的例子是由其众多的状态变量,内能、体积和质量组成指定的系统。根据定义,它们是时不变的。根据定义,它们与它们的共轭状态密集函数的时不变名义值相结合,反向温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广泛的状态变量的值,不足以提供这些名义值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
<br />
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The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
<br />
"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有时间趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的标称值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微波动期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。非已知属于平衡状态的标称值,否则根据单一的度量无法进行判断。<br />
<br />
It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.<br />
<br />
可以承认,在重复测量这些共轭强度函数时,发现它们的值随时间略有不同。这种可变性被认为是由于内部波动。不同测量值平均到其名义值。<br />
<br />
<br />
<br />
If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<ref>Buchdahl, H.A. (1966), p. 16.</ref><br />
<br />
如果这个系统真的像经典热力学所假定的那样是宏观的,那么这个系统的波动太小了,宏观上无法检测到。这就是所谓的热力学极限。实际上,物质的分子性质和动量转移的量子性质由于它们太小而看不见,已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中,平衡的波动概念是没有位置的。”<br />
<br />
<br />
If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
<br />
如果系统被重复细分,最终产生的系统足够小,可以表现出明显的波动。这是一个介观层面的研究。波动则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
<br />
An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process." This illustrates the importance for thermodynamics of the concept of temperature.<br />
<br />
热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
<br />
<br />
<br />
If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在波动过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,即需要量子统计力学。波动可以变得相对占主导地位,测量问题变得重要。<br />
<br />
Thermal equilibrium is achieved when two systems in thermal contact with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<br />
<br />
当两个相互热接触的系统不再有净能量交换时,就会产生热平衡。因此,如果两个系统处于热平衡,那么它们的温度是相同的。<br />
<br />
<br />
<br />
The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
<br />
"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有时间趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的标称值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微波动期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。非已知属于平衡状态的标称值,否则根据单一的度量无法进行判断。<br />
<br />
Thermal equilibrium occurs when a system's macroscopic thermal observables have ceased to change with time. For example, an ideal gas whose distribution function has stabilised to a specific Maxwell–Boltzmann distribution would be in thermal equilibrium. This outcome allows a single temperature and pressure to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<br />
<br />
当系统的宏观热观测值不再随着时间变化时,就会出现热平衡。例如,一种分布函数稳定到一个特定的麦克斯韦-波兹曼分布的理想气体即处于热平衡状态。这个结果可以将单一的温度和压力归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是很有可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
<br />
=== Thermal equilibrium ===<br />
热平衡<br />
{{Main|Thermal equilibrium}}<br />
<br />
<br />
<br />
An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process."<ref>Eu, B.C. (2002), page 13.</ref> This illustrates the importance for thermodynamics of the concept of temperature.<br />
<br />
热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
<br />
A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<br />
<br />
一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数。<br />
<br />
<br />
<br />
[[Thermal equilibrium]] is achieved when two systems in [[thermal contact]] with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<ref>[[Raj Pathria|R. K. Pathria]], 1996</ref><br />
<br />
当两个相互'''<font color="#ff8000">热接触 Thermal Contact</font>'''的系统不再有净能量交换时,就会产生'''<font color="#ff8000">热平衡 Thermal Equilibrium</font>'''。因此,如果两个系统处于热平衡,那么它们的温度是相同的<br />
<br />
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
<br />
非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
<br />
<br />
<br />
Thermal equilibrium occurs when a system's [[macroscopic]] thermal observables have ceased to change with time. For example, an [[ideal gas]] whose [[Distribution function (physics)|distribution function]] has stabilised to a specific [[Maxwell–Boltzmann distribution]] would be in thermal equilibrium. This outcome allows a single [[temperature]] and [[pressure]] to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<ref>de Groot, S.R., Mazur, P. (1962), p. 44.</ref><br />
<br />
当一个系统的'''<font color="#ff8000">宏观 Macroscopic</font>'''热观测值不再随时间变化时,就会出现热平衡。例如,一种'''<font color="#ff8000">分布函数 Distribution Function</font>'''稳定到一个特定的'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''的'''<font color="#ff8000">理想气体 Ideal Gas</font>'''即处于热平衡状态。这个结果可以将单一的'''<font color="#ff8000">温度 Temperature</font>'''和'''<font color="#ff8000">压力 Pressure</font>'''归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
<br />
Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle. It states that a non-equilibrium system evolves such as to maximize its entropy production.<br />
<br />
定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
<br />
==Non-equilibrium==<br />
非平衡<br />
{{Main|Non-equilibrium thermodynamics}}<br />
<br />
<br />
<br />
Thermodynamic models <br />
<br />
热力学模型<br />
<br />
A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<ref>de Groot, S.R., Mazur, P. (1962), p. 43.</ref><br />
<br />
一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数<br />
<br />
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
<br />
非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
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<br />
Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle.<ref>{{cite book|last1=Ziegler|first1=H.|title=An Introduction to Thermomechanics.|date=1983|location=North Holland, Amsterdam.}}</ref><ref>{{cite journal|last1=Onsager|first1=Lars|title=Reciprocal Relations in Irreversible Processes|journal=Phys. Rev.|date=1931|volume=37|issue=4|doi=10.1103/PhysRev.37.405|bibcode=1931PhRv...37..405O|pages=405–426|doi-access=free}}</ref> It states that a non-equilibrium system evolves such as to maximize its entropy production.<ref>{{cite book|last1=Kleidon|first1=A.|last2=et.|first2=al.|title=Non-equilibrium Thermodynamics and the Production of Entropy.|date=2005|edition=Heidelberg: Springer.}}</ref><ref>{{cite journal|last1=Belkin|first1=Andrey|last2=et.|first2=al.|title=Self-Assembled Wiggling Nano-Structures and the Principle of Maximum Entropy Production|journal=Sci. Rep.|doi=10.1038/srep08323|bibcode=2015NatSR...5E8323B|pmc=4321171|pmid=25662746|volume=5|year=2015|page=8323}}</ref><br />
<br />
定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
<br />
Topics in control theory<br />
<br />
控制理论主题<br />
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==See also ==<br />
<br />
{{Portal|Chemistry}}<br />
<br />
;Thermodynamic models 热力学模型<br />
<br />
{{colbegin}}<br />
<br />
* [[Non-random two-liquid model]] (NRTL model) - Phase equilibrium calculations 非随机两液模型(NRTL 模型)-相平衡计算<br />
<br />
* [[UNIQUAC]] model - Phase equilibrium calculations UNIQUAC 模型-相平衡计算<br />
<br />
* [[Time crystal]] 时间晶体<br />
<br />
{{colend}}<br />
<br />
;Topics in control theory 控制理论主题<br />
<br />
{{colbegin}}<br />
<br />
* [[Steady state]] 稳态<br />
<br />
* [[Transient state]] 瞬态<br />
<br />
* [[Coefficient diagram method]] 系数图法<br />
<br />
* [[Control reconfiguration]] 控制重构<br />
<br />
* [[Cut-insertion theorem]] 切入定理<br />
<br />
* [[Feedback]] 反馈<br />
<br />
* [[H infinity]] H 无限<br />
<br />
* [[Hankel singular value]] 汉克尔奇异值<br />
<br />
* [[Krener's theorem]] 克雷纳定理<br />
<br />
* [[Lead-lag compensator]] 超前滞后补偿器<br />
<br />
* [[Minor loop feedback]] 小循环反馈<br />
<br />
* [[Minor loop feedback|Multi-loop feedback]] 小循环反馈 | 多循环反馈<br />
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* [[Positive systems]] 正向系统<br />
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* [[Radial basis function]] 径向基底函数<br />
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Other related topics<br />
<br />
其他相关话题<br />
<br />
* [[Root locus]] 根轨迹<br />
<br />
* [[Signal-flow graph]]s 信号流图<br />
<br />
* [[Stable polynomial]] 稳定多项式<br />
<br />
* [[State space representation]] 状态空间<br />
<br />
* [[Underactuation]] 欠驱动<br />
<br />
* [[Youla–Kucera parametrization]] 尤拉-库切拉参数化<br />
<br />
* [[Markov chain approximation method]] 马尔可夫链近似法<br />
<br />
{{colend}}<br />
<br />
;Other related topics<br />
其他相关话题<br />
<br />
{{colbegin}}<br />
<br />
* [[Automation and remote control]] 自动化和远程控制<br />
<br />
* [[Bond graph]] 键合图<br />
<br />
* [[Control engineering]] 控制工程<br />
<br />
* [[Control–feedback–abort loop]] 控制-反馈-中止循环<br />
<br />
* [[Controller (control theory)]] 控制器(控制理论)<br />
<br />
* [[Cybernetics]] 控制论<br />
<br />
* [[Intelligent control]] 智能控制<br />
<br />
* [[Mathematical system theory]] 数学系统论<br />
<br />
* [[Negative feedback amplifier]] 负反馈放大器<br />
<br />
* [[People in systems and control]] 系统和控制中的人<br />
<br />
* [[Perceptual control theory]] 知觉控制理论<br />
<br />
* [[Systems theory]] 系统论<br />
<br />
* [[Time scale calculus]] 时间尺度演算<br />
<br />
{{colend}}<br />
<br />
<br />
<br />
== 编者推荐 ==<br />
===集智文章推荐===<br />
<br />
====[https://swarma.org/?p=21322 什么是非平衡态热力学 | 集智百科]====<br />
非平衡态热力学 Non-equilibrium thermodynamics 是热力学的一个分支,研究某些不处于热力学平衡中的物理系统<br />
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<br />
<br />
<br />
==General references==<br />
<br />
* Cesare Barbieri (2007) ''Fundamentals of Astronomy''. First Edition (QB43.3.B37 2006) CRC Press {{ISBN|0-7503-0886-9}}, {{ISBN|978-0-7503-0886-1}}<br />
<br />
* Hans R. Griem (2005) ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}<br />
<br />
* C. Michael Hogan, Leda C. Patmore and Harry Seidman (1973) ''Statistical Prediction of Dynamic Thermal Equilibrium Temperatures using Standard Meteorological Data Bases'', Second Edition (EPA-660/2-73-003 2006) United States Environmental Protection Agency Office of Research and Development, Washington, D.C. [http://library.wur.nl/WebQuery/catalog/lang/1851848]<br />
<br />
* F. Mandl (1988) ''Statistical Physics'', Second Edition, John Wiley & Sons<br />
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<br />
<br />
==References==<br />
<br />
{{Reflist|colwidth=35em}}<br />
<br />
<br />
<br />
==Cited bibliography==<br />
<br />
<br />
<br />
*Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', third edition, McGraw-Hill, London, {{ISBN|0-521-25445-0}}.<br />
<br />
*Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, {{ISBN|0-88318-797-3}}.<br />
<br />
*Beattie, J.A., Oppenheim, I. (1979). ''Principles of Thermodynamics'', Elsevier Scientific Publishing, Amsterdam, {{ISBN|0-444-41806-7}}.<br />
<br />
*[[Ludwig Boltzmann|Boltzmann, L.]] (1896/1964). ''Lectures on Gas Theory'', translated by S.G. Brush, University of California Press, Berkeley.<br />
<br />
*Buchdahl, H.A. (1966). ''The Concepts of Classical Thermodynamics'', Cambridge University Press, Cambridge UK.<br />
<br />
*[[Herbert Callen|Callen, H.B.]] (1960/1985). ''Thermodynamics and an Introduction to Thermostatistics'', (1st edition 1960) 2nd edition 1985, Wiley, New York, {{ISBN|0-471-86256-8}}.<br />
<br />
*[[Constantin Carathéodory|Carathéodory, C.]] (1909). [https://web.archive.org/web/20160304213645/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0067&DMDID=DMDLOG_0033&L=1 Untersuchungen über die Grundlagen der Thermodynamik], ''[[Mathematische Annalen]]'', '''67''': 355–386. A translation may be found [http://neo-classical-physics.info/uploads/3/0/6/5/3065888/caratheodory_-_thermodynamics.pdf here]. Also a mostly reliable [https://books.google.com/books?id=xwBRAAAAMAAJ&q=Investigation+into+the+foundations translation is to be found] at Kestin, J. (1976). ''The Second Law of Thermodynamics'', Dowden, Hutchinson & Ross, Stroudsburg PA.<br />
<br />
*[[Sydney Chapman (mathematician)|Chapman, S.]], [[Thomas George Cowling|Cowling, T.G.]] (1939/1970). ''The Mathematical Theory of Non-uniform gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases'', third edition 1970, Cambridge University Press, London.<br />
<br />
*Crawford, F.H. (1963). ''Heat, Thermodynamics, and Statistical Physics'', Rupert Hart-Davis, London, Harcourt, Brace & World, Inc.<br />
<br />
*de Groot, S.R., Mazur, P. (1962). ''Non-equilibrium Thermodynamics'', North-Holland, Amsterdam. Reprinted (1984), Dover Publications Inc., New York, {{ISBN|0486647412}}.<br />
<br />
*Denbigh, K.G. (1951). ''Thermodynamics of the Steady State'', Methuen, London.<br />
<br />
*Eu, B.C. (2002). ''Generalized Thermodynamics. The Thermodynamics of Irreversible Processes and Generalized Hydrodynamics'', Kluwer Academic Publishers, Dordrecht, {{ISBN|1-4020-0788-4}}.<br />
<br />
*Fitts, D.D. (1962). ''Nonequilibrium thermodynamics. A Phenomenological Theory of Irreversible Processes in Fluid Systems'', McGraw-Hill, New York.<br />
<br />
*[[Josiah Willard Gibbs|Gibbs, J.W.]] (1876/1878). On the equilibrium of heterogeneous substances, ''Trans. Conn. Acad.'', '''3''': 108–248, 343–524, reprinted in ''The Collected Works of J. Willard Gibbs, Ph.D, LL. D.'', edited by W.R. Longley, R.G. Van Name, Longmans, Green & Co., New York, 1928, volume 1, pp.&nbsp;55–353.<br />
<br />
*Griem, H.R. (2005). ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}.<br />
<br />
*[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', fifth revised edition, North-Holland, Amsterdam.<br />
<br />
*Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of ''Thermodynamics'', pages 1–97 of volume 1, ed. W. Jost, of ''Physical Chemistry. An Advanced Treatise'', ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081.<br />
<br />
*[[John Gamble Kirkwood|Kirkwood, J.G.]], Oppenheim, I. (1961). ''Chemical Thermodynamics'', McGraw-Hill Book Company, New York.<br />
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*Landsberg, P.T. (1961). ''Thermodynamics with Quantum Statistical Illustrations'', Interscience, New York.<br />
<br />
*{{cite journal |last1=Lieb |first1=E. H. |last2=Yngvason |first2=J. |year=1999 |title=The Physics and Mathematics of the Second Law of Thermodynamics |journal=Phys. Rep. |volume=310 |issue= 1|pages=1–96 |doi= 10.1016/S0370-1573(98)00082-9|arxiv = cond-mat/9708200 |bibcode = 1999PhR...310....1L |s2cid=119620408 }}<br />
<br />
*Levine, I.N. (1983), ''Physical Chemistry'', second edition, McGraw-Hill, New York, {{ISBN|978-0072538625}}.<br />
<br />
*{{cite journal | last1 = Maxwell | first1 = J.C. | authorlink = James Clerk Maxwell | year = 1867 | title = On the dynamical theory of gases | url = | journal = Phil. Trans. Roy. Soc. London | volume = 157 | issue = | pages = 49–88 }}<br />
<br />
*[[Philip M. Morse|Morse, P.M.]] (1969). ''Thermal Physics'', second edition, W.A. Benjamin, Inc, New York.<br />
<br />
*Münster, A. (1970). ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London.<br />
<br />
*[[J.R. Partington|Partington, J.R.]] (1949). ''An Advanced Treatise on Physical Chemistry'', volume 1, ''Fundamental Principles. The Properties of Gases'', Longmans, Green and Co., London.<br />
<br />
*[[Brian Pippard|Pippard, A.B.]] (1957/1966). ''The Elements of Classical Thermodynamics'', reprinted with corrections 1966, Cambridge University Press, London.<br />
<br />
* [[Max Planck|Planck. M.]] (1914). [https://archive.org/details/theoryofheatradi00planrich ''The Theory of Heat Radiation''], a translation by Masius, M. of the second German edition, P. Blakiston's Son & Co., Philadelphia.<br />
<br />
*[[Ilya Prigogine|Prigogine, I.]] (1947). ''Étude Thermodynamique des Phénomènes irréversibles'', Dunod, Paris, and Desoers, Liège.<br />
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*[[Ilya Prigogine|Prigogine, I.]], Defay, R. (1950/1954). ''Chemical Thermodynamics'', Longmans, Green & Co, London.<br />
<br />
*Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005). ''Physical Chemistry'', fourth edition, Wiley, Hoboken NJ.<br />
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*[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966). ''Elements of Thermodynamics'', Addison-Wesley Publishing, Reading MA.<br />
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*{{cite journal|last=Thomson|first=W.|author-link=William Thomson, 1st Baron Kelvin|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Transactions of the Royal Society of Edinburgh|date=March 1851|volume=XX|issue=part II|pages=261–268; 289–298}} Also published in {{cite journal|last=Thomson|first=W.|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Phil. Mag. |date=December 1852 |volume=IV |series=4 |issue=22 |pages=8–21 |url=https://archive.org/details/londonedinburghp04maga |accessdate=25 June 2012}}<br />
<br />
*[[László Tisza|Tisza, L.]] (1966). ''Generalized Thermodynamics'', M.I.T Press, Cambridge MA.<br />
<br />
*[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963). ''Lectures in Statistical Mechanics'', American Mathematical Society, Providence RI.<br />
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*Waldram, J.R. (1985). ''The Theory of Thermodynamics'', Cambridge University Press, Cambridge UK, {{ISBN|0-521-24575-3}}.<br />
<br />
*[[Mark Zemansky|Zemansky, M.]] (1937/1968). ''Heat and Thermodynamics. An Intermediate Textbook'', fifth edition 1967, McGraw–Hill Book Company, New York.<br />
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== External links ==<br />
<br />
Category:Equilibrium chemistry<br />
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类别: 平衡化学<br />
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*[http://ads.harvard.edu/books/1989fsa..book/AbookC15.pdf Breakdown of Local Thermodynamic Equilibrium] George W. Collins, The Fundamentals of Stellar Astrophysics, Chapter 15<br />
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Category:Thermodynamic cycles<br />
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类别: 热力循环<br />
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*[http://spiff.rit.edu/classes/phys440/lectures/lte/lte.html Thermodynamic Equilibrium, Local and otherwise] lecture by Michael Richmond<br />
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Category:Thermodynamic processes<br />
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类别: 热力学过程<br />
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*[http://journals.ametsoc.org/doi/abs/10.1175/1520-0469%281970%29027%3C0711:NLTEIC%3E2.0.CO%3B2 Non-Local Thermodynamic Equilibrium in Cloudy Planetary Atmospheres] Paper by R. E. Samueison quantifying the effects due to non-LTE in an atmosphere<br />
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Category:Thermodynamic systems<br />
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类别: 热力学系统<br />
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*[http://scienceworld.wolfram.com/physics/LocalThermodynamicEquilibrium.html Local Thermodynamic Equilibrium]<br />
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Category:Thermodynamics<br />
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分类: 热力学<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Thermodynamic equilibrium]]. Its edit history can be viewed at [[平衡热力学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%B9%B3%E8%A1%A1%E7%83%AD%E5%8A%9B%E5%AD%A6&diff=21482平衡热力学2021-01-31T01:48:25Z<p>Jxzhou:/* Characteristics of a state of internal thermodynamic equilibrium */</p>
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<div>此词条暂由小竹凉翻译,翻译字数共5339,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{short description|State of thermodynamic system(s) where no net macroscopic flow of matter or energy occurs}}<br />
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'''Thermodynamic equilibrium''' is an [[axiomatic]] concept of [[thermodynamics]]. It is an internal [[State variables|state]] of a single [[thermodynamic system]], or a relation between several thermodynamic systems connected by more or less permeable or impermeable [[Thermodynamic system#Walls|walls]]. In thermodynamic equilibrium there are no net [[macroscopic]] [[Flow (mathematics)|flows]] of [[matter]] or of [[energy]], either within a system or between systems. <br />
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Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium there are no net macroscopic flows of matter or of energy, either within a system or between systems. <br />
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'''热力学平衡'''是'''<font color="#ff8000">热力学 Thermodynamics</font>'''的一个'''<font color="#ff8000">不言自明的 Axiomatic</font>'''概念。它是单个'''<font color="#ff8000">热力学系统 Thermodynamic System</font>'''的内部'''<font color="#ff8000">状态 State</font>''',或者是几个热力学系统之间通过或多或少的渗透或不渗透的'''<font color="#ff8000">壁 Wall</font>'''连接的关系。无论是在一个系统内还是在系统之间,在热力学平衡中不存在'''<font color="#ff8000">物质 Matter</font>'''或'''<font color="#ff8000">能量 Energy</font>'''的净'''<font color="#ff8000">宏观 Macroscopic</font>''' '''<font color="#ff8000">流动 Flow</font>'''。<br />
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In a system that is in its own state of internal thermodynamic equilibrium, no [[macroscopic]] change occurs. <br />
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In a system that is in its own state of internal thermodynamic equilibrium, no macroscopic change occurs. <br />
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在一个处于内部热力学平衡状态的系统中,不会发生'''<font color="#ff8000">宏观 Macroscopic</font>'''变化。<br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual [[Thermal equilibrium|thermal]], [[Mechanical equilibrium|mechanical]], [[Chemical equilibrium|chemical]], and [[Radiative equilibrium|radiative]] equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a [[thermodynamic operation]]. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a thermodynamic operation. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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相互热力学平衡的体系同时处于互相之间的'''<font color="#ff8000">热 Thermal</font>'''平衡、'''<font color="#ff8000">力学 Mechanical</font>'''平衡、'''<font color="#ff8000">化学 Chemical</font>'''平衡和'''<font color="#ff8000">辐射 Radiative</font>'''平衡。系统可以处于其中一种相互平衡状态,尽管其他状态未平衡。在热力学平衡中所有的平衡同时并且无限期地保持,直到被'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''打破。在一个宏观平衡中,微观交换是完全或几乎完全平衡的;这是对宏观平衡概念的物理解释。<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform [[temperature]]. Its [[Intensive and extensive properties|intensive properties]], other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform temperature. Its intensive properties, other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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一个处于内部热力学状态平衡的热力学系统具有空间均匀的'''<font color="#ff8000">温度 Temperature</font>'''。除了温度以外,它的'''<font color="#ff8000">强度性质 Intensive Properties</font>'''可以由于周围环境施加的不变的长程力场而导致空间不均匀性。<br />
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In systems that are at a state of [[non-equilibrium]] there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a '''meta-stable equilibrium'''.<br />
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In systems that are at a state of non-equilibrium there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a meta-stable equilibrium.<br />
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相比之下,处于'''<font color="#ff8000">非平衡状态 non-equilibrium</font>'''的系统中有物质或能量的净流动。如果这些变化可以在一个还没有发生的系统中被触发,那么这个系统就被称为处于一个'''亚稳定的平衡状态'''。<br />
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Though not a widely named a "law," it is an [[axiom]] of thermodynamics that there exist states of thermodynamic equilibrium. The [[second law of thermodynamics]] states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the [[entropy|entropies]] of the portions.<br />
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Though not a widely named a "law," it is an axiom of thermodynamics that there exist states of thermodynamic equilibrium. The second law of thermodynamics states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the entropies of the portions.<br />
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虽然不是一个广泛命名的“定律” ,但存在热力学平衡状态是一个热力学'''<font color="#ff8000">公理 Axiom</font>'''。'''<font color="#ff8000">热力学第二定律 second law of thermodynamics</font>'''指出,当一个物质体从一个平衡状态开始,在这个状态中,它的一部分被或多或少渗透或不渗透的分区保持在不同的状态,并且是孤立的,热力学操作移除分区或使分区更具渗透性,然后它会自发地达到自己内部热力学平衡的新状态,并伴随着部分'''<font color="#ff8000">熵 Entropy</font>'''的总和增加。<br />
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== Overview 概览==<br />
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{{Thermodynamics|cTopic=[[Thermodynamic system|Systems]]}}<br />
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Classical thermodynamics deals with states of [[dynamic equilibrium]]. The state of a system at thermodynamic equilibrium is the one for which some [[thermodynamic potential]] is minimized, or for which the [[entropy]] (''S'') is maximized, for specified conditions. One such potential is the [[Helmholtz free energy]] (''A''), for a system with surroundings at controlled constant temperature and volume:<br />
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Classical thermodynamics deals with states of dynamic equilibrium. The state of a system at thermodynamic equilibrium is the one for which some thermodynamic potential is minimized, or for which the entropy (S) is maximized, for specified conditions. One such potential is the Helmholtz free energy (A), for a system with surroundings at controlled constant temperature and volume:<br />
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经典热力学研究'''<font color="#ff8000">动态平衡 Dynamic Equilibrium</font>'''的状态。系统的热力学平衡状态是对于特定的条件,一些'''<font color="#ff8000">热力学势 Thermodynamic Potential</font>'''被最小化,或者'''<font color="#ff8000">熵 Entropy</font>'''(S)被最大化。对于一个周围环境温度和体积恒定的系统,其中一个这样的热力学势是'''<font color="#ff8000">亥姆霍兹自由能 Helmholtz Free Energy</font>'''(A):<br />
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:<math>A = U - TS</math><br />
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<math>A = U - TS</math><br />
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A = U-TS<br />
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Another potential, the [[Gibbs free energy]] (''G''), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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Another potential, the Gibbs free energy (G), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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在恒定温度和压力的系统中,另一个热力学势'''<font color="#ff8000">吉布斯自由能 Gibbs Free Energy</font>'''(G)在热力学平衡状态最小:<br />
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:<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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where ''T'' denotes the absolute thermodynamic temperature, ''P'' the pressure, ''S'' the entropy, ''V'' the volume, and ''U'' the internal energy of the system.<br />
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where T denotes the absolute thermodynamic temperature, P the pressure, S the entropy, V the volume, and U the internal energy of the system.<br />
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其中 T 表示热力学绝对温度,P 表示压强,S 表示熵,V 表示体积,U 表示体系的内能。<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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热力学平衡是一种独特的稳定定态,当系统长时间与周围环境相互作用时,它可以被接近或最终到达。上述势能是数学构造的热力学量,在特定的环境条件下最小化。<br />
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== Conditions 条件==<br />
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* For a completely isolated system, ''S'' is maximum at thermodynamic equilibrium. 对于一个完全孤立的系统,S在热力学平衡中取最大值。<br />
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* For a system with controlled constant temperature and volume, ''A'' is minimum at thermodynamic equilibrium. 对于一个恒定温度和体积的系统来说,A在热力学平衡中取最小值。<br />
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* For a system with controlled constant temperature and pressure, ''G'' is minimum at thermodynamic equilibrium. 对于一个恒温恒压的系统,G在热力学平衡中取最小值。<br />
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The various types of equilibriums are achieved as follows:<br />
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The various types of equilibriums are achieved as follows:<br />
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实现各种类型的平衡的方法如下:<br />
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*Two systems are in ''thermal equilibrium'' when their [[temperature]]s are the same. 当两个系统的'''<font color="#ff8000">温度 Temperature</font>'''相同时,它们就处于''热平衡状态''<br />
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*Two systems are in ''mechanical equilibrium'' when their [[pressure]]s are the same. 当两个体系的'''<font color="#ff8000">压力 Pressure</font>'''相同时,它们就处于''力学平衡''<br />
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*Two systems are in ''diffusive equilibrium'' when their [[chemical potential]]s are the same. 当两个题体系的'''<font color="#ff8000">化学势 Chemical Potential</font>'''相同时,它们就处于''扩散平衡''<br />
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*All [[forces]] are balanced and there is no significant external driving force.<br />
所有的'''<font color="#ff8000">力 Force</font>'''都是平衡的,没有明显的外部驱动力<br />
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==Relation of exchange equilibrium between systems 系统之间的交换均衡关系==<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability.<ref name="Nster_a">Münster, A. (1970), p. 49.</ref> When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability. When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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通常,热力学系统的周围环境也可以被看作是另一个热力学系统。在这种观点中,我们可以把系统及其周围环境看作是相互接触的两个系统,远程作用力也将它们联系在一起。系统的包围物是两个系统之间的接触面或边界。在热力学形式中,该表面被认为具有特定的渗透性质。例如,接触的表面可能被认为只能透热,使能量只能作为热传递。当远程力在时间上不发生变化,两个系统之间的热量传递减慢并最终永久停止时,这两个系统被称为热平衡; 这就是接触平衡的一个例子。其它类型的接触平衡可用其它类型的比渗透率来定义。当两个系统对于某一特定类型的渗透率处于接触平衡时,它们具有属于该特定类型渗透率的强变量的共同值。这种强度变量的例子有温度、压力、化学势。<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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接触平衡也可视为交换平衡。在接触平衡状态下,两系统之间某些量的传递速率存在零平衡。例如,对于只能透热的壁,内能作为热在两个系统之间的扩散速率是相等并反向的。两个系统之间的绝热壁只对作为功传递的能量有渗透作用; 在力学平衡,两个系统之间作为功的能量传递速率相等且相反。如果是一个简单的壁,那么通过它的体积转移率也是相等且相反的; 即它两边的压力是相等的。如果绝热壁比较复杂,有一种杠杆,有一个面积比,那么两个体系在交换平衡中的压力与体积交换比成反比,这使得转移率的零平衡作功。<br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<ref name="Planck 1914 40">[[Max Planck|Planck. M.]] (1914), p. 40.</ref><br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<br />
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辐射交换可以发生在两个不同的系统之间。当两个体系温度相同时,辐射交换平衡占优势。<br />
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==Thermodynamic state of internal equilibrium of a system 系统内部平衡的热力学状态==<br />
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A collection of matter may be entirely [[Isolated system|isolated]] from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium.<ref>Haase, R. (1971), p. 4.</ref><ref>Callen, H.B. (1960/1985), p. 26.</ref> (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics.<ref>{{Cite journal |doi = 10.1119/1.4914528|bibcode = 2015AmJPh..83..628M|title = Time and irreversibility in axiomatic thermodynamics|year = 2015|last1 = Marsland|first1 = Robert|last2 = Brown|first2 = Harvey R.|last3 = Valente|first3 = Giovanni|journal = American Journal of Physics|volume = 83|issue = 7|pages = 628–634}}</ref> One textbook<ref>[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963), p. 5.</ref> calls it the "zeroth law", remarking that the authors think this more befitting that title than its [[Zeroth law of thermodynamics|more customary definition]], which apparently was suggested by [[Ralph H. Fowler|Fowler]].)<br />
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A collection of matter may be entirely isolated from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium. (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics. One textbook calls it the "zeroth law", remarking that the authors think this more befitting that title than its more customary definition, which apparently was suggested by Fowler.)<br />
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物质的集合可能与其周围的环境完全'''<font color="#ff8000">孤立 Isolated</font>'''。如果它在无限长的时间内一直保持不受干扰,按照经典热力学假定,它处于一个没有发生任何变化,没有流动的状态,即内部平衡的热力学状态。(这种假设有时被称为“负第一”热力学定律,但并不常见。有教科书称之为“第零定律” ,作者'''<font color="#ff8000">福勒 Fowler</font>'''认为这个名称是'''<font color="#ff8000">更符合惯例的定义 More Customary Definition</font>'''。)<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a [[thermodynamic operation]] be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a thermodynamic operation be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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这种状态是所谓的经典热力学或平衡态热力学的主要关注点,因为它们是系统中被认为在这门学科中得到很好定义的唯一状态。一个与另一个系统处于接触平衡状态可以被一个'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''隔离,在隔离发生时,其内部不会发生任何变化。因此,一个与另一个系统处于接触平衡状态时也可以被视为处于其自身的内部热力学平衡状态。<br />
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==Multiple contact equilibrium 多点接触平衡==<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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热力学形式允许一个系统同时与其他多个系统接触,这些系统可能有也可能没有相互接触,且这些接触具有不同的渗透性。如果这些系统都与世界其他部分相互隔离,那么它们彼此之间就会达到各自的接触平衡。<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy.<ref name="Caratheodory">Carathéodory, C. (1909).</ref><ref>Prigogine, I. (1947), p. 48.</ref><ref>Landsberg, P. T. (1961), pp. 128–142.</ref><ref>Tisza, L. (1966), p. 108.</ref> Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy. Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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如果几个系统彼此之间没有绝热壁,但是它们与世界其他部分共同隔离,那么它们就会达到多重接触平衡状态,且有共同的温度,总的内能和熵。在众多强度量中,这是温度的一个独特性质。即使在远距离作用力存在的情况下,它也是有效的。(也就是说,没有“力”可以维持温度的差异。)举个例子,在热力学平衡的一个垂直的引力场系统中,顶部壁面的压力比底部壁面的压力小,但是各处的温度都是一样的。<br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural [[thermodynamic process]].<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), § 1.12.</ref> It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings.<ref>Levine, I.N. (1983), p. 40.</ref><ref>Lieb, E.H., Yngvason, J. (1999), pp. 17–18.</ref> The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of [[Second law of thermodynamics#Description#Kelvin statement|"inanimate" agency]]; a system in thermodynamic equilibrium is inanimate.<ref>[[William Thomson, 1st Baron Kelvin|Thomson, W.]] (1851).</ref><br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural thermodynamic process. It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings. The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of "inanimate" agency; a system in thermodynamic equilibrium is inanimate.<br />
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热力操作可能作为一个事件发生在周围环境的壁上,既不直接影响与周围环境联系的壁,也不直接影响其内部,且发生在一个明确的有限的时间内。例如,一个固定的绝热壁可以在环境中被放置或拆除。由于这种操作仅限于周围环境,系统可能会在一段时间内远离自身最初的内部状态---- 热力学平衡。根据热力学第二定律的说法,整体经历了变化并最终与周围环境达到了新的平衡。继Planck之后,这一连串的事件被称为自然'''<font color="#ff8000">热力学过程 Thermodynamic Process</font>'''。即使在这个过程中,当系统和周围环境都不处于明确的内部平衡状态时,存在着暂时偏离热力学平衡的现象,由于初始状态和最终状态都是热力学平衡的,这在平衡热力学中也是允许的。一个自然过程在其主要部分中以有限的速率进行,因此,它从根本上不同于虚构的准静态“过程”;即不在整个过程中无限缓慢地进行而且虚构地“可逆”。经典热力学允许,即使一个过程可能需要很长的时间才能达到热力学平衡,如果主要部分的过程是在一个有限的比率中,那么它被认为是自然的,并受制于热力学第二定律,即不可逆的。工程设计的机器、人工设备和操作是允许在周围环境中进行的。允许在环境中而不是在系统中进行此类操作和设备,是开尔文在他的一个热力学第二定律的陈述中提到'''<font color="#ff8000">无生命机构 Inanimate Agency</font>'''的原因; 在热力学平衡的系统是无生命的。<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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否则,热力操作可能会直接影响系统的壁。<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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通常可以很方便地假设周围的某些子系统比系统大得多,以至于这个过程只能影响周围子系统的强度变量,然后将这些子系统称为相关强度变量的储备库。<br />
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== Local and global equilibrium 局部和全局均衡==<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by [[intensive quantity|intensive]] parameters. As an example, [[temperature]] controls [[Heat equation|heat exchanges]]. ''Global thermodynamic equilibrium'' (GTE) means that those [[intensive quantity|intensive]] parameters are homogeneous throughout the whole system, while ''local thermodynamic equilibrium'' (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by intensive parameters. As an example, temperature controls heat exchanges. Global thermodynamic equilibrium (GTE) means that those intensive parameters are homogeneous throughout the whole system, while local thermodynamic equilibrium (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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区分全局性和局部性热力学平衡是很有用的。在热力学中,系统内部和系统与外部之间的交换是由'''<font color="#ff8000">强度 Intensive</font>'''参数控制的。例如,'''<font color="#ff8000">温度 Temperature</font>'''控制'''<font color="#ff8000">热交换 Heat Equation</font>'''。全局热力学平衡(GTE)意味着这些'''<font color="#ff8000">强度 Intensive</font>'''参数在整个系统中是均匀的,而局部热力学平衡(LTE)意味着这些强度参数在空间和时间上是变化的,但变化如此缓慢,以至于对于任何一点,人们都可以假设在该点的某个邻域存在热力学平衡。<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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如果对系统的描述要求强度参数的变化过大,那么这些强度参数的定义所依据的假设本身就会失效,系统将既不处于全局平衡,也不处于局部平衡。例如,粒子需要一定数量的碰撞来平衡其周围环境。如果在这些碰撞中移动的平均距离使它离开平衡邻域,它将永远不会平衡,也就不会有 LTE。根据定义,温度与平衡邻域的平均内部能量成正比。由于没有达到平衡邻域,温度的概念就不成立,温度也就变得无法定义。<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to [[massive]] particles. In a [[radiation|radiating]] gas, the [[photon]]s being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to massive particles. In a radiating gas, the photons being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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值得注意的是,这种局部平衡可能只适用于系统中的某个粒子子集。例如,LTE 通常只适用于'''<font color="#ff8000">大 Massive</font>'''质量粒子。在'''<font color="#ff8000">辐射 Radiation</font>'''气体中,被气体发射和吸收的'''<font color="#ff8000">光子 Photon</font>'''不需要彼此在一个热力学平衡内,或与气体中的大量粒子在一起,LTE 才能存在。在某些情况下,自由电子并不需要与大得多的原子或分子处于平衡状态,LTE 才能存在。<br />
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As an example, LTE will exist in a glass of water that contains a melting [[ice cube]]. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the [[Maxwell–Boltzmann distribution]] for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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As an example, LTE will exist in a glass of water that contains a melting ice cube. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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例如,LTE 将存在于一个装有正在融化的'''<font color="#ff8000">冰块 Ice Cube</font>'''的水杯中。玻璃杯内的温度可以在任何时候定义,但是离冰块近的地方要比离冰块远的地方冷。如果观察到位于给定点附近的分子的能量,它们将按照麦克斯韦-波兹曼分布在一定温度下的分布。如果观察到位于另一点附近的分子的能量,它们将按照'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''分布到另一个温度。<br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural [[transport phenomena]] may lead a system from local to global thermodynamic equilibrium. Going back to our example, the [[diffusion]] of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<ref>H.R. Griem, 2005</ref><br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural transport phenomena may lead a system from local to global thermodynamic equilibrium. Going back to our example, the diffusion of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<br />
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局部热力学平衡不需要局部或全局的平稳性。换句话说,每一个小区域不需要有一个恒定的温度。然而,它确实要求每个小的局部变化缓慢到足以维持其局部麦克斯韦-波尔兹曼速度分布。全局非平衡态只有通过系统与外界的交换才能保持稳定。例如,通过在水杯中不断添加细粉冰来补偿熔化,并持续排出融水,可以保持全局稳定的静态。自然'''<font color="#ff8000">输运现象 Transport Phenomena</font>'''会使一个局部热力学平衡系统逐渐达到全局的热力学平衡。回顾我们的例子,热量的扩散将导致我们的玻璃杯水流向全局热力学平衡,在这种状态下,玻璃杯的温度是完全均匀的。<br />
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==Reservations 保留意见==<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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学识渊博的笔者在热力学领域对热力学平衡描述时,经常对他们的描述附加条件或保留意见。有些笔者含蓄地保留了或多或少的空白,以待说明。<br />
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For example, one widely cited writer, [[Herbert Callen|H. B. Callen]] writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. ''Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!''"<ref>Callen, H.B. (1960/1985), p. 15.</ref><br />
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For example, one widely cited writer, H. B. Callen writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!"<br />
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例如,一位被广泛引用的作家'''<font color="#ff8000">H.B.卡伦 H.B.Callen</font>'''在这里写道: “实际上,很少有系统处于绝对和真正的平衡状态。”他提到了放射性过程,认为它们可能需要“宇宙时间才能完成,因此通常可以忽略”。他补充道: “在实践中,平衡的标准是循环的。在操作上,如果一个系统的性质一致地用热力学理论来描述,那么它就处于平衡状态! ”<br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<ref>Beattie, J.A., Oppenheim, I. (1979), p. 3.</ref><br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<br />
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J.A.贝蒂和 I.奥本海姆写道: “坚持对平衡定义的严格解释,将排除热力学应用于实际系统的所有状态。”<br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment",<ref>Callen, H.B. (1960/1985), p. 485.</ref> and cited by Adkins as having written a "classic text",<ref>Adkins, C.J. (1968/1983), p. ''xiii''.</ref> [[Brian Pippard|A.B. Pippard]] writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<ref>Pippard, A.B. (1957/1966), p. 6.</ref><br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment", and cited by Adkins as having written a "classic text", A.B. Pippard writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<br />
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Callen引用另一位作者的话说,他给出了“学术且严谨的论述” ,Adkins引用他的话说,他写了一本“经典著作”—— '''<font color="#ff8000">A.B.皮帕德 A.B.Pippard</font>'''在文中写道: “只要时间足够长,过冷水蒸汽最终会凝结,... ..。时间可能是漫长的,也许长达10年或者更长。就大多数目的而言,只要这种迅速的变化不是人为地刺激,这些系统就可以被视为处于平衡状态。”<br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster">Münster, A. (1970), p. 53.</ref><br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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另一位作者A.Münster,写道。他观察到热核反应发生的速度非常缓慢,以至于在热力学中可以忽略不计。他评论道: “‘绝对平衡’或‘所有可想象过程的平衡’的概念没有物理意义。”他说: “ ... 我们只能考虑特定过程和确定的实验条件下的平衡。”<br />
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According to [[László Tisza|L. Tisza]]: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<ref>Tisza, L. (1966), p. 119.</ref><br />
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According to L. Tisza: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<br />
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根据'''<font color="#ff8000">L.缇莎 L.Tisza</font>'''的说法: “ ... 在讨论接近绝对零度的现象时。经典理论的绝对预测变得特别模糊,因为在非平衡状态下发生冻结是非常普遍的。”<br />
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==Definitions 定义==<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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一个系统最普遍的热力学平衡是通过与周围环境的接触,允许所有化学物质和各种能量同时通过。热力学平衡中的系统可能以均匀加速度在空间中运动,但此时不能改变其形状或大小; 因此它是由空间中的刚性体积来定义的。它可能存在于外力场中,由远远大于系统本身的外部因素决定,因此系统内的事件不会对外力场产生相当大的影响。只有当外力场是均匀的,并且确定了它的均匀加速度,或者它处于一个非均匀力场中,但是由于表面的局部力,例如机械压力,使它保持静止时,这个系统才能处于热力学平衡。<br />
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Thermodynamic equilibrium is a [[primitive notion]] of the theory of thermodynamics. According to [[Philip M. Morse|P.M. Morse]]: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are ''not'' conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments."<ref>[[Philip M. Morse|Morse, P.M.]] (1969), p. 7.</ref> This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<ref>Bailyn, M. (1994), p. 20.</ref><br />
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Thermodynamic equilibrium is a primitive notion of the theory of thermodynamics. According to P.M. Morse: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are not conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments." This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<br />
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热力学平衡是热力学理论的一个'''<font color="#ff8000">基本概念 Primitive Notion</font>'''。'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''说: “应该强调的是,存在热力学状态这一事实,以及存在由平衡态唯一指定的热力学变量这一事实,并不是从某些哲学第一原理得出的逻辑结论。这些结论不可避免地来自两个多世纪的实验。”这意味着热力学平衡不能仅仅用热力学的其他理论概念来定义。M.Bailyn提出了一个基本的热力学定律理论,它定义并假设了热力学平衡的存在。<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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热力学平衡的教科书定义通常被仔细说明,并有些保留。<br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<ref>Münster, A. (1970), p. 52.</ref><br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<br />
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例如,A. Münster写道:“当一个孤立系统中没有以可测量的速率发生状态变化时,系统处于热力学平衡状态。”这里有两项保留:系统是孤立的;任何状态的变化都是不可测量的缓慢。他通过对在室温且没有催化剂的情况下混合氧和氢的说明,讨论了第二个条件。Münster指出,描述热力学平衡状态所需要的宏观变量比给定系统任何其他状态都少。这是部分,但不完全是,因为系统内和流过系统的所有流都是零。<br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in ''equilibrium''.<ref>Haase, R. (1971), pp. 3–4.</ref><br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in equilibrium.<br />
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R. Haase's的热力学演示并不从对热力学平衡的限制开始,因为他打算考虑非平衡态热力学。他考虑一个具有时间不变性质的任意系统。他通过切断除外力场以外的所有外部影响来测试它的热力学平衡。如果在绝缘之后,没有任何变化,他说,系统处于平衡状态。<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness".<ref>Callen, H.B. (1960/1985), p. 13.</ref> This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness". This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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在一个标题为“热力学平衡”的章节中,H.B. Callen在一个段落中定义了平衡状态.他指出,它们“是由系统内部的内在因素决定的”。它们是“终端状态” ,随着时间的推移,系统会以“冰川般缓慢”的速度朝着这个终端状态演化。这个说法并没有明确,对于热力学平衡系统必须是孤立的;;Callen也没有说明他所说的“内在因素”是什么意思。<br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<ref>Adkins, C.J. (1968/1983), p. ''7''.</ref><br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<br />
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另一位教科书作者,C.J.Adkins,明确允许热力学平衡在非孤立的系统中发生。然而,他的系统在物质转移方面是封闭的。他写道: “一般来说,热力学平衡的方法包括热和类似功的形式与周围环境的相互作用。”他将这种热力学平衡与只有通过热接触才能进行能量传递的热平衡相区别。<br />
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Another textbook author, [[J.R. Partington]], writes: "(i) ''An equilibrium state is one which is independent of time''." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..."<ref>Partington, J.R. (1949), p. 161.</ref> This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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Another textbook author, J.R. Partington, writes: "(i) An equilibrium state is one which is independent of time." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..." This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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另一位教科书作者'''<font color="#ff8000">J.R.帕廷顿 J.R.Partington</font>'''写道: “(i)平衡状态是独立于时间的状态。”但是,在提到“只是明显处于平衡状态”的系统时,他补充说: “这样的系统处于‘虚假平衡’状态。帕廷顿的陈述没有明确指出平衡是指一个孤立的系统。和Münster一样,Partington也指的是氧和氢的混合物。他补充说:“在一个真正的平衡状态,任何影响状态的外部条件的微小变化都会产生一个微小的状态变化... ... ”这个条件意味着热力学平衡必须在小的扰动下保持稳定; 这个要求对于热力学平衡的严格意义是必不可少的。<br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, ''thermodynamic—equilibrium.''"<ref>Crawford, F.H. (1963), p. 5.</ref><br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, thermodynamic—equilibrium."<br />
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在F.H.Crawford的一本学生教科书中,有一个标题为“热力学平衡”的章节。它区分了几种流动的驱动因素,然后说: “这些是孤立系统明显普遍趋向于完全机械、热、化学和电力状态的例子——或者简单地说,热力学平衡状态。”<br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in ''equilibrium''."<ref>Buchdahl, H.A. (1966), p. 8.</ref> Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being ''in equilibrium'' so long as experimental tests show that 'slow' transitions are in effect reversible."<ref>Buchdahl, H.A. (1966), p. 111.</ref> It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<ref>Adkins, C.J. (1968/1983), p. 8.</ref><br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in equilibrium." Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being in equilibrium so long as experimental tests show that 'slow' transitions are in effect reversible." It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<br />
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H.A. Buchdahl的一本关于经典热力学的专著考虑了热力学系统的平衡,而实际上并没有写热力学平衡一词。Buchdahl在提到封闭的物质交换系统时写道: “如果一个系统处于一个适当的静态状态,那么它将被称为处于平衡状态。”出于热力学描述的目的,Buchdahl的专著也讨论了非晶态玻璃。它说: “更准确地说,只要实验测试表明‘慢’跃迁实际上是可逆的,玻璃就可以被认为处于平衡状态。”通常来说不会将这一条件作为热力学平衡定义的一部分,而是假定相反的情况:如果热力学平衡中的一个物体受到足够慢的过程的影响,则该过程可被视为足够接近可逆,并且该物体在过程中足够接近热力学平衡。<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of ''contact equilibrium''. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by [[Constantin Carathéodory|C. Carathéodory]], and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster" /> Thermodynamic equilibrium for an open system means that, with respect to every relevant kind of selectively permeable wall, contact equilibrium exists when the respective intensive parameters of the system and surroundings are equal.<ref name="Nster_a" /> This definition does not consider the most general kind of thermodynamic equilibrium, which is through unselective contacts. This definition does not simply state that no current of matter or energy exists in the interior or at the boundaries; but it is compatible with the following definition, which does so state.<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of contact equilibrium. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by C. Carathéodory, and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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通过引入接触平衡的概念,A. Münster仔细地扩展了孤立系统热力学平衡的定义。这指定了在考虑非孤立系统的热力学平衡时允许的特定过程,并特别关心开放系统,这些开放系统可能从周围环境获得或丢失物质。感兴趣的系统和周围系统之间的接触平衡,通过一种特殊的壁与之接触,其余的连接系统是孤立的。这种特殊类型的壁也被'''<font color="#ff8000">C.喀喇西奥多里 C.Carathéodory</font>'''考虑过,其他作家也提到过。它们具有选择渗透性。它们可能只对机械功有渗透性,或者只对热有渗透性,或者只对某种特定的化学物质有渗透性。每个接触平衡定义了一个强度参数; 例如,只能透热的壁定义了一个经验温度。对于感兴趣的体系中每一种化学成分,都可以存在接触平衡。在接触平衡中,尽管有可能通过选择性渗透壁进行交换,但是感兴趣的系统是不变的,好像它处在孤立的热力学平衡。这个方案遵循的一般规则是: “ ... ... 我们只能考虑特定过程和特定实验条件下的平衡。”<br />
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[[Mark Zemansky|M. Zemansky]] also distinguishes mechanical, chemical, and thermal equilibrium. He then writes: "When the conditions for all three types of equilibrium are satisfied, the system is said to be in a state of thermodynamic equilibrium".<ref>[[Mark Zemansky|Zemansky, M.]] (1937/1968), p. 27.</ref><br />
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'''<font color="#ff8000">M.泽曼斯基 M.Zemansky</font>'''还区分了力学、化学和热平衡。他接着写道: “当这三种均衡的条件都满足时,系统就处于热力学平衡状态。”<br />
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P.M. Morse writes that thermodynamics is concerned with "states of thermodynamic equilibrium". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<br />
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[[Philip M. Morse|P.M. Morse]] writes that thermodynamics is concerned with "''states of thermodynamic equilibrium''". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<ref>[[Philip M. Morse|Morse, P.M.]] (1969), pp. 6, 37.</ref><br />
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'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''写道,热力学关注的是“热力学平衡状态”。在讨论物体与周围热源之间的热量传递时,他也使用了“热平衡”这个短语,尽管没有明确定义一个特殊的术语“热平衡”<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "full thermodynamic equilibrium state".<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "''full'' thermodynamic equilibrium state".<ref>Waldram, J.R. (1985), p. 5.</ref><br />
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J.R. Waldram写到了“一个明确的热力学状态”。他将一个系统定义为“当其观测量随时间停止变化时”的“热平衡”。但是在这个定义之下不久,他写到一块玻璃还没有达到“完全的热力学平衡状态”。<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, thermodynamic equilibrium is said to exist." He is not here considering the presence of an external force field.<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, ''thermodynamic equilibrium'' is said to exist." He is not here considering the presence of an external force field.<ref>Bailyn, M. (1994), p. 21.</ref><br />
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考虑到平衡状态,M.Bailyn写道: “每个强度变量都有自己的平衡类型。”然后他定义了热平衡、力学平衡和物质平衡。因此,他写道: “如果所有的强度变量都是一致的,那么热力学平衡就是存在的。”他在这里没有考虑外力场的存在。<br />
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J.G. Kirkwood and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of thermodynamic equilibrium if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<br />
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[[John Gamble Kirkwood|J.G. Kirkwood]] and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of ''thermodynamic equilibrium'' if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<ref>Kirkwood, J.G., Oppenheim, I. (1961), p. 2</ref><br />
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'''<font color="#ff8000">J.G.柯克伍德 J.G.Kirkwood</font>'''和 I.Oppenheim 将热力学平衡定义为: “一个系统处于热力学平衡状态,如果,在实验的时间内,(a)它强度特性与时间无关,(b)它的内部或与周围环境的边界处没有物质或能量流。”显然,他们没有把定义限制在孤立的或封闭的系统。它们不讨论“缓慢”发生变化的可能性,并且超出了分配给实验的时间范围。他们注意到,对于两个相接触的系统,存在一个强度性质的小子类,如果这个小子类的所有子类都相等,那么所有各自的强度性质都相等。只要满足其他一些条件,热力学平衡状态可以由这个子类定义。<br />
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==Characteristics of a state of internal thermodynamic equilibrium 内部热力学平衡状态的特征==<br />
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A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous. Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface." As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.<br />
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在内部热力学平衡中,没有外力的情况下由单相组成的热力学系统是均匀的。Planck在论文中简要介绍了热量、温度和热平衡,然后宣布: “在下文中,我们将主要讨论任何形式的均匀、各向同性的物体,它们在整个物质中具有相同的温度和密度,并受到到处垂直于表面的均匀压力作用。”和 Carathéodory 一样,Planck 将表面效应、外场和各向异性晶体排除在外。虽然Planck提到了温度,但并没有明确提到热力学平衡的概念。相比之下,Carathéodory 关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ,虽然没有明确地使用短语‘热力学平衡’,也没有明确地假设存在一个温度来定义它。<br />
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===Homogeneity in the absence of external forces===<br />
在没有外力的情况下的同质性<br />
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A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous.<ref name="Planck 1903 3"/> This means that the material in any small volume element of the system can be interchanged with the material of any other geometrically congruent volume element of the system, and the effect is to leave the system thermodynamically unchanged. In general, a strong external force field makes a system of a single phase in its own internal thermodynamic equilibrium inhomogeneous with respect to some [[Intensive and extensive properties|intensive variables]]. For example, a relatively dense component of a mixture can be concentrated by centrifugation.<br />
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在没有外力的情况下,由单一相组成的热力学系统,在其自身的内部热力学平衡中是均匀的。这意味着系统中任何小体积单元中的材料可以与系统中任何其他几何相等的体积单元中的材料互换,其效果是使系统在热力学上保持不变。一般来说,一个强外力场使得一个单相系统在其自身的内部热力学平衡中对于一些'''<font color="#ff8000">强变量 Intensive Variable</font>'''是不均匀的。例如,可以通过离心来浓缩混合物中相对密度较大的组分。<br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform. Considerations of kinetic theory or statistical mechanics also support this statement.<br />
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热力学平衡系统中的温度在空间和时间上是均匀的。在一个系统内部热力学平衡状态下,没有净内部宏观流动。特别是,这意味着系统的所有局部部分处于相互辐射交换平衡状态。这意味着系统的温度在空间上是均匀的。动力学理论或统计力学也支持这种说法。<br />
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===Uniform temperature===<br />
均匀温度<br />
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In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium. As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.<br />
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为了使一个系统处于它自己的内部热力学平衡状态,它处于自己内部的热平衡状态当然是必要的,但不是充分的;系统在达到内部热平衡之前,可以达到内部机械平衡。如上所述,根据 A.Münster的说法,对于给定的孤立系统的任何状态,定义一个热力学平衡所需的变量数是最少的。如上所述,J.G.Kirkwood 和 I.Oppenheim 指出,热力学平衡状态可以由一个特殊的子类的强变量定义,该子类中有一定数量的成员。<br />
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Such equilibrium inhomogeneity, induced by external forces, does not occur for the intensive variable [[temperature]]. According to [[Edward A. Guggenheim|E.A. Guggenheim]], "The most important conception of thermodynamics is temperature."<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), p.5.</ref> Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface."<ref name="Planck 1903 3">[[Max Planck|Planck, M.]] (1897/1927), p.3.</ref> As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.<br />
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这种由外力引起的平衡不均匀性,在强烈变化的'''<font color="#ff8000">温度 Temperature</font>'''下不会发生。'''<font color="#ff8000">E.A.古根海姆 E.A. Guggenheim</font>'''认为,“热力学最重要的概念是温度。“Planck在介绍他的论文时,简要叙述了热、温度和热平衡,然后宣布: ”在下文中,我们将主要讨论任何形式的均匀、各向同性的物体,它们的物质具有相同的温度和密度,并受到到处垂直于表面的均匀压力的作用和Carathéodory 一样,Planck将表面效应、外场和各向异性晶体排除在外。虽然Planck提到了温度,但并没有明确提到热力学平衡的概念。相比之下,Carathéodory关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ,虽然没有明确地使用短语‘热力学平衡’ ,也没有明确地假设存在一个温度来定义它。<br />
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If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.<br />
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如果热力学平衡位于一个外力场中,那么通常只有温度在空间上是均匀的。如果外力场非零,温度以外的强度变量通常是不均匀的。在这种情况下,一般需要附加变量来描述空间非均匀性。<br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform.<ref name="Planck 1914 40"/> This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers.<ref>Gibbs, J.W. (1876/1878), pp. 144-150.</ref><ref>[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966), pp. 127–130.</ref><ref>Münster, A. (1970), pp. 309–310.</ref><ref>Bailyn, M. (1994), pp. 254-256.</ref><ref>{{cite journal | last1 = Verkley | first1 = W.T.M. | last2 = Gerkema | first2 = T. | year = 2004 | title = On maximum entropy profiles | journal = J. Atmos. Sci. | volume = 61 | issue = 8| pages = 931–936 | doi=10.1175/1520-0469(2004)061<0931:omep>2.0.co;2| bibcode = 2004JAtS...61..931V | doi-access = free }}</ref><ref>{{cite journal | last1 = Akmaev | first1 = R.A. | year = 2008 | title = On the energetics of maximum-entropy temperature profiles | url = | journal = Q. J. R. Meteorol. Soc. | volume = 134 | issue = 630| pages = 187–197 | doi=10.1002/qj.209| bibcode = 2008QJRMS.134..187A }}</ref> Considerations of kinetic theory or statistical mechanics also support this statement.<ref>Maxwell, J.C. (1867).</ref><ref>Boltzmann, L. (1896/1964), p. 143.</ref><ref>Chapman, S., Cowling, T.G. (1939/1970), Section 4.14, pp. 75–78.</ref><ref>[[J. R. Partington|Partington, J.R.]] (1949), pp. 275–278.</ref><ref>{{cite journal | last1 = Coombes | first1 = C.A. | last2 = Laue | first2 = H. | year = 1985 | title = A paradox concerning the temperature distribution of a gas in a gravitational field | url = | journal = Am. J. Phys. | volume = 53 | issue = 3| pages = 272–273 | doi=10.1119/1.14138| bibcode = 1985AmJPh..53..272C }}</ref><ref>{{cite journal | last1 = Román | first1 = F.L. | last2 = White | first2 = J.A. | last3 = Velasco | first3 = S. | year = 1995 | title = Microcanonical single-particle distributions for an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 16 | issue = 2| pages = 83–90 | doi=10.1088/0143-0807/16/2/008| bibcode = 1995EJPh...16...83R }}</ref><ref>{{cite journal | last1 = Velasco | first1 = S. | last2 = Román | first2 = F.L. | last3 = White | first3 = J.A. | year = 1996 | title = On a paradox concerning the temperature distribution of an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 17 | issue = | pages = 43–44 | doi=10.1088/0143-0807/17/1/008}}</ref><br />
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热力学平衡系统内的温度在时间和空间上都是均匀的。在一个处于内部热力学平衡的系统中,不存在净的内部宏观流动。特别是,这意味着系统的所有局部都处于相互辐射交换平衡。这意味着系统的温度在空间上是均匀的。这在所有情况下都是如此,包括那些非均匀外力场。对于外部施加的引力场,这可以通过使用朗朗日乘数的方法通过变化的演算在宏观热力学术语中证明。动力学理论或统计力学也支持这种说法。<br />
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In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium.<ref name="Fitts 43"/><br />
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为了使一个系统处于它自己的内部热力学平衡状态,它必须处于它自己的内部热平衡状态是必要不充分的; 一个系统在到达内部热平衡之前到达内部机械平衡是可能的。<br />
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As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.<br />
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如上所述,j.r. Partington 指出热力学平衡状态在小的瞬态扰动下是稳定的。如果没有这个条件,一般来说,研究热力学平衡系统的实验就会遇到巨大的困难。<br />
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===Number of real variables needed for specification===<br />
规范所需的实变量数目<br />
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In his exposition of his scheme of closed system equilibrium thermodynamics, C. Carathéodory initially postulates that experiment reveals that a definite number of real variables define the states that are the points of the manifold of equilibria.<ref name="Caratheodory" /> In the words of Prigogine and Defay (1945): "It is a matter of experience that when we have specified a certain number of macroscopic properties of a system, then all the other properties are fixed."<ref>Prigogine, I., Defay, R. (1950/1954), p. 1.</ref><ref>Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005), p. 4.</ref> As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.<br />
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在他关于封闭系统平衡态热力学方案的论述中,C.Carathéodory 最初假定实验揭示了一定数量的实变量定义了作为平衡态流形点的状态。用 Prigogine 和 Defay (1945)的话说: “这是一个经验问题,当我们确定了一个系统一定数量的宏观属性时,那么所有其他属性都是固定的。如上所述,A. Münster认为,定义热力学平衡所需的变量数量对于给定孤立系统的任何状态来说都是最少的。如上所述,J.G. Kirkwood 和 I. Oppenheim 指出,热力学平衡状态可以由一个特殊子类的强度变量来定义,该子类中有一定数量的成员。<br />
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When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium. Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<br />
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当一个物质体从不均匀的非平衡状态或化学非平衡状态开始,然后被孤立,它自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如,在这种演变的许多情况下,内部机械平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是,在这种演变的许多情况下,热平衡的发展要比化学平衡快得多。<br />
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If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.<br />
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如果热力学平衡位于一个外力场中,那么通常只有温度在空间上是均匀的。如果外力场非零,温度以外的强度变量通常是不均匀的。在这种情况下,一般需要附加变量来描述空间非均匀性。<br />
<br />
===Stability against small perturbations===<br />
对小扰动的稳定性<br />
<br />
In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
<br />
在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
<br />
As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.<br />
<br />
如上所述,J.R. Partington 指出热力学平衡状态在小的瞬态扰动下是稳定的。如果没有这个条件,一般来说,研究热力学平衡系统的实验就会遇到严重的困难。<br />
<br />
<br />
To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics. But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
<br />
考虑孤立热力学系统中的波动概念,一个方便的例子是由其广泛的状态变量、内能、体积和质量组成指定的系统。根据定义,它们是时不变的。根据定义,它们与它们的共轭状态密集函数的时不变名义值相结合,反向温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广泛的状态变量的值,不足以提供这些名义值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
<br />
===Approach to thermodynamic equilibrium within an isolated system===<br />
孤立系统中的热力学平衡<br />
<br />
<br />
It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.<br />
<br />
可以承认,在重复测量这些共轭强度函数时,发现它们的值随时间略有不同。这种可变性被认为是由于内部波动。不同测量值平均到其名义值。<br />
<br />
When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium.<ref name="Fitts 43">Fitts, D.D. (1962), p. 43.</ref> Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<ref>Denbigh, K.G. (1951), p. 42.</ref><br />
<br />
当一个物质体从不均匀的非平衡状态或化学非平衡状态开始,然后被孤立,它自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如,在这种演变的许多情况下,内部机械平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是,在这种演变的许多情况下,热平衡的发展要比化学平衡快得多。<br />
<br />
If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<br />
<br />
如果这个系统真的像经典热力学所假定的那样是宏观的,那么这个系统的波动太小了,宏观上无法检测到。这就是所谓的热力学极限。实际上,物质的分子性质和动量转移的量子性质由于它们太小而看不见,已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中,平衡的波动概念是没有位置的。”<br />
<br />
===Fluctuations within an isolated system in its own internal thermodynamic equilibrium===<br />
孤立系统内部热力学平衡的波动<br />
<br />
<br />
If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
<br />
如果系统被重复细分,最终产生的系统足够小,可以表现出明显的波动。这是一个介观层面的研究。波动则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
<br />
In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
<br />
在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
<br />
<br />
If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
<br />
如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在波动过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,即需要量子统计力学。波动可以变得相对占主导地位,测量问题变得重要。<br />
<br />
To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics.<ref>Tschoegl, N.W. (2000). ''Fundamentals of Equilibrium and Steady-State Thermodynamics'', Elsevier, Amsterdam, {{ISBN|0-444-50426-5}}, p. 21.</ref> But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
<br />
考虑孤立热力学系统中的波动概念,一个方便的例子是由其众多的状态变量,内能、体积和质量组成指定的系统。根据定义,它们是时不变的。根据定义,它们与它们的共轭状态密集函数的时不变名义值相结合,反向温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广泛的状态变量的值,不足以提供这些名义值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
<br />
<br />
The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
<br />
"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有时间趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的标称值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微波动期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。非已知属于平衡状态的标称值,否则根据单一的度量无法进行判断。<br />
<br />
It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.<br />
<br />
可以承认,在重复测量这些共轭强度函数时,发现它们的值随时间略有不同。这种可变性被认为是由于内部波动。不同测量值平均到其名义值。<br />
<br />
<br />
<br />
If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<ref>Buchdahl, H.A. (1966), p. 16.</ref><br />
<br />
如果这个系统真的像经典热力学所假定的那样是宏观的,那么这个系统的波动太小了,宏观上无法检测到。这就是所谓的热力学极限。实际上,物质的分子性质和动量转移的量子性质由于它们太小而看不见,已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中,平衡的波动概念是没有位置的。”<br />
<br />
<br />
If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
<br />
如果系统被重复细分,最终产生的系统足够小,可以表现出明显的波动。这是一个介观层面的研究。波动则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
<br />
An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process." This illustrates the importance for thermodynamics of the concept of temperature.<br />
<br />
热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
<br />
<br />
<br />
If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在波动过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,即需要量子统计力学。波动可以变得相对占主导地位,测量问题变得重要。<br />
<br />
Thermal equilibrium is achieved when two systems in thermal contact with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<br />
<br />
当两个相互热接触的系统不再有净能量交换时,就会产生热平衡。因此,如果两个系统处于热平衡,那么它们的温度是相同的。<br />
<br />
<br />
<br />
The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
<br />
"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有时间趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的标称值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微波动期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。非已知属于平衡状态的标称值,否则根据单一的度量无法进行判断。<br />
<br />
Thermal equilibrium occurs when a system's macroscopic thermal observables have ceased to change with time. For example, an ideal gas whose distribution function has stabilised to a specific Maxwell–Boltzmann distribution would be in thermal equilibrium. This outcome allows a single temperature and pressure to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<br />
<br />
当系统的宏观热观测值不再随着时间变化时,就会出现热平衡。例如,一种分布函数稳定到一个特定的麦克斯韦-波兹曼分布的理想气体即处于热平衡状态。这个结果可以将单一的温度和压力归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是很有可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
<br />
=== Thermal equilibrium ===<br />
热平衡<br />
{{Main|Thermal equilibrium}}<br />
<br />
<br />
<br />
An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process."<ref>Eu, B.C. (2002), page 13.</ref> This illustrates the importance for thermodynamics of the concept of temperature.<br />
<br />
热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
<br />
A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<br />
<br />
一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数。<br />
<br />
<br />
<br />
[[Thermal equilibrium]] is achieved when two systems in [[thermal contact]] with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<ref>[[Raj Pathria|R. K. Pathria]], 1996</ref><br />
<br />
当两个相互'''<font color="#ff8000">热接触 Thermal Contact</font>'''的系统不再有净能量交换时,就会产生'''<font color="#ff8000">热平衡 Thermal Equilibrium</font>'''。因此,如果两个系统处于热平衡,那么它们的温度是相同的<br />
<br />
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
<br />
非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
<br />
<br />
<br />
Thermal equilibrium occurs when a system's [[macroscopic]] thermal observables have ceased to change with time. For example, an [[ideal gas]] whose [[Distribution function (physics)|distribution function]] has stabilised to a specific [[Maxwell–Boltzmann distribution]] would be in thermal equilibrium. This outcome allows a single [[temperature]] and [[pressure]] to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<ref>de Groot, S.R., Mazur, P. (1962), p. 44.</ref><br />
<br />
当一个系统的'''<font color="#ff8000">宏观 Macroscopic</font>'''热观测值不再随时间变化时,就会出现热平衡。例如,一种'''<font color="#ff8000">分布函数 Distribution Function</font>'''稳定到一个特定的'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''的'''<font color="#ff8000">理想气体 Ideal Gas</font>'''即处于热平衡状态。这个结果可以将单一的'''<font color="#ff8000">温度 Temperature</font>'''和'''<font color="#ff8000">压力 Pressure</font>'''归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
<br />
Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle. It states that a non-equilibrium system evolves such as to maximize its entropy production.<br />
<br />
定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
<br />
==Non-equilibrium==<br />
非平衡<br />
{{Main|Non-equilibrium thermodynamics}}<br />
<br />
<br />
<br />
Thermodynamic models <br />
<br />
热力学模型<br />
<br />
A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<ref>de Groot, S.R., Mazur, P. (1962), p. 43.</ref><br />
<br />
一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数<br />
<br />
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
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Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle.<ref>{{cite book|last1=Ziegler|first1=H.|title=An Introduction to Thermomechanics.|date=1983|location=North Holland, Amsterdam.}}</ref><ref>{{cite journal|last1=Onsager|first1=Lars|title=Reciprocal Relations in Irreversible Processes|journal=Phys. Rev.|date=1931|volume=37|issue=4|doi=10.1103/PhysRev.37.405|bibcode=1931PhRv...37..405O|pages=405–426|doi-access=free}}</ref> It states that a non-equilibrium system evolves such as to maximize its entropy production.<ref>{{cite book|last1=Kleidon|first1=A.|last2=et.|first2=al.|title=Non-equilibrium Thermodynamics and the Production of Entropy.|date=2005|edition=Heidelberg: Springer.}}</ref><ref>{{cite journal|last1=Belkin|first1=Andrey|last2=et.|first2=al.|title=Self-Assembled Wiggling Nano-Structures and the Principle of Maximum Entropy Production|journal=Sci. Rep.|doi=10.1038/srep08323|bibcode=2015NatSR...5E8323B|pmc=4321171|pmid=25662746|volume=5|year=2015|page=8323}}</ref><br />
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定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
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Topics in control theory<br />
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控制理论主题<br />
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==See also ==<br />
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{{Portal|Chemistry}}<br />
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;Thermodynamic models 热力学模型<br />
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* [[Non-random two-liquid model]] (NRTL model) - Phase equilibrium calculations 非随机两液模型(NRTL 模型)-相平衡计算<br />
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* [[UNIQUAC]] model - Phase equilibrium calculations UNIQUAC 模型-相平衡计算<br />
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* [[Time crystal]] 时间晶体<br />
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;Topics in control theory 控制理论主题<br />
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* [[Steady state]] 稳态<br />
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* [[Transient state]] 瞬态<br />
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* [[Coefficient diagram method]] 系数图法<br />
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* [[Control reconfiguration]] 控制重构<br />
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* [[Cut-insertion theorem]] 切入定理<br />
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* [[Feedback]] 反馈<br />
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* [[H infinity]] H 无限<br />
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* [[Hankel singular value]] 汉克尔奇异值<br />
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* [[Krener's theorem]] 克雷纳定理<br />
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* [[Lead-lag compensator]] 超前滞后补偿器<br />
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* [[Minor loop feedback]] 小循环反馈<br />
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* [[Minor loop feedback|Multi-loop feedback]] 小循环反馈 | 多循环反馈<br />
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* [[Positive systems]] 正向系统<br />
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* [[Radial basis function]] 径向基底函数<br />
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Other related topics<br />
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其他相关话题<br />
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* [[Root locus]] 根轨迹<br />
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* [[Signal-flow graph]]s 信号流图<br />
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* [[Stable polynomial]] 稳定多项式<br />
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* [[State space representation]] 状态空间<br />
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* [[Underactuation]] 欠驱动<br />
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* [[Youla–Kucera parametrization]] 尤拉-库切拉参数化<br />
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* [[Markov chain approximation method]] 马尔可夫链近似法<br />
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{{colend}}<br />
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;Other related topics<br />
其他相关话题<br />
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* [[Automation and remote control]] 自动化和远程控制<br />
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* [[Bond graph]] 键合图<br />
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* [[Control engineering]] 控制工程<br />
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* [[Control–feedback–abort loop]] 控制-反馈-中止循环<br />
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* [[Controller (control theory)]] 控制器(控制理论)<br />
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* [[Cybernetics]] 控制论<br />
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* [[Intelligent control]] 智能控制<br />
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* [[Mathematical system theory]] 数学系统论<br />
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* [[Negative feedback amplifier]] 负反馈放大器<br />
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* [[People in systems and control]] 系统和控制中的人<br />
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* [[Perceptual control theory]] 知觉控制理论<br />
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* [[Systems theory]] 系统论<br />
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* [[Time scale calculus]] 时间尺度演算<br />
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{{colend}}<br />
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== 编者推荐 ==<br />
===集智文章推荐===<br />
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====[https://swarma.org/?p=21322 什么是非平衡态热力学 | 集智百科]====<br />
非平衡态热力学 Non-equilibrium thermodynamics 是热力学的一个分支,研究某些不处于热力学平衡中的物理系统<br />
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==General references==<br />
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* Cesare Barbieri (2007) ''Fundamentals of Astronomy''. First Edition (QB43.3.B37 2006) CRC Press {{ISBN|0-7503-0886-9}}, {{ISBN|978-0-7503-0886-1}}<br />
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* Hans R. Griem (2005) ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}<br />
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* C. Michael Hogan, Leda C. Patmore and Harry Seidman (1973) ''Statistical Prediction of Dynamic Thermal Equilibrium Temperatures using Standard Meteorological Data Bases'', Second Edition (EPA-660/2-73-003 2006) United States Environmental Protection Agency Office of Research and Development, Washington, D.C. [http://library.wur.nl/WebQuery/catalog/lang/1851848]<br />
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* F. Mandl (1988) ''Statistical Physics'', Second Edition, John Wiley & Sons<br />
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==References==<br />
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{{Reflist|colwidth=35em}}<br />
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==Cited bibliography==<br />
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*Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', third edition, McGraw-Hill, London, {{ISBN|0-521-25445-0}}.<br />
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*Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, {{ISBN|0-88318-797-3}}.<br />
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*Beattie, J.A., Oppenheim, I. (1979). ''Principles of Thermodynamics'', Elsevier Scientific Publishing, Amsterdam, {{ISBN|0-444-41806-7}}.<br />
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*[[Ludwig Boltzmann|Boltzmann, L.]] (1896/1964). ''Lectures on Gas Theory'', translated by S.G. Brush, University of California Press, Berkeley.<br />
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*Buchdahl, H.A. (1966). ''The Concepts of Classical Thermodynamics'', Cambridge University Press, Cambridge UK.<br />
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*[[Herbert Callen|Callen, H.B.]] (1960/1985). ''Thermodynamics and an Introduction to Thermostatistics'', (1st edition 1960) 2nd edition 1985, Wiley, New York, {{ISBN|0-471-86256-8}}.<br />
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*[[Constantin Carathéodory|Carathéodory, C.]] (1909). [https://web.archive.org/web/20160304213645/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0067&DMDID=DMDLOG_0033&L=1 Untersuchungen über die Grundlagen der Thermodynamik], ''[[Mathematische Annalen]]'', '''67''': 355–386. A translation may be found [http://neo-classical-physics.info/uploads/3/0/6/5/3065888/caratheodory_-_thermodynamics.pdf here]. Also a mostly reliable [https://books.google.com/books?id=xwBRAAAAMAAJ&q=Investigation+into+the+foundations translation is to be found] at Kestin, J. (1976). ''The Second Law of Thermodynamics'', Dowden, Hutchinson & Ross, Stroudsburg PA.<br />
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*[[Sydney Chapman (mathematician)|Chapman, S.]], [[Thomas George Cowling|Cowling, T.G.]] (1939/1970). ''The Mathematical Theory of Non-uniform gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases'', third edition 1970, Cambridge University Press, London.<br />
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*Crawford, F.H. (1963). ''Heat, Thermodynamics, and Statistical Physics'', Rupert Hart-Davis, London, Harcourt, Brace & World, Inc.<br />
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*de Groot, S.R., Mazur, P. (1962). ''Non-equilibrium Thermodynamics'', North-Holland, Amsterdam. Reprinted (1984), Dover Publications Inc., New York, {{ISBN|0486647412}}.<br />
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*Denbigh, K.G. (1951). ''Thermodynamics of the Steady State'', Methuen, London.<br />
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*Eu, B.C. (2002). ''Generalized Thermodynamics. The Thermodynamics of Irreversible Processes and Generalized Hydrodynamics'', Kluwer Academic Publishers, Dordrecht, {{ISBN|1-4020-0788-4}}.<br />
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*Fitts, D.D. (1962). ''Nonequilibrium thermodynamics. A Phenomenological Theory of Irreversible Processes in Fluid Systems'', McGraw-Hill, New York.<br />
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*[[Josiah Willard Gibbs|Gibbs, J.W.]] (1876/1878). On the equilibrium of heterogeneous substances, ''Trans. Conn. Acad.'', '''3''': 108–248, 343–524, reprinted in ''The Collected Works of J. Willard Gibbs, Ph.D, LL. D.'', edited by W.R. Longley, R.G. Van Name, Longmans, Green & Co., New York, 1928, volume 1, pp.&nbsp;55–353.<br />
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*Griem, H.R. (2005). ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}.<br />
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*[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', fifth revised edition, North-Holland, Amsterdam.<br />
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*Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of ''Thermodynamics'', pages 1–97 of volume 1, ed. W. Jost, of ''Physical Chemistry. An Advanced Treatise'', ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081.<br />
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*[[John Gamble Kirkwood|Kirkwood, J.G.]], Oppenheim, I. (1961). ''Chemical Thermodynamics'', McGraw-Hill Book Company, New York.<br />
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*Landsberg, P.T. (1961). ''Thermodynamics with Quantum Statistical Illustrations'', Interscience, New York.<br />
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*{{cite journal |last1=Lieb |first1=E. H. |last2=Yngvason |first2=J. |year=1999 |title=The Physics and Mathematics of the Second Law of Thermodynamics |journal=Phys. Rep. |volume=310 |issue= 1|pages=1–96 |doi= 10.1016/S0370-1573(98)00082-9|arxiv = cond-mat/9708200 |bibcode = 1999PhR...310....1L |s2cid=119620408 }}<br />
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*Levine, I.N. (1983), ''Physical Chemistry'', second edition, McGraw-Hill, New York, {{ISBN|978-0072538625}}.<br />
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*{{cite journal | last1 = Maxwell | first1 = J.C. | authorlink = James Clerk Maxwell | year = 1867 | title = On the dynamical theory of gases | url = | journal = Phil. Trans. Roy. Soc. London | volume = 157 | issue = | pages = 49–88 }}<br />
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*[[Philip M. Morse|Morse, P.M.]] (1969). ''Thermal Physics'', second edition, W.A. Benjamin, Inc, New York.<br />
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*Münster, A. (1970). ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London.<br />
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*[[J.R. Partington|Partington, J.R.]] (1949). ''An Advanced Treatise on Physical Chemistry'', volume 1, ''Fundamental Principles. The Properties of Gases'', Longmans, Green and Co., London.<br />
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*[[Brian Pippard|Pippard, A.B.]] (1957/1966). ''The Elements of Classical Thermodynamics'', reprinted with corrections 1966, Cambridge University Press, London.<br />
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* [[Max Planck|Planck. M.]] (1914). [https://archive.org/details/theoryofheatradi00planrich ''The Theory of Heat Radiation''], a translation by Masius, M. of the second German edition, P. Blakiston's Son & Co., Philadelphia.<br />
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*[[Ilya Prigogine|Prigogine, I.]] (1947). ''Étude Thermodynamique des Phénomènes irréversibles'', Dunod, Paris, and Desoers, Liège.<br />
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*[[Ilya Prigogine|Prigogine, I.]], Defay, R. (1950/1954). ''Chemical Thermodynamics'', Longmans, Green & Co, London.<br />
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*Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005). ''Physical Chemistry'', fourth edition, Wiley, Hoboken NJ.<br />
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*[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966). ''Elements of Thermodynamics'', Addison-Wesley Publishing, Reading MA.<br />
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*{{cite journal|last=Thomson|first=W.|author-link=William Thomson, 1st Baron Kelvin|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Transactions of the Royal Society of Edinburgh|date=March 1851|volume=XX|issue=part II|pages=261–268; 289–298}} Also published in {{cite journal|last=Thomson|first=W.|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Phil. Mag. |date=December 1852 |volume=IV |series=4 |issue=22 |pages=8–21 |url=https://archive.org/details/londonedinburghp04maga |accessdate=25 June 2012}}<br />
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*[[László Tisza|Tisza, L.]] (1966). ''Generalized Thermodynamics'', M.I.T Press, Cambridge MA.<br />
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*[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963). ''Lectures in Statistical Mechanics'', American Mathematical Society, Providence RI.<br />
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*Waldram, J.R. (1985). ''The Theory of Thermodynamics'', Cambridge University Press, Cambridge UK, {{ISBN|0-521-24575-3}}.<br />
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*[[Mark Zemansky|Zemansky, M.]] (1937/1968). ''Heat and Thermodynamics. An Intermediate Textbook'', fifth edition 1967, McGraw–Hill Book Company, New York.<br />
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== External links ==<br />
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Category:Equilibrium chemistry<br />
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类别: 平衡化学<br />
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*[http://ads.harvard.edu/books/1989fsa..book/AbookC15.pdf Breakdown of Local Thermodynamic Equilibrium] George W. Collins, The Fundamentals of Stellar Astrophysics, Chapter 15<br />
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Category:Thermodynamic cycles<br />
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类别: 热力循环<br />
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*[http://spiff.rit.edu/classes/phys440/lectures/lte/lte.html Thermodynamic Equilibrium, Local and otherwise] lecture by Michael Richmond<br />
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Category:Thermodynamic processes<br />
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类别: 热力学过程<br />
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*[http://journals.ametsoc.org/doi/abs/10.1175/1520-0469%281970%29027%3C0711:NLTEIC%3E2.0.CO%3B2 Non-Local Thermodynamic Equilibrium in Cloudy Planetary Atmospheres] Paper by R. E. Samueison quantifying the effects due to non-LTE in an atmosphere<br />
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Category:Thermodynamic systems<br />
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类别: 热力学系统<br />
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*[http://scienceworld.wolfram.com/physics/LocalThermodynamicEquilibrium.html Local Thermodynamic Equilibrium]<br />
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Category:Thermodynamics<br />
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分类: 热力学<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Thermodynamic equilibrium]]. Its edit history can be viewed at [[平衡热力学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%B9%B3%E8%A1%A1%E7%83%AD%E5%8A%9B%E5%AD%A6&diff=21480平衡热力学2021-01-30T14:13:02Z<p>Jxzhou:/* Definitions */</p>
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<div>此词条暂由小竹凉翻译,翻译字数共5339,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{short description|State of thermodynamic system(s) where no net macroscopic flow of matter or energy occurs}}<br />
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'''Thermodynamic equilibrium''' is an [[axiomatic]] concept of [[thermodynamics]]. It is an internal [[State variables|state]] of a single [[thermodynamic system]], or a relation between several thermodynamic systems connected by more or less permeable or impermeable [[Thermodynamic system#Walls|walls]]. In thermodynamic equilibrium there are no net [[macroscopic]] [[Flow (mathematics)|flows]] of [[matter]] or of [[energy]], either within a system or between systems. <br />
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Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium there are no net macroscopic flows of matter or of energy, either within a system or between systems. <br />
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'''热力学平衡'''是'''<font color="#ff8000">热力学 Thermodynamics</font>'''的一个'''<font color="#ff8000">不言自明的 Axiomatic</font>'''概念。它是单个'''<font color="#ff8000">热力学系统 Thermodynamic System</font>'''的内部'''<font color="#ff8000">状态 State</font>''',或者是几个热力学系统之间通过或多或少的渗透或不渗透的'''<font color="#ff8000">壁 Wall</font>'''连接的关系。无论是在一个系统内还是在系统之间,在热力学平衡中不存在'''<font color="#ff8000">物质 Matter</font>'''或'''<font color="#ff8000">能量 Energy</font>'''的净'''<font color="#ff8000">宏观 Macroscopic</font>''' '''<font color="#ff8000">流动 Flow</font>'''。<br />
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In a system that is in its own state of internal thermodynamic equilibrium, no [[macroscopic]] change occurs. <br />
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In a system that is in its own state of internal thermodynamic equilibrium, no macroscopic change occurs. <br />
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在一个处于内部热力学平衡状态的系统中,不会发生'''<font color="#ff8000">宏观 Macroscopic</font>'''变化。<br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual [[Thermal equilibrium|thermal]], [[Mechanical equilibrium|mechanical]], [[Chemical equilibrium|chemical]], and [[Radiative equilibrium|radiative]] equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a [[thermodynamic operation]]. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a thermodynamic operation. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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相互热力学平衡的体系同时处于互相之间的'''<font color="#ff8000">热 Thermal</font>'''平衡、'''<font color="#ff8000">力学 Mechanical</font>'''平衡、'''<font color="#ff8000">化学 Chemical</font>'''平衡和'''<font color="#ff8000">辐射 Radiative</font>'''平衡。系统可以处于其中一种相互平衡状态,尽管其他状态未平衡。在热力学平衡中所有的平衡同时并且无限期地保持,直到被'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''打破。在一个宏观平衡中,微观交换是完全或几乎完全平衡的;这是对宏观平衡概念的物理解释。<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform [[temperature]]. Its [[Intensive and extensive properties|intensive properties]], other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform temperature. Its intensive properties, other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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一个处于内部热力学状态平衡的热力学系统具有空间均匀的'''<font color="#ff8000">温度 Temperature</font>'''。除了温度以外,它的'''<font color="#ff8000">强度性质 Intensive Properties</font>'''可以由于周围环境施加的不变的长程力场而导致空间不均匀性。<br />
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In systems that are at a state of [[non-equilibrium]] there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a '''meta-stable equilibrium'''.<br />
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In systems that are at a state of non-equilibrium there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a meta-stable equilibrium.<br />
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相比之下,处于'''<font color="#ff8000">非平衡状态 non-equilibrium</font>'''的系统中有物质或能量的净流动。如果这些变化可以在一个还没有发生的系统中被触发,那么这个系统就被称为处于一个'''亚稳定的平衡状态'''。<br />
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Though not a widely named a "law," it is an [[axiom]] of thermodynamics that there exist states of thermodynamic equilibrium. The [[second law of thermodynamics]] states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the [[entropy|entropies]] of the portions.<br />
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Though not a widely named a "law," it is an axiom of thermodynamics that there exist states of thermodynamic equilibrium. The second law of thermodynamics states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the entropies of the portions.<br />
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虽然不是一个广泛命名的“定律” ,但存在热力学平衡状态是一个热力学'''<font color="#ff8000">公理 Axiom</font>'''。'''<font color="#ff8000">热力学第二定律 second law of thermodynamics</font>'''指出,当一个物质体从一个平衡状态开始,在这个状态中,它的一部分被或多或少渗透或不渗透的分区保持在不同的状态,并且是孤立的,热力学操作移除分区或使分区更具渗透性,然后它会自发地达到自己内部热力学平衡的新状态,并伴随着部分'''<font color="#ff8000">熵 Entropy</font>'''的总和增加。<br />
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== Overview 概览==<br />
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{{Thermodynamics|cTopic=[[Thermodynamic system|Systems]]}}<br />
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Classical thermodynamics deals with states of [[dynamic equilibrium]]. The state of a system at thermodynamic equilibrium is the one for which some [[thermodynamic potential]] is minimized, or for which the [[entropy]] (''S'') is maximized, for specified conditions. One such potential is the [[Helmholtz free energy]] (''A''), for a system with surroundings at controlled constant temperature and volume:<br />
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Classical thermodynamics deals with states of dynamic equilibrium. The state of a system at thermodynamic equilibrium is the one for which some thermodynamic potential is minimized, or for which the entropy (S) is maximized, for specified conditions. One such potential is the Helmholtz free energy (A), for a system with surroundings at controlled constant temperature and volume:<br />
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经典热力学研究'''<font color="#ff8000">动态平衡 Dynamic Equilibrium</font>'''的状态。系统的热力学平衡状态是对于特定的条件,一些'''<font color="#ff8000">热力学势 Thermodynamic Potential</font>'''被最小化,或者'''<font color="#ff8000">熵 Entropy</font>'''(S)被最大化。对于一个周围环境温度和体积恒定的系统,其中一个这样的热力学势是'''<font color="#ff8000">亥姆霍兹自由能 Helmholtz Free Energy</font>'''(A):<br />
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:<math>A = U - TS</math><br />
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<math>A = U - TS</math><br />
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A = U-TS<br />
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Another potential, the [[Gibbs free energy]] (''G''), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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Another potential, the Gibbs free energy (G), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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在恒定温度和压力的系统中,另一个热力学势'''<font color="#ff8000">吉布斯自由能 Gibbs Free Energy</font>'''(G)在热力学平衡状态最小:<br />
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:<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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where ''T'' denotes the absolute thermodynamic temperature, ''P'' the pressure, ''S'' the entropy, ''V'' the volume, and ''U'' the internal energy of the system.<br />
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where T denotes the absolute thermodynamic temperature, P the pressure, S the entropy, V the volume, and U the internal energy of the system.<br />
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其中 T 表示热力学绝对温度,P 表示压强,S 表示熵,V 表示体积,U 表示体系的内能。<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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热力学平衡是一种独特的稳定定态,当系统长时间与周围环境相互作用时,它可以被接近或最终到达。上述势能是数学构造的热力学量,在特定的环境条件下最小化。<br />
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== Conditions 条件==<br />
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* For a completely isolated system, ''S'' is maximum at thermodynamic equilibrium. 对于一个完全孤立的系统,S在热力学平衡中取最大值。<br />
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* For a system with controlled constant temperature and volume, ''A'' is minimum at thermodynamic equilibrium. 对于一个恒定温度和体积的系统来说,A在热力学平衡中取最小值。<br />
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* For a system with controlled constant temperature and pressure, ''G'' is minimum at thermodynamic equilibrium. 对于一个恒温恒压的系统,G在热力学平衡中取最小值。<br />
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The various types of equilibriums are achieved as follows:<br />
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The various types of equilibriums are achieved as follows:<br />
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实现各种类型的平衡的方法如下:<br />
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*Two systems are in ''thermal equilibrium'' when their [[temperature]]s are the same. 当两个系统的'''<font color="#ff8000">温度 Temperature</font>'''相同时,它们就处于''热平衡状态''<br />
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*Two systems are in ''mechanical equilibrium'' when their [[pressure]]s are the same. 当两个体系的'''<font color="#ff8000">压力 Pressure</font>'''相同时,它们就处于''力学平衡''<br />
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*Two systems are in ''diffusive equilibrium'' when their [[chemical potential]]s are the same. 当两个题体系的'''<font color="#ff8000">化学势 Chemical Potential</font>'''相同时,它们就处于''扩散平衡''<br />
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*All [[forces]] are balanced and there is no significant external driving force.<br />
所有的'''<font color="#ff8000">力 Force</font>'''都是平衡的,没有明显的外部驱动力<br />
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==Relation of exchange equilibrium between systems 系统之间的交换均衡关系==<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability.<ref name="Nster_a">Münster, A. (1970), p. 49.</ref> When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability. When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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通常,热力学系统的周围环境也可以被看作是另一个热力学系统。在这种观点中,我们可以把系统及其周围环境看作是相互接触的两个系统,远程作用力也将它们联系在一起。系统的包围物是两个系统之间的接触面或边界。在热力学形式中,该表面被认为具有特定的渗透性质。例如,接触的表面可能被认为只能透热,使能量只能作为热传递。当远程力在时间上不发生变化,两个系统之间的热量传递减慢并最终永久停止时,这两个系统被称为热平衡; 这就是接触平衡的一个例子。其它类型的接触平衡可用其它类型的比渗透率来定义。当两个系统对于某一特定类型的渗透率处于接触平衡时,它们具有属于该特定类型渗透率的强变量的共同值。这种强度变量的例子有温度、压力、化学势。<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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接触平衡也可视为交换平衡。在接触平衡状态下,两系统之间某些量的传递速率存在零平衡。例如,对于只能透热的壁,内能作为热在两个系统之间的扩散速率是相等并反向的。两个系统之间的绝热壁只对作为功传递的能量有渗透作用; 在力学平衡,两个系统之间作为功的能量传递速率相等且相反。如果是一个简单的壁,那么通过它的体积转移率也是相等且相反的; 即它两边的压力是相等的。如果绝热壁比较复杂,有一种杠杆,有一个面积比,那么两个体系在交换平衡中的压力与体积交换比成反比,这使得转移率的零平衡作功。<br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<ref name="Planck 1914 40">[[Max Planck|Planck. M.]] (1914), p. 40.</ref><br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<br />
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辐射交换可以发生在两个不同的系统之间。当两个体系温度相同时,辐射交换平衡占优势。<br />
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==Thermodynamic state of internal equilibrium of a system 系统内部平衡的热力学状态==<br />
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A collection of matter may be entirely [[Isolated system|isolated]] from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium.<ref>Haase, R. (1971), p. 4.</ref><ref>Callen, H.B. (1960/1985), p. 26.</ref> (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics.<ref>{{Cite journal |doi = 10.1119/1.4914528|bibcode = 2015AmJPh..83..628M|title = Time and irreversibility in axiomatic thermodynamics|year = 2015|last1 = Marsland|first1 = Robert|last2 = Brown|first2 = Harvey R.|last3 = Valente|first3 = Giovanni|journal = American Journal of Physics|volume = 83|issue = 7|pages = 628–634}}</ref> One textbook<ref>[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963), p. 5.</ref> calls it the "zeroth law", remarking that the authors think this more befitting that title than its [[Zeroth law of thermodynamics|more customary definition]], which apparently was suggested by [[Ralph H. Fowler|Fowler]].)<br />
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A collection of matter may be entirely isolated from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium. (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics. One textbook calls it the "zeroth law", remarking that the authors think this more befitting that title than its more customary definition, which apparently was suggested by Fowler.)<br />
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物质的集合可能与其周围的环境完全'''<font color="#ff8000">孤立 Isolated</font>'''。如果它在无限长的时间内一直保持不受干扰,按照经典热力学假定,它处于一个没有发生任何变化,没有流动的状态,即内部平衡的热力学状态。(这种假设有时被称为“负第一”热力学定律,但并不常见。有教科书称之为“第零定律” ,作者'''<font color="#ff8000">福勒 Fowler</font>'''认为这个名称是'''<font color="#ff8000">更符合惯例的定义 More Customary Definition</font>'''。)<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a [[thermodynamic operation]] be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a thermodynamic operation be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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这种状态是所谓的经典热力学或平衡态热力学的主要关注点,因为它们是系统中被认为在这门学科中得到很好定义的唯一状态。一个与另一个系统处于接触平衡状态可以被一个'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''隔离,在隔离发生时,其内部不会发生任何变化。因此,一个与另一个系统处于接触平衡状态时也可以被视为处于其自身的内部热力学平衡状态。<br />
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==Multiple contact equilibrium 多点接触平衡==<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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热力学形式允许一个系统同时与其他多个系统接触,这些系统可能有也可能没有相互接触,且这些接触具有不同的渗透性。如果这些系统都与世界其他部分相互隔离,那么它们彼此之间就会达到各自的接触平衡。<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy.<ref name="Caratheodory">Carathéodory, C. (1909).</ref><ref>Prigogine, I. (1947), p. 48.</ref><ref>Landsberg, P. T. (1961), pp. 128–142.</ref><ref>Tisza, L. (1966), p. 108.</ref> Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy. Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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如果几个系统彼此之间没有绝热壁,但是它们与世界其他部分共同隔离,那么它们就会达到多重接触平衡状态,且有共同的温度,总的内能和熵。在众多强度量中,这是温度的一个独特性质。即使在远距离作用力存在的情况下,它也是有效的。(也就是说,没有“力”可以维持温度的差异。)举个例子,在热力学平衡的一个垂直的引力场系统中,顶部壁面的压力比底部壁面的压力小,但是各处的温度都是一样的。<br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural [[thermodynamic process]].<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), § 1.12.</ref> It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings.<ref>Levine, I.N. (1983), p. 40.</ref><ref>Lieb, E.H., Yngvason, J. (1999), pp. 17–18.</ref> The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of [[Second law of thermodynamics#Description#Kelvin statement|"inanimate" agency]]; a system in thermodynamic equilibrium is inanimate.<ref>[[William Thomson, 1st Baron Kelvin|Thomson, W.]] (1851).</ref><br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural thermodynamic process. It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings. The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of "inanimate" agency; a system in thermodynamic equilibrium is inanimate.<br />
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热力操作可能作为一个事件发生在周围环境的壁上,既不直接影响与周围环境联系的壁,也不直接影响其内部,且发生在一个明确的有限的时间内。例如,一个固定的绝热壁可以在环境中被放置或拆除。由于这种操作仅限于周围环境,系统可能会在一段时间内远离自身最初的内部状态---- 热力学平衡。根据热力学第二定律的说法,整体经历了变化并最终与周围环境达到了新的平衡。继Planck之后,这一连串的事件被称为自然'''<font color="#ff8000">热力学过程 Thermodynamic Process</font>'''。即使在这个过程中,当系统和周围环境都不处于明确的内部平衡状态时,存在着暂时偏离热力学平衡的现象,由于初始状态和最终状态都是热力学平衡的,这在平衡热力学中也是允许的。一个自然过程在其主要部分中以有限的速率进行,因此,它从根本上不同于虚构的准静态“过程”;即不在整个过程中无限缓慢地进行而且虚构地“可逆”。经典热力学允许,即使一个过程可能需要很长的时间才能达到热力学平衡,如果主要部分的过程是在一个有限的比率中,那么它被认为是自然的,并受制于热力学第二定律,即不可逆的。工程设计的机器、人工设备和操作是允许在周围环境中进行的。允许在环境中而不是在系统中进行此类操作和设备,是开尔文在他的一个热力学第二定律的陈述中提到'''<font color="#ff8000">无生命机构 Inanimate Agency</font>'''的原因; 在热力学平衡的系统是无生命的。<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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否则,热力操作可能会直接影响系统的壁。<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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通常可以很方便地假设周围的某些子系统比系统大得多,以至于这个过程只能影响周围子系统的强度变量,然后将这些子系统称为相关强度变量的储备库。<br />
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== Local and global equilibrium 局部和全局均衡==<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by [[intensive quantity|intensive]] parameters. As an example, [[temperature]] controls [[Heat equation|heat exchanges]]. ''Global thermodynamic equilibrium'' (GTE) means that those [[intensive quantity|intensive]] parameters are homogeneous throughout the whole system, while ''local thermodynamic equilibrium'' (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by intensive parameters. As an example, temperature controls heat exchanges. Global thermodynamic equilibrium (GTE) means that those intensive parameters are homogeneous throughout the whole system, while local thermodynamic equilibrium (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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区分全局性和局部性热力学平衡是很有用的。在热力学中,系统内部和系统与外部之间的交换是由'''<font color="#ff8000">强度 Intensive</font>'''参数控制的。例如,'''<font color="#ff8000">温度 Temperature</font>'''控制'''<font color="#ff8000">热交换 Heat Equation</font>'''。全局热力学平衡(GTE)意味着这些'''<font color="#ff8000">强度 Intensive</font>'''参数在整个系统中是均匀的,而局部热力学平衡(LTE)意味着这些强度参数在空间和时间上是变化的,但变化如此缓慢,以至于对于任何一点,人们都可以假设在该点的某个邻域存在热力学平衡。<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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如果对系统的描述要求强度参数的变化过大,那么这些强度参数的定义所依据的假设本身就会失效,系统将既不处于全局平衡,也不处于局部平衡。例如,粒子需要一定数量的碰撞来平衡其周围环境。如果在这些碰撞中移动的平均距离使它离开平衡邻域,它将永远不会平衡,也就不会有 LTE。根据定义,温度与平衡邻域的平均内部能量成正比。由于没有达到平衡邻域,温度的概念就不成立,温度也就变得无法定义。<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to [[massive]] particles. In a [[radiation|radiating]] gas, the [[photon]]s being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to massive particles. In a radiating gas, the photons being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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值得注意的是,这种局部平衡可能只适用于系统中的某个粒子子集。例如,LTE 通常只适用于'''<font color="#ff8000">大 Massive</font>'''质量粒子。在'''<font color="#ff8000">辐射 Radiation</font>'''气体中,被气体发射和吸收的'''<font color="#ff8000">光子 Photon</font>'''不需要彼此在一个热力学平衡内,或与气体中的大量粒子在一起,LTE 才能存在。在某些情况下,自由电子并不需要与大得多的原子或分子处于平衡状态,LTE 才能存在。<br />
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As an example, LTE will exist in a glass of water that contains a melting [[ice cube]]. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the [[Maxwell–Boltzmann distribution]] for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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As an example, LTE will exist in a glass of water that contains a melting ice cube. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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例如,LTE 将存在于一个装有正在融化的'''<font color="#ff8000">冰块 Ice Cube</font>'''的水杯中。玻璃杯内的温度可以在任何时候定义,但是离冰块近的地方要比离冰块远的地方冷。如果观察到位于给定点附近的分子的能量,它们将按照麦克斯韦-波兹曼分布在一定温度下的分布。如果观察到位于另一点附近的分子的能量,它们将按照'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''分布到另一个温度。<br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural [[transport phenomena]] may lead a system from local to global thermodynamic equilibrium. Going back to our example, the [[diffusion]] of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<ref>H.R. Griem, 2005</ref><br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural transport phenomena may lead a system from local to global thermodynamic equilibrium. Going back to our example, the diffusion of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<br />
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局部热力学平衡不需要局部或全局的平稳性。换句话说,每一个小区域不需要有一个恒定的温度。然而,它确实要求每个小的局部变化缓慢到足以维持其局部麦克斯韦-波尔兹曼速度分布。全局非平衡态只有通过系统与外界的交换才能保持稳定。例如,通过在水杯中不断添加细粉冰来补偿熔化,并持续排出融水,可以保持全局稳定的静态。自然'''<font color="#ff8000">输运现象 Transport Phenomena</font>'''会使一个局部热力学平衡系统逐渐达到全局的热力学平衡。回顾我们的例子,热量的扩散将导致我们的玻璃杯水流向全局热力学平衡,在这种状态下,玻璃杯的温度是完全均匀的。<br />
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==Reservations 保留意见==<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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学识渊博的笔者在热力学领域对热力学平衡描述时,经常对他们的描述附加条件或保留意见。有些笔者含蓄地保留了或多或少的空白,以待说明。<br />
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For example, one widely cited writer, [[Herbert Callen|H. B. Callen]] writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. ''Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!''"<ref>Callen, H.B. (1960/1985), p. 15.</ref><br />
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For example, one widely cited writer, H. B. Callen writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!"<br />
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例如,一位被广泛引用的作家'''<font color="#ff8000">H.B.卡伦 H.B.Callen</font>'''在这里写道: “实际上,很少有系统处于绝对和真正的平衡状态。”他提到了放射性过程,认为它们可能需要“宇宙时间才能完成,因此通常可以忽略”。他补充道: “在实践中,平衡的标准是循环的。在操作上,如果一个系统的性质一致地用热力学理论来描述,那么它就处于平衡状态! ”<br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<ref>Beattie, J.A., Oppenheim, I. (1979), p. 3.</ref><br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<br />
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J.A.贝蒂和 I.奥本海姆写道: “坚持对平衡定义的严格解释,将排除热力学应用于实际系统的所有状态。”<br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment",<ref>Callen, H.B. (1960/1985), p. 485.</ref> and cited by Adkins as having written a "classic text",<ref>Adkins, C.J. (1968/1983), p. ''xiii''.</ref> [[Brian Pippard|A.B. Pippard]] writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<ref>Pippard, A.B. (1957/1966), p. 6.</ref><br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment", and cited by Adkins as having written a "classic text", A.B. Pippard writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<br />
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Callen引用另一位作者的话说,他给出了“学术且严谨的论述” ,Adkins引用他的话说,他写了一本“经典著作”—— '''<font color="#ff8000">A.B.皮帕德 A.B.Pippard</font>'''在文中写道: “只要时间足够长,过冷水蒸汽最终会凝结,... ..。时间可能是漫长的,也许长达10年或者更长。就大多数目的而言,只要这种迅速的变化不是人为地刺激,这些系统就可以被视为处于平衡状态。”<br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster">Münster, A. (1970), p. 53.</ref><br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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另一位作者A.Münster,写道。他观察到热核反应发生的速度非常缓慢,以至于在热力学中可以忽略不计。他评论道: “‘绝对平衡’或‘所有可想象过程的平衡’的概念没有物理意义。”他说: “ ... 我们只能考虑特定过程和确定的实验条件下的平衡。”<br />
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According to [[László Tisza|L. Tisza]]: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<ref>Tisza, L. (1966), p. 119.</ref><br />
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According to L. Tisza: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<br />
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根据'''<font color="#ff8000">L.缇莎 L.Tisza</font>'''的说法: “ ... 在讨论接近绝对零度的现象时。经典理论的绝对预测变得特别模糊,因为在非平衡状态下发生冻结是非常普遍的。”<br />
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==Definitions 定义==<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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一个系统最普遍的热力学平衡是通过与周围环境的接触,允许所有化学物质和各种能量同时通过。热力学平衡中的系统可能以均匀加速度在空间中运动,但此时不能改变其形状或大小; 因此它是由空间中的刚性体积来定义的。它可能存在于外力场中,由远远大于系统本身的外部因素决定,因此系统内的事件不会对外力场产生相当大的影响。只有当外力场是均匀的,并且确定了它的均匀加速度,或者它处于一个非均匀力场中,但是由于表面的局部力,例如机械压力,使它保持静止时,这个系统才能处于热力学平衡。<br />
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Thermodynamic equilibrium is a [[primitive notion]] of the theory of thermodynamics. According to [[Philip M. Morse|P.M. Morse]]: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are ''not'' conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments."<ref>[[Philip M. Morse|Morse, P.M.]] (1969), p. 7.</ref> This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<ref>Bailyn, M. (1994), p. 20.</ref><br />
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Thermodynamic equilibrium is a primitive notion of the theory of thermodynamics. According to P.M. Morse: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are not conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments." This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<br />
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热力学平衡是热力学理论的一个'''<font color="#ff8000">基本概念 Primitive Notion</font>'''。'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''说: “应该强调的是,存在热力学状态这一事实,以及存在由平衡态唯一指定的热力学变量这一事实,并不是从某些哲学第一原理得出的逻辑结论。这些结论不可避免地来自两个多世纪的实验。”这意味着热力学平衡不能仅仅用热力学的其他理论概念来定义。M.Bailyn提出了一个基本的热力学定律理论,它定义并假设了热力学平衡的存在。<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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热力学平衡的教科书定义通常被仔细说明,并有些保留。<br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<ref>Münster, A. (1970), p. 52.</ref><br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<br />
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例如,A. Münster写道:“当一个孤立系统中没有以可测量的速率发生状态变化时,系统处于热力学平衡状态。”这里有两项保留:系统是孤立的;任何状态的变化都是不可测量的缓慢。他通过对在室温且没有催化剂的情况下混合氧和氢的说明,讨论了第二个条件。Münster指出,描述热力学平衡状态所需要的宏观变量比给定系统任何其他状态都少。这是部分,但不完全是,因为系统内和流过系统的所有流都是零。<br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in ''equilibrium''.<ref>Haase, R. (1971), pp. 3–4.</ref><br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in equilibrium.<br />
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R. Haase's的热力学演示并不从对热力学平衡的限制开始,因为他打算考虑非平衡态热力学。他考虑一个具有时间不变性质的任意系统。他通过切断除外力场以外的所有外部影响来测试它的热力学平衡。如果在绝缘之后,没有任何变化,他说,系统处于平衡状态。<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness".<ref>Callen, H.B. (1960/1985), p. 13.</ref> This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness". This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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在一个标题为“热力学平衡”的章节中,H.B. Callen在一个段落中定义了平衡状态.他指出,它们“是由系统内部的内在因素决定的”。它们是“终端状态” ,随着时间的推移,系统会以“冰川般缓慢”的速度朝着这个终端状态演化。这个说法并没有明确,对于热力学平衡系统必须是孤立的;;Callen也没有说明他所说的“内在因素”是什么意思。<br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<ref>Adkins, C.J. (1968/1983), p. ''7''.</ref><br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<br />
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另一位教科书作者,C.J.Adkins,明确允许热力学平衡在非孤立的系统中发生。然而,他的系统在物质转移方面是封闭的。他写道: “一般来说,热力学平衡的方法包括热和类似功的形式与周围环境的相互作用。”他将这种热力学平衡与只有通过热接触才能进行能量传递的热平衡相区别。<br />
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Another textbook author, [[J.R. Partington]], writes: "(i) ''An equilibrium state is one which is independent of time''." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..."<ref>Partington, J.R. (1949), p. 161.</ref> This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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Another textbook author, J.R. Partington, writes: "(i) An equilibrium state is one which is independent of time." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..." This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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另一位教科书作者'''<font color="#ff8000">J.R.帕廷顿 J.R.Partington</font>'''写道: “(i)平衡状态是独立于时间的状态。”但是,在提到“只是明显处于平衡状态”的系统时,他补充说: “这样的系统处于‘虚假平衡’状态。帕廷顿的陈述没有明确指出平衡是指一个孤立的系统。和Münster一样,Partington也指的是氧和氢的混合物。他补充说:“在一个真正的平衡状态,任何影响状态的外部条件的微小变化都会产生一个微小的状态变化... ... ”这个条件意味着热力学平衡必须在小的扰动下保持稳定; 这个要求对于热力学平衡的严格意义是必不可少的。<br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, ''thermodynamic—equilibrium.''"<ref>Crawford, F.H. (1963), p. 5.</ref><br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, thermodynamic—equilibrium."<br />
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在F.H.Crawford的一本学生教科书中,有一个标题为“热力学平衡”的章节。它区分了几种流动的驱动因素,然后说: “这些是孤立系统明显普遍趋向于完全机械、热、化学和电力状态的例子——或者简单地说,热力学平衡状态。”<br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in ''equilibrium''."<ref>Buchdahl, H.A. (1966), p. 8.</ref> Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being ''in equilibrium'' so long as experimental tests show that 'slow' transitions are in effect reversible."<ref>Buchdahl, H.A. (1966), p. 111.</ref> It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<ref>Adkins, C.J. (1968/1983), p. 8.</ref><br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in equilibrium." Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being in equilibrium so long as experimental tests show that 'slow' transitions are in effect reversible." It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<br />
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H.A. Buchdahl的一本关于经典热力学的专著考虑了热力学系统的平衡,而实际上并没有写热力学平衡一词。Buchdahl在提到封闭的物质交换系统时写道: “如果一个系统处于一个适当的静态状态,那么它将被称为处于平衡状态。”出于热力学描述的目的,Buchdahl的专著也讨论了非晶态玻璃。它说: “更准确地说,只要实验测试表明‘慢’跃迁实际上是可逆的,玻璃就可以被认为处于平衡状态。”通常来说不会将这一条件作为热力学平衡定义的一部分,而是假定相反的情况:如果热力学平衡中的一个物体受到足够慢的过程的影响,则该过程可被视为足够接近可逆,并且该物体在过程中足够接近热力学平衡。<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of ''contact equilibrium''. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by [[Constantin Carathéodory|C. Carathéodory]], and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster" /> Thermodynamic equilibrium for an open system means that, with respect to every relevant kind of selectively permeable wall, contact equilibrium exists when the respective intensive parameters of the system and surroundings are equal.<ref name="Nster_a" /> This definition does not consider the most general kind of thermodynamic equilibrium, which is through unselective contacts. This definition does not simply state that no current of matter or energy exists in the interior or at the boundaries; but it is compatible with the following definition, which does so state.<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of contact equilibrium. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by C. Carathéodory, and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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通过引入接触平衡的概念,A. Münster仔细地扩展了孤立系统热力学平衡的定义。这指定了在考虑非孤立系统的热力学平衡时允许的特定过程,并特别关心开放系统,这些开放系统可能从周围环境获得或丢失物质。感兴趣的系统和周围系统之间的接触平衡,通过一种特殊的壁与之接触,其余的连接系统是孤立的。这种特殊类型的壁也被'''<font color="#ff8000">C.喀喇西奥多里 C.Carathéodory</font>'''考虑过,其他作家也提到过。它们具有选择渗透性。它们可能只对机械功有渗透性,或者只对热有渗透性,或者只对某种特定的化学物质有渗透性。每个接触平衡定义了一个强度参数; 例如,只能透热的壁定义了一个经验温度。对于感兴趣的体系中每一种化学成分,都可以存在接触平衡。在接触平衡中,尽管有可能通过选择性渗透壁进行交换,但是感兴趣的系统是不变的,好像它处在孤立的热力学平衡。这个方案遵循的一般规则是: “ ... ... 我们只能考虑特定过程和特定实验条件下的平衡。”<br />
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[[Mark Zemansky|M. Zemansky]] also distinguishes mechanical, chemical, and thermal equilibrium. He then writes: "When the conditions for all three types of equilibrium are satisfied, the system is said to be in a state of thermodynamic equilibrium".<ref>[[Mark Zemansky|Zemansky, M.]] (1937/1968), p. 27.</ref><br />
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'''<font color="#ff8000">M.泽曼斯基 M.Zemansky</font>'''还区分了力学、化学和热平衡。他接着写道: “当这三种均衡的条件都满足时,系统就处于热力学平衡状态。”<br />
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P.M. Morse writes that thermodynamics is concerned with "states of thermodynamic equilibrium". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<br />
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[[Philip M. Morse|P.M. Morse]] writes that thermodynamics is concerned with "''states of thermodynamic equilibrium''". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<ref>[[Philip M. Morse|Morse, P.M.]] (1969), pp. 6, 37.</ref><br />
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'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''写道,热力学关注的是“热力学平衡状态”。在讨论物体与周围热源之间的热量传递时,他也使用了“热平衡”这个短语,尽管没有明确定义一个特殊的术语“热平衡”<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "full thermodynamic equilibrium state".<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "''full'' thermodynamic equilibrium state".<ref>Waldram, J.R. (1985), p. 5.</ref><br />
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J.R. Waldram写到了“一个明确的热力学状态”。他将一个系统定义为“当其观测量随时间停止变化时”的“热平衡”。但是在这个定义之下不久,他写到一块玻璃还没有达到“完全的热力学平衡状态”。<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, thermodynamic equilibrium is said to exist." He is not here considering the presence of an external force field.<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, ''thermodynamic equilibrium'' is said to exist." He is not here considering the presence of an external force field.<ref>Bailyn, M. (1994), p. 21.</ref><br />
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考虑到平衡状态,M.Bailyn写道: “每个强度变量都有自己的平衡类型。”然后他定义了热平衡、力学平衡和物质平衡。因此,他写道: “如果所有的强度变量都是一致的,那么热力学平衡就是存在的。”他在这里没有考虑外力场的存在。<br />
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J.G. Kirkwood and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of thermodynamic equilibrium if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<br />
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[[John Gamble Kirkwood|J.G. Kirkwood]] and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of ''thermodynamic equilibrium'' if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<ref>Kirkwood, J.G., Oppenheim, I. (1961), p. 2</ref><br />
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'''<font color="#ff8000">J.G.柯克伍德 J.G.Kirkwood</font>'''和 I.Oppenheim 将热力学平衡定义为: “一个系统处于热力学平衡状态,如果,在实验的时间内,(a)它强度特性与时间无关,(b)它的内部或与周围环境的边界处没有物质或能量流。”显然,他们没有把定义限制在孤立的或封闭的系统。它们不讨论“缓慢”发生变化的可能性,并且超出了分配给实验的时间范围。他们注意到,对于两个相接触的系统,存在一个强度性质的小子类,如果这个小子类的所有子类都相等,那么所有各自的强度性质都相等。只要满足其他一些条件,热力学平衡状态可以由这个子类定义。<br />
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==Characteristics of a state of internal thermodynamic equilibrium==<br />
内部热力学平衡状态的特征<br />
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A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous. Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface." As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.<br />
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在内部热力学平衡中,没有外力的情况下由单相组成的热力学系统是均匀的。Planck在论文中简要介绍了热量、温度和热平衡,然后宣布: “在下文中,我们将主要讨论任何形式的均匀、各向同性的物体,它们在整个物质中具有相同的温度和密度,并受到到处垂直于表面的均匀压力作用。”和 Carathéodory 一样,Planck 将表面效应、外场和各向异性晶体排除在外。虽然Planck提到了温度,但并没有明确提到热力学平衡的概念。相比之下,Carathéodory 关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ,虽然没有明确地使用短语‘热力学平衡’,也没有明确地假设存在一个温度来定义它。<br />
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===Homogeneity in the absence of external forces===<br />
在没有外力的情况下的同质性<br />
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A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous.<ref name="Planck 1903 3"/> This means that the material in any small volume element of the system can be interchanged with the material of any other geometrically congruent volume element of the system, and the effect is to leave the system thermodynamically unchanged. In general, a strong external force field makes a system of a single phase in its own internal thermodynamic equilibrium inhomogeneous with respect to some [[Intensive and extensive properties|intensive variables]]. For example, a relatively dense component of a mixture can be concentrated by centrifugation.<br />
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在没有外力的情况下,由单一相组成的热力学系统,在其自身的内部热力学平衡中是均匀的。这意味着系统中任何小体积单元中的材料可以与系统中任何其他几何相等的体积单元中的材料互换,其效果是使系统在热力学上保持不变。一般来说,一个强外力场使得一个单相系统在其自身的内部热力学平衡中对于一些'''<font color="#ff8000">强变量 Intensive Variable</font>'''是不均匀的。例如,可以通过离心来浓缩混合物中相对密度较大的组分。<br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform. Considerations of kinetic theory or statistical mechanics also support this statement.<br />
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热力学平衡系统中的温度在空间和时间上是均匀的。在一个系统内部热力学平衡状态下,没有净内部宏观流动。特别是,这意味着系统的所有局部部分处于相互辐射交换平衡状态。这意味着系统的温度在空间上是均匀的。动力学理论或统计力学也支持这种说法。<br />
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===Uniform temperature===<br />
均匀温度<br />
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In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium. As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.<br />
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为了使一个系统处于它自己的内部热力学平衡状态,它处于自己内部的热平衡状态当然是必要的,但不是充分的;系统在达到内部热平衡之前,可以达到内部机械平衡。如上所述,根据 A.Münster的说法,对于给定的孤立系统的任何状态,定义一个热力学平衡所需的变量数是最少的。如上所述,J.G.Kirkwood 和 I.Oppenheim 指出,热力学平衡状态可以由一个特殊的子类的强变量定义,该子类中有一定数量的成员。<br />
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Such equilibrium inhomogeneity, induced by external forces, does not occur for the intensive variable [[temperature]]. According to [[Edward A. Guggenheim|E.A. Guggenheim]], "The most important conception of thermodynamics is temperature."<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), p.5.</ref> Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface."<ref name="Planck 1903 3">[[Max Planck|Planck, M.]] (1897/1927), p.3.</ref> As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.<br />
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这种由外力引起的平衡不均匀性,在强烈变化的'''<font color="#ff8000">温度 Temperature</font>'''下不会发生。'''<font color="#ff8000">E.A.古根海姆 E.A. Guggenheim</font>'''认为,“热力学最重要的概念是温度。“Planck在介绍他的论文时,简要叙述了热、温度和热平衡,然后宣布: ”在下文中,我们将主要讨论任何形式的均匀、各向同性的物体,它们的物质具有相同的温度和密度,并受到到处垂直于表面的均匀压力的作用和Carathéodory 一样,Planck将表面效应、外场和各向异性晶体排除在外。虽然Planck提到了温度,但并没有明确提到热力学平衡的概念。相比之下,Carathéodory关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ,虽然没有明确地使用短语‘热力学平衡’ ,也没有明确地假设存在一个温度来定义它。<br />
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If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.<br />
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如果热力学平衡位于一个外力场中,那么通常只有温度在空间上是均匀的。如果外力场非零,温度以外的强度变量通常是不均匀的。在这种情况下,一般需要附加变量来描述空间非均匀性。<br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform.<ref name="Planck 1914 40"/> This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers.<ref>Gibbs, J.W. (1876/1878), pp. 144-150.</ref><ref>[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966), pp. 127–130.</ref><ref>Münster, A. (1970), pp. 309–310.</ref><ref>Bailyn, M. (1994), pp. 254-256.</ref><ref>{{cite journal | last1 = Verkley | first1 = W.T.M. | last2 = Gerkema | first2 = T. | year = 2004 | title = On maximum entropy profiles | journal = J. Atmos. Sci. | volume = 61 | issue = 8| pages = 931–936 | doi=10.1175/1520-0469(2004)061<0931:omep>2.0.co;2| bibcode = 2004JAtS...61..931V | doi-access = free }}</ref><ref>{{cite journal | last1 = Akmaev | first1 = R.A. | year = 2008 | title = On the energetics of maximum-entropy temperature profiles | url = | journal = Q. J. R. Meteorol. Soc. | volume = 134 | issue = 630| pages = 187–197 | doi=10.1002/qj.209| bibcode = 2008QJRMS.134..187A }}</ref> Considerations of kinetic theory or statistical mechanics also support this statement.<ref>Maxwell, J.C. (1867).</ref><ref>Boltzmann, L. (1896/1964), p. 143.</ref><ref>Chapman, S., Cowling, T.G. (1939/1970), Section 4.14, pp. 75–78.</ref><ref>[[J. R. Partington|Partington, J.R.]] (1949), pp. 275–278.</ref><ref>{{cite journal | last1 = Coombes | first1 = C.A. | last2 = Laue | first2 = H. | year = 1985 | title = A paradox concerning the temperature distribution of a gas in a gravitational field | url = | journal = Am. J. Phys. | volume = 53 | issue = 3| pages = 272–273 | doi=10.1119/1.14138| bibcode = 1985AmJPh..53..272C }}</ref><ref>{{cite journal | last1 = Román | first1 = F.L. | last2 = White | first2 = J.A. | last3 = Velasco | first3 = S. | year = 1995 | title = Microcanonical single-particle distributions for an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 16 | issue = 2| pages = 83–90 | doi=10.1088/0143-0807/16/2/008| bibcode = 1995EJPh...16...83R }}</ref><ref>{{cite journal | last1 = Velasco | first1 = S. | last2 = Román | first2 = F.L. | last3 = White | first3 = J.A. | year = 1996 | title = On a paradox concerning the temperature distribution of an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 17 | issue = | pages = 43–44 | doi=10.1088/0143-0807/17/1/008}}</ref><br />
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热力学平衡系统内的温度在时间和空间上都是均匀的。在一个处于内部热力学平衡的系统中,不存在净的内部宏观流动。特别是,这意味着系统的所有局部都处于相互辐射交换平衡。这意味着系统的温度在空间上是均匀的。这在所有情况下都是如此,包括那些非均匀外力场。对于外部施加的引力场,这可以通过使用朗朗日乘数的方法通过变化的演算在宏观热力学术语中证明。动力学理论或统计力学也支持这种说法。<br />
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In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium.<ref name="Fitts 43"/><br />
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为了使一个系统处于它自己的内部热力学平衡状态,它必须处于它自己的内部热平衡状态是必要不充分的; 一个系统在到达内部热平衡之前到达内部机械平衡是可能的。<br />
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As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.<br />
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如上所述,j.r. Partington 指出热力学平衡状态在小的瞬态扰动下是稳定的。如果没有这个条件,一般来说,研究热力学平衡系统的实验就会遇到巨大的困难。<br />
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===Number of real variables needed for specification===<br />
规范所需的实变量数目<br />
<br />
<br />
In his exposition of his scheme of closed system equilibrium thermodynamics, C. Carathéodory initially postulates that experiment reveals that a definite number of real variables define the states that are the points of the manifold of equilibria.<ref name="Caratheodory" /> In the words of Prigogine and Defay (1945): "It is a matter of experience that when we have specified a certain number of macroscopic properties of a system, then all the other properties are fixed."<ref>Prigogine, I., Defay, R. (1950/1954), p. 1.</ref><ref>Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005), p. 4.</ref> As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.<br />
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在他关于封闭系统平衡态热力学方案的论述中,C.Carathéodory 最初假定实验揭示了一定数量的实变量定义了作为平衡态流形点的状态。用 Prigogine 和 Defay (1945)的话说: “这是一个经验问题,当我们确定了一个系统一定数量的宏观属性时,那么所有其他属性都是固定的。如上所述,A. Münster认为,定义热力学平衡所需的变量数量对于给定孤立系统的任何状态来说都是最少的。如上所述,J.G. Kirkwood 和 I. Oppenheim 指出,热力学平衡状态可以由一个特殊子类的强度变量来定义,该子类中有一定数量的成员。<br />
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When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium. Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<br />
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当一个物质体从不均匀的非平衡状态或化学非平衡状态开始,然后被孤立,它自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如,在这种演变的许多情况下,内部机械平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是,在这种演变的许多情况下,热平衡的发展要比化学平衡快得多。<br />
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If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.<br />
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如果热力学平衡位于一个外力场中,那么通常只有温度在空间上是均匀的。如果外力场非零,温度以外的强度变量通常是不均匀的。在这种情况下,一般需要附加变量来描述空间非均匀性。<br />
<br />
===Stability against small perturbations===<br />
对小扰动的稳定性<br />
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In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
<br />
在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
<br />
As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.<br />
<br />
如上所述,J.R. Partington 指出热力学平衡状态在小的瞬态扰动下是稳定的。如果没有这个条件,一般来说,研究热力学平衡系统的实验就会遇到严重的困难。<br />
<br />
<br />
To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics. But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
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考虑孤立热力学系统中的波动概念,一个方便的例子是由其广泛的状态变量、内能、体积和质量组成指定的系统。根据定义,它们是时不变的。根据定义,它们与它们的共轭状态密集函数的时不变名义值相结合,反向温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广泛的状态变量的值,不足以提供这些名义值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
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===Approach to thermodynamic equilibrium within an isolated system===<br />
孤立系统中的热力学平衡<br />
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It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.<br />
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可以承认,在重复测量这些共轭强度函数时,发现它们的值随时间略有不同。这种可变性被认为是由于内部波动。不同测量值平均到其名义值。<br />
<br />
When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium.<ref name="Fitts 43">Fitts, D.D. (1962), p. 43.</ref> Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<ref>Denbigh, K.G. (1951), p. 42.</ref><br />
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当一个物质体从不均匀的非平衡状态或化学非平衡状态开始,然后被孤立,它自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如,在这种演变的许多情况下,内部机械平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是,在这种演变的许多情况下,热平衡的发展要比化学平衡快得多。<br />
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If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<br />
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如果这个系统真的像经典热力学所假定的那样是宏观的,那么这个系统的波动太小了,宏观上无法检测到。这就是所谓的热力学极限。实际上,物质的分子性质和动量转移的量子性质由于它们太小而看不见,已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中,平衡的波动概念是没有位置的。”<br />
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===Fluctuations within an isolated system in its own internal thermodynamic equilibrium===<br />
孤立系统内部热力学平衡的波动<br />
<br />
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If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
<br />
如果系统被重复细分,最终产生的系统足够小,可以表现出明显的波动。这是一个介观层面的研究。波动则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
<br />
In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
<br />
在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
<br />
<br />
If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
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如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在波动过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,即需要量子统计力学。波动可以变得相对占主导地位,测量问题变得重要。<br />
<br />
To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics.<ref>Tschoegl, N.W. (2000). ''Fundamentals of Equilibrium and Steady-State Thermodynamics'', Elsevier, Amsterdam, {{ISBN|0-444-50426-5}}, p. 21.</ref> But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
<br />
考虑孤立热力学系统中的波动概念,一个方便的例子是由其众多的状态变量,内能、体积和质量组成指定的系统。根据定义,它们是时不变的。根据定义,它们与它们的共轭状态密集函数的时不变名义值相结合,反向温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广泛的状态变量的值,不足以提供这些名义值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
<br />
<br />
The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
<br />
"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有时间趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的标称值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微波动期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。非已知属于平衡状态的标称值,否则根据单一的度量无法进行判断。<br />
<br />
It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.<br />
<br />
可以承认,在重复测量这些共轭强度函数时,发现它们的值随时间略有不同。这种可变性被认为是由于内部波动。不同测量值平均到其名义值。<br />
<br />
<br />
<br />
If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<ref>Buchdahl, H.A. (1966), p. 16.</ref><br />
<br />
如果这个系统真的像经典热力学所假定的那样是宏观的,那么这个系统的波动太小了,宏观上无法检测到。这就是所谓的热力学极限。实际上,物质的分子性质和动量转移的量子性质由于它们太小而看不见,已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中,平衡的波动概念是没有位置的。”<br />
<br />
<br />
If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
<br />
如果系统被重复细分,最终产生的系统足够小,可以表现出明显的波动。这是一个介观层面的研究。波动则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
<br />
An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process." This illustrates the importance for thermodynamics of the concept of temperature.<br />
<br />
热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
<br />
<br />
<br />
If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在波动过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,即需要量子统计力学。波动可以变得相对占主导地位,测量问题变得重要。<br />
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Thermal equilibrium is achieved when two systems in thermal contact with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<br />
<br />
当两个相互热接触的系统不再有净能量交换时,就会产生热平衡。因此,如果两个系统处于热平衡,那么它们的温度是相同的。<br />
<br />
<br />
<br />
The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
<br />
"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有时间趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的标称值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微波动期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。非已知属于平衡状态的标称值,否则根据单一的度量无法进行判断。<br />
<br />
Thermal equilibrium occurs when a system's macroscopic thermal observables have ceased to change with time. For example, an ideal gas whose distribution function has stabilised to a specific Maxwell–Boltzmann distribution would be in thermal equilibrium. This outcome allows a single temperature and pressure to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<br />
<br />
当系统的宏观热观测值不再随着时间变化时,就会出现热平衡。例如,一种分布函数稳定到一个特定的麦克斯韦-波兹曼分布的理想气体即处于热平衡状态。这个结果可以将单一的温度和压力归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是很有可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
<br />
=== Thermal equilibrium ===<br />
热平衡<br />
{{Main|Thermal equilibrium}}<br />
<br />
<br />
<br />
An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process."<ref>Eu, B.C. (2002), page 13.</ref> This illustrates the importance for thermodynamics of the concept of temperature.<br />
<br />
热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
<br />
A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<br />
<br />
一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数。<br />
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[[Thermal equilibrium]] is achieved when two systems in [[thermal contact]] with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<ref>[[Raj Pathria|R. K. Pathria]], 1996</ref><br />
<br />
当两个相互'''<font color="#ff8000">热接触 Thermal Contact</font>'''的系统不再有净能量交换时,就会产生'''<font color="#ff8000">热平衡 Thermal Equilibrium</font>'''。因此,如果两个系统处于热平衡,那么它们的温度是相同的<br />
<br />
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
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Thermal equilibrium occurs when a system's [[macroscopic]] thermal observables have ceased to change with time. For example, an [[ideal gas]] whose [[Distribution function (physics)|distribution function]] has stabilised to a specific [[Maxwell–Boltzmann distribution]] would be in thermal equilibrium. This outcome allows a single [[temperature]] and [[pressure]] to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<ref>de Groot, S.R., Mazur, P. (1962), p. 44.</ref><br />
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当一个系统的'''<font color="#ff8000">宏观 Macroscopic</font>'''热观测值不再随时间变化时,就会出现热平衡。例如,一种'''<font color="#ff8000">分布函数 Distribution Function</font>'''稳定到一个特定的'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''的'''<font color="#ff8000">理想气体 Ideal Gas</font>'''即处于热平衡状态。这个结果可以将单一的'''<font color="#ff8000">温度 Temperature</font>'''和'''<font color="#ff8000">压力 Pressure</font>'''归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
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Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle. It states that a non-equilibrium system evolves such as to maximize its entropy production.<br />
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定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
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==Non-equilibrium==<br />
非平衡<br />
{{Main|Non-equilibrium thermodynamics}}<br />
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Thermodynamic models <br />
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热力学模型<br />
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A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<ref>de Groot, S.R., Mazur, P. (1962), p. 43.</ref><br />
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一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数<br />
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Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
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Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle.<ref>{{cite book|last1=Ziegler|first1=H.|title=An Introduction to Thermomechanics.|date=1983|location=North Holland, Amsterdam.}}</ref><ref>{{cite journal|last1=Onsager|first1=Lars|title=Reciprocal Relations in Irreversible Processes|journal=Phys. Rev.|date=1931|volume=37|issue=4|doi=10.1103/PhysRev.37.405|bibcode=1931PhRv...37..405O|pages=405–426|doi-access=free}}</ref> It states that a non-equilibrium system evolves such as to maximize its entropy production.<ref>{{cite book|last1=Kleidon|first1=A.|last2=et.|first2=al.|title=Non-equilibrium Thermodynamics and the Production of Entropy.|date=2005|edition=Heidelberg: Springer.}}</ref><ref>{{cite journal|last1=Belkin|first1=Andrey|last2=et.|first2=al.|title=Self-Assembled Wiggling Nano-Structures and the Principle of Maximum Entropy Production|journal=Sci. Rep.|doi=10.1038/srep08323|bibcode=2015NatSR...5E8323B|pmc=4321171|pmid=25662746|volume=5|year=2015|page=8323}}</ref><br />
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定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
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Topics in control theory<br />
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控制理论主题<br />
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==See also ==<br />
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{{Portal|Chemistry}}<br />
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;Thermodynamic models 热力学模型<br />
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* [[Non-random two-liquid model]] (NRTL model) - Phase equilibrium calculations 非随机两液模型(NRTL 模型)-相平衡计算<br />
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* [[UNIQUAC]] model - Phase equilibrium calculations UNIQUAC 模型-相平衡计算<br />
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* [[Time crystal]] 时间晶体<br />
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;Topics in control theory 控制理论主题<br />
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* [[Steady state]] 稳态<br />
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* [[Transient state]] 瞬态<br />
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* [[Coefficient diagram method]] 系数图法<br />
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* [[Control reconfiguration]] 控制重构<br />
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* [[Cut-insertion theorem]] 切入定理<br />
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* [[Feedback]] 反馈<br />
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* [[H infinity]] H 无限<br />
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* [[Hankel singular value]] 汉克尔奇异值<br />
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* [[Krener's theorem]] 克雷纳定理<br />
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* [[Lead-lag compensator]] 超前滞后补偿器<br />
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* [[Minor loop feedback]] 小循环反馈<br />
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* [[Minor loop feedback|Multi-loop feedback]] 小循环反馈 | 多循环反馈<br />
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* [[Positive systems]] 正向系统<br />
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* [[Radial basis function]] 径向基底函数<br />
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Other related topics<br />
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其他相关话题<br />
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* [[Root locus]] 根轨迹<br />
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* [[Signal-flow graph]]s 信号流图<br />
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* [[Stable polynomial]] 稳定多项式<br />
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* [[State space representation]] 状态空间<br />
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* [[Underactuation]] 欠驱动<br />
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* [[Youla–Kucera parametrization]] 尤拉-库切拉参数化<br />
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* [[Markov chain approximation method]] 马尔可夫链近似法<br />
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{{colend}}<br />
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;Other related topics<br />
其他相关话题<br />
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* [[Automation and remote control]] 自动化和远程控制<br />
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* [[Bond graph]] 键合图<br />
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* [[Control engineering]] 控制工程<br />
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* [[Control–feedback–abort loop]] 控制-反馈-中止循环<br />
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* [[Controller (control theory)]] 控制器(控制理论)<br />
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* [[Cybernetics]] 控制论<br />
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* [[Intelligent control]] 智能控制<br />
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* [[Mathematical system theory]] 数学系统论<br />
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* [[Negative feedback amplifier]] 负反馈放大器<br />
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* [[People in systems and control]] 系统和控制中的人<br />
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* [[Perceptual control theory]] 知觉控制理论<br />
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* [[Systems theory]] 系统论<br />
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* [[Time scale calculus]] 时间尺度演算<br />
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{{colend}}<br />
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== 编者推荐 ==<br />
===集智文章推荐===<br />
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====[https://swarma.org/?p=21322 什么是非平衡态热力学 | 集智百科]====<br />
非平衡态热力学 Non-equilibrium thermodynamics 是热力学的一个分支,研究某些不处于热力学平衡中的物理系统<br />
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==General references==<br />
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* Cesare Barbieri (2007) ''Fundamentals of Astronomy''. First Edition (QB43.3.B37 2006) CRC Press {{ISBN|0-7503-0886-9}}, {{ISBN|978-0-7503-0886-1}}<br />
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* Hans R. Griem (2005) ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}<br />
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* C. Michael Hogan, Leda C. Patmore and Harry Seidman (1973) ''Statistical Prediction of Dynamic Thermal Equilibrium Temperatures using Standard Meteorological Data Bases'', Second Edition (EPA-660/2-73-003 2006) United States Environmental Protection Agency Office of Research and Development, Washington, D.C. [http://library.wur.nl/WebQuery/catalog/lang/1851848]<br />
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* F. Mandl (1988) ''Statistical Physics'', Second Edition, John Wiley & Sons<br />
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==References==<br />
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{{Reflist|colwidth=35em}}<br />
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==Cited bibliography==<br />
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*Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', third edition, McGraw-Hill, London, {{ISBN|0-521-25445-0}}.<br />
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*Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, {{ISBN|0-88318-797-3}}.<br />
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*Beattie, J.A., Oppenheim, I. (1979). ''Principles of Thermodynamics'', Elsevier Scientific Publishing, Amsterdam, {{ISBN|0-444-41806-7}}.<br />
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*[[Ludwig Boltzmann|Boltzmann, L.]] (1896/1964). ''Lectures on Gas Theory'', translated by S.G. Brush, University of California Press, Berkeley.<br />
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*Buchdahl, H.A. (1966). ''The Concepts of Classical Thermodynamics'', Cambridge University Press, Cambridge UK.<br />
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*[[Herbert Callen|Callen, H.B.]] (1960/1985). ''Thermodynamics and an Introduction to Thermostatistics'', (1st edition 1960) 2nd edition 1985, Wiley, New York, {{ISBN|0-471-86256-8}}.<br />
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*[[Constantin Carathéodory|Carathéodory, C.]] (1909). [https://web.archive.org/web/20160304213645/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0067&DMDID=DMDLOG_0033&L=1 Untersuchungen über die Grundlagen der Thermodynamik], ''[[Mathematische Annalen]]'', '''67''': 355–386. A translation may be found [http://neo-classical-physics.info/uploads/3/0/6/5/3065888/caratheodory_-_thermodynamics.pdf here]. Also a mostly reliable [https://books.google.com/books?id=xwBRAAAAMAAJ&q=Investigation+into+the+foundations translation is to be found] at Kestin, J. (1976). ''The Second Law of Thermodynamics'', Dowden, Hutchinson & Ross, Stroudsburg PA.<br />
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*[[Sydney Chapman (mathematician)|Chapman, S.]], [[Thomas George Cowling|Cowling, T.G.]] (1939/1970). ''The Mathematical Theory of Non-uniform gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases'', third edition 1970, Cambridge University Press, London.<br />
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*Crawford, F.H. (1963). ''Heat, Thermodynamics, and Statistical Physics'', Rupert Hart-Davis, London, Harcourt, Brace & World, Inc.<br />
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*de Groot, S.R., Mazur, P. (1962). ''Non-equilibrium Thermodynamics'', North-Holland, Amsterdam. Reprinted (1984), Dover Publications Inc., New York, {{ISBN|0486647412}}.<br />
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*Denbigh, K.G. (1951). ''Thermodynamics of the Steady State'', Methuen, London.<br />
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*Eu, B.C. (2002). ''Generalized Thermodynamics. The Thermodynamics of Irreversible Processes and Generalized Hydrodynamics'', Kluwer Academic Publishers, Dordrecht, {{ISBN|1-4020-0788-4}}.<br />
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*Fitts, D.D. (1962). ''Nonequilibrium thermodynamics. A Phenomenological Theory of Irreversible Processes in Fluid Systems'', McGraw-Hill, New York.<br />
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*[[Josiah Willard Gibbs|Gibbs, J.W.]] (1876/1878). On the equilibrium of heterogeneous substances, ''Trans. Conn. Acad.'', '''3''': 108–248, 343–524, reprinted in ''The Collected Works of J. Willard Gibbs, Ph.D, LL. D.'', edited by W.R. Longley, R.G. Van Name, Longmans, Green & Co., New York, 1928, volume 1, pp.&nbsp;55–353.<br />
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*Griem, H.R. (2005). ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}.<br />
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*[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', fifth revised edition, North-Holland, Amsterdam.<br />
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*Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of ''Thermodynamics'', pages 1–97 of volume 1, ed. W. Jost, of ''Physical Chemistry. An Advanced Treatise'', ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081.<br />
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*[[John Gamble Kirkwood|Kirkwood, J.G.]], Oppenheim, I. (1961). ''Chemical Thermodynamics'', McGraw-Hill Book Company, New York.<br />
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*Landsberg, P.T. (1961). ''Thermodynamics with Quantum Statistical Illustrations'', Interscience, New York.<br />
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*{{cite journal |last1=Lieb |first1=E. H. |last2=Yngvason |first2=J. |year=1999 |title=The Physics and Mathematics of the Second Law of Thermodynamics |journal=Phys. Rep. |volume=310 |issue= 1|pages=1–96 |doi= 10.1016/S0370-1573(98)00082-9|arxiv = cond-mat/9708200 |bibcode = 1999PhR...310....1L |s2cid=119620408 }}<br />
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*Levine, I.N. (1983), ''Physical Chemistry'', second edition, McGraw-Hill, New York, {{ISBN|978-0072538625}}.<br />
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*{{cite journal | last1 = Maxwell | first1 = J.C. | authorlink = James Clerk Maxwell | year = 1867 | title = On the dynamical theory of gases | url = | journal = Phil. Trans. Roy. Soc. London | volume = 157 | issue = | pages = 49–88 }}<br />
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*[[Philip M. Morse|Morse, P.M.]] (1969). ''Thermal Physics'', second edition, W.A. Benjamin, Inc, New York.<br />
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*Münster, A. (1970). ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London.<br />
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*[[J.R. Partington|Partington, J.R.]] (1949). ''An Advanced Treatise on Physical Chemistry'', volume 1, ''Fundamental Principles. The Properties of Gases'', Longmans, Green and Co., London.<br />
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*[[Brian Pippard|Pippard, A.B.]] (1957/1966). ''The Elements of Classical Thermodynamics'', reprinted with corrections 1966, Cambridge University Press, London.<br />
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* [[Max Planck|Planck. M.]] (1914). [https://archive.org/details/theoryofheatradi00planrich ''The Theory of Heat Radiation''], a translation by Masius, M. of the second German edition, P. Blakiston's Son & Co., Philadelphia.<br />
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*[[Ilya Prigogine|Prigogine, I.]] (1947). ''Étude Thermodynamique des Phénomènes irréversibles'', Dunod, Paris, and Desoers, Liège.<br />
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*[[Ilya Prigogine|Prigogine, I.]], Defay, R. (1950/1954). ''Chemical Thermodynamics'', Longmans, Green & Co, London.<br />
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*Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005). ''Physical Chemistry'', fourth edition, Wiley, Hoboken NJ.<br />
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*[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966). ''Elements of Thermodynamics'', Addison-Wesley Publishing, Reading MA.<br />
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*{{cite journal|last=Thomson|first=W.|author-link=William Thomson, 1st Baron Kelvin|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Transactions of the Royal Society of Edinburgh|date=March 1851|volume=XX|issue=part II|pages=261–268; 289–298}} Also published in {{cite journal|last=Thomson|first=W.|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Phil. Mag. |date=December 1852 |volume=IV |series=4 |issue=22 |pages=8–21 |url=https://archive.org/details/londonedinburghp04maga |accessdate=25 June 2012}}<br />
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*[[László Tisza|Tisza, L.]] (1966). ''Generalized Thermodynamics'', M.I.T Press, Cambridge MA.<br />
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*[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963). ''Lectures in Statistical Mechanics'', American Mathematical Society, Providence RI.<br />
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*Waldram, J.R. (1985). ''The Theory of Thermodynamics'', Cambridge University Press, Cambridge UK, {{ISBN|0-521-24575-3}}.<br />
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*[[Mark Zemansky|Zemansky, M.]] (1937/1968). ''Heat and Thermodynamics. An Intermediate Textbook'', fifth edition 1967, McGraw–Hill Book Company, New York.<br />
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== External links ==<br />
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Category:Equilibrium chemistry<br />
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类别: 平衡化学<br />
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*[http://ads.harvard.edu/books/1989fsa..book/AbookC15.pdf Breakdown of Local Thermodynamic Equilibrium] George W. Collins, The Fundamentals of Stellar Astrophysics, Chapter 15<br />
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Category:Thermodynamic cycles<br />
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类别: 热力循环<br />
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*[http://spiff.rit.edu/classes/phys440/lectures/lte/lte.html Thermodynamic Equilibrium, Local and otherwise] lecture by Michael Richmond<br />
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Category:Thermodynamic processes<br />
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类别: 热力学过程<br />
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*[http://journals.ametsoc.org/doi/abs/10.1175/1520-0469%281970%29027%3C0711:NLTEIC%3E2.0.CO%3B2 Non-Local Thermodynamic Equilibrium in Cloudy Planetary Atmospheres] Paper by R. E. Samueison quantifying the effects due to non-LTE in an atmosphere<br />
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Category:Thermodynamic systems<br />
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类别: 热力学系统<br />
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*[http://scienceworld.wolfram.com/physics/LocalThermodynamicEquilibrium.html Local Thermodynamic Equilibrium]<br />
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Category:Thermodynamics<br />
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分类: 热力学<br />
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<small>This page was moved from [[wikipedia:en:Thermodynamic equilibrium]]. Its edit history can be viewed at [[平衡热力学/edithistory]]</small></noinclude><br />
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<div>此词条暂由小竹凉翻译,翻译字数共5339,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{short description|State of thermodynamic system(s) where no net macroscopic flow of matter or energy occurs}}<br />
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'''Thermodynamic equilibrium''' is an [[axiomatic]] concept of [[thermodynamics]]. It is an internal [[State variables|state]] of a single [[thermodynamic system]], or a relation between several thermodynamic systems connected by more or less permeable or impermeable [[Thermodynamic system#Walls|walls]]. In thermodynamic equilibrium there are no net [[macroscopic]] [[Flow (mathematics)|flows]] of [[matter]] or of [[energy]], either within a system or between systems. <br />
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Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium there are no net macroscopic flows of matter or of energy, either within a system or between systems. <br />
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'''热力学平衡'''是'''<font color="#ff8000">热力学 Thermodynamics</font>'''的一个'''<font color="#ff8000">不言自明的 Axiomatic</font>'''概念。它是单个'''<font color="#ff8000">热力学系统 Thermodynamic System</font>'''的内部'''<font color="#ff8000">状态 State</font>''',或者是几个热力学系统之间通过或多或少的渗透或不渗透的'''<font color="#ff8000">壁 Wall</font>'''连接的关系。无论是在一个系统内还是在系统之间,在热力学平衡中不存在'''<font color="#ff8000">物质 Matter</font>'''或'''<font color="#ff8000">能量 Energy</font>'''的净'''<font color="#ff8000">宏观 Macroscopic</font>''' '''<font color="#ff8000">流动 Flow</font>'''。<br />
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In a system that is in its own state of internal thermodynamic equilibrium, no [[macroscopic]] change occurs. <br />
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In a system that is in its own state of internal thermodynamic equilibrium, no macroscopic change occurs. <br />
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在一个处于内部热力学平衡状态的系统中,不会发生'''<font color="#ff8000">宏观 Macroscopic</font>'''变化。<br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual [[Thermal equilibrium|thermal]], [[Mechanical equilibrium|mechanical]], [[Chemical equilibrium|chemical]], and [[Radiative equilibrium|radiative]] equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a [[thermodynamic operation]]. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a thermodynamic operation. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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相互热力学平衡的体系同时处于互相之间的'''<font color="#ff8000">热 Thermal</font>'''平衡、'''<font color="#ff8000">力学 Mechanical</font>'''平衡、'''<font color="#ff8000">化学 Chemical</font>'''平衡和'''<font color="#ff8000">辐射 Radiative</font>'''平衡。系统可以处于其中一种相互平衡状态,尽管其他状态未平衡。在热力学平衡中所有的平衡同时并且无限期地保持,直到被'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''打破。在一个宏观平衡中,微观交换是完全或几乎完全平衡的;这是对宏观平衡概念的物理解释。<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform [[temperature]]. Its [[Intensive and extensive properties|intensive properties]], other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform temperature. Its intensive properties, other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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一个处于内部热力学状态平衡的热力学系统具有空间均匀的'''<font color="#ff8000">温度 Temperature</font>'''。除了温度以外,它的'''<font color="#ff8000">强度性质 Intensive Properties</font>'''可以由于周围环境施加的不变的长程力场而导致空间不均匀性。<br />
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In systems that are at a state of [[non-equilibrium]] there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a '''meta-stable equilibrium'''.<br />
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In systems that are at a state of non-equilibrium there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a meta-stable equilibrium.<br />
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相比之下,处于'''<font color="#ff8000">非平衡状态 non-equilibrium</font>'''的系统中有物质或能量的净流动。如果这些变化可以在一个还没有发生的系统中被触发,那么这个系统就被称为处于一个'''亚稳定的平衡状态'''。<br />
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Though not a widely named a "law," it is an [[axiom]] of thermodynamics that there exist states of thermodynamic equilibrium. The [[second law of thermodynamics]] states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the [[entropy|entropies]] of the portions.<br />
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Though not a widely named a "law," it is an axiom of thermodynamics that there exist states of thermodynamic equilibrium. The second law of thermodynamics states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the entropies of the portions.<br />
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虽然不是一个广泛命名的“定律” ,但存在热力学平衡状态是一个热力学'''<font color="#ff8000">公理 Axiom</font>'''。'''<font color="#ff8000">热力学第二定律 second law of thermodynamics</font>'''指出,当一个物质体从一个平衡状态开始,在这个状态中,它的一部分被或多或少渗透或不渗透的分区保持在不同的状态,并且是孤立的,热力学操作移除分区或使分区更具渗透性,然后它会自发地达到自己内部热力学平衡的新状态,并伴随着部分'''<font color="#ff8000">熵 Entropy</font>'''的总和增加。<br />
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== Overview 概览==<br />
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{{Thermodynamics|cTopic=[[Thermodynamic system|Systems]]}}<br />
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Classical thermodynamics deals with states of [[dynamic equilibrium]]. The state of a system at thermodynamic equilibrium is the one for which some [[thermodynamic potential]] is minimized, or for which the [[entropy]] (''S'') is maximized, for specified conditions. One such potential is the [[Helmholtz free energy]] (''A''), for a system with surroundings at controlled constant temperature and volume:<br />
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Classical thermodynamics deals with states of dynamic equilibrium. The state of a system at thermodynamic equilibrium is the one for which some thermodynamic potential is minimized, or for which the entropy (S) is maximized, for specified conditions. One such potential is the Helmholtz free energy (A), for a system with surroundings at controlled constant temperature and volume:<br />
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经典热力学研究'''<font color="#ff8000">动态平衡 Dynamic Equilibrium</font>'''的状态。系统的热力学平衡状态是对于特定的条件,一些'''<font color="#ff8000">热力学势 Thermodynamic Potential</font>'''被最小化,或者'''<font color="#ff8000">熵 Entropy</font>'''(S)被最大化。对于一个周围环境温度和体积恒定的系统,其中一个这样的热力学势是'''<font color="#ff8000">亥姆霍兹自由能 Helmholtz Free Energy</font>'''(A):<br />
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:<math>A = U - TS</math><br />
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<math>A = U - TS</math><br />
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A = U-TS<br />
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Another potential, the [[Gibbs free energy]] (''G''), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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Another potential, the Gibbs free energy (G), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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在恒定温度和压力的系统中,另一个热力学势'''<font color="#ff8000">吉布斯自由能 Gibbs Free Energy</font>'''(G)在热力学平衡状态最小:<br />
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:<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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where ''T'' denotes the absolute thermodynamic temperature, ''P'' the pressure, ''S'' the entropy, ''V'' the volume, and ''U'' the internal energy of the system.<br />
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where T denotes the absolute thermodynamic temperature, P the pressure, S the entropy, V the volume, and U the internal energy of the system.<br />
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其中 T 表示热力学绝对温度,P 表示压强,S 表示熵,V 表示体积,U 表示体系的内能。<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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热力学平衡是一种独特的稳定定态,当系统长时间与周围环境相互作用时,它可以被接近或最终到达。上述势能是数学构造的热力学量,在特定的环境条件下最小化。<br />
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== Conditions 条件==<br />
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* For a completely isolated system, ''S'' is maximum at thermodynamic equilibrium. 对于一个完全孤立的系统,S在热力学平衡中取最大值。<br />
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* For a system with controlled constant temperature and volume, ''A'' is minimum at thermodynamic equilibrium. 对于一个恒定温度和体积的系统来说,A在热力学平衡中取最小值。<br />
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* For a system with controlled constant temperature and pressure, ''G'' is minimum at thermodynamic equilibrium. 对于一个恒温恒压的系统,G在热力学平衡中取最小值。<br />
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The various types of equilibriums are achieved as follows:<br />
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The various types of equilibriums are achieved as follows:<br />
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实现各种类型的平衡的方法如下:<br />
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*Two systems are in ''thermal equilibrium'' when their [[temperature]]s are the same. 当两个系统的'''<font color="#ff8000">温度 Temperature</font>'''相同时,它们就处于''热平衡状态''<br />
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*Two systems are in ''mechanical equilibrium'' when their [[pressure]]s are the same. 当两个体系的'''<font color="#ff8000">压力 Pressure</font>'''相同时,它们就处于''力学平衡''<br />
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*Two systems are in ''diffusive equilibrium'' when their [[chemical potential]]s are the same. 当两个题体系的'''<font color="#ff8000">化学势 Chemical Potential</font>'''相同时,它们就处于''扩散平衡''<br />
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*All [[forces]] are balanced and there is no significant external driving force.<br />
所有的'''<font color="#ff8000">力 Force</font>'''都是平衡的,没有明显的外部驱动力<br />
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==Relation of exchange equilibrium between systems 系统之间的交换均衡关系==<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability.<ref name="Nster_a">Münster, A. (1970), p. 49.</ref> When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability. When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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通常,热力学系统的周围环境也可以被看作是另一个热力学系统。在这种观点中,我们可以把系统及其周围环境看作是相互接触的两个系统,远程作用力也将它们联系在一起。系统的包围物是两个系统之间的接触面或边界。在热力学形式中,该表面被认为具有特定的渗透性质。例如,接触的表面可能被认为只能透热,使能量只能作为热传递。当远程力在时间上不发生变化,两个系统之间的热量传递减慢并最终永久停止时,这两个系统被称为热平衡; 这就是接触平衡的一个例子。其它类型的接触平衡可用其它类型的比渗透率来定义。当两个系统对于某一特定类型的渗透率处于接触平衡时,它们具有属于该特定类型渗透率的强变量的共同值。这种强度变量的例子有温度、压力、化学势。<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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接触平衡也可视为交换平衡。在接触平衡状态下,两系统之间某些量的传递速率存在零平衡。例如,对于只能透热的壁,内能作为热在两个系统之间的扩散速率是相等并反向的。两个系统之间的绝热壁只对作为功传递的能量有渗透作用; 在力学平衡,两个系统之间作为功的能量传递速率相等且相反。如果是一个简单的壁,那么通过它的体积转移率也是相等且相反的; 即它两边的压力是相等的。如果绝热壁比较复杂,有一种杠杆,有一个面积比,那么两个体系在交换平衡中的压力与体积交换比成反比,这使得转移率的零平衡作功。<br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<ref name="Planck 1914 40">[[Max Planck|Planck. M.]] (1914), p. 40.</ref><br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<br />
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辐射交换可以发生在两个不同的系统之间。当两个体系温度相同时,辐射交换平衡占优势。<br />
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==Thermodynamic state of internal equilibrium of a system 系统内部平衡的热力学状态==<br />
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A collection of matter may be entirely [[Isolated system|isolated]] from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium.<ref>Haase, R. (1971), p. 4.</ref><ref>Callen, H.B. (1960/1985), p. 26.</ref> (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics.<ref>{{Cite journal |doi = 10.1119/1.4914528|bibcode = 2015AmJPh..83..628M|title = Time and irreversibility in axiomatic thermodynamics|year = 2015|last1 = Marsland|first1 = Robert|last2 = Brown|first2 = Harvey R.|last3 = Valente|first3 = Giovanni|journal = American Journal of Physics|volume = 83|issue = 7|pages = 628–634}}</ref> One textbook<ref>[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963), p. 5.</ref> calls it the "zeroth law", remarking that the authors think this more befitting that title than its [[Zeroth law of thermodynamics|more customary definition]], which apparently was suggested by [[Ralph H. Fowler|Fowler]].)<br />
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A collection of matter may be entirely isolated from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium. (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics. One textbook calls it the "zeroth law", remarking that the authors think this more befitting that title than its more customary definition, which apparently was suggested by Fowler.)<br />
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物质的集合可能与其周围的环境完全'''<font color="#ff8000">孤立 Isolated</font>'''。如果它在无限长的时间内一直保持不受干扰,按照经典热力学假定,它处于一个没有发生任何变化,没有流动的状态,即内部平衡的热力学状态。(这种假设有时被称为“负第一”热力学定律,但并不常见。有教科书称之为“第零定律” ,作者'''<font color="#ff8000">福勒 Fowler</font>'''认为这个名称是'''<font color="#ff8000">更符合惯例的定义 More Customary Definition</font>'''。)<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a [[thermodynamic operation]] be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a thermodynamic operation be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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这种状态是所谓的经典热力学或平衡态热力学的主要关注点,因为它们是系统中被认为在这门学科中得到很好定义的唯一状态。一个与另一个系统处于接触平衡状态可以被一个'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''隔离,在隔离发生时,其内部不会发生任何变化。因此,一个与另一个系统处于接触平衡状态时也可以被视为处于其自身的内部热力学平衡状态。<br />
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==Multiple contact equilibrium 多点接触平衡==<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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热力学形式允许一个系统同时与其他多个系统接触,这些系统可能有也可能没有相互接触,且这些接触具有不同的渗透性。如果这些系统都与世界其他部分相互隔离,那么它们彼此之间就会达到各自的接触平衡。<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy.<ref name="Caratheodory">Carathéodory, C. (1909).</ref><ref>Prigogine, I. (1947), p. 48.</ref><ref>Landsberg, P. T. (1961), pp. 128–142.</ref><ref>Tisza, L. (1966), p. 108.</ref> Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy. Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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如果几个系统彼此之间没有绝热壁,但是它们与世界其他部分共同隔离,那么它们就会达到多重接触平衡状态,且有共同的温度,总的内能和熵。在众多强度量中,这是温度的一个独特性质。即使在远距离作用力存在的情况下,它也是有效的。(也就是说,没有“力”可以维持温度的差异。)举个例子,在热力学平衡的一个垂直的引力场系统中,顶部壁面的压力比底部壁面的压力小,但是各处的温度都是一样的。<br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural [[thermodynamic process]].<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), § 1.12.</ref> It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings.<ref>Levine, I.N. (1983), p. 40.</ref><ref>Lieb, E.H., Yngvason, J. (1999), pp. 17–18.</ref> The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of [[Second law of thermodynamics#Description#Kelvin statement|"inanimate" agency]]; a system in thermodynamic equilibrium is inanimate.<ref>[[William Thomson, 1st Baron Kelvin|Thomson, W.]] (1851).</ref><br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural thermodynamic process. It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings. The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of "inanimate" agency; a system in thermodynamic equilibrium is inanimate.<br />
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热力操作可能作为一个事件发生在周围环境的壁上,既不直接影响与周围环境联系的壁,也不直接影响其内部,且发生在一个明确的有限的时间内。例如,一个固定的绝热壁可以在环境中被放置或拆除。由于这种操作仅限于周围环境,系统可能会在一段时间内远离自身最初的内部状态---- 热力学平衡。根据热力学第二定律的说法,整体经历了变化并最终与周围环境达到了新的平衡。继Planck之后,这一连串的事件被称为自然'''<font color="#ff8000">热力学过程 Thermodynamic Process</font>'''。即使在这个过程中,当系统和周围环境都不处于明确的内部平衡状态时,存在着暂时偏离热力学平衡的现象,由于初始状态和最终状态都是热力学平衡的,这在平衡热力学中也是允许的。一个自然过程在其主要部分中以有限的速率进行,因此,它从根本上不同于虚构的准静态“过程”;即不在整个过程中无限缓慢地进行而且虚构地“可逆”。经典热力学允许,即使一个过程可能需要很长的时间才能达到热力学平衡,如果主要部分的过程是在一个有限的比率中,那么它被认为是自然的,并受制于热力学第二定律,即不可逆的。工程设计的机器、人工设备和操作是允许在周围环境中进行的。允许在环境中而不是在系统中进行此类操作和设备,是开尔文在他的一个热力学第二定律的陈述中提到'''<font color="#ff8000">无生命机构 Inanimate Agency</font>'''的原因; 在热力学平衡的系统是无生命的。<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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否则,热力操作可能会直接影响系统的壁。<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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通常可以很方便地假设周围的某些子系统比系统大得多,以至于这个过程只能影响周围子系统的强度变量,然后将这些子系统称为相关强度变量的储备库。<br />
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== Local and global equilibrium 局部和全局均衡==<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by [[intensive quantity|intensive]] parameters. As an example, [[temperature]] controls [[Heat equation|heat exchanges]]. ''Global thermodynamic equilibrium'' (GTE) means that those [[intensive quantity|intensive]] parameters are homogeneous throughout the whole system, while ''local thermodynamic equilibrium'' (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by intensive parameters. As an example, temperature controls heat exchanges. Global thermodynamic equilibrium (GTE) means that those intensive parameters are homogeneous throughout the whole system, while local thermodynamic equilibrium (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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区分全局性和局部性热力学平衡是很有用的。在热力学中,系统内部和系统与外部之间的交换是由'''<font color="#ff8000">强度 Intensive</font>'''参数控制的。例如,'''<font color="#ff8000">温度 Temperature</font>'''控制'''<font color="#ff8000">热交换 Heat Equation</font>'''。全局热力学平衡(GTE)意味着这些'''<font color="#ff8000">强度 Intensive</font>'''参数在整个系统中是均匀的,而局部热力学平衡(LTE)意味着这些强度参数在空间和时间上是变化的,但变化如此缓慢,以至于对于任何一点,人们都可以假设在该点的某个邻域存在热力学平衡。<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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如果对系统的描述要求强度参数的变化过大,那么这些强度参数的定义所依据的假设本身就会失效,系统将既不处于全局平衡,也不处于局部平衡。例如,粒子需要一定数量的碰撞来平衡其周围环境。如果在这些碰撞中移动的平均距离使它离开平衡邻域,它将永远不会平衡,也就不会有 LTE。根据定义,温度与平衡邻域的平均内部能量成正比。由于没有达到平衡邻域,温度的概念就不成立,温度也就变得无法定义。<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to [[massive]] particles. In a [[radiation|radiating]] gas, the [[photon]]s being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to massive particles. In a radiating gas, the photons being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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值得注意的是,这种局部平衡可能只适用于系统中的某个粒子子集。例如,LTE 通常只适用于'''<font color="#ff8000">大 Massive</font>'''质量粒子。在'''<font color="#ff8000">辐射 Radiation</font>'''气体中,被气体发射和吸收的'''<font color="#ff8000">光子 Photon</font>'''不需要彼此在一个热力学平衡内,或与气体中的大量粒子在一起,LTE 才能存在。在某些情况下,自由电子并不需要与大得多的原子或分子处于平衡状态,LTE 才能存在。<br />
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As an example, LTE will exist in a glass of water that contains a melting [[ice cube]]. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the [[Maxwell–Boltzmann distribution]] for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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As an example, LTE will exist in a glass of water that contains a melting ice cube. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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例如,LTE 将存在于一个装有正在融化的'''<font color="#ff8000">冰块 Ice Cube</font>'''的水杯中。玻璃杯内的温度可以在任何时候定义,但是离冰块近的地方要比离冰块远的地方冷。如果观察到位于给定点附近的分子的能量,它们将按照麦克斯韦-波兹曼分布在一定温度下的分布。如果观察到位于另一点附近的分子的能量,它们将按照'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''分布到另一个温度。<br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural [[transport phenomena]] may lead a system from local to global thermodynamic equilibrium. Going back to our example, the [[diffusion]] of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<ref>H.R. Griem, 2005</ref><br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural transport phenomena may lead a system from local to global thermodynamic equilibrium. Going back to our example, the diffusion of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<br />
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局部热力学平衡不需要局部或全局的平稳性。换句话说,每一个小区域不需要有一个恒定的温度。然而,它确实要求每个小的局部变化缓慢到足以维持其局部麦克斯韦-波尔兹曼速度分布。全局非平衡态只有通过系统与外界的交换才能保持稳定。例如,通过在水杯中不断添加细粉冰来补偿熔化,并持续排出融水,可以保持全局稳定的静态。自然'''<font color="#ff8000">输运现象 Transport Phenomena</font>'''会使一个局部热力学平衡系统逐渐达到全局的热力学平衡。回顾我们的例子,热量的扩散将导致我们的玻璃杯水流向全局热力学平衡,在这种状态下,玻璃杯的温度是完全均匀的。<br />
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==Reservations 保留意见==<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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学识渊博的笔者在热力学领域对热力学平衡描述时,经常对他们的描述附加条件或保留意见。有些笔者含蓄地保留了或多或少的空白,以待说明。<br />
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For example, one widely cited writer, [[Herbert Callen|H. B. Callen]] writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. ''Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!''"<ref>Callen, H.B. (1960/1985), p. 15.</ref><br />
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For example, one widely cited writer, H. B. Callen writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!"<br />
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例如,一位被广泛引用的作家'''<font color="#ff8000">H.B.卡伦 H.B.Callen</font>'''在这里写道: “实际上,很少有系统处于绝对和真正的平衡状态。”他提到了放射性过程,认为它们可能需要“宇宙时间才能完成,因此通常可以忽略”。他补充道: “在实践中,平衡的标准是循环的。在操作上,如果一个系统的性质一致地用热力学理论来描述,那么它就处于平衡状态! ”<br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<ref>Beattie, J.A., Oppenheim, I. (1979), p. 3.</ref><br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<br />
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J.A.贝蒂和 I.奥本海姆写道: “坚持对平衡定义的严格解释,将排除热力学应用于实际系统的所有状态。”<br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment",<ref>Callen, H.B. (1960/1985), p. 485.</ref> and cited by Adkins as having written a "classic text",<ref>Adkins, C.J. (1968/1983), p. ''xiii''.</ref> [[Brian Pippard|A.B. Pippard]] writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<ref>Pippard, A.B. (1957/1966), p. 6.</ref><br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment", and cited by Adkins as having written a "classic text", A.B. Pippard writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<br />
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Callen引用另一位作者的话说,他给出了“学术且严谨的论述” ,Adkins引用他的话说,他写了一本“经典著作”—— '''<font color="#ff8000">A.B.皮帕德 A.B.Pippard</font>'''在文中写道: “只要时间足够长,过冷水蒸汽最终会凝结,... ..。时间可能是漫长的,也许长达10年或者更长。就大多数目的而言,只要这种迅速的变化不是人为地刺激,这些系统就可以被视为处于平衡状态。”<br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster">Münster, A. (1970), p. 53.</ref><br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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另一位作者A.Münster,写道。他观察到热核反应发生的速度非常缓慢,以至于在热力学中可以忽略不计。他评论道: “‘绝对平衡’或‘所有可想象过程的平衡’的概念没有物理意义。”他说: “ ... 我们只能考虑特定过程和确定的实验条件下的平衡。”<br />
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According to [[László Tisza|L. Tisza]]: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<ref>Tisza, L. (1966), p. 119.</ref><br />
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According to L. Tisza: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<br />
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根据'''<font color="#ff8000">L.缇莎 L.Tisza</font>'''的说法: “ ... 在讨论接近绝对零度的现象时。经典理论的绝对预测变得特别模糊,因为在非平衡状态下发生冻结是非常普遍的。”<br />
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==Definitions==<br />
定义<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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一个系统最普遍的热力学平衡是通过与周围环境的接触,允许所有化学物质和各种能量同时通过。热力学平衡中的系统以均匀加速度在空间中运动,但此时不能改变其形状或大小; 因此它是由空间中的刚性体积来定义的。它可能存在于外力场中,由远远大于系统本身的外部因素决定,因此系统内的事件不会对外力场产生相当大的影响。只有当外力场是均匀的,并且确定了它的均匀加速度,或者它处于一个非均匀力场中,但是由于表面的局部力,例如机械压力,使它保持静止时,这个系统才能处于热力学平衡。<br />
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Thermodynamic equilibrium is a [[primitive notion]] of the theory of thermodynamics. According to [[Philip M. Morse|P.M. Morse]]: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are ''not'' conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments."<ref>[[Philip M. Morse|Morse, P.M.]] (1969), p. 7.</ref> This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<ref>Bailyn, M. (1994), p. 20.</ref><br />
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Thermodynamic equilibrium is a primitive notion of the theory of thermodynamics. According to P.M. Morse: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are not conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments." This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<br />
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热力学平衡是热力学理论的一个'''<font color="#ff8000">基本概念 Primitive Notion</font>'''。'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''说: “应该强调的是,存在热力学状态这一事实,以及存在由平衡态唯一指定的热力学变量这一事实,并不是从某些哲学第一原理得出的逻辑结论。这些结论不可避免地来自两个多世纪的实验。”这意味着热力学平衡不能仅仅用热力学的其他理论概念来定义。M.Bailyn提出了一个基本的热力学定律理论,它定义并假设了热力学平衡的存在。<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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热力学平衡的教科书定义通常被仔细说明,并有些保留。<br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<ref>Münster, A. (1970), p. 52.</ref><br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<br />
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例如,A. Münster写道:“当系统中没有以可测量的速度发生状态变化时,隔离系统处于热力学平衡状态。”这里有两项保留:系统是孤立的;任何状态的变化都是不可估量的缓慢。他通过对在室温且没有催化剂的情况下混合氧和氢的说明,讨论了第二个条件。Münster指出,热力学平衡状态所描述的宏观变量比给定系统任何其他状态都少。这是部分,但不完全是,因为系统内和系统内的所有流都是零。<br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in ''equilibrium''.<ref>Haase, R. (1971), pp. 3–4.</ref><br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in equilibrium.<br />
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R. Haase's的热力学演示并不从对热力学平衡的限制开始,因为他打算考虑非平衡态热力学。他考虑一个具有时间不变性质的任意系统。他通过切断除外力场以外的所有外部影响来测试它的热力学平衡。如果在绝缘之后,没有任何变化,他说,系统处于平衡状态。<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness".<ref>Callen, H.B. (1960/1985), p. 13.</ref> This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness". This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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在一个标题为“热力学平衡”的章节中,H.B. Callen在段落定义了平衡状态.他指出,它们“是由系统内部的内在因素决定的”。它们是“终端状态” ,随着时间的推移,系统会以“冰川般缓慢”的速度朝着这个终端状态演化。这个说法并没有明确,对于热力学平衡系统必须是孤立的;;Callen也没有说明他所说的“内在因素”是什么意思。<br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<ref>Adkins, C.J. (1968/1983), p. ''7''.</ref><br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<br />
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另一位教科书作者,C.J.Adkins,明确允许热力学平衡在非孤立的系统中发生。然而,他的系统在物质转移方面是封闭的。他写道: “一般来说,热力学平衡的方法包括热和类似变动与周围环境的相互作用。”他将这种热力学平衡与只有通过热接触才能进行能量传递的热平衡相区别。<br />
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Another textbook author, [[J.R. Partington]], writes: "(i) ''An equilibrium state is one which is independent of time''." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..."<ref>Partington, J.R. (1949), p. 161.</ref> This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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Another textbook author, J.R. Partington, writes: "(i) An equilibrium state is one which is independent of time." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..." This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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另一位教科书作者'''<font color="#ff8000">J.R.帕廷顿 J.R.Partington</font>'''写道: “(i)平衡状态是独立于时间的状态。”但是,在提到“只是明显处于平衡状态”的系统时,他补充说: “这样的系统处于‘虚假平衡’状态。帕廷顿的陈述没有明确指出平衡是指一个孤立的系统。和Münster一样,Partington也指的是氧和氢的混合物。他补充说:“在一个真正的平衡状态,任何影响状态的外部条件的最小变化都会产生一个微小的状态变化... ... ”这个条件意味着热力学平衡必须在小的扰动下保持稳定; 这个要求对于热力学平衡的严格意义是必不可少的。<br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, ''thermodynamic—equilibrium.''"<ref>Crawford, F.H. (1963), p. 5.</ref><br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, thermodynamic—equilibrium."<br />
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在F.H.Crawford的一本学生教科书中,有一个标题为“热力学平衡”的章节。它区分了几种流动的驱动因素,然后说: “这些是孤立系统明显普遍趋向于完全机械、热、化学和电力状态的例子——或者简单地说,热力学平衡状态。”<br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in ''equilibrium''."<ref>Buchdahl, H.A. (1966), p. 8.</ref> Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being ''in equilibrium'' so long as experimental tests show that 'slow' transitions are in effect reversible."<ref>Buchdahl, H.A. (1966), p. 111.</ref> It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<ref>Adkins, C.J. (1968/1983), p. 8.</ref><br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in equilibrium." Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being in equilibrium so long as experimental tests show that 'slow' transitions are in effect reversible." It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<br />
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H.A. Buchdahl的一本关于经典热力学的专著考虑了热力学系统的平衡,而实际上并没有写热力学平衡一词。Buchdahl在提到封闭的物质交换系统时写道: “如果一个系统处于一个适当的静态状态,那么它将被称为处于平衡状态。”出于热力学描述的目的,Buchdahl的专著也讨论了非晶态玻璃。它说: “更准确地说,只要实验测试表明‘慢’跃迁实际上是可逆的,玻璃就可以被认为处于平衡状态。”通常来说不会将这一条件作为热力学平衡定义的一部分,而是假定相反的情况:如果热力学平衡中的一个体受到足够慢的过程的影响,则该过程可被视为足够接近可逆,并且该物体在过程中足够接近热力学平衡。<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of ''contact equilibrium''. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by [[Constantin Carathéodory|C. Carathéodory]], and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster" /> Thermodynamic equilibrium for an open system means that, with respect to every relevant kind of selectively permeable wall, contact equilibrium exists when the respective intensive parameters of the system and surroundings are equal.<ref name="Nster_a" /> This definition does not consider the most general kind of thermodynamic equilibrium, which is through unselective contacts. This definition does not simply state that no current of matter or energy exists in the interior or at the boundaries; but it is compatible with the following definition, which does so state.<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of contact equilibrium. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by C. Carathéodory, and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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通过引入接触平衡的概念,A. Münster仔细地扩展了孤立系统热力学平衡的定义。这指定了在考虑非孤立系统的热力学平衡时允许的特定过程,并特别关心开放系统,这些开放系统可能从周围环境获得或丢失物质。利益系统和周围系统之间的接触平衡,通过一种特殊的壁与利益系统接触,其余的连接系统是孤立的。这种特殊类型的壁也被'''<font color="#ff8000">C.喀喇西奥多里 C.Carathéodory</font>'''考虑过,其他作家也提到过。它们具有选择渗透性。它们可能只对机械工作有渗透性,或者只对热有渗透性,或者只对某种特定的化学物质有渗透性。每个接触平衡定义了一个强度参数; 例如,只能透热的壁定义了一个经验温度。对于感兴趣的体系中每一种化学成分,都可以存在接触平衡。在接触平衡中,尽管有可能通过选择性渗透壁进行交换,感兴趣的系统是不变的,好像它处在孤立的热力学平衡。这个方案遵循的一般规则是: “ ... ... 我们只能考虑特定过程和特定实验条件下的平衡。”<br />
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[[Mark Zemansky|M. Zemansky]] also distinguishes mechanical, chemical, and thermal equilibrium. He then writes: "When the conditions for all three types of equilibrium are satisfied, the system is said to be in a state of thermodynamic equilibrium".<ref>[[Mark Zemansky|Zemansky, M.]] (1937/1968), p. 27.</ref><br />
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'''<font color="#ff8000">M.泽曼斯基 M.Zemansky</font>'''还区分了机械、化学和热平衡。他接着写道: “当这三种均衡的条件都满足时,系统就处于热力学平衡状态。”<br />
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P.M. Morse writes that thermodynamics is concerned with "states of thermodynamic equilibrium". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<br />
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[[Philip M. Morse|P.M. Morse]] writes that thermodynamics is concerned with "''states of thermodynamic equilibrium''". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<ref>[[Philip M. Morse|Morse, P.M.]] (1969), pp. 6, 37.</ref><br />
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'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''写道,热力学关注的是“热力学平衡状态”。在讨论物体与周围热源之间的热量传递时,他也使用了“热平衡”这个短语,尽管没有明确定义一个特殊的术语“热平衡”<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "full thermodynamic equilibrium state".<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "''full'' thermodynamic equilibrium state".<ref>Waldram, J.R. (1985), p. 5.</ref><br />
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J.R. Waldram写到了“一个明确的热力学状态”。他将一个系统定义为“当其观测量随时间停止变化时”的“热平衡”。但是在这个定义之下不久,他写到一块玻璃还没有达到“完全的热力学平衡状态”。<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, thermodynamic equilibrium is said to exist." He is not here considering the presence of an external force field.<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, ''thermodynamic equilibrium'' is said to exist." He is not here considering the presence of an external force field.<ref>Bailyn, M. (1994), p. 21.</ref><br />
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考虑到平衡状态,M.Bailyn写道: “每个强度变量都有自己的平衡类型。”然后他定义了热平衡、机械平衡和物质平衡。因此,他写道: “如果所有的强度变量都是一致的,那么热力学平衡就是存在的。”他在这里没有考虑外力场的存在。<br />
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J.G. Kirkwood and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of thermodynamic equilibrium if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<br />
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[[John Gamble Kirkwood|J.G. Kirkwood]] and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of ''thermodynamic equilibrium'' if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<ref>Kirkwood, J.G., Oppenheim, I. (1961), p. 2</ref><br />
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'''<font color="#ff8000">J.G.柯克伍德 J.G.Kirkwood</font>'''和 I.Oppenheim 将热力学平衡定义为: “一个系统处于热力学平衡状态,如果,在分配给实验的时间内,(a)它强度特性与时间无关,(b)它的内部或与周围环境的边界处没有物质或能量流。”显然,他们没有把定义限制在孤立的或封闭的系统。它们不讨论“缓慢”发生变化的可能性,并且超出了分配给实验的时间范围。他们注意到,对于两个相接触的系统,存在一个强度性质的小子类,如果这个小子类的所有子类都相等,那么所有各自的强度性质都相等。只要满足其他一些条件,热力学平衡状态可以由这个子类定义。<br />
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==Characteristics of a state of internal thermodynamic equilibrium==<br />
内部热力学平衡状态的特征<br />
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A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous. Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface." As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.<br />
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在内部热力学平衡中,没有外力的情况下由单相组成的热力学系统是均匀的。Planck在论文中简要介绍了热量、温度和热平衡,然后宣布: “在下文中,我们将主要讨论任何形式的均匀、各向同性的物体,它们在整个物质中具有相同的温度和密度,并受到到处垂直于表面的均匀压力作用。”和 Carathéodory 一样,Planck 将表面效应、外场和各向异性晶体排除在外。虽然Planck提到了温度,但并没有明确提到热力学平衡的概念。相比之下,Carathéodory 关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ,虽然没有明确地使用短语‘热力学平衡’,也没有明确地假设存在一个温度来定义它。<br />
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===Homogeneity in the absence of external forces===<br />
在没有外力的情况下的同质性<br />
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A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous.<ref name="Planck 1903 3"/> This means that the material in any small volume element of the system can be interchanged with the material of any other geometrically congruent volume element of the system, and the effect is to leave the system thermodynamically unchanged. In general, a strong external force field makes a system of a single phase in its own internal thermodynamic equilibrium inhomogeneous with respect to some [[Intensive and extensive properties|intensive variables]]. For example, a relatively dense component of a mixture can be concentrated by centrifugation.<br />
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在没有外力的情况下,由单一相组成的热力学系统,在其自身的内部热力学平衡中是均匀的。这意味着系统中任何小体积单元中的材料可以与系统中任何其他几何相等的体积单元中的材料互换,其效果是使系统在热力学上保持不变。一般来说,一个强外力场使得一个单相系统在其自身的内部热力学平衡中对于一些'''<font color="#ff8000">强变量 Intensive Variable</font>'''是不均匀的。例如,可以通过离心来浓缩混合物中相对密度较大的组分。<br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform. Considerations of kinetic theory or statistical mechanics also support this statement.<br />
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热力学平衡系统中的温度在空间和时间上是均匀的。在一个系统内部热力学平衡状态下,没有净内部宏观流动。特别是,这意味着系统的所有局部部分处于相互辐射交换平衡状态。这意味着系统的温度在空间上是均匀的。动力学理论或统计力学也支持这种说法。<br />
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===Uniform temperature===<br />
均匀温度<br />
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In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium. As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.<br />
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为了使一个系统处于它自己的内部热力学平衡状态,它处于自己内部的热平衡状态当然是必要的,但不是充分的;系统在达到内部热平衡之前,可以达到内部机械平衡。如上所述,根据 A.Münster的说法,对于给定的孤立系统的任何状态,定义一个热力学平衡所需的变量数是最少的。如上所述,J.G.Kirkwood 和 I.Oppenheim 指出,热力学平衡状态可以由一个特殊的子类的强变量定义,该子类中有一定数量的成员。<br />
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Such equilibrium inhomogeneity, induced by external forces, does not occur for the intensive variable [[temperature]]. According to [[Edward A. Guggenheim|E.A. Guggenheim]], "The most important conception of thermodynamics is temperature."<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), p.5.</ref> Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface."<ref name="Planck 1903 3">[[Max Planck|Planck, M.]] (1897/1927), p.3.</ref> As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.<br />
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这种由外力引起的平衡不均匀性,在强烈变化的'''<font color="#ff8000">温度 Temperature</font>'''下不会发生。'''<font color="#ff8000">E.A.古根海姆 E.A. Guggenheim</font>'''认为,“热力学最重要的概念是温度。“Planck在介绍他的论文时,简要叙述了热、温度和热平衡,然后宣布: ”在下文中,我们将主要讨论任何形式的均匀、各向同性的物体,它们的物质具有相同的温度和密度,并受到到处垂直于表面的均匀压力的作用和Carathéodory 一样,Planck将表面效应、外场和各向异性晶体排除在外。虽然Planck提到了温度,但并没有明确提到热力学平衡的概念。相比之下,Carathéodory关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ,虽然没有明确地使用短语‘热力学平衡’ ,也没有明确地假设存在一个温度来定义它。<br />
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<br />
If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.<br />
<br />
如果热力学平衡位于一个外力场中,那么通常只有温度在空间上是均匀的。如果外力场非零,温度以外的强度变量通常是不均匀的。在这种情况下,一般需要附加变量来描述空间非均匀性。<br />
<br />
The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform.<ref name="Planck 1914 40"/> This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers.<ref>Gibbs, J.W. (1876/1878), pp. 144-150.</ref><ref>[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966), pp. 127–130.</ref><ref>Münster, A. (1970), pp. 309–310.</ref><ref>Bailyn, M. (1994), pp. 254-256.</ref><ref>{{cite journal | last1 = Verkley | first1 = W.T.M. | last2 = Gerkema | first2 = T. | year = 2004 | title = On maximum entropy profiles | journal = J. Atmos. Sci. | volume = 61 | issue = 8| pages = 931–936 | doi=10.1175/1520-0469(2004)061<0931:omep>2.0.co;2| bibcode = 2004JAtS...61..931V | doi-access = free }}</ref><ref>{{cite journal | last1 = Akmaev | first1 = R.A. | year = 2008 | title = On the energetics of maximum-entropy temperature profiles | url = | journal = Q. J. R. Meteorol. Soc. | volume = 134 | issue = 630| pages = 187–197 | doi=10.1002/qj.209| bibcode = 2008QJRMS.134..187A }}</ref> Considerations of kinetic theory or statistical mechanics also support this statement.<ref>Maxwell, J.C. (1867).</ref><ref>Boltzmann, L. (1896/1964), p. 143.</ref><ref>Chapman, S., Cowling, T.G. (1939/1970), Section 4.14, pp. 75–78.</ref><ref>[[J. R. Partington|Partington, J.R.]] (1949), pp. 275–278.</ref><ref>{{cite journal | last1 = Coombes | first1 = C.A. | last2 = Laue | first2 = H. | year = 1985 | title = A paradox concerning the temperature distribution of a gas in a gravitational field | url = | journal = Am. J. Phys. | volume = 53 | issue = 3| pages = 272–273 | doi=10.1119/1.14138| bibcode = 1985AmJPh..53..272C }}</ref><ref>{{cite journal | last1 = Román | first1 = F.L. | last2 = White | first2 = J.A. | last3 = Velasco | first3 = S. | year = 1995 | title = Microcanonical single-particle distributions for an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 16 | issue = 2| pages = 83–90 | doi=10.1088/0143-0807/16/2/008| bibcode = 1995EJPh...16...83R }}</ref><ref>{{cite journal | last1 = Velasco | first1 = S. | last2 = Román | first2 = F.L. | last3 = White | first3 = J.A. | year = 1996 | title = On a paradox concerning the temperature distribution of an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 17 | issue = | pages = 43–44 | doi=10.1088/0143-0807/17/1/008}}</ref><br />
<br />
热力学平衡系统内的温度在时间和空间上都是均匀的。在一个处于内部热力学平衡的系统中,不存在净的内部宏观流动。特别是,这意味着系统的所有局部都处于相互辐射交换平衡。这意味着系统的温度在空间上是均匀的。这在所有情况下都是如此,包括那些非均匀外力场。对于外部施加的引力场,这可以通过使用朗朗日乘数的方法通过变化的演算在宏观热力学术语中证明。动力学理论或统计力学也支持这种说法。<br />
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<br />
In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium.<ref name="Fitts 43"/><br />
<br />
为了使一个系统处于它自己的内部热力学平衡状态,它必须处于它自己的内部热平衡状态是必要不充分的; 一个系统在到达内部热平衡之前到达内部机械平衡是可能的。<br />
<br />
As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.<br />
<br />
如上所述,j.r. Partington 指出热力学平衡状态在小的瞬态扰动下是稳定的。如果没有这个条件,一般来说,研究热力学平衡系统的实验就会遇到巨大的困难。<br />
<br />
===Number of real variables needed for specification===<br />
规范所需的实变量数目<br />
<br />
<br />
In his exposition of his scheme of closed system equilibrium thermodynamics, C. Carathéodory initially postulates that experiment reveals that a definite number of real variables define the states that are the points of the manifold of equilibria.<ref name="Caratheodory" /> In the words of Prigogine and Defay (1945): "It is a matter of experience that when we have specified a certain number of macroscopic properties of a system, then all the other properties are fixed."<ref>Prigogine, I., Defay, R. (1950/1954), p. 1.</ref><ref>Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005), p. 4.</ref> As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.<br />
<br />
在他关于封闭系统平衡态热力学方案的论述中,C.Carathéodory 最初假定实验揭示了一定数量的实变量定义了作为平衡态流形点的状态。用 Prigogine 和 Defay (1945)的话说: “这是一个经验问题,当我们确定了一个系统一定数量的宏观属性时,那么所有其他属性都是固定的。如上所述,A. Münster认为,定义热力学平衡所需的变量数量对于给定孤立系统的任何状态来说都是最少的。如上所述,J.G. Kirkwood 和 I. Oppenheim 指出,热力学平衡状态可以由一个特殊子类的强度变量来定义,该子类中有一定数量的成员。<br />
<br />
When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium. Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<br />
<br />
当一个物质体从不均匀的非平衡状态或化学非平衡状态开始,然后被孤立,它自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如,在这种演变的许多情况下,内部机械平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是,在这种演变的许多情况下,热平衡的发展要比化学平衡快得多。<br />
<br />
<br />
<br />
If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.<br />
<br />
如果热力学平衡位于一个外力场中,那么通常只有温度在空间上是均匀的。如果外力场非零,温度以外的强度变量通常是不均匀的。在这种情况下,一般需要附加变量来描述空间非均匀性。<br />
<br />
===Stability against small perturbations===<br />
对小扰动的稳定性<br />
<br />
In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
<br />
在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
<br />
As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.<br />
<br />
如上所述,J.R. Partington 指出热力学平衡状态在小的瞬态扰动下是稳定的。如果没有这个条件,一般来说,研究热力学平衡系统的实验就会遇到严重的困难。<br />
<br />
<br />
To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics. But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
<br />
考虑孤立热力学系统中的波动概念,一个方便的例子是由其广泛的状态变量、内能、体积和质量组成指定的系统。根据定义,它们是时不变的。根据定义,它们与它们的共轭状态密集函数的时不变名义值相结合,反向温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广泛的状态变量的值,不足以提供这些名义值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
<br />
===Approach to thermodynamic equilibrium within an isolated system===<br />
孤立系统中的热力学平衡<br />
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It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.<br />
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可以承认,在重复测量这些共轭强度函数时,发现它们的值随时间略有不同。这种可变性被认为是由于内部波动。不同测量值平均到其名义值。<br />
<br />
When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium.<ref name="Fitts 43">Fitts, D.D. (1962), p. 43.</ref> Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<ref>Denbigh, K.G. (1951), p. 42.</ref><br />
<br />
当一个物质体从不均匀的非平衡状态或化学非平衡状态开始,然后被孤立,它自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如,在这种演变的许多情况下,内部机械平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是,在这种演变的许多情况下,热平衡的发展要比化学平衡快得多。<br />
<br />
If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<br />
<br />
如果这个系统真的像经典热力学所假定的那样是宏观的,那么这个系统的波动太小了,宏观上无法检测到。这就是所谓的热力学极限。实际上,物质的分子性质和动量转移的量子性质由于它们太小而看不见,已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中,平衡的波动概念是没有位置的。”<br />
<br />
===Fluctuations within an isolated system in its own internal thermodynamic equilibrium===<br />
孤立系统内部热力学平衡的波动<br />
<br />
<br />
If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
<br />
如果系统被重复细分,最终产生的系统足够小,可以表现出明显的波动。这是一个介观层面的研究。波动则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
<br />
In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
<br />
在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
<br />
<br />
If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
<br />
如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在波动过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,即需要量子统计力学。波动可以变得相对占主导地位,测量问题变得重要。<br />
<br />
To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics.<ref>Tschoegl, N.W. (2000). ''Fundamentals of Equilibrium and Steady-State Thermodynamics'', Elsevier, Amsterdam, {{ISBN|0-444-50426-5}}, p. 21.</ref> But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
<br />
考虑孤立热力学系统中的波动概念,一个方便的例子是由其众多的状态变量,内能、体积和质量组成指定的系统。根据定义,它们是时不变的。根据定义,它们与它们的共轭状态密集函数的时不变名义值相结合,反向温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广泛的状态变量的值,不足以提供这些名义值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
<br />
<br />
The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
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"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有时间趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的标称值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微波动期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。非已知属于平衡状态的标称值,否则根据单一的度量无法进行判断。<br />
<br />
It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.<br />
<br />
可以承认,在重复测量这些共轭强度函数时,发现它们的值随时间略有不同。这种可变性被认为是由于内部波动。不同测量值平均到其名义值。<br />
<br />
<br />
<br />
If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<ref>Buchdahl, H.A. (1966), p. 16.</ref><br />
<br />
如果这个系统真的像经典热力学所假定的那样是宏观的,那么这个系统的波动太小了,宏观上无法检测到。这就是所谓的热力学极限。实际上,物质的分子性质和动量转移的量子性质由于它们太小而看不见,已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中,平衡的波动概念是没有位置的。”<br />
<br />
<br />
If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
<br />
如果系统被重复细分,最终产生的系统足够小,可以表现出明显的波动。这是一个介观层面的研究。波动则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
<br />
An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process." This illustrates the importance for thermodynamics of the concept of temperature.<br />
<br />
热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
<br />
<br />
<br />
If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在波动过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,即需要量子统计力学。波动可以变得相对占主导地位,测量问题变得重要。<br />
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Thermal equilibrium is achieved when two systems in thermal contact with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<br />
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当两个相互热接触的系统不再有净能量交换时,就会产生热平衡。因此,如果两个系统处于热平衡,那么它们的温度是相同的。<br />
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The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
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"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有时间趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的标称值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微波动期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。非已知属于平衡状态的标称值,否则根据单一的度量无法进行判断。<br />
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Thermal equilibrium occurs when a system's macroscopic thermal observables have ceased to change with time. For example, an ideal gas whose distribution function has stabilised to a specific Maxwell–Boltzmann distribution would be in thermal equilibrium. This outcome allows a single temperature and pressure to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<br />
<br />
当系统的宏观热观测值不再随着时间变化时,就会出现热平衡。例如,一种分布函数稳定到一个特定的麦克斯韦-波兹曼分布的理想气体即处于热平衡状态。这个结果可以将单一的温度和压力归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是很有可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
<br />
=== Thermal equilibrium ===<br />
热平衡<br />
{{Main|Thermal equilibrium}}<br />
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<br />
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An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process."<ref>Eu, B.C. (2002), page 13.</ref> This illustrates the importance for thermodynamics of the concept of temperature.<br />
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热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
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A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<br />
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一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数。<br />
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[[Thermal equilibrium]] is achieved when two systems in [[thermal contact]] with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<ref>[[Raj Pathria|R. K. Pathria]], 1996</ref><br />
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当两个相互'''<font color="#ff8000">热接触 Thermal Contact</font>'''的系统不再有净能量交换时,就会产生'''<font color="#ff8000">热平衡 Thermal Equilibrium</font>'''。因此,如果两个系统处于热平衡,那么它们的温度是相同的<br />
<br />
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
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Thermal equilibrium occurs when a system's [[macroscopic]] thermal observables have ceased to change with time. For example, an [[ideal gas]] whose [[Distribution function (physics)|distribution function]] has stabilised to a specific [[Maxwell–Boltzmann distribution]] would be in thermal equilibrium. This outcome allows a single [[temperature]] and [[pressure]] to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<ref>de Groot, S.R., Mazur, P. (1962), p. 44.</ref><br />
<br />
当一个系统的'''<font color="#ff8000">宏观 Macroscopic</font>'''热观测值不再随时间变化时,就会出现热平衡。例如,一种'''<font color="#ff8000">分布函数 Distribution Function</font>'''稳定到一个特定的'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''的'''<font color="#ff8000">理想气体 Ideal Gas</font>'''即处于热平衡状态。这个结果可以将单一的'''<font color="#ff8000">温度 Temperature</font>'''和'''<font color="#ff8000">压力 Pressure</font>'''归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
<br />
Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle. It states that a non-equilibrium system evolves such as to maximize its entropy production.<br />
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定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
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==Non-equilibrium==<br />
非平衡<br />
{{Main|Non-equilibrium thermodynamics}}<br />
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Thermodynamic models <br />
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热力学模型<br />
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A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<ref>de Groot, S.R., Mazur, P. (1962), p. 43.</ref><br />
<br />
一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数<br />
<br />
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
<br />
非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
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Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle.<ref>{{cite book|last1=Ziegler|first1=H.|title=An Introduction to Thermomechanics.|date=1983|location=North Holland, Amsterdam.}}</ref><ref>{{cite journal|last1=Onsager|first1=Lars|title=Reciprocal Relations in Irreversible Processes|journal=Phys. Rev.|date=1931|volume=37|issue=4|doi=10.1103/PhysRev.37.405|bibcode=1931PhRv...37..405O|pages=405–426|doi-access=free}}</ref> It states that a non-equilibrium system evolves such as to maximize its entropy production.<ref>{{cite book|last1=Kleidon|first1=A.|last2=et.|first2=al.|title=Non-equilibrium Thermodynamics and the Production of Entropy.|date=2005|edition=Heidelberg: Springer.}}</ref><ref>{{cite journal|last1=Belkin|first1=Andrey|last2=et.|first2=al.|title=Self-Assembled Wiggling Nano-Structures and the Principle of Maximum Entropy Production|journal=Sci. Rep.|doi=10.1038/srep08323|bibcode=2015NatSR...5E8323B|pmc=4321171|pmid=25662746|volume=5|year=2015|page=8323}}</ref><br />
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定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
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Topics in control theory<br />
<br />
控制理论主题<br />
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==See also ==<br />
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{{Portal|Chemistry}}<br />
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;Thermodynamic models 热力学模型<br />
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{{colbegin}}<br />
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* [[Non-random two-liquid model]] (NRTL model) - Phase equilibrium calculations 非随机两液模型(NRTL 模型)-相平衡计算<br />
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* [[UNIQUAC]] model - Phase equilibrium calculations UNIQUAC 模型-相平衡计算<br />
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* [[Time crystal]] 时间晶体<br />
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{{colend}}<br />
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;Topics in control theory 控制理论主题<br />
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{{colbegin}}<br />
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* [[Steady state]] 稳态<br />
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* [[Transient state]] 瞬态<br />
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* [[Coefficient diagram method]] 系数图法<br />
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* [[Control reconfiguration]] 控制重构<br />
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* [[Cut-insertion theorem]] 切入定理<br />
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* [[Feedback]] 反馈<br />
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* [[H infinity]] H 无限<br />
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* [[Hankel singular value]] 汉克尔奇异值<br />
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* [[Krener's theorem]] 克雷纳定理<br />
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* [[Lead-lag compensator]] 超前滞后补偿器<br />
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* [[Minor loop feedback]] 小循环反馈<br />
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* [[Minor loop feedback|Multi-loop feedback]] 小循环反馈 | 多循环反馈<br />
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* [[Positive systems]] 正向系统<br />
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* [[Radial basis function]] 径向基底函数<br />
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Other related topics<br />
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其他相关话题<br />
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* [[Root locus]] 根轨迹<br />
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* [[Signal-flow graph]]s 信号流图<br />
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* [[Stable polynomial]] 稳定多项式<br />
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* [[State space representation]] 状态空间<br />
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* [[Underactuation]] 欠驱动<br />
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* [[Youla–Kucera parametrization]] 尤拉-库切拉参数化<br />
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* [[Markov chain approximation method]] 马尔可夫链近似法<br />
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{{colend}}<br />
<br />
;Other related topics<br />
其他相关话题<br />
<br />
{{colbegin}}<br />
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* [[Automation and remote control]] 自动化和远程控制<br />
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* [[Bond graph]] 键合图<br />
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* [[Control engineering]] 控制工程<br />
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* [[Control–feedback–abort loop]] 控制-反馈-中止循环<br />
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* [[Controller (control theory)]] 控制器(控制理论)<br />
<br />
* [[Cybernetics]] 控制论<br />
<br />
* [[Intelligent control]] 智能控制<br />
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* [[Mathematical system theory]] 数学系统论<br />
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* [[Negative feedback amplifier]] 负反馈放大器<br />
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* [[People in systems and control]] 系统和控制中的人<br />
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* [[Perceptual control theory]] 知觉控制理论<br />
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* [[Systems theory]] 系统论<br />
<br />
* [[Time scale calculus]] 时间尺度演算<br />
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{{colend}}<br />
<br />
<br />
<br />
== 编者推荐 ==<br />
===集智文章推荐===<br />
<br />
====[https://swarma.org/?p=21322 什么是非平衡态热力学 | 集智百科]====<br />
非平衡态热力学 Non-equilibrium thermodynamics 是热力学的一个分支,研究某些不处于热力学平衡中的物理系统<br />
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<br />
==General references==<br />
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* Cesare Barbieri (2007) ''Fundamentals of Astronomy''. First Edition (QB43.3.B37 2006) CRC Press {{ISBN|0-7503-0886-9}}, {{ISBN|978-0-7503-0886-1}}<br />
<br />
* Hans R. Griem (2005) ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}<br />
<br />
* C. Michael Hogan, Leda C. Patmore and Harry Seidman (1973) ''Statistical Prediction of Dynamic Thermal Equilibrium Temperatures using Standard Meteorological Data Bases'', Second Edition (EPA-660/2-73-003 2006) United States Environmental Protection Agency Office of Research and Development, Washington, D.C. [http://library.wur.nl/WebQuery/catalog/lang/1851848]<br />
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* F. Mandl (1988) ''Statistical Physics'', Second Edition, John Wiley & Sons<br />
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==References==<br />
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{{Reflist|colwidth=35em}}<br />
<br />
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==Cited bibliography==<br />
<br />
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<br />
*Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', third edition, McGraw-Hill, London, {{ISBN|0-521-25445-0}}.<br />
<br />
*Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, {{ISBN|0-88318-797-3}}.<br />
<br />
*Beattie, J.A., Oppenheim, I. (1979). ''Principles of Thermodynamics'', Elsevier Scientific Publishing, Amsterdam, {{ISBN|0-444-41806-7}}.<br />
<br />
*[[Ludwig Boltzmann|Boltzmann, L.]] (1896/1964). ''Lectures on Gas Theory'', translated by S.G. Brush, University of California Press, Berkeley.<br />
<br />
*Buchdahl, H.A. (1966). ''The Concepts of Classical Thermodynamics'', Cambridge University Press, Cambridge UK.<br />
<br />
*[[Herbert Callen|Callen, H.B.]] (1960/1985). ''Thermodynamics and an Introduction to Thermostatistics'', (1st edition 1960) 2nd edition 1985, Wiley, New York, {{ISBN|0-471-86256-8}}.<br />
<br />
*[[Constantin Carathéodory|Carathéodory, C.]] (1909). [https://web.archive.org/web/20160304213645/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0067&DMDID=DMDLOG_0033&L=1 Untersuchungen über die Grundlagen der Thermodynamik], ''[[Mathematische Annalen]]'', '''67''': 355–386. A translation may be found [http://neo-classical-physics.info/uploads/3/0/6/5/3065888/caratheodory_-_thermodynamics.pdf here]. Also a mostly reliable [https://books.google.com/books?id=xwBRAAAAMAAJ&q=Investigation+into+the+foundations translation is to be found] at Kestin, J. (1976). ''The Second Law of Thermodynamics'', Dowden, Hutchinson & Ross, Stroudsburg PA.<br />
<br />
*[[Sydney Chapman (mathematician)|Chapman, S.]], [[Thomas George Cowling|Cowling, T.G.]] (1939/1970). ''The Mathematical Theory of Non-uniform gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases'', third edition 1970, Cambridge University Press, London.<br />
<br />
*Crawford, F.H. (1963). ''Heat, Thermodynamics, and Statistical Physics'', Rupert Hart-Davis, London, Harcourt, Brace & World, Inc.<br />
<br />
*de Groot, S.R., Mazur, P. (1962). ''Non-equilibrium Thermodynamics'', North-Holland, Amsterdam. Reprinted (1984), Dover Publications Inc., New York, {{ISBN|0486647412}}.<br />
<br />
*Denbigh, K.G. (1951). ''Thermodynamics of the Steady State'', Methuen, London.<br />
<br />
*Eu, B.C. (2002). ''Generalized Thermodynamics. The Thermodynamics of Irreversible Processes and Generalized Hydrodynamics'', Kluwer Academic Publishers, Dordrecht, {{ISBN|1-4020-0788-4}}.<br />
<br />
*Fitts, D.D. (1962). ''Nonequilibrium thermodynamics. A Phenomenological Theory of Irreversible Processes in Fluid Systems'', McGraw-Hill, New York.<br />
<br />
*[[Josiah Willard Gibbs|Gibbs, J.W.]] (1876/1878). On the equilibrium of heterogeneous substances, ''Trans. Conn. Acad.'', '''3''': 108–248, 343–524, reprinted in ''The Collected Works of J. Willard Gibbs, Ph.D, LL. D.'', edited by W.R. Longley, R.G. Van Name, Longmans, Green & Co., New York, 1928, volume 1, pp.&nbsp;55–353.<br />
<br />
*Griem, H.R. (2005). ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}.<br />
<br />
*[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', fifth revised edition, North-Holland, Amsterdam.<br />
<br />
*Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of ''Thermodynamics'', pages 1–97 of volume 1, ed. W. Jost, of ''Physical Chemistry. An Advanced Treatise'', ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081.<br />
<br />
*[[John Gamble Kirkwood|Kirkwood, J.G.]], Oppenheim, I. (1961). ''Chemical Thermodynamics'', McGraw-Hill Book Company, New York.<br />
<br />
*Landsberg, P.T. (1961). ''Thermodynamics with Quantum Statistical Illustrations'', Interscience, New York.<br />
<br />
*{{cite journal |last1=Lieb |first1=E. H. |last2=Yngvason |first2=J. |year=1999 |title=The Physics and Mathematics of the Second Law of Thermodynamics |journal=Phys. Rep. |volume=310 |issue= 1|pages=1–96 |doi= 10.1016/S0370-1573(98)00082-9|arxiv = cond-mat/9708200 |bibcode = 1999PhR...310....1L |s2cid=119620408 }}<br />
<br />
*Levine, I.N. (1983), ''Physical Chemistry'', second edition, McGraw-Hill, New York, {{ISBN|978-0072538625}}.<br />
<br />
*{{cite journal | last1 = Maxwell | first1 = J.C. | authorlink = James Clerk Maxwell | year = 1867 | title = On the dynamical theory of gases | url = | journal = Phil. Trans. Roy. Soc. London | volume = 157 | issue = | pages = 49–88 }}<br />
<br />
*[[Philip M. Morse|Morse, P.M.]] (1969). ''Thermal Physics'', second edition, W.A. Benjamin, Inc, New York.<br />
<br />
*Münster, A. (1970). ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London.<br />
<br />
*[[J.R. Partington|Partington, J.R.]] (1949). ''An Advanced Treatise on Physical Chemistry'', volume 1, ''Fundamental Principles. The Properties of Gases'', Longmans, Green and Co., London.<br />
<br />
*[[Brian Pippard|Pippard, A.B.]] (1957/1966). ''The Elements of Classical Thermodynamics'', reprinted with corrections 1966, Cambridge University Press, London.<br />
<br />
* [[Max Planck|Planck. M.]] (1914). [https://archive.org/details/theoryofheatradi00planrich ''The Theory of Heat Radiation''], a translation by Masius, M. of the second German edition, P. Blakiston's Son & Co., Philadelphia.<br />
<br />
*[[Ilya Prigogine|Prigogine, I.]] (1947). ''Étude Thermodynamique des Phénomènes irréversibles'', Dunod, Paris, and Desoers, Liège.<br />
<br />
*[[Ilya Prigogine|Prigogine, I.]], Defay, R. (1950/1954). ''Chemical Thermodynamics'', Longmans, Green & Co, London.<br />
<br />
*Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005). ''Physical Chemistry'', fourth edition, Wiley, Hoboken NJ.<br />
<br />
*[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966). ''Elements of Thermodynamics'', Addison-Wesley Publishing, Reading MA.<br />
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*{{cite journal|last=Thomson|first=W.|author-link=William Thomson, 1st Baron Kelvin|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Transactions of the Royal Society of Edinburgh|date=March 1851|volume=XX|issue=part II|pages=261–268; 289–298}} Also published in {{cite journal|last=Thomson|first=W.|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Phil. Mag. |date=December 1852 |volume=IV |series=4 |issue=22 |pages=8–21 |url=https://archive.org/details/londonedinburghp04maga |accessdate=25 June 2012}}<br />
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*[[László Tisza|Tisza, L.]] (1966). ''Generalized Thermodynamics'', M.I.T Press, Cambridge MA.<br />
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*[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963). ''Lectures in Statistical Mechanics'', American Mathematical Society, Providence RI.<br />
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*Waldram, J.R. (1985). ''The Theory of Thermodynamics'', Cambridge University Press, Cambridge UK, {{ISBN|0-521-24575-3}}.<br />
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*[[Mark Zemansky|Zemansky, M.]] (1937/1968). ''Heat and Thermodynamics. An Intermediate Textbook'', fifth edition 1967, McGraw–Hill Book Company, New York.<br />
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== External links ==<br />
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Category:Equilibrium chemistry<br />
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类别: 平衡化学<br />
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*[http://ads.harvard.edu/books/1989fsa..book/AbookC15.pdf Breakdown of Local Thermodynamic Equilibrium] George W. Collins, The Fundamentals of Stellar Astrophysics, Chapter 15<br />
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Category:Thermodynamic cycles<br />
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类别: 热力循环<br />
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*[http://spiff.rit.edu/classes/phys440/lectures/lte/lte.html Thermodynamic Equilibrium, Local and otherwise] lecture by Michael Richmond<br />
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Category:Thermodynamic processes<br />
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类别: 热力学过程<br />
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*[http://journals.ametsoc.org/doi/abs/10.1175/1520-0469%281970%29027%3C0711:NLTEIC%3E2.0.CO%3B2 Non-Local Thermodynamic Equilibrium in Cloudy Planetary Atmospheres] Paper by R. E. Samueison quantifying the effects due to non-LTE in an atmosphere<br />
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Category:Thermodynamic systems<br />
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类别: 热力学系统<br />
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*[http://scienceworld.wolfram.com/physics/LocalThermodynamicEquilibrium.html Local Thermodynamic Equilibrium]<br />
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Category:Thermodynamics<br />
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分类: 热力学<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Thermodynamic equilibrium]]. Its edit history can be viewed at [[平衡热力学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%B9%B3%E8%A1%A1%E7%83%AD%E5%8A%9B%E5%AD%A6&diff=21468平衡热力学2021-01-30T12:29:47Z<p>Jxzhou:/* Local and global equilibrium */</p>
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<div>此词条暂由小竹凉翻译,翻译字数共5339,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{short description|State of thermodynamic system(s) where no net macroscopic flow of matter or energy occurs}}<br />
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'''Thermodynamic equilibrium''' is an [[axiomatic]] concept of [[thermodynamics]]. It is an internal [[State variables|state]] of a single [[thermodynamic system]], or a relation between several thermodynamic systems connected by more or less permeable or impermeable [[Thermodynamic system#Walls|walls]]. In thermodynamic equilibrium there are no net [[macroscopic]] [[Flow (mathematics)|flows]] of [[matter]] or of [[energy]], either within a system or between systems. <br />
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Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium there are no net macroscopic flows of matter or of energy, either within a system or between systems. <br />
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'''热力学平衡'''是'''<font color="#ff8000">热力学 Thermodynamics</font>'''的一个'''<font color="#ff8000">不言自明的 Axiomatic</font>'''概念。它是单个'''<font color="#ff8000">热力学系统 Thermodynamic System</font>'''的内部'''<font color="#ff8000">状态 State</font>''',或者是几个热力学系统之间通过或多或少的渗透或不渗透的'''<font color="#ff8000">壁 Wall</font>'''连接的关系。无论是在一个系统内还是在系统之间,在热力学平衡中不存在'''<font color="#ff8000">物质 Matter</font>'''或'''<font color="#ff8000">能量 Energy</font>'''的净'''<font color="#ff8000">宏观 Macroscopic</font>''' '''<font color="#ff8000">流动 Flow</font>'''。<br />
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In a system that is in its own state of internal thermodynamic equilibrium, no [[macroscopic]] change occurs. <br />
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In a system that is in its own state of internal thermodynamic equilibrium, no macroscopic change occurs. <br />
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在一个处于内部热力学平衡状态的系统中,不会发生'''<font color="#ff8000">宏观 Macroscopic</font>'''变化。<br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual [[Thermal equilibrium|thermal]], [[Mechanical equilibrium|mechanical]], [[Chemical equilibrium|chemical]], and [[Radiative equilibrium|radiative]] equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a [[thermodynamic operation]]. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a thermodynamic operation. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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相互热力学平衡的体系同时处于互相之间的'''<font color="#ff8000">热 Thermal</font>'''平衡、'''<font color="#ff8000">力学 Mechanical</font>'''平衡、'''<font color="#ff8000">化学 Chemical</font>'''平衡和'''<font color="#ff8000">辐射 Radiative</font>'''平衡。系统可以处于其中一种相互平衡状态,尽管其他状态未平衡。在热力学平衡中所有的平衡同时并且无限期地保持,直到被'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''打破。在一个宏观平衡中,微观交换是完全或几乎完全平衡的;这是对宏观平衡概念的物理解释。<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform [[temperature]]. Its [[Intensive and extensive properties|intensive properties]], other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform temperature. Its intensive properties, other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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一个处于内部热力学状态平衡的热力学系统具有空间均匀的'''<font color="#ff8000">温度 Temperature</font>'''。除了温度以外,它的'''<font color="#ff8000">强度性质 Intensive Properties</font>'''可以由于周围环境施加的不变的长程力场而导致空间不均匀性。<br />
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In systems that are at a state of [[non-equilibrium]] there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a '''meta-stable equilibrium'''.<br />
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In systems that are at a state of non-equilibrium there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a meta-stable equilibrium.<br />
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相比之下,处于'''<font color="#ff8000">非平衡状态 non-equilibrium</font>'''的系统中有物质或能量的净流动。如果这些变化可以在一个还没有发生的系统中被触发,那么这个系统就被称为处于一个'''亚稳定的平衡状态'''。<br />
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Though not a widely named a "law," it is an [[axiom]] of thermodynamics that there exist states of thermodynamic equilibrium. The [[second law of thermodynamics]] states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the [[entropy|entropies]] of the portions.<br />
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Though not a widely named a "law," it is an axiom of thermodynamics that there exist states of thermodynamic equilibrium. The second law of thermodynamics states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the entropies of the portions.<br />
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虽然不是一个广泛命名的“定律” ,但存在热力学平衡状态是一个热力学'''<font color="#ff8000">公理 Axiom</font>'''。'''<font color="#ff8000">热力学第二定律 second law of thermodynamics</font>'''指出,当一个物质体从一个平衡状态开始,在这个状态中,它的一部分被或多或少渗透或不渗透的分区保持在不同的状态,并且是孤立的,热力学操作移除分区或使分区更具渗透性,然后它会自发地达到自己内部热力学平衡的新状态,并伴随着部分'''<font color="#ff8000">熵 Entropy</font>'''的总和增加。<br />
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== Overview 概览==<br />
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{{Thermodynamics|cTopic=[[Thermodynamic system|Systems]]}}<br />
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Classical thermodynamics deals with states of [[dynamic equilibrium]]. The state of a system at thermodynamic equilibrium is the one for which some [[thermodynamic potential]] is minimized, or for which the [[entropy]] (''S'') is maximized, for specified conditions. One such potential is the [[Helmholtz free energy]] (''A''), for a system with surroundings at controlled constant temperature and volume:<br />
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Classical thermodynamics deals with states of dynamic equilibrium. The state of a system at thermodynamic equilibrium is the one for which some thermodynamic potential is minimized, or for which the entropy (S) is maximized, for specified conditions. One such potential is the Helmholtz free energy (A), for a system with surroundings at controlled constant temperature and volume:<br />
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经典热力学研究'''<font color="#ff8000">动态平衡 Dynamic Equilibrium</font>'''的状态。系统的热力学平衡状态是对于特定的条件,一些'''<font color="#ff8000">热力学势 Thermodynamic Potential</font>'''被最小化,或者'''<font color="#ff8000">熵 Entropy</font>'''(S)被最大化。对于一个周围环境温度和体积恒定的系统,其中一个这样的热力学势是'''<font color="#ff8000">亥姆霍兹自由能 Helmholtz Free Energy</font>'''(A):<br />
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:<math>A = U - TS</math><br />
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<math>A = U - TS</math><br />
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A = U-TS<br />
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Another potential, the [[Gibbs free energy]] (''G''), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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Another potential, the Gibbs free energy (G), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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在恒定温度和压力的系统中,另一个热力学势'''<font color="#ff8000">吉布斯自由能 Gibbs Free Energy</font>'''(G)在热力学平衡状态最小:<br />
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:<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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where ''T'' denotes the absolute thermodynamic temperature, ''P'' the pressure, ''S'' the entropy, ''V'' the volume, and ''U'' the internal energy of the system.<br />
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where T denotes the absolute thermodynamic temperature, P the pressure, S the entropy, V the volume, and U the internal energy of the system.<br />
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其中 T 表示热力学绝对温度,P 表示压强,S 表示熵,V 表示体积,U 表示体系的内能。<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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热力学平衡是一种独特的稳定定态,当系统长时间与周围环境相互作用时,它可以被接近或最终到达。上述势能是数学构造的热力学量,在特定的环境条件下最小化。<br />
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== Conditions 条件==<br />
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* For a completely isolated system, ''S'' is maximum at thermodynamic equilibrium. 对于一个完全孤立的系统,S在热力学平衡中取最大值。<br />
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* For a system with controlled constant temperature and volume, ''A'' is minimum at thermodynamic equilibrium. 对于一个恒定温度和体积的系统来说,A在热力学平衡中取最小值。<br />
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* For a system with controlled constant temperature and pressure, ''G'' is minimum at thermodynamic equilibrium. 对于一个恒温恒压的系统,G在热力学平衡中取最小值。<br />
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The various types of equilibriums are achieved as follows:<br />
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The various types of equilibriums are achieved as follows:<br />
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实现各种类型的平衡的方法如下:<br />
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*Two systems are in ''thermal equilibrium'' when their [[temperature]]s are the same. 当两个系统的'''<font color="#ff8000">温度 Temperature</font>'''相同时,它们就处于''热平衡状态''<br />
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*Two systems are in ''mechanical equilibrium'' when their [[pressure]]s are the same. 当两个体系的'''<font color="#ff8000">压力 Pressure</font>'''相同时,它们就处于''力学平衡''<br />
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*Two systems are in ''diffusive equilibrium'' when their [[chemical potential]]s are the same. 当两个题体系的'''<font color="#ff8000">化学势 Chemical Potential</font>'''相同时,它们就处于''扩散平衡''<br />
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*All [[forces]] are balanced and there is no significant external driving force.<br />
所有的'''<font color="#ff8000">力 Force</font>'''都是平衡的,没有明显的外部驱动力<br />
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==Relation of exchange equilibrium between systems 系统之间的交换均衡关系==<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability.<ref name="Nster_a">Münster, A. (1970), p. 49.</ref> When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability. When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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通常,热力学系统的周围环境也可以被看作是另一个热力学系统。在这种观点中,我们可以把系统及其周围环境看作是相互接触的两个系统,远程作用力也将它们联系在一起。系统的包围物是两个系统之间的接触面或边界。在热力学形式中,该表面被认为具有特定的渗透性质。例如,接触的表面可能被认为只能透热,使能量只能作为热传递。当远程力在时间上不发生变化,两个系统之间的热量传递减慢并最终永久停止时,这两个系统被称为热平衡; 这就是接触平衡的一个例子。其它类型的接触平衡可用其它类型的比渗透率来定义。当两个系统对于某一特定类型的渗透率处于接触平衡时,它们具有属于该特定类型渗透率的强变量的共同值。这种强度变量的例子有温度、压力、化学势。<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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接触平衡也可视为交换平衡。在接触平衡状态下,两系统之间某些量的传递速率存在零平衡。例如,对于只能透热的壁,内能作为热在两个系统之间的扩散速率是相等并反向的。两个系统之间的绝热壁只对作为功传递的能量有渗透作用; 在力学平衡,两个系统之间作为功的能量传递速率相等且相反。如果是一个简单的壁,那么通过它的体积转移率也是相等且相反的; 即它两边的压力是相等的。如果绝热壁比较复杂,有一种杠杆,有一个面积比,那么两个体系在交换平衡中的压力与体积交换比成反比,这使得转移率的零平衡作功。<br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<ref name="Planck 1914 40">[[Max Planck|Planck. M.]] (1914), p. 40.</ref><br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<br />
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辐射交换可以发生在两个不同的系统之间。当两个体系温度相同时,辐射交换平衡占优势。<br />
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==Thermodynamic state of internal equilibrium of a system 系统内部平衡的热力学状态==<br />
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A collection of matter may be entirely [[Isolated system|isolated]] from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium.<ref>Haase, R. (1971), p. 4.</ref><ref>Callen, H.B. (1960/1985), p. 26.</ref> (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics.<ref>{{Cite journal |doi = 10.1119/1.4914528|bibcode = 2015AmJPh..83..628M|title = Time and irreversibility in axiomatic thermodynamics|year = 2015|last1 = Marsland|first1 = Robert|last2 = Brown|first2 = Harvey R.|last3 = Valente|first3 = Giovanni|journal = American Journal of Physics|volume = 83|issue = 7|pages = 628–634}}</ref> One textbook<ref>[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963), p. 5.</ref> calls it the "zeroth law", remarking that the authors think this more befitting that title than its [[Zeroth law of thermodynamics|more customary definition]], which apparently was suggested by [[Ralph H. Fowler|Fowler]].)<br />
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A collection of matter may be entirely isolated from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium. (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics. One textbook calls it the "zeroth law", remarking that the authors think this more befitting that title than its more customary definition, which apparently was suggested by Fowler.)<br />
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物质的集合可能与其周围的环境完全'''<font color="#ff8000">孤立 Isolated</font>'''。如果它在无限长的时间内一直保持不受干扰,按照经典热力学假定,它处于一个没有发生任何变化,没有流动的状态,即内部平衡的热力学状态。(这种假设有时被称为“负第一”热力学定律,但并不常见。有教科书称之为“第零定律” ,作者'''<font color="#ff8000">福勒 Fowler</font>'''认为这个名称是'''<font color="#ff8000">更符合惯例的定义 More Customary Definition</font>'''。)<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a [[thermodynamic operation]] be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a thermodynamic operation be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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这种状态是所谓的经典热力学或平衡态热力学的主要关注点,因为它们是系统中被认为在这门学科中得到很好定义的唯一状态。一个与另一个系统处于接触平衡状态可以被一个'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''隔离,在隔离发生时,其内部不会发生任何变化。因此,一个与另一个系统处于接触平衡状态时也可以被视为处于其自身的内部热力学平衡状态。<br />
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==Multiple contact equilibrium 多点接触平衡==<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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热力学形式允许一个系统同时与其他多个系统接触,这些系统可能有也可能没有相互接触,且这些接触具有不同的渗透性。如果这些系统都与世界其他部分相互隔离,那么它们彼此之间就会达到各自的接触平衡。<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy.<ref name="Caratheodory">Carathéodory, C. (1909).</ref><ref>Prigogine, I. (1947), p. 48.</ref><ref>Landsberg, P. T. (1961), pp. 128–142.</ref><ref>Tisza, L. (1966), p. 108.</ref> Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy. Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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如果几个系统彼此之间没有绝热壁,但是它们与世界其他部分共同隔离,那么它们就会达到多重接触平衡状态,且有共同的温度,总的内能和熵。在众多强度量中,这是温度的一个独特性质。即使在远距离作用力存在的情况下,它也是有效的。(也就是说,没有“力”可以维持温度的差异。)举个例子,在热力学平衡的一个垂直的引力场系统中,顶部壁面的压力比底部壁面的压力小,但是各处的温度都是一样的。<br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural [[thermodynamic process]].<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), § 1.12.</ref> It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings.<ref>Levine, I.N. (1983), p. 40.</ref><ref>Lieb, E.H., Yngvason, J. (1999), pp. 17–18.</ref> The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of [[Second law of thermodynamics#Description#Kelvin statement|"inanimate" agency]]; a system in thermodynamic equilibrium is inanimate.<ref>[[William Thomson, 1st Baron Kelvin|Thomson, W.]] (1851).</ref><br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural thermodynamic process. It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings. The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of "inanimate" agency; a system in thermodynamic equilibrium is inanimate.<br />
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热力操作可能作为一个事件发生在周围环境的壁上,既不直接影响与周围环境联系的壁,也不直接影响其内部,且发生在一个明确的有限的时间内。例如,一个固定的绝热壁可以在环境中被放置或拆除。由于这种操作仅限于周围环境,系统可能会在一段时间内远离自身最初的内部状态---- 热力学平衡。根据热力学第二定律的说法,整体经历了变化并最终与周围环境达到了新的平衡。继Planck之后,这一连串的事件被称为自然'''<font color="#ff8000">热力学过程 Thermodynamic Process</font>'''。即使在这个过程中,当系统和周围环境都不处于明确的内部平衡状态时,存在着暂时偏离热力学平衡的现象,由于初始状态和最终状态都是热力学平衡的,这在平衡热力学中也是允许的。一个自然过程在其主要部分中以有限的速率进行,因此,它从根本上不同于虚构的准静态“过程”;即不在整个过程中无限缓慢地进行而且虚构地“可逆”。经典热力学允许,即使一个过程可能需要很长的时间才能达到热力学平衡,如果主要部分的过程是在一个有限的比率中,那么它被认为是自然的,并受制于热力学第二定律,即不可逆的。工程设计的机器、人工设备和操作是允许在周围环境中进行的。允许在环境中而不是在系统中进行此类操作和设备,是开尔文在他的一个热力学第二定律的陈述中提到'''<font color="#ff8000">无生命机构 Inanimate Agency</font>'''的原因; 在热力学平衡的系统是无生命的。<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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否则,热力操作可能会直接影响系统的壁。<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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通常可以很方便地假设周围的某些子系统比系统大得多,以至于这个过程只能影响周围子系统的强度变量,然后将这些子系统称为相关强度变量的储备库。<br />
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== Local and global equilibrium 局部和全局均衡==<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by [[intensive quantity|intensive]] parameters. As an example, [[temperature]] controls [[Heat equation|heat exchanges]]. ''Global thermodynamic equilibrium'' (GTE) means that those [[intensive quantity|intensive]] parameters are homogeneous throughout the whole system, while ''local thermodynamic equilibrium'' (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by intensive parameters. As an example, temperature controls heat exchanges. Global thermodynamic equilibrium (GTE) means that those intensive parameters are homogeneous throughout the whole system, while local thermodynamic equilibrium (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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区分全局性和局部性热力学平衡是很有用的。在热力学中,系统内部和系统与外部之间的交换是由'''<font color="#ff8000">强度 Intensive</font>'''参数控制的。例如,'''<font color="#ff8000">温度 Temperature</font>'''控制'''<font color="#ff8000">热交换 Heat Equation</font>'''。全局热力学平衡(GTE)意味着这些'''<font color="#ff8000">强度 Intensive</font>'''参数在整个系统中是均匀的,而局部热力学平衡(LTE)意味着这些强度参数在空间和时间上是变化的,但变化如此缓慢,以至于对于任何一点,人们都可以假设在该点的某个邻域存在热力学平衡。<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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如果对系统的描述要求强度参数的变化过大,那么这些强度参数的定义所依据的假设本身就会失效,系统将既不处于全局平衡,也不处于局部平衡。例如,粒子需要一定数量的碰撞来平衡其周围环境。如果在这些碰撞中移动的平均距离使它离开平衡邻域,它将永远不会平衡,也就不会有 LTE。根据定义,温度与平衡邻域的平均内部能量成正比。由于没有达到平衡邻域,温度的概念就不成立,温度也就变得无法定义。<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to [[massive]] particles. In a [[radiation|radiating]] gas, the [[photon]]s being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to massive particles. In a radiating gas, the photons being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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值得注意的是,这种局部平衡可能只适用于系统中的某个粒子子集。例如,LTE 通常只适用于'''<font color="#ff8000">大 Massive</font>'''质量粒子。在'''<font color="#ff8000">辐射 Radiation</font>'''气体中,被气体发射和吸收的'''<font color="#ff8000">光子 Photon</font>'''不需要彼此在一个热力学平衡内,或与气体中的大量粒子在一起,LTE 才能存在。在某些情况下,自由电子并不需要与大得多的原子或分子处于平衡状态,LTE 才能存在。<br />
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As an example, LTE will exist in a glass of water that contains a melting [[ice cube]]. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the [[Maxwell–Boltzmann distribution]] for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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As an example, LTE will exist in a glass of water that contains a melting ice cube. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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例如,LTE 将存在于一个装有正在融化的'''<font color="#ff8000">冰块 Ice Cube</font>'''的水杯中。玻璃杯内的温度可以在任何时候定义,但是离冰块近的地方要比离冰块远的地方冷。如果观察到位于给定点附近的分子的能量,它们将按照麦克斯韦-波兹曼分布在一定温度下的分布。如果观察到位于另一点附近的分子的能量,它们将按照'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''分布到另一个温度。<br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural [[transport phenomena]] may lead a system from local to global thermodynamic equilibrium. Going back to our example, the [[diffusion]] of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<ref>H.R. Griem, 2005</ref><br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural transport phenomena may lead a system from local to global thermodynamic equilibrium. Going back to our example, the diffusion of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<br />
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局部热力学平衡不需要局部或全局的平稳性。换句话说,每一个小区域不需要有一个恒定的温度。然而,它确实要求每个小的局部变化缓慢到足以维持其局部麦克斯韦-波尔兹曼速度分布。全局非平衡态只有通过系统与外界的交换才能保持稳定。例如,通过在水杯中不断添加细粉冰来补偿熔化,并持续排出融水,可以保持全局稳定的静态。自然'''<font color="#ff8000">输运现象 Transport Phenomena</font>'''会使一个局部热力学平衡系统逐渐达到全局的热力学平衡。回顾我们的例子,热量的扩散将导致我们的玻璃杯水流向全局热力学平衡,在这种状态下,玻璃杯的温度是完全均匀的。<br />
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==Reservations==<br />
保留意见<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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学识渊博的笔者在热力学领域对热力学平衡描述时,经常对他们的描述附加条件或保留意见。有些笔者含蓄地保留了或多或少的空白,以待说明。<br />
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For example, one widely cited writer, [[Herbert Callen|H. B. Callen]] writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. ''Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!''"<ref>Callen, H.B. (1960/1985), p. 15.</ref><br />
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For example, one widely cited writer, H. B. Callen writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!"<br />
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例如,一位被广泛引用的作家'''<font color="#ff8000">H.B.卡伦 H.B.Callen</font>'''在这里写道: “实际上,很少有系统处于绝对和真正的平衡状态。”他提到了放射性过程,认为它们可能需要“宇宙时间才能完成,因此通常可以忽略”。他补充道: “在实践中,平衡的标准是循环的。在操作上,如果一个系统的性质一致地用热力学理论来描述,那么它就处于平衡状态! ”<br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<ref>Beattie, J.A., Oppenheim, I. (1979), p. 3.</ref><br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<br />
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J.A.贝蒂和 I.奥本海姆写道: “坚持对平衡定义的严格解释,将排除热力学应用于实际系统的所有状态。”<br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment",<ref>Callen, H.B. (1960/1985), p. 485.</ref> and cited by Adkins as having written a "classic text",<ref>Adkins, C.J. (1968/1983), p. ''xiii''.</ref> [[Brian Pippard|A.B. Pippard]] writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<ref>Pippard, A.B. (1957/1966), p. 6.</ref><br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment", and cited by Adkins as having written a "classic text", A.B. Pippard writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<br />
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Callen引用另一位作者的话说,他给出了“学术且严谨的论述” ,Adkins引用他的话说,他写了一本“经典著作”—— '''<font color="#ff8000">A.B.皮帕德 A.B.Pippard</font>'''在文中写道: “只要时间足够长,过冷水蒸汽最终会凝结,... ..。时间可能是漫长的,也许长达10年或者更长。就大多数目的而言,只要这种迅速的变化不是人为地刺激,这些系统就可以被视为处于平衡状态。”<br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster">Münster, A. (1970), p. 53.</ref><br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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另一位作者A.Münster,写道。他观察到热核反应发生的速度非常缓慢,以至于在热力学中可以忽略不计。他评论道: “‘绝对平衡’或‘所有可想象过程的平衡’的概念没有物理意义。”他说: “ ... 我们只能考虑特定过程和确定的实验条件下的平衡。”<br />
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According to [[László Tisza|L. Tisza]]: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<ref>Tisza, L. (1966), p. 119.</ref><br />
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According to L. Tisza: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<br />
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根据'''<font color="#ff8000">L.缇莎 L.Tisza</font>'''的说法: “ ... 在讨论接近绝对零度的现象时。经典理论的绝对预测变得特别模糊,因为在非平衡状态下发生冻结是非常普遍的。”<br />
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==Definitions==<br />
定义<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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一个系统最普遍的热力学平衡是通过与周围环境的接触,允许所有化学物质和各种能量同时通过。热力学平衡中的系统以均匀加速度在空间中运动,但此时不能改变其形状或大小; 因此它是由空间中的刚性体积来定义的。它可能存在于外力场中,由远远大于系统本身的外部因素决定,因此系统内的事件不会对外力场产生相当大的影响。只有当外力场是均匀的,并且确定了它的均匀加速度,或者它处于一个非均匀力场中,但是由于表面的局部力,例如机械压力,使它保持静止时,这个系统才能处于热力学平衡。<br />
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Thermodynamic equilibrium is a [[primitive notion]] of the theory of thermodynamics. According to [[Philip M. Morse|P.M. Morse]]: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are ''not'' conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments."<ref>[[Philip M. Morse|Morse, P.M.]] (1969), p. 7.</ref> This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<ref>Bailyn, M. (1994), p. 20.</ref><br />
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Thermodynamic equilibrium is a primitive notion of the theory of thermodynamics. According to P.M. Morse: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are not conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments." This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<br />
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热力学平衡是热力学理论的一个'''<font color="#ff8000">基本概念 Primitive Notion</font>'''。'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''说: “应该强调的是,存在热力学状态这一事实,以及存在由平衡态唯一指定的热力学变量这一事实,并不是从某些哲学第一原理得出的逻辑结论。这些结论不可避免地来自两个多世纪的实验。”这意味着热力学平衡不能仅仅用热力学的其他理论概念来定义。M.Bailyn提出了一个基本的热力学定律理论,它定义并假设了热力学平衡的存在。<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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热力学平衡的教科书定义通常被仔细说明,并有些保留。<br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<ref>Münster, A. (1970), p. 52.</ref><br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<br />
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例如,A. Münster写道:“当系统中没有以可测量的速度发生状态变化时,隔离系统处于热力学平衡状态。”这里有两项保留:系统是孤立的;任何状态的变化都是不可估量的缓慢。他通过对在室温且没有催化剂的情况下混合氧和氢的说明,讨论了第二个条件。Münster指出,热力学平衡状态所描述的宏观变量比给定系统任何其他状态都少。这是部分,但不完全是,因为系统内和系统内的所有流都是零。<br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in ''equilibrium''.<ref>Haase, R. (1971), pp. 3–4.</ref><br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in equilibrium.<br />
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R. Haase's的热力学演示并不从对热力学平衡的限制开始,因为他打算考虑非平衡态热力学。他考虑一个具有时间不变性质的任意系统。他通过切断除外力场以外的所有外部影响来测试它的热力学平衡。如果在绝缘之后,没有任何变化,他说,系统处于平衡状态。<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness".<ref>Callen, H.B. (1960/1985), p. 13.</ref> This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness". This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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在一个标题为“热力学平衡”的章节中,H.B. Callen在段落定义了平衡状态.他指出,它们“是由系统内部的内在因素决定的”。它们是“终端状态” ,随着时间的推移,系统会以“冰川般缓慢”的速度朝着这个终端状态演化。这个说法并没有明确,对于热力学平衡系统必须是孤立的;;Callen也没有说明他所说的“内在因素”是什么意思。<br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<ref>Adkins, C.J. (1968/1983), p. ''7''.</ref><br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<br />
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另一位教科书作者,C.J.Adkins,明确允许热力学平衡在非孤立的系统中发生。然而,他的系统在物质转移方面是封闭的。他写道: “一般来说,热力学平衡的方法包括热和类似变动与周围环境的相互作用。”他将这种热力学平衡与只有通过热接触才能进行能量传递的热平衡相区别。<br />
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Another textbook author, [[J.R. Partington]], writes: "(i) ''An equilibrium state is one which is independent of time''." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..."<ref>Partington, J.R. (1949), p. 161.</ref> This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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Another textbook author, J.R. Partington, writes: "(i) An equilibrium state is one which is independent of time." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..." This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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另一位教科书作者'''<font color="#ff8000">J.R.帕廷顿 J.R.Partington</font>'''写道: “(i)平衡状态是独立于时间的状态。”但是,在提到“只是明显处于平衡状态”的系统时,他补充说: “这样的系统处于‘虚假平衡’状态。帕廷顿的陈述没有明确指出平衡是指一个孤立的系统。和Münster一样,Partington也指的是氧和氢的混合物。他补充说:“在一个真正的平衡状态,任何影响状态的外部条件的最小变化都会产生一个微小的状态变化... ... ”这个条件意味着热力学平衡必须在小的扰动下保持稳定; 这个要求对于热力学平衡的严格意义是必不可少的。<br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, ''thermodynamic—equilibrium.''"<ref>Crawford, F.H. (1963), p. 5.</ref><br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, thermodynamic—equilibrium."<br />
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在F.H.Crawford的一本学生教科书中,有一个标题为“热力学平衡”的章节。它区分了几种流动的驱动因素,然后说: “这些是孤立系统明显普遍趋向于完全机械、热、化学和电力状态的例子——或者简单地说,热力学平衡状态。”<br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in ''equilibrium''."<ref>Buchdahl, H.A. (1966), p. 8.</ref> Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being ''in equilibrium'' so long as experimental tests show that 'slow' transitions are in effect reversible."<ref>Buchdahl, H.A. (1966), p. 111.</ref> It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<ref>Adkins, C.J. (1968/1983), p. 8.</ref><br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in equilibrium." Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being in equilibrium so long as experimental tests show that 'slow' transitions are in effect reversible." It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<br />
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H.A. Buchdahl的一本关于经典热力学的专著考虑了热力学系统的平衡,而实际上并没有写热力学平衡一词。Buchdahl在提到封闭的物质交换系统时写道: “如果一个系统处于一个适当的静态状态,那么它将被称为处于平衡状态。”出于热力学描述的目的,Buchdahl的专著也讨论了非晶态玻璃。它说: “更准确地说,只要实验测试表明‘慢’跃迁实际上是可逆的,玻璃就可以被认为处于平衡状态。”通常来说不会将这一条件作为热力学平衡定义的一部分,而是假定相反的情况:如果热力学平衡中的一个体受到足够慢的过程的影响,则该过程可被视为足够接近可逆,并且该物体在过程中足够接近热力学平衡。<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of ''contact equilibrium''. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by [[Constantin Carathéodory|C. Carathéodory]], and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster" /> Thermodynamic equilibrium for an open system means that, with respect to every relevant kind of selectively permeable wall, contact equilibrium exists when the respective intensive parameters of the system and surroundings are equal.<ref name="Nster_a" /> This definition does not consider the most general kind of thermodynamic equilibrium, which is through unselective contacts. This definition does not simply state that no current of matter or energy exists in the interior or at the boundaries; but it is compatible with the following definition, which does so state.<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of contact equilibrium. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by C. Carathéodory, and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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通过引入接触平衡的概念,A. Münster仔细地扩展了孤立系统热力学平衡的定义。这指定了在考虑非孤立系统的热力学平衡时允许的特定过程,并特别关心开放系统,这些开放系统可能从周围环境获得或丢失物质。利益系统和周围系统之间的接触平衡,通过一种特殊的壁与利益系统接触,其余的连接系统是孤立的。这种特殊类型的壁也被'''<font color="#ff8000">C.喀喇西奥多里 C.Carathéodory</font>'''考虑过,其他作家也提到过。它们具有选择渗透性。它们可能只对机械工作有渗透性,或者只对热有渗透性,或者只对某种特定的化学物质有渗透性。每个接触平衡定义了一个强度参数; 例如,只能透热的壁定义了一个经验温度。对于感兴趣的体系中每一种化学成分,都可以存在接触平衡。在接触平衡中,尽管有可能通过选择性渗透壁进行交换,感兴趣的系统是不变的,好像它处在孤立的热力学平衡。这个方案遵循的一般规则是: “ ... ... 我们只能考虑特定过程和特定实验条件下的平衡。”<br />
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[[Mark Zemansky|M. Zemansky]] also distinguishes mechanical, chemical, and thermal equilibrium. He then writes: "When the conditions for all three types of equilibrium are satisfied, the system is said to be in a state of thermodynamic equilibrium".<ref>[[Mark Zemansky|Zemansky, M.]] (1937/1968), p. 27.</ref><br />
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'''<font color="#ff8000">M.泽曼斯基 M.Zemansky</font>'''还区分了机械、化学和热平衡。他接着写道: “当这三种均衡的条件都满足时,系统就处于热力学平衡状态。”<br />
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P.M. Morse writes that thermodynamics is concerned with "states of thermodynamic equilibrium". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<br />
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[[Philip M. Morse|P.M. Morse]] writes that thermodynamics is concerned with "''states of thermodynamic equilibrium''". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<ref>[[Philip M. Morse|Morse, P.M.]] (1969), pp. 6, 37.</ref><br />
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'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''写道,热力学关注的是“热力学平衡状态”。在讨论物体与周围热源之间的热量传递时,他也使用了“热平衡”这个短语,尽管没有明确定义一个特殊的术语“热平衡”<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "full thermodynamic equilibrium state".<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "''full'' thermodynamic equilibrium state".<ref>Waldram, J.R. (1985), p. 5.</ref><br />
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J.R. Waldram写到了“一个明确的热力学状态”。他将一个系统定义为“当其观测量随时间停止变化时”的“热平衡”。但是在这个定义之下不久,他写到一块玻璃还没有达到“完全的热力学平衡状态”。<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, thermodynamic equilibrium is said to exist." He is not here considering the presence of an external force field.<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, ''thermodynamic equilibrium'' is said to exist." He is not here considering the presence of an external force field.<ref>Bailyn, M. (1994), p. 21.</ref><br />
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考虑到平衡状态,M.Bailyn写道: “每个强度变量都有自己的平衡类型。”然后他定义了热平衡、机械平衡和物质平衡。因此,他写道: “如果所有的强度变量都是一致的,那么热力学平衡就是存在的。”他在这里没有考虑外力场的存在。<br />
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J.G. Kirkwood and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of thermodynamic equilibrium if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<br />
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[[John Gamble Kirkwood|J.G. Kirkwood]] and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of ''thermodynamic equilibrium'' if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<ref>Kirkwood, J.G., Oppenheim, I. (1961), p. 2</ref><br />
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'''<font color="#ff8000">J.G.柯克伍德 J.G.Kirkwood</font>'''和 I.Oppenheim 将热力学平衡定义为: “一个系统处于热力学平衡状态,如果,在分配给实验的时间内,(a)它强度特性与时间无关,(b)它的内部或与周围环境的边界处没有物质或能量流。”显然,他们没有把定义限制在孤立的或封闭的系统。它们不讨论“缓慢”发生变化的可能性,并且超出了分配给实验的时间范围。他们注意到,对于两个相接触的系统,存在一个强度性质的小子类,如果这个小子类的所有子类都相等,那么所有各自的强度性质都相等。只要满足其他一些条件,热力学平衡状态可以由这个子类定义。<br />
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==Characteristics of a state of internal thermodynamic equilibrium==<br />
内部热力学平衡状态的特征<br />
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A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous. Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface." As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.<br />
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在内部热力学平衡中,没有外力的情况下由单相组成的热力学系统是均匀的。Planck在论文中简要介绍了热量、温度和热平衡,然后宣布: “在下文中,我们将主要讨论任何形式的均匀、各向同性的物体,它们在整个物质中具有相同的温度和密度,并受到到处垂直于表面的均匀压力作用。”和 Carathéodory 一样,Planck 将表面效应、外场和各向异性晶体排除在外。虽然Planck提到了温度,但并没有明确提到热力学平衡的概念。相比之下,Carathéodory 关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ,虽然没有明确地使用短语‘热力学平衡’,也没有明确地假设存在一个温度来定义它。<br />
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===Homogeneity in the absence of external forces===<br />
在没有外力的情况下的同质性<br />
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A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous.<ref name="Planck 1903 3"/> This means that the material in any small volume element of the system can be interchanged with the material of any other geometrically congruent volume element of the system, and the effect is to leave the system thermodynamically unchanged. In general, a strong external force field makes a system of a single phase in its own internal thermodynamic equilibrium inhomogeneous with respect to some [[Intensive and extensive properties|intensive variables]]. For example, a relatively dense component of a mixture can be concentrated by centrifugation.<br />
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在没有外力的情况下,由单一相组成的热力学系统,在其自身的内部热力学平衡中是均匀的。这意味着系统中任何小体积单元中的材料可以与系统中任何其他几何相等的体积单元中的材料互换,其效果是使系统在热力学上保持不变。一般来说,一个强外力场使得一个单相系统在其自身的内部热力学平衡中对于一些'''<font color="#ff8000">强变量 Intensive Variable</font>'''是不均匀的。例如,可以通过离心来浓缩混合物中相对密度较大的组分。<br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform. Considerations of kinetic theory or statistical mechanics also support this statement.<br />
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热力学平衡系统中的温度在空间和时间上是均匀的。在一个系统内部热力学平衡状态下,没有净内部宏观流动。特别是,这意味着系统的所有局部部分处于相互辐射交换平衡状态。这意味着系统的温度在空间上是均匀的。动力学理论或统计力学也支持这种说法。<br />
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===Uniform temperature===<br />
均匀温度<br />
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In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium. As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.<br />
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为了使一个系统处于它自己的内部热力学平衡状态,它处于自己内部的热平衡状态当然是必要的,但不是充分的;系统在达到内部热平衡之前,可以达到内部机械平衡。如上所述,根据 A.Münster的说法,对于给定的孤立系统的任何状态,定义一个热力学平衡所需的变量数是最少的。如上所述,J.G.Kirkwood 和 I.Oppenheim 指出,热力学平衡状态可以由一个特殊的子类的强变量定义,该子类中有一定数量的成员。<br />
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Such equilibrium inhomogeneity, induced by external forces, does not occur for the intensive variable [[temperature]]. According to [[Edward A. Guggenheim|E.A. Guggenheim]], "The most important conception of thermodynamics is temperature."<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), p.5.</ref> Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface."<ref name="Planck 1903 3">[[Max Planck|Planck, M.]] (1897/1927), p.3.</ref> As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.<br />
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这种由外力引起的平衡不均匀性,在强烈变化的'''<font color="#ff8000">温度 Temperature</font>'''下不会发生。'''<font color="#ff8000">E.A.古根海姆 E.A. Guggenheim</font>'''认为,“热力学最重要的概念是温度。“Planck在介绍他的论文时,简要叙述了热、温度和热平衡,然后宣布: ”在下文中,我们将主要讨论任何形式的均匀、各向同性的物体,它们的物质具有相同的温度和密度,并受到到处垂直于表面的均匀压力的作用和Carathéodory 一样,Planck将表面效应、外场和各向异性晶体排除在外。虽然Planck提到了温度,但并没有明确提到热力学平衡的概念。相比之下,Carathéodory关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ,虽然没有明确地使用短语‘热力学平衡’ ,也没有明确地假设存在一个温度来定义它。<br />
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<br />
If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.<br />
<br />
如果热力学平衡位于一个外力场中,那么通常只有温度在空间上是均匀的。如果外力场非零,温度以外的强度变量通常是不均匀的。在这种情况下,一般需要附加变量来描述空间非均匀性。<br />
<br />
The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform.<ref name="Planck 1914 40"/> This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers.<ref>Gibbs, J.W. (1876/1878), pp. 144-150.</ref><ref>[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966), pp. 127–130.</ref><ref>Münster, A. (1970), pp. 309–310.</ref><ref>Bailyn, M. (1994), pp. 254-256.</ref><ref>{{cite journal | last1 = Verkley | first1 = W.T.M. | last2 = Gerkema | first2 = T. | year = 2004 | title = On maximum entropy profiles | journal = J. Atmos. Sci. | volume = 61 | issue = 8| pages = 931–936 | doi=10.1175/1520-0469(2004)061<0931:omep>2.0.co;2| bibcode = 2004JAtS...61..931V | doi-access = free }}</ref><ref>{{cite journal | last1 = Akmaev | first1 = R.A. | year = 2008 | title = On the energetics of maximum-entropy temperature profiles | url = | journal = Q. J. R. Meteorol. Soc. | volume = 134 | issue = 630| pages = 187–197 | doi=10.1002/qj.209| bibcode = 2008QJRMS.134..187A }}</ref> Considerations of kinetic theory or statistical mechanics also support this statement.<ref>Maxwell, J.C. (1867).</ref><ref>Boltzmann, L. (1896/1964), p. 143.</ref><ref>Chapman, S., Cowling, T.G. (1939/1970), Section 4.14, pp. 75–78.</ref><ref>[[J. R. Partington|Partington, J.R.]] (1949), pp. 275–278.</ref><ref>{{cite journal | last1 = Coombes | first1 = C.A. | last2 = Laue | first2 = H. | year = 1985 | title = A paradox concerning the temperature distribution of a gas in a gravitational field | url = | journal = Am. J. Phys. | volume = 53 | issue = 3| pages = 272–273 | doi=10.1119/1.14138| bibcode = 1985AmJPh..53..272C }}</ref><ref>{{cite journal | last1 = Román | first1 = F.L. | last2 = White | first2 = J.A. | last3 = Velasco | first3 = S. | year = 1995 | title = Microcanonical single-particle distributions for an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 16 | issue = 2| pages = 83–90 | doi=10.1088/0143-0807/16/2/008| bibcode = 1995EJPh...16...83R }}</ref><ref>{{cite journal | last1 = Velasco | first1 = S. | last2 = Román | first2 = F.L. | last3 = White | first3 = J.A. | year = 1996 | title = On a paradox concerning the temperature distribution of an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 17 | issue = | pages = 43–44 | doi=10.1088/0143-0807/17/1/008}}</ref><br />
<br />
热力学平衡系统内的温度在时间和空间上都是均匀的。在一个处于内部热力学平衡的系统中,不存在净的内部宏观流动。特别是,这意味着系统的所有局部都处于相互辐射交换平衡。这意味着系统的温度在空间上是均匀的。这在所有情况下都是如此,包括那些非均匀外力场。对于外部施加的引力场,这可以通过使用朗朗日乘数的方法通过变化的演算在宏观热力学术语中证明。动力学理论或统计力学也支持这种说法。<br />
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In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium.<ref name="Fitts 43"/><br />
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为了使一个系统处于它自己的内部热力学平衡状态,它必须处于它自己的内部热平衡状态是必要不充分的; 一个系统在到达内部热平衡之前到达内部机械平衡是可能的。<br />
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As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.<br />
<br />
如上所述,j.r. Partington 指出热力学平衡状态在小的瞬态扰动下是稳定的。如果没有这个条件,一般来说,研究热力学平衡系统的实验就会遇到巨大的困难。<br />
<br />
===Number of real variables needed for specification===<br />
规范所需的实变量数目<br />
<br />
<br />
In his exposition of his scheme of closed system equilibrium thermodynamics, C. Carathéodory initially postulates that experiment reveals that a definite number of real variables define the states that are the points of the manifold of equilibria.<ref name="Caratheodory" /> In the words of Prigogine and Defay (1945): "It is a matter of experience that when we have specified a certain number of macroscopic properties of a system, then all the other properties are fixed."<ref>Prigogine, I., Defay, R. (1950/1954), p. 1.</ref><ref>Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005), p. 4.</ref> As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.<br />
<br />
在他关于封闭系统平衡态热力学方案的论述中,C.Carathéodory 最初假定实验揭示了一定数量的实变量定义了作为平衡态流形点的状态。用 Prigogine 和 Defay (1945)的话说: “这是一个经验问题,当我们确定了一个系统一定数量的宏观属性时,那么所有其他属性都是固定的。如上所述,A. Münster认为,定义热力学平衡所需的变量数量对于给定孤立系统的任何状态来说都是最少的。如上所述,J.G. Kirkwood 和 I. Oppenheim 指出,热力学平衡状态可以由一个特殊子类的强度变量来定义,该子类中有一定数量的成员。<br />
<br />
When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium. Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<br />
<br />
当一个物质体从不均匀的非平衡状态或化学非平衡状态开始,然后被孤立,它自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如,在这种演变的许多情况下,内部机械平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是,在这种演变的许多情况下,热平衡的发展要比化学平衡快得多。<br />
<br />
<br />
<br />
If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.<br />
<br />
如果热力学平衡位于一个外力场中,那么通常只有温度在空间上是均匀的。如果外力场非零,温度以外的强度变量通常是不均匀的。在这种情况下,一般需要附加变量来描述空间非均匀性。<br />
<br />
===Stability against small perturbations===<br />
对小扰动的稳定性<br />
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In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
<br />
在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
<br />
As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.<br />
<br />
如上所述,J.R. Partington 指出热力学平衡状态在小的瞬态扰动下是稳定的。如果没有这个条件,一般来说,研究热力学平衡系统的实验就会遇到严重的困难。<br />
<br />
<br />
To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics. But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
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考虑孤立热力学系统中的波动概念,一个方便的例子是由其广泛的状态变量、内能、体积和质量组成指定的系统。根据定义,它们是时不变的。根据定义,它们与它们的共轭状态密集函数的时不变名义值相结合,反向温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广泛的状态变量的值,不足以提供这些名义值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
<br />
===Approach to thermodynamic equilibrium within an isolated system===<br />
孤立系统中的热力学平衡<br />
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It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.<br />
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可以承认,在重复测量这些共轭强度函数时,发现它们的值随时间略有不同。这种可变性被认为是由于内部波动。不同测量值平均到其名义值。<br />
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When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium.<ref name="Fitts 43">Fitts, D.D. (1962), p. 43.</ref> Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<ref>Denbigh, K.G. (1951), p. 42.</ref><br />
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当一个物质体从不均匀的非平衡状态或化学非平衡状态开始,然后被孤立,它自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如,在这种演变的许多情况下,内部机械平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是,在这种演变的许多情况下,热平衡的发展要比化学平衡快得多。<br />
<br />
If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<br />
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如果这个系统真的像经典热力学所假定的那样是宏观的,那么这个系统的波动太小了,宏观上无法检测到。这就是所谓的热力学极限。实际上,物质的分子性质和动量转移的量子性质由于它们太小而看不见,已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中,平衡的波动概念是没有位置的。”<br />
<br />
===Fluctuations within an isolated system in its own internal thermodynamic equilibrium===<br />
孤立系统内部热力学平衡的波动<br />
<br />
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If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
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如果系统被重复细分,最终产生的系统足够小,可以表现出明显的波动。这是一个介观层面的研究。波动则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
<br />
In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
<br />
在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
<br />
<br />
If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
<br />
如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在波动过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,即需要量子统计力学。波动可以变得相对占主导地位,测量问题变得重要。<br />
<br />
To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics.<ref>Tschoegl, N.W. (2000). ''Fundamentals of Equilibrium and Steady-State Thermodynamics'', Elsevier, Amsterdam, {{ISBN|0-444-50426-5}}, p. 21.</ref> But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
<br />
考虑孤立热力学系统中的波动概念,一个方便的例子是由其众多的状态变量,内能、体积和质量组成指定的系统。根据定义,它们是时不变的。根据定义,它们与它们的共轭状态密集函数的时不变名义值相结合,反向温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广泛的状态变量的值,不足以提供这些名义值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
<br />
<br />
The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
<br />
"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有时间趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的标称值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微波动期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。非已知属于平衡状态的标称值,否则根据单一的度量无法进行判断。<br />
<br />
It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.<br />
<br />
可以承认,在重复测量这些共轭强度函数时,发现它们的值随时间略有不同。这种可变性被认为是由于内部波动。不同测量值平均到其名义值。<br />
<br />
<br />
<br />
If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<ref>Buchdahl, H.A. (1966), p. 16.</ref><br />
<br />
如果这个系统真的像经典热力学所假定的那样是宏观的,那么这个系统的波动太小了,宏观上无法检测到。这就是所谓的热力学极限。实际上,物质的分子性质和动量转移的量子性质由于它们太小而看不见,已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中,平衡的波动概念是没有位置的。”<br />
<br />
<br />
If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
<br />
如果系统被重复细分,最终产生的系统足够小,可以表现出明显的波动。这是一个介观层面的研究。波动则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
<br />
An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process." This illustrates the importance for thermodynamics of the concept of temperature.<br />
<br />
热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
<br />
<br />
<br />
If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在波动过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,即需要量子统计力学。波动可以变得相对占主导地位,测量问题变得重要。<br />
<br />
Thermal equilibrium is achieved when two systems in thermal contact with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<br />
<br />
当两个相互热接触的系统不再有净能量交换时,就会产生热平衡。因此,如果两个系统处于热平衡,那么它们的温度是相同的。<br />
<br />
<br />
<br />
The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
<br />
"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有时间趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的标称值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微波动期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。非已知属于平衡状态的标称值,否则根据单一的度量无法进行判断。<br />
<br />
Thermal equilibrium occurs when a system's macroscopic thermal observables have ceased to change with time. For example, an ideal gas whose distribution function has stabilised to a specific Maxwell–Boltzmann distribution would be in thermal equilibrium. This outcome allows a single temperature and pressure to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<br />
<br />
当系统的宏观热观测值不再随着时间变化时,就会出现热平衡。例如,一种分布函数稳定到一个特定的麦克斯韦-波兹曼分布的理想气体即处于热平衡状态。这个结果可以将单一的温度和压力归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是很有可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
<br />
=== Thermal equilibrium ===<br />
热平衡<br />
{{Main|Thermal equilibrium}}<br />
<br />
<br />
<br />
An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process."<ref>Eu, B.C. (2002), page 13.</ref> This illustrates the importance for thermodynamics of the concept of temperature.<br />
<br />
热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
<br />
A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<br />
<br />
一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数。<br />
<br />
<br />
<br />
[[Thermal equilibrium]] is achieved when two systems in [[thermal contact]] with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<ref>[[Raj Pathria|R. K. Pathria]], 1996</ref><br />
<br />
当两个相互'''<font color="#ff8000">热接触 Thermal Contact</font>'''的系统不再有净能量交换时,就会产生'''<font color="#ff8000">热平衡 Thermal Equilibrium</font>'''。因此,如果两个系统处于热平衡,那么它们的温度是相同的<br />
<br />
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
<br />
非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
<br />
<br />
<br />
Thermal equilibrium occurs when a system's [[macroscopic]] thermal observables have ceased to change with time. For example, an [[ideal gas]] whose [[Distribution function (physics)|distribution function]] has stabilised to a specific [[Maxwell–Boltzmann distribution]] would be in thermal equilibrium. This outcome allows a single [[temperature]] and [[pressure]] to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<ref>de Groot, S.R., Mazur, P. (1962), p. 44.</ref><br />
<br />
当一个系统的'''<font color="#ff8000">宏观 Macroscopic</font>'''热观测值不再随时间变化时,就会出现热平衡。例如,一种'''<font color="#ff8000">分布函数 Distribution Function</font>'''稳定到一个特定的'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''的'''<font color="#ff8000">理想气体 Ideal Gas</font>'''即处于热平衡状态。这个结果可以将单一的'''<font color="#ff8000">温度 Temperature</font>'''和'''<font color="#ff8000">压力 Pressure</font>'''归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
<br />
Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle. It states that a non-equilibrium system evolves such as to maximize its entropy production.<br />
<br />
定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
<br />
==Non-equilibrium==<br />
非平衡<br />
{{Main|Non-equilibrium thermodynamics}}<br />
<br />
<br />
<br />
Thermodynamic models <br />
<br />
热力学模型<br />
<br />
A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<ref>de Groot, S.R., Mazur, P. (1962), p. 43.</ref><br />
<br />
一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数<br />
<br />
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
<br />
非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
<br />
<br />
Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle.<ref>{{cite book|last1=Ziegler|first1=H.|title=An Introduction to Thermomechanics.|date=1983|location=North Holland, Amsterdam.}}</ref><ref>{{cite journal|last1=Onsager|first1=Lars|title=Reciprocal Relations in Irreversible Processes|journal=Phys. Rev.|date=1931|volume=37|issue=4|doi=10.1103/PhysRev.37.405|bibcode=1931PhRv...37..405O|pages=405–426|doi-access=free}}</ref> It states that a non-equilibrium system evolves such as to maximize its entropy production.<ref>{{cite book|last1=Kleidon|first1=A.|last2=et.|first2=al.|title=Non-equilibrium Thermodynamics and the Production of Entropy.|date=2005|edition=Heidelberg: Springer.}}</ref><ref>{{cite journal|last1=Belkin|first1=Andrey|last2=et.|first2=al.|title=Self-Assembled Wiggling Nano-Structures and the Principle of Maximum Entropy Production|journal=Sci. Rep.|doi=10.1038/srep08323|bibcode=2015NatSR...5E8323B|pmc=4321171|pmid=25662746|volume=5|year=2015|page=8323}}</ref><br />
<br />
定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
<br />
Topics in control theory<br />
<br />
控制理论主题<br />
<br />
==See also ==<br />
<br />
{{Portal|Chemistry}}<br />
<br />
;Thermodynamic models 热力学模型<br />
<br />
{{colbegin}}<br />
<br />
* [[Non-random two-liquid model]] (NRTL model) - Phase equilibrium calculations 非随机两液模型(NRTL 模型)-相平衡计算<br />
<br />
* [[UNIQUAC]] model - Phase equilibrium calculations UNIQUAC 模型-相平衡计算<br />
<br />
* [[Time crystal]] 时间晶体<br />
<br />
{{colend}}<br />
<br />
;Topics in control theory 控制理论主题<br />
<br />
{{colbegin}}<br />
<br />
* [[Steady state]] 稳态<br />
<br />
* [[Transient state]] 瞬态<br />
<br />
* [[Coefficient diagram method]] 系数图法<br />
<br />
* [[Control reconfiguration]] 控制重构<br />
<br />
* [[Cut-insertion theorem]] 切入定理<br />
<br />
* [[Feedback]] 反馈<br />
<br />
* [[H infinity]] H 无限<br />
<br />
* [[Hankel singular value]] 汉克尔奇异值<br />
<br />
* [[Krener's theorem]] 克雷纳定理<br />
<br />
* [[Lead-lag compensator]] 超前滞后补偿器<br />
<br />
* [[Minor loop feedback]] 小循环反馈<br />
<br />
* [[Minor loop feedback|Multi-loop feedback]] 小循环反馈 | 多循环反馈<br />
<br />
* [[Positive systems]] 正向系统<br />
<br />
* [[Radial basis function]] 径向基底函数<br />
<br />
Other related topics<br />
<br />
其他相关话题<br />
<br />
* [[Root locus]] 根轨迹<br />
<br />
* [[Signal-flow graph]]s 信号流图<br />
<br />
* [[Stable polynomial]] 稳定多项式<br />
<br />
* [[State space representation]] 状态空间<br />
<br />
* [[Underactuation]] 欠驱动<br />
<br />
* [[Youla–Kucera parametrization]] 尤拉-库切拉参数化<br />
<br />
* [[Markov chain approximation method]] 马尔可夫链近似法<br />
<br />
{{colend}}<br />
<br />
;Other related topics<br />
其他相关话题<br />
<br />
{{colbegin}}<br />
<br />
* [[Automation and remote control]] 自动化和远程控制<br />
<br />
* [[Bond graph]] 键合图<br />
<br />
* [[Control engineering]] 控制工程<br />
<br />
* [[Control–feedback–abort loop]] 控制-反馈-中止循环<br />
<br />
* [[Controller (control theory)]] 控制器(控制理论)<br />
<br />
* [[Cybernetics]] 控制论<br />
<br />
* [[Intelligent control]] 智能控制<br />
<br />
* [[Mathematical system theory]] 数学系统论<br />
<br />
* [[Negative feedback amplifier]] 负反馈放大器<br />
<br />
* [[People in systems and control]] 系统和控制中的人<br />
<br />
* [[Perceptual control theory]] 知觉控制理论<br />
<br />
* [[Systems theory]] 系统论<br />
<br />
* [[Time scale calculus]] 时间尺度演算<br />
<br />
{{colend}}<br />
<br />
<br />
<br />
== 编者推荐 ==<br />
===集智文章推荐===<br />
<br />
====[https://swarma.org/?p=21322 什么是非平衡态热力学 | 集智百科]====<br />
非平衡态热力学 Non-equilibrium thermodynamics 是热力学的一个分支,研究某些不处于热力学平衡中的物理系统<br />
<br />
<br />
<br />
<br />
==General references==<br />
<br />
* Cesare Barbieri (2007) ''Fundamentals of Astronomy''. First Edition (QB43.3.B37 2006) CRC Press {{ISBN|0-7503-0886-9}}, {{ISBN|978-0-7503-0886-1}}<br />
<br />
* Hans R. Griem (2005) ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}<br />
<br />
* C. Michael Hogan, Leda C. Patmore and Harry Seidman (1973) ''Statistical Prediction of Dynamic Thermal Equilibrium Temperatures using Standard Meteorological Data Bases'', Second Edition (EPA-660/2-73-003 2006) United States Environmental Protection Agency Office of Research and Development, Washington, D.C. [http://library.wur.nl/WebQuery/catalog/lang/1851848]<br />
<br />
* F. Mandl (1988) ''Statistical Physics'', Second Edition, John Wiley & Sons<br />
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<br />
==References==<br />
<br />
{{Reflist|colwidth=35em}}<br />
<br />
<br />
<br />
==Cited bibliography==<br />
<br />
<br />
<br />
*Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', third edition, McGraw-Hill, London, {{ISBN|0-521-25445-0}}.<br />
<br />
*Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, {{ISBN|0-88318-797-3}}.<br />
<br />
*Beattie, J.A., Oppenheim, I. (1979). ''Principles of Thermodynamics'', Elsevier Scientific Publishing, Amsterdam, {{ISBN|0-444-41806-7}}.<br />
<br />
*[[Ludwig Boltzmann|Boltzmann, L.]] (1896/1964). ''Lectures on Gas Theory'', translated by S.G. Brush, University of California Press, Berkeley.<br />
<br />
*Buchdahl, H.A. (1966). ''The Concepts of Classical Thermodynamics'', Cambridge University Press, Cambridge UK.<br />
<br />
*[[Herbert Callen|Callen, H.B.]] (1960/1985). ''Thermodynamics and an Introduction to Thermostatistics'', (1st edition 1960) 2nd edition 1985, Wiley, New York, {{ISBN|0-471-86256-8}}.<br />
<br />
*[[Constantin Carathéodory|Carathéodory, C.]] (1909). [https://web.archive.org/web/20160304213645/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0067&DMDID=DMDLOG_0033&L=1 Untersuchungen über die Grundlagen der Thermodynamik], ''[[Mathematische Annalen]]'', '''67''': 355–386. A translation may be found [http://neo-classical-physics.info/uploads/3/0/6/5/3065888/caratheodory_-_thermodynamics.pdf here]. Also a mostly reliable [https://books.google.com/books?id=xwBRAAAAMAAJ&q=Investigation+into+the+foundations translation is to be found] at Kestin, J. (1976). ''The Second Law of Thermodynamics'', Dowden, Hutchinson & Ross, Stroudsburg PA.<br />
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*[[Sydney Chapman (mathematician)|Chapman, S.]], [[Thomas George Cowling|Cowling, T.G.]] (1939/1970). ''The Mathematical Theory of Non-uniform gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases'', third edition 1970, Cambridge University Press, London.<br />
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*Crawford, F.H. (1963). ''Heat, Thermodynamics, and Statistical Physics'', Rupert Hart-Davis, London, Harcourt, Brace & World, Inc.<br />
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*de Groot, S.R., Mazur, P. (1962). ''Non-equilibrium Thermodynamics'', North-Holland, Amsterdam. Reprinted (1984), Dover Publications Inc., New York, {{ISBN|0486647412}}.<br />
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*Denbigh, K.G. (1951). ''Thermodynamics of the Steady State'', Methuen, London.<br />
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*Eu, B.C. (2002). ''Generalized Thermodynamics. The Thermodynamics of Irreversible Processes and Generalized Hydrodynamics'', Kluwer Academic Publishers, Dordrecht, {{ISBN|1-4020-0788-4}}.<br />
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*Fitts, D.D. (1962). ''Nonequilibrium thermodynamics. A Phenomenological Theory of Irreversible Processes in Fluid Systems'', McGraw-Hill, New York.<br />
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*[[Josiah Willard Gibbs|Gibbs, J.W.]] (1876/1878). On the equilibrium of heterogeneous substances, ''Trans. Conn. Acad.'', '''3''': 108–248, 343–524, reprinted in ''The Collected Works of J. Willard Gibbs, Ph.D, LL. D.'', edited by W.R. Longley, R.G. Van Name, Longmans, Green & Co., New York, 1928, volume 1, pp.&nbsp;55–353.<br />
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*Griem, H.R. (2005). ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}.<br />
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*[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', fifth revised edition, North-Holland, Amsterdam.<br />
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*Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of ''Thermodynamics'', pages 1–97 of volume 1, ed. W. Jost, of ''Physical Chemistry. An Advanced Treatise'', ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081.<br />
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*[[John Gamble Kirkwood|Kirkwood, J.G.]], Oppenheim, I. (1961). ''Chemical Thermodynamics'', McGraw-Hill Book Company, New York.<br />
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*Landsberg, P.T. (1961). ''Thermodynamics with Quantum Statistical Illustrations'', Interscience, New York.<br />
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*{{cite journal |last1=Lieb |first1=E. H. |last2=Yngvason |first2=J. |year=1999 |title=The Physics and Mathematics of the Second Law of Thermodynamics |journal=Phys. Rep. |volume=310 |issue= 1|pages=1–96 |doi= 10.1016/S0370-1573(98)00082-9|arxiv = cond-mat/9708200 |bibcode = 1999PhR...310....1L |s2cid=119620408 }}<br />
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*Levine, I.N. (1983), ''Physical Chemistry'', second edition, McGraw-Hill, New York, {{ISBN|978-0072538625}}.<br />
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*{{cite journal | last1 = Maxwell | first1 = J.C. | authorlink = James Clerk Maxwell | year = 1867 | title = On the dynamical theory of gases | url = | journal = Phil. Trans. Roy. Soc. London | volume = 157 | issue = | pages = 49–88 }}<br />
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*[[Philip M. Morse|Morse, P.M.]] (1969). ''Thermal Physics'', second edition, W.A. Benjamin, Inc, New York.<br />
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*Münster, A. (1970). ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London.<br />
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*[[J.R. Partington|Partington, J.R.]] (1949). ''An Advanced Treatise on Physical Chemistry'', volume 1, ''Fundamental Principles. The Properties of Gases'', Longmans, Green and Co., London.<br />
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*[[Brian Pippard|Pippard, A.B.]] (1957/1966). ''The Elements of Classical Thermodynamics'', reprinted with corrections 1966, Cambridge University Press, London.<br />
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* [[Max Planck|Planck. M.]] (1914). [https://archive.org/details/theoryofheatradi00planrich ''The Theory of Heat Radiation''], a translation by Masius, M. of the second German edition, P. Blakiston's Son & Co., Philadelphia.<br />
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*[[Ilya Prigogine|Prigogine, I.]] (1947). ''Étude Thermodynamique des Phénomènes irréversibles'', Dunod, Paris, and Desoers, Liège.<br />
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*[[Ilya Prigogine|Prigogine, I.]], Defay, R. (1950/1954). ''Chemical Thermodynamics'', Longmans, Green & Co, London.<br />
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*Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005). ''Physical Chemistry'', fourth edition, Wiley, Hoboken NJ.<br />
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*[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966). ''Elements of Thermodynamics'', Addison-Wesley Publishing, Reading MA.<br />
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*{{cite journal|last=Thomson|first=W.|author-link=William Thomson, 1st Baron Kelvin|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Transactions of the Royal Society of Edinburgh|date=March 1851|volume=XX|issue=part II|pages=261–268; 289–298}} Also published in {{cite journal|last=Thomson|first=W.|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Phil. Mag. |date=December 1852 |volume=IV |series=4 |issue=22 |pages=8–21 |url=https://archive.org/details/londonedinburghp04maga |accessdate=25 June 2012}}<br />
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*[[László Tisza|Tisza, L.]] (1966). ''Generalized Thermodynamics'', M.I.T Press, Cambridge MA.<br />
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*[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963). ''Lectures in Statistical Mechanics'', American Mathematical Society, Providence RI.<br />
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*Waldram, J.R. (1985). ''The Theory of Thermodynamics'', Cambridge University Press, Cambridge UK, {{ISBN|0-521-24575-3}}.<br />
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*[[Mark Zemansky|Zemansky, M.]] (1937/1968). ''Heat and Thermodynamics. An Intermediate Textbook'', fifth edition 1967, McGraw–Hill Book Company, New York.<br />
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== External links ==<br />
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Category:Equilibrium chemistry<br />
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类别: 平衡化学<br />
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*[http://ads.harvard.edu/books/1989fsa..book/AbookC15.pdf Breakdown of Local Thermodynamic Equilibrium] George W. Collins, The Fundamentals of Stellar Astrophysics, Chapter 15<br />
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Category:Thermodynamic cycles<br />
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类别: 热力循环<br />
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*[http://spiff.rit.edu/classes/phys440/lectures/lte/lte.html Thermodynamic Equilibrium, Local and otherwise] lecture by Michael Richmond<br />
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Category:Thermodynamic processes<br />
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类别: 热力学过程<br />
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*[http://journals.ametsoc.org/doi/abs/10.1175/1520-0469%281970%29027%3C0711:NLTEIC%3E2.0.CO%3B2 Non-Local Thermodynamic Equilibrium in Cloudy Planetary Atmospheres] Paper by R. E. Samueison quantifying the effects due to non-LTE in an atmosphere<br />
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Category:Thermodynamic systems<br />
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类别: 热力学系统<br />
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*[http://scienceworld.wolfram.com/physics/LocalThermodynamicEquilibrium.html Local Thermodynamic Equilibrium]<br />
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Category:Thermodynamics<br />
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分类: 热力学<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Thermodynamic equilibrium]]. Its edit history can be viewed at [[平衡热力学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%B9%B3%E8%A1%A1%E7%83%AD%E5%8A%9B%E5%AD%A6&diff=21464平衡热力学2021-01-30T11:55:01Z<p>Jxzhou:/* Multiple contact equilibrium */</p>
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<div>此词条暂由小竹凉翻译,翻译字数共5339,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{short description|State of thermodynamic system(s) where no net macroscopic flow of matter or energy occurs}}<br />
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'''Thermodynamic equilibrium''' is an [[axiomatic]] concept of [[thermodynamics]]. It is an internal [[State variables|state]] of a single [[thermodynamic system]], or a relation between several thermodynamic systems connected by more or less permeable or impermeable [[Thermodynamic system#Walls|walls]]. In thermodynamic equilibrium there are no net [[macroscopic]] [[Flow (mathematics)|flows]] of [[matter]] or of [[energy]], either within a system or between systems. <br />
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Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium there are no net macroscopic flows of matter or of energy, either within a system or between systems. <br />
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'''热力学平衡'''是'''<font color="#ff8000">热力学 Thermodynamics</font>'''的一个'''<font color="#ff8000">不言自明的 Axiomatic</font>'''概念。它是单个'''<font color="#ff8000">热力学系统 Thermodynamic System</font>'''的内部'''<font color="#ff8000">状态 State</font>''',或者是几个热力学系统之间通过或多或少的渗透或不渗透的'''<font color="#ff8000">壁 Wall</font>'''连接的关系。无论是在一个系统内还是在系统之间,在热力学平衡中不存在'''<font color="#ff8000">物质 Matter</font>'''或'''<font color="#ff8000">能量 Energy</font>'''的净'''<font color="#ff8000">宏观 Macroscopic</font>''' '''<font color="#ff8000">流动 Flow</font>'''。<br />
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In a system that is in its own state of internal thermodynamic equilibrium, no [[macroscopic]] change occurs. <br />
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In a system that is in its own state of internal thermodynamic equilibrium, no macroscopic change occurs. <br />
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在一个处于内部热力学平衡状态的系统中,不会发生'''<font color="#ff8000">宏观 Macroscopic</font>'''变化。<br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual [[Thermal equilibrium|thermal]], [[Mechanical equilibrium|mechanical]], [[Chemical equilibrium|chemical]], and [[Radiative equilibrium|radiative]] equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a [[thermodynamic operation]]. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a thermodynamic operation. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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相互热力学平衡的体系同时处于互相之间的'''<font color="#ff8000">热 Thermal</font>'''平衡、'''<font color="#ff8000">力学 Mechanical</font>'''平衡、'''<font color="#ff8000">化学 Chemical</font>'''平衡和'''<font color="#ff8000">辐射 Radiative</font>'''平衡。系统可以处于其中一种相互平衡状态,尽管其他状态未平衡。在热力学平衡中所有的平衡同时并且无限期地保持,直到被'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''打破。在一个宏观平衡中,微观交换是完全或几乎完全平衡的;这是对宏观平衡概念的物理解释。<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform [[temperature]]. Its [[Intensive and extensive properties|intensive properties]], other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform temperature. Its intensive properties, other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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一个处于内部热力学状态平衡的热力学系统具有空间均匀的'''<font color="#ff8000">温度 Temperature</font>'''。除了温度以外,它的'''<font color="#ff8000">强度性质 Intensive Properties</font>'''可以由于周围环境施加的不变的长程力场而导致空间不均匀性。<br />
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In systems that are at a state of [[non-equilibrium]] there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a '''meta-stable equilibrium'''.<br />
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In systems that are at a state of non-equilibrium there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a meta-stable equilibrium.<br />
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相比之下,处于'''<font color="#ff8000">非平衡状态 non-equilibrium</font>'''的系统中有物质或能量的净流动。如果这些变化可以在一个还没有发生的系统中被触发,那么这个系统就被称为处于一个'''亚稳定的平衡状态'''。<br />
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Though not a widely named a "law," it is an [[axiom]] of thermodynamics that there exist states of thermodynamic equilibrium. The [[second law of thermodynamics]] states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the [[entropy|entropies]] of the portions.<br />
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Though not a widely named a "law," it is an axiom of thermodynamics that there exist states of thermodynamic equilibrium. The second law of thermodynamics states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the entropies of the portions.<br />
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虽然不是一个广泛命名的“定律” ,但存在热力学平衡状态是一个热力学'''<font color="#ff8000">公理 Axiom</font>'''。'''<font color="#ff8000">热力学第二定律 second law of thermodynamics</font>'''指出,当一个物质体从一个平衡状态开始,在这个状态中,它的一部分被或多或少渗透或不渗透的分区保持在不同的状态,并且是孤立的,热力学操作移除分区或使分区更具渗透性,然后它会自发地达到自己内部热力学平衡的新状态,并伴随着部分'''<font color="#ff8000">熵 Entropy</font>'''的总和增加。<br />
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== Overview 概览==<br />
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{{Thermodynamics|cTopic=[[Thermodynamic system|Systems]]}}<br />
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Classical thermodynamics deals with states of [[dynamic equilibrium]]. The state of a system at thermodynamic equilibrium is the one for which some [[thermodynamic potential]] is minimized, or for which the [[entropy]] (''S'') is maximized, for specified conditions. One such potential is the [[Helmholtz free energy]] (''A''), for a system with surroundings at controlled constant temperature and volume:<br />
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Classical thermodynamics deals with states of dynamic equilibrium. The state of a system at thermodynamic equilibrium is the one for which some thermodynamic potential is minimized, or for which the entropy (S) is maximized, for specified conditions. One such potential is the Helmholtz free energy (A), for a system with surroundings at controlled constant temperature and volume:<br />
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经典热力学研究'''<font color="#ff8000">动态平衡 Dynamic Equilibrium</font>'''的状态。系统的热力学平衡状态是对于特定的条件,一些'''<font color="#ff8000">热力学势 Thermodynamic Potential</font>'''被最小化,或者'''<font color="#ff8000">熵 Entropy</font>'''(S)被最大化。对于一个周围环境温度和体积恒定的系统,其中一个这样的热力学势是'''<font color="#ff8000">亥姆霍兹自由能 Helmholtz Free Energy</font>'''(A):<br />
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:<math>A = U - TS</math><br />
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<math>A = U - TS</math><br />
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A = U-TS<br />
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Another potential, the [[Gibbs free energy]] (''G''), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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Another potential, the Gibbs free energy (G), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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在恒定温度和压力的系统中,另一个热力学势'''<font color="#ff8000">吉布斯自由能 Gibbs Free Energy</font>'''(G)在热力学平衡状态最小:<br />
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:<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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where ''T'' denotes the absolute thermodynamic temperature, ''P'' the pressure, ''S'' the entropy, ''V'' the volume, and ''U'' the internal energy of the system.<br />
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where T denotes the absolute thermodynamic temperature, P the pressure, S the entropy, V the volume, and U the internal energy of the system.<br />
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其中 T 表示热力学绝对温度,P 表示压强,S 表示熵,V 表示体积,U 表示体系的内能。<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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热力学平衡是一种独特的稳定定态,当系统长时间与周围环境相互作用时,它可以被接近或最终到达。上述势能是数学构造的热力学量,在特定的环境条件下最小化。<br />
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== Conditions 条件==<br />
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* For a completely isolated system, ''S'' is maximum at thermodynamic equilibrium. 对于一个完全孤立的系统,S在热力学平衡中取最大值。<br />
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* For a system with controlled constant temperature and volume, ''A'' is minimum at thermodynamic equilibrium. 对于一个恒定温度和体积的系统来说,A在热力学平衡中取最小值。<br />
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* For a system with controlled constant temperature and pressure, ''G'' is minimum at thermodynamic equilibrium. 对于一个恒温恒压的系统,G在热力学平衡中取最小值。<br />
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The various types of equilibriums are achieved as follows:<br />
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The various types of equilibriums are achieved as follows:<br />
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实现各种类型的平衡的方法如下:<br />
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*Two systems are in ''thermal equilibrium'' when their [[temperature]]s are the same. 当两个系统的'''<font color="#ff8000">温度 Temperature</font>'''相同时,它们就处于''热平衡状态''<br />
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*Two systems are in ''mechanical equilibrium'' when their [[pressure]]s are the same. 当两个体系的'''<font color="#ff8000">压力 Pressure</font>'''相同时,它们就处于''力学平衡''<br />
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*Two systems are in ''diffusive equilibrium'' when their [[chemical potential]]s are the same. 当两个题体系的'''<font color="#ff8000">化学势 Chemical Potential</font>'''相同时,它们就处于''扩散平衡''<br />
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*All [[forces]] are balanced and there is no significant external driving force.<br />
所有的'''<font color="#ff8000">力 Force</font>'''都是平衡的,没有明显的外部驱动力<br />
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==Relation of exchange equilibrium between systems 系统之间的交换均衡关系==<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability.<ref name="Nster_a">Münster, A. (1970), p. 49.</ref> When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability. When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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通常,热力学系统的周围环境也可以被看作是另一个热力学系统。在这种观点中,我们可以把系统及其周围环境看作是相互接触的两个系统,远程作用力也将它们联系在一起。系统的包围物是两个系统之间的接触面或边界。在热力学形式中,该表面被认为具有特定的渗透性质。例如,接触的表面可能被认为只能透热,使能量只能作为热传递。当远程力在时间上不发生变化,两个系统之间的热量传递减慢并最终永久停止时,这两个系统被称为热平衡; 这就是接触平衡的一个例子。其它类型的接触平衡可用其它类型的比渗透率来定义。当两个系统对于某一特定类型的渗透率处于接触平衡时,它们具有属于该特定类型渗透率的强变量的共同值。这种强度变量的例子有温度、压力、化学势。<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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接触平衡也可视为交换平衡。在接触平衡状态下,两系统之间某些量的传递速率存在零平衡。例如,对于只能透热的壁,内能作为热在两个系统之间的扩散速率是相等并反向的。两个系统之间的绝热壁只对作为功传递的能量有渗透作用; 在力学平衡,两个系统之间作为功的能量传递速率相等且相反。如果是一个简单的壁,那么通过它的体积转移率也是相等且相反的; 即它两边的压力是相等的。如果绝热壁比较复杂,有一种杠杆,有一个面积比,那么两个体系在交换平衡中的压力与体积交换比成反比,这使得转移率的零平衡作功。<br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<ref name="Planck 1914 40">[[Max Planck|Planck. M.]] (1914), p. 40.</ref><br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<br />
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辐射交换可以发生在两个不同的系统之间。当两个体系温度相同时,辐射交换平衡占优势。<br />
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==Thermodynamic state of internal equilibrium of a system 系统内部平衡的热力学状态==<br />
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A collection of matter may be entirely [[Isolated system|isolated]] from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium.<ref>Haase, R. (1971), p. 4.</ref><ref>Callen, H.B. (1960/1985), p. 26.</ref> (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics.<ref>{{Cite journal |doi = 10.1119/1.4914528|bibcode = 2015AmJPh..83..628M|title = Time and irreversibility in axiomatic thermodynamics|year = 2015|last1 = Marsland|first1 = Robert|last2 = Brown|first2 = Harvey R.|last3 = Valente|first3 = Giovanni|journal = American Journal of Physics|volume = 83|issue = 7|pages = 628–634}}</ref> One textbook<ref>[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963), p. 5.</ref> calls it the "zeroth law", remarking that the authors think this more befitting that title than its [[Zeroth law of thermodynamics|more customary definition]], which apparently was suggested by [[Ralph H. Fowler|Fowler]].)<br />
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A collection of matter may be entirely isolated from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium. (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics. One textbook calls it the "zeroth law", remarking that the authors think this more befitting that title than its more customary definition, which apparently was suggested by Fowler.)<br />
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物质的集合可能与其周围的环境完全'''<font color="#ff8000">孤立 Isolated</font>'''。如果它在无限长的时间内一直保持不受干扰,按照经典热力学假定,它处于一个没有发生任何变化,没有流动的状态,即内部平衡的热力学状态。(这种假设有时被称为“负第一”热力学定律,但并不常见。有教科书称之为“第零定律” ,作者'''<font color="#ff8000">福勒 Fowler</font>'''认为这个名称是'''<font color="#ff8000">更符合惯例的定义 More Customary Definition</font>'''。)<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a [[thermodynamic operation]] be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a thermodynamic operation be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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这种状态是所谓的经典热力学或平衡态热力学的主要关注点,因为它们是系统中被认为在这门学科中得到很好定义的唯一状态。一个与另一个系统处于接触平衡状态可以被一个'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''隔离,在隔离发生时,其内部不会发生任何变化。因此,一个与另一个系统处于接触平衡状态时也可以被视为处于其自身的内部热力学平衡状态。<br />
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==Multiple contact equilibrium 多点接触平衡==<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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热力学形式允许一个系统同时与其他多个系统接触,这些系统可能有也可能没有相互接触,且这些接触具有不同的渗透性。如果这些系统都与世界其他部分相互隔离,那么它们彼此之间就会达到各自的接触平衡。<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy.<ref name="Caratheodory">Carathéodory, C. (1909).</ref><ref>Prigogine, I. (1947), p. 48.</ref><ref>Landsberg, P. T. (1961), pp. 128–142.</ref><ref>Tisza, L. (1966), p. 108.</ref> Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy. Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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如果几个系统彼此之间没有绝热壁,但是它们与世界其他部分共同隔离,那么它们就会达到多重接触平衡状态,且有共同的温度,总的内能和熵。在众多强度量中,这是温度的一个独特性质。即使在远距离作用力存在的情况下,它也是有效的。(也就是说,没有“力”可以维持温度的差异。)举个例子,在热力学平衡的一个垂直的引力场系统中,顶部壁面的压力比底部壁面的压力小,但是各处的温度都是一样的。<br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural [[thermodynamic process]].<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), § 1.12.</ref> It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings.<ref>Levine, I.N. (1983), p. 40.</ref><ref>Lieb, E.H., Yngvason, J. (1999), pp. 17–18.</ref> The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of [[Second law of thermodynamics#Description#Kelvin statement|"inanimate" agency]]; a system in thermodynamic equilibrium is inanimate.<ref>[[William Thomson, 1st Baron Kelvin|Thomson, W.]] (1851).</ref><br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural thermodynamic process. It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings. The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of "inanimate" agency; a system in thermodynamic equilibrium is inanimate.<br />
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热力操作可能作为一个事件发生在周围环境的壁上,既不直接影响与周围环境联系的壁,也不直接影响其内部,且发生在一个明确的有限的时间内。例如,一个固定的绝热壁可以在环境中被放置或拆除。由于这种操作仅限于周围环境,系统可能会在一段时间内远离自身最初的内部状态---- 热力学平衡。根据热力学第二定律的说法,整体经历了变化并最终与周围环境达到了新的平衡。继Planck之后,这一连串的事件被称为自然'''<font color="#ff8000">热力学过程 Thermodynamic Process</font>'''。即使在这个过程中,当系统和周围环境都不处于明确的内部平衡状态时,存在着暂时偏离热力学平衡的现象,由于初始状态和最终状态都是热力学平衡的,这在平衡热力学中也是允许的。一个自然过程在其主要部分中以有限的速率进行,因此,它从根本上不同于虚构的准静态“过程”;即不在整个过程中无限缓慢地进行而且虚构地“可逆”。经典热力学允许,即使一个过程可能需要很长的时间才能达到热力学平衡,如果主要部分的过程是在一个有限的比率中,那么它被认为是自然的,并受制于热力学第二定律,即不可逆的。工程设计的机器、人工设备和操作是允许在周围环境中进行的。允许在环境中而不是在系统中进行此类操作和设备,是开尔文在他的一个热力学第二定律的陈述中提到'''<font color="#ff8000">无生命机构 Inanimate Agency</font>'''的原因; 在热力学平衡的系统是无生命的。<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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否则,热力操作可能会直接影响系统的壁。<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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通常可以很方便地假设周围的某些子系统比系统大得多,以至于这个过程只能影响周围子系统的强度变量,然后将这些子系统称为相关强度变量的储备库。<br />
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== Local and global equilibrium ==<br />
局部和全局均衡<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by [[intensive quantity|intensive]] parameters. As an example, [[temperature]] controls [[Heat equation|heat exchanges]]. ''Global thermodynamic equilibrium'' (GTE) means that those [[intensive quantity|intensive]] parameters are homogeneous throughout the whole system, while ''local thermodynamic equilibrium'' (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by intensive parameters. As an example, temperature controls heat exchanges. Global thermodynamic equilibrium (GTE) means that those intensive parameters are homogeneous throughout the whole system, while local thermodynamic equilibrium (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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区分全局性和局部性热力学平衡是很有用的。在热力学中,系统内部和系统与外部之间的交换是由'''<font color="#ff8000">强度 Intensive</font>'''参数控制的。例如,'''<font color="#ff8000">温度 Temperature</font>'''控制'''<font color="#ff8000">热交换 Heat Equation</font>'''。全局热力学平衡(GTE)意味着这些'''<font color="#ff8000">强度 Intensive</font>'''参数在整个系统中是均匀的,而局部热力学平衡(LTE)意味着这些强度参数在空间和时间上是变化的,但变化如此缓慢,以至于对于任何一点,人们都可以假设在某个邻近的某个热力学平衡。<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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如果对系统的描述要求强度参数的变化过大,那么这些强度参数的定义所依据的假设本身就会破裂,系统将既不处于全局平衡,也不处于局部平衡。例如,粒子需要一定数量的碰撞来平衡其周围环境。如果在这些碰撞中移动的平均距离使它离开平衡邻域,它将永远不会平衡,也就不会有 LTE。根据定义,温度与平衡邻域的平均内部能量成正比。由于没有达到平衡邻域,温度的概念就不成立,温度也就变得不确定。<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to [[massive]] particles. In a [[radiation|radiating]] gas, the [[photon]]s being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to massive particles. In a radiating gas, the photons being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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值得注意的是,这种局部平衡可能只适用于系统中的某个粒子子集。例如,LTE 通常只适用于'''<font color="#ff8000">大 Massive</font>'''质量粒子。在'''<font color="#ff8000">辐射 Radiation</font>'''气体中,被气体发射和吸收的'''<font color="#ff8000">光子 Photon</font>'''不需要彼此在一个热力学平衡内,或与气体中的大量粒子在一起,LTE 才能存在。在某些情况下,自由电子并不需要与大得多的原子或分子处于平衡状态,LTE 才能存在。<br />
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As an example, LTE will exist in a glass of water that contains a melting [[ice cube]]. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the [[Maxwell–Boltzmann distribution]] for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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As an example, LTE will exist in a glass of water that contains a melting ice cube. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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例如,LTE 将存在于一个装有融化的'''<font color="#ff8000">冰块 Ice Cube</font>'''的水杯中。玻璃杯内的温度可以在任何时候定义,但是离冰块近的地方要比离冰块远的地方冷。如果观察到位于给定点附近的分子的能量,它们将按照麦克斯韦-波兹曼分布在一定温度下的分布。如果观察到位于另一点附近的分子的能量,它们将按照'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''分布到另一个温度。<br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural [[transport phenomena]] may lead a system from local to global thermodynamic equilibrium. Going back to our example, the [[diffusion]] of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<ref>H.R. Griem, 2005</ref><br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural transport phenomena may lead a system from local to global thermodynamic equilibrium. Going back to our example, the diffusion of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<br />
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局部热力学平衡不需要局部或全局的平稳性。换句话说,每一个小区域不需要有一个恒定的温度。然而,它确实要求每个小的局部变化缓慢到足以维持其局部麦克斯韦-波兹曼分布的分子速度。全局非平衡态只有通过系统与外界的交换才能保持稳定。例如,通过在水杯中不断添加细粉冰来补偿熔化,并持续排出融水,可以保持全球稳定的静止状态。自然'''<font color="#ff8000">迁移现象 Transport Phenomena</font>'''可能导致一个从局部到全局的热力学平衡系统。回顾我们的例子,热量的扩散将导致我们的玻璃杯水流向全局热力学平衡,在这种状态下,玻璃杯的温度是完全均匀的。<br />
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==Reservations==<br />
保留意见<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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学识渊博的笔者在热力学领域对热力学平衡描述时,经常对他们的描述附加条件或保留意见。有些笔者含蓄地保留了或多或少的空白,以待说明。<br />
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For example, one widely cited writer, [[Herbert Callen|H. B. Callen]] writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. ''Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!''"<ref>Callen, H.B. (1960/1985), p. 15.</ref><br />
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For example, one widely cited writer, H. B. Callen writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!"<br />
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例如,一位被广泛引用的作家'''<font color="#ff8000">H.B.卡伦 H.B.Callen</font>'''在这里写道: “实际上,很少有系统处于绝对和真正的平衡状态。”他提到了放射性过程,认为它们可能需要“宇宙时间才能完成,因此通常可以忽略”。他补充道: “在实践中,平衡的标准是循环的。在操作上,如果一个系统的性质一致地用热力学理论来描述,那么它就处于平衡状态! ”<br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<ref>Beattie, J.A., Oppenheim, I. (1979), p. 3.</ref><br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<br />
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J.A.贝蒂和 I.奥本海姆写道: “坚持对平衡定义的严格解释,将排除热力学应用于实际系统的所有状态。”<br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment",<ref>Callen, H.B. (1960/1985), p. 485.</ref> and cited by Adkins as having written a "classic text",<ref>Adkins, C.J. (1968/1983), p. ''xiii''.</ref> [[Brian Pippard|A.B. Pippard]] writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<ref>Pippard, A.B. (1957/1966), p. 6.</ref><br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment", and cited by Adkins as having written a "classic text", A.B. Pippard writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<br />
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Callen引用另一位作者的话说,他给出了“学术且严谨的论述” ,Adkins引用他的话说,他写了一本“经典著作”—— '''<font color="#ff8000">A.B.皮帕德 A.B.Pippard</font>'''在文中写道: “只要时间足够长,过冷水蒸汽最终会凝结,... ..。时间可能是漫长的,也许长达10年或者更长。就大多数目的而言,只要这种迅速的变化不是人为地刺激,这些系统就可以被视为处于平衡状态。”<br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster">Münster, A. (1970), p. 53.</ref><br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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另一位作者A.Münster,写道。他观察到热核反应发生的速度非常缓慢,以至于在热力学中可以忽略不计。他评论道: “‘绝对平衡’或‘所有可想象过程的平衡’的概念没有物理意义。”他说: “ ... 我们只能考虑特定过程和确定的实验条件下的平衡。”<br />
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According to [[László Tisza|L. Tisza]]: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<ref>Tisza, L. (1966), p. 119.</ref><br />
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According to L. Tisza: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<br />
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根据'''<font color="#ff8000">L.缇莎 L.Tisza</font>'''的说法: “ ... 在讨论接近绝对零度的现象时。经典理论的绝对预测变得特别模糊,因为在非平衡状态下发生冻结是非常普遍的。”<br />
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==Definitions==<br />
定义<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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一个系统最普遍的热力学平衡是通过与周围环境的接触,允许所有化学物质和各种能量同时通过。热力学平衡中的系统以均匀加速度在空间中运动,但此时不能改变其形状或大小; 因此它是由空间中的刚性体积来定义的。它可能存在于外力场中,由远远大于系统本身的外部因素决定,因此系统内的事件不会对外力场产生相当大的影响。只有当外力场是均匀的,并且确定了它的均匀加速度,或者它处于一个非均匀力场中,但是由于表面的局部力,例如机械压力,使它保持静止时,这个系统才能处于热力学平衡。<br />
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Thermodynamic equilibrium is a [[primitive notion]] of the theory of thermodynamics. According to [[Philip M. Morse|P.M. Morse]]: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are ''not'' conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments."<ref>[[Philip M. Morse|Morse, P.M.]] (1969), p. 7.</ref> This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<ref>Bailyn, M. (1994), p. 20.</ref><br />
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Thermodynamic equilibrium is a primitive notion of the theory of thermodynamics. According to P.M. Morse: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are not conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments." This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<br />
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热力学平衡是热力学理论的一个'''<font color="#ff8000">基本概念 Primitive Notion</font>'''。'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''说: “应该强调的是,存在热力学状态这一事实,以及存在由平衡态唯一指定的热力学变量这一事实,并不是从某些哲学第一原理得出的逻辑结论。这些结论不可避免地来自两个多世纪的实验。”这意味着热力学平衡不能仅仅用热力学的其他理论概念来定义。M.Bailyn提出了一个基本的热力学定律理论,它定义并假设了热力学平衡的存在。<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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热力学平衡的教科书定义通常被仔细说明,并有些保留。<br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<ref>Münster, A. (1970), p. 52.</ref><br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<br />
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例如,A. Münster写道:“当系统中没有以可测量的速度发生状态变化时,隔离系统处于热力学平衡状态。”这里有两项保留:系统是孤立的;任何状态的变化都是不可估量的缓慢。他通过对在室温且没有催化剂的情况下混合氧和氢的说明,讨论了第二个条件。Münster指出,热力学平衡状态所描述的宏观变量比给定系统任何其他状态都少。这是部分,但不完全是,因为系统内和系统内的所有流都是零。<br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in ''equilibrium''.<ref>Haase, R. (1971), pp. 3–4.</ref><br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in equilibrium.<br />
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R. Haase's的热力学演示并不从对热力学平衡的限制开始,因为他打算考虑非平衡态热力学。他考虑一个具有时间不变性质的任意系统。他通过切断除外力场以外的所有外部影响来测试它的热力学平衡。如果在绝缘之后,没有任何变化,他说,系统处于平衡状态。<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness".<ref>Callen, H.B. (1960/1985), p. 13.</ref> This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness". This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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在一个标题为“热力学平衡”的章节中,H.B. Callen在段落定义了平衡状态.他指出,它们“是由系统内部的内在因素决定的”。它们是“终端状态” ,随着时间的推移,系统会以“冰川般缓慢”的速度朝着这个终端状态演化。这个说法并没有明确,对于热力学平衡系统必须是孤立的;;Callen也没有说明他所说的“内在因素”是什么意思。<br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<ref>Adkins, C.J. (1968/1983), p. ''7''.</ref><br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<br />
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另一位教科书作者,C.J.Adkins,明确允许热力学平衡在非孤立的系统中发生。然而,他的系统在物质转移方面是封闭的。他写道: “一般来说,热力学平衡的方法包括热和类似变动与周围环境的相互作用。”他将这种热力学平衡与只有通过热接触才能进行能量传递的热平衡相区别。<br />
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Another textbook author, [[J.R. Partington]], writes: "(i) ''An equilibrium state is one which is independent of time''." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..."<ref>Partington, J.R. (1949), p. 161.</ref> This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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Another textbook author, J.R. Partington, writes: "(i) An equilibrium state is one which is independent of time." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..." This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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另一位教科书作者'''<font color="#ff8000">J.R.帕廷顿 J.R.Partington</font>'''写道: “(i)平衡状态是独立于时间的状态。”但是,在提到“只是明显处于平衡状态”的系统时,他补充说: “这样的系统处于‘虚假平衡’状态。帕廷顿的陈述没有明确指出平衡是指一个孤立的系统。和Münster一样,Partington也指的是氧和氢的混合物。他补充说:“在一个真正的平衡状态,任何影响状态的外部条件的最小变化都会产生一个微小的状态变化... ... ”这个条件意味着热力学平衡必须在小的扰动下保持稳定; 这个要求对于热力学平衡的严格意义是必不可少的。<br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, ''thermodynamic—equilibrium.''"<ref>Crawford, F.H. (1963), p. 5.</ref><br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, thermodynamic—equilibrium."<br />
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在F.H.Crawford的一本学生教科书中,有一个标题为“热力学平衡”的章节。它区分了几种流动的驱动因素,然后说: “这些是孤立系统明显普遍趋向于完全机械、热、化学和电力状态的例子——或者简单地说,热力学平衡状态。”<br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in ''equilibrium''."<ref>Buchdahl, H.A. (1966), p. 8.</ref> Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being ''in equilibrium'' so long as experimental tests show that 'slow' transitions are in effect reversible."<ref>Buchdahl, H.A. (1966), p. 111.</ref> It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<ref>Adkins, C.J. (1968/1983), p. 8.</ref><br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in equilibrium." Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being in equilibrium so long as experimental tests show that 'slow' transitions are in effect reversible." It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<br />
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H.A. Buchdahl的一本关于经典热力学的专著考虑了热力学系统的平衡,而实际上并没有写热力学平衡一词。Buchdahl在提到封闭的物质交换系统时写道: “如果一个系统处于一个适当的静态状态,那么它将被称为处于平衡状态。”出于热力学描述的目的,Buchdahl的专著也讨论了非晶态玻璃。它说: “更准确地说,只要实验测试表明‘慢’跃迁实际上是可逆的,玻璃就可以被认为处于平衡状态。”通常来说不会将这一条件作为热力学平衡定义的一部分,而是假定相反的情况:如果热力学平衡中的一个体受到足够慢的过程的影响,则该过程可被视为足够接近可逆,并且该物体在过程中足够接近热力学平衡。<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of ''contact equilibrium''. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by [[Constantin Carathéodory|C. Carathéodory]], and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster" /> Thermodynamic equilibrium for an open system means that, with respect to every relevant kind of selectively permeable wall, contact equilibrium exists when the respective intensive parameters of the system and surroundings are equal.<ref name="Nster_a" /> This definition does not consider the most general kind of thermodynamic equilibrium, which is through unselective contacts. This definition does not simply state that no current of matter or energy exists in the interior or at the boundaries; but it is compatible with the following definition, which does so state.<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of contact equilibrium. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by C. Carathéodory, and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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通过引入接触平衡的概念,A. Münster仔细地扩展了孤立系统热力学平衡的定义。这指定了在考虑非孤立系统的热力学平衡时允许的特定过程,并特别关心开放系统,这些开放系统可能从周围环境获得或丢失物质。利益系统和周围系统之间的接触平衡,通过一种特殊的壁与利益系统接触,其余的连接系统是孤立的。这种特殊类型的壁也被'''<font color="#ff8000">C.喀喇西奥多里 C.Carathéodory</font>'''考虑过,其他作家也提到过。它们具有选择渗透性。它们可能只对机械工作有渗透性,或者只对热有渗透性,或者只对某种特定的化学物质有渗透性。每个接触平衡定义了一个强度参数; 例如,只能透热的壁定义了一个经验温度。对于感兴趣的体系中每一种化学成分,都可以存在接触平衡。在接触平衡中,尽管有可能通过选择性渗透壁进行交换,感兴趣的系统是不变的,好像它处在孤立的热力学平衡。这个方案遵循的一般规则是: “ ... ... 我们只能考虑特定过程和特定实验条件下的平衡。”<br />
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[[Mark Zemansky|M. Zemansky]] also distinguishes mechanical, chemical, and thermal equilibrium. He then writes: "When the conditions for all three types of equilibrium are satisfied, the system is said to be in a state of thermodynamic equilibrium".<ref>[[Mark Zemansky|Zemansky, M.]] (1937/1968), p. 27.</ref><br />
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'''<font color="#ff8000">M.泽曼斯基 M.Zemansky</font>'''还区分了机械、化学和热平衡。他接着写道: “当这三种均衡的条件都满足时,系统就处于热力学平衡状态。”<br />
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P.M. Morse writes that thermodynamics is concerned with "states of thermodynamic equilibrium". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<br />
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[[Philip M. Morse|P.M. Morse]] writes that thermodynamics is concerned with "''states of thermodynamic equilibrium''". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<ref>[[Philip M. Morse|Morse, P.M.]] (1969), pp. 6, 37.</ref><br />
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'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''写道,热力学关注的是“热力学平衡状态”。在讨论物体与周围热源之间的热量传递时,他也使用了“热平衡”这个短语,尽管没有明确定义一个特殊的术语“热平衡”<br />
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<br />
J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "full thermodynamic equilibrium state".<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "''full'' thermodynamic equilibrium state".<ref>Waldram, J.R. (1985), p. 5.</ref><br />
<br />
J.R. Waldram写到了“一个明确的热力学状态”。他将一个系统定义为“当其观测量随时间停止变化时”的“热平衡”。但是在这个定义之下不久,他写到一块玻璃还没有达到“完全的热力学平衡状态”。<br />
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<br />
Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, thermodynamic equilibrium is said to exist." He is not here considering the presence of an external force field.<br />
<br />
Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, ''thermodynamic equilibrium'' is said to exist." He is not here considering the presence of an external force field.<ref>Bailyn, M. (1994), p. 21.</ref><br />
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考虑到平衡状态,M.Bailyn写道: “每个强度变量都有自己的平衡类型。”然后他定义了热平衡、机械平衡和物质平衡。因此,他写道: “如果所有的强度变量都是一致的,那么热力学平衡就是存在的。”他在这里没有考虑外力场的存在。<br />
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<br />
J.G. Kirkwood and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of thermodynamic equilibrium if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<br />
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[[John Gamble Kirkwood|J.G. Kirkwood]] and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of ''thermodynamic equilibrium'' if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<ref>Kirkwood, J.G., Oppenheim, I. (1961), p. 2</ref><br />
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'''<font color="#ff8000">J.G.柯克伍德 J.G.Kirkwood</font>'''和 I.Oppenheim 将热力学平衡定义为: “一个系统处于热力学平衡状态,如果,在分配给实验的时间内,(a)它强度特性与时间无关,(b)它的内部或与周围环境的边界处没有物质或能量流。”显然,他们没有把定义限制在孤立的或封闭的系统。它们不讨论“缓慢”发生变化的可能性,并且超出了分配给实验的时间范围。他们注意到,对于两个相接触的系统,存在一个强度性质的小子类,如果这个小子类的所有子类都相等,那么所有各自的强度性质都相等。只要满足其他一些条件,热力学平衡状态可以由这个子类定义。<br />
<br />
==Characteristics of a state of internal thermodynamic equilibrium==<br />
内部热力学平衡状态的特征<br />
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<br />
A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous. Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface." As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.<br />
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在内部热力学平衡中,没有外力的情况下由单相组成的热力学系统是均匀的。Planck在论文中简要介绍了热量、温度和热平衡,然后宣布: “在下文中,我们将主要讨论任何形式的均匀、各向同性的物体,它们在整个物质中具有相同的温度和密度,并受到到处垂直于表面的均匀压力作用。”和 Carathéodory 一样,Planck 将表面效应、外场和各向异性晶体排除在外。虽然Planck提到了温度,但并没有明确提到热力学平衡的概念。相比之下,Carathéodory 关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ,虽然没有明确地使用短语‘热力学平衡’,也没有明确地假设存在一个温度来定义它。<br />
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===Homogeneity in the absence of external forces===<br />
在没有外力的情况下的同质性<br />
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A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous.<ref name="Planck 1903 3"/> This means that the material in any small volume element of the system can be interchanged with the material of any other geometrically congruent volume element of the system, and the effect is to leave the system thermodynamically unchanged. In general, a strong external force field makes a system of a single phase in its own internal thermodynamic equilibrium inhomogeneous with respect to some [[Intensive and extensive properties|intensive variables]]. For example, a relatively dense component of a mixture can be concentrated by centrifugation.<br />
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在没有外力的情况下,由单一相组成的热力学系统,在其自身的内部热力学平衡中是均匀的。这意味着系统中任何小体积单元中的材料可以与系统中任何其他几何相等的体积单元中的材料互换,其效果是使系统在热力学上保持不变。一般来说,一个强外力场使得一个单相系统在其自身的内部热力学平衡中对于一些'''<font color="#ff8000">强变量 Intensive Variable</font>'''是不均匀的。例如,可以通过离心来浓缩混合物中相对密度较大的组分。<br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform. Considerations of kinetic theory or statistical mechanics also support this statement.<br />
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热力学平衡系统中的温度在空间和时间上是均匀的。在一个系统内部热力学平衡状态下,没有净内部宏观流动。特别是,这意味着系统的所有局部部分处于相互辐射交换平衡状态。这意味着系统的温度在空间上是均匀的。动力学理论或统计力学也支持这种说法。<br />
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===Uniform temperature===<br />
均匀温度<br />
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In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium. As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.<br />
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为了使一个系统处于它自己的内部热力学平衡状态,它处于自己内部的热平衡状态当然是必要的,但不是充分的;系统在达到内部热平衡之前,可以达到内部机械平衡。如上所述,根据 A.Münster的说法,对于给定的孤立系统的任何状态,定义一个热力学平衡所需的变量数是最少的。如上所述,J.G.Kirkwood 和 I.Oppenheim 指出,热力学平衡状态可以由一个特殊的子类的强变量定义,该子类中有一定数量的成员。<br />
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Such equilibrium inhomogeneity, induced by external forces, does not occur for the intensive variable [[temperature]]. According to [[Edward A. Guggenheim|E.A. Guggenheim]], "The most important conception of thermodynamics is temperature."<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), p.5.</ref> Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface."<ref name="Planck 1903 3">[[Max Planck|Planck, M.]] (1897/1927), p.3.</ref> As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.<br />
<br />
这种由外力引起的平衡不均匀性,在强烈变化的'''<font color="#ff8000">温度 Temperature</font>'''下不会发生。'''<font color="#ff8000">E.A.古根海姆 E.A. Guggenheim</font>'''认为,“热力学最重要的概念是温度。“Planck在介绍他的论文时,简要叙述了热、温度和热平衡,然后宣布: ”在下文中,我们将主要讨论任何形式的均匀、各向同性的物体,它们的物质具有相同的温度和密度,并受到到处垂直于表面的均匀压力的作用和Carathéodory 一样,Planck将表面效应、外场和各向异性晶体排除在外。虽然Planck提到了温度,但并没有明确提到热力学平衡的概念。相比之下,Carathéodory关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ,虽然没有明确地使用短语‘热力学平衡’ ,也没有明确地假设存在一个温度来定义它。<br />
<br />
<br />
If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.<br />
<br />
如果热力学平衡位于一个外力场中,那么通常只有温度在空间上是均匀的。如果外力场非零,温度以外的强度变量通常是不均匀的。在这种情况下,一般需要附加变量来描述空间非均匀性。<br />
<br />
The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform.<ref name="Planck 1914 40"/> This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers.<ref>Gibbs, J.W. (1876/1878), pp. 144-150.</ref><ref>[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966), pp. 127–130.</ref><ref>Münster, A. (1970), pp. 309–310.</ref><ref>Bailyn, M. (1994), pp. 254-256.</ref><ref>{{cite journal | last1 = Verkley | first1 = W.T.M. | last2 = Gerkema | first2 = T. | year = 2004 | title = On maximum entropy profiles | journal = J. Atmos. Sci. | volume = 61 | issue = 8| pages = 931–936 | doi=10.1175/1520-0469(2004)061<0931:omep>2.0.co;2| bibcode = 2004JAtS...61..931V | doi-access = free }}</ref><ref>{{cite journal | last1 = Akmaev | first1 = R.A. | year = 2008 | title = On the energetics of maximum-entropy temperature profiles | url = | journal = Q. J. R. Meteorol. Soc. | volume = 134 | issue = 630| pages = 187–197 | doi=10.1002/qj.209| bibcode = 2008QJRMS.134..187A }}</ref> Considerations of kinetic theory or statistical mechanics also support this statement.<ref>Maxwell, J.C. (1867).</ref><ref>Boltzmann, L. (1896/1964), p. 143.</ref><ref>Chapman, S., Cowling, T.G. (1939/1970), Section 4.14, pp. 75–78.</ref><ref>[[J. R. Partington|Partington, J.R.]] (1949), pp. 275–278.</ref><ref>{{cite journal | last1 = Coombes | first1 = C.A. | last2 = Laue | first2 = H. | year = 1985 | title = A paradox concerning the temperature distribution of a gas in a gravitational field | url = | journal = Am. J. Phys. | volume = 53 | issue = 3| pages = 272–273 | doi=10.1119/1.14138| bibcode = 1985AmJPh..53..272C }}</ref><ref>{{cite journal | last1 = Román | first1 = F.L. | last2 = White | first2 = J.A. | last3 = Velasco | first3 = S. | year = 1995 | title = Microcanonical single-particle distributions for an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 16 | issue = 2| pages = 83–90 | doi=10.1088/0143-0807/16/2/008| bibcode = 1995EJPh...16...83R }}</ref><ref>{{cite journal | last1 = Velasco | first1 = S. | last2 = Román | first2 = F.L. | last3 = White | first3 = J.A. | year = 1996 | title = On a paradox concerning the temperature distribution of an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 17 | issue = | pages = 43–44 | doi=10.1088/0143-0807/17/1/008}}</ref><br />
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热力学平衡系统内的温度在时间和空间上都是均匀的。在一个处于内部热力学平衡的系统中,不存在净的内部宏观流动。特别是,这意味着系统的所有局部都处于相互辐射交换平衡。这意味着系统的温度在空间上是均匀的。这在所有情况下都是如此,包括那些非均匀外力场。对于外部施加的引力场,这可以通过使用朗朗日乘数的方法通过变化的演算在宏观热力学术语中证明。动力学理论或统计力学也支持这种说法。<br />
<br />
<br />
In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium.<ref name="Fitts 43"/><br />
<br />
为了使一个系统处于它自己的内部热力学平衡状态,它必须处于它自己的内部热平衡状态是必要不充分的; 一个系统在到达内部热平衡之前到达内部机械平衡是可能的。<br />
<br />
As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.<br />
<br />
如上所述,j.r. Partington 指出热力学平衡状态在小的瞬态扰动下是稳定的。如果没有这个条件,一般来说,研究热力学平衡系统的实验就会遇到巨大的困难。<br />
<br />
===Number of real variables needed for specification===<br />
规范所需的实变量数目<br />
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<br />
In his exposition of his scheme of closed system equilibrium thermodynamics, C. Carathéodory initially postulates that experiment reveals that a definite number of real variables define the states that are the points of the manifold of equilibria.<ref name="Caratheodory" /> In the words of Prigogine and Defay (1945): "It is a matter of experience that when we have specified a certain number of macroscopic properties of a system, then all the other properties are fixed."<ref>Prigogine, I., Defay, R. (1950/1954), p. 1.</ref><ref>Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005), p. 4.</ref> As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.<br />
<br />
在他关于封闭系统平衡态热力学方案的论述中,C.Carathéodory 最初假定实验揭示了一定数量的实变量定义了作为平衡态流形点的状态。用 Prigogine 和 Defay (1945)的话说: “这是一个经验问题,当我们确定了一个系统一定数量的宏观属性时,那么所有其他属性都是固定的。如上所述,A. Münster认为,定义热力学平衡所需的变量数量对于给定孤立系统的任何状态来说都是最少的。如上所述,J.G. Kirkwood 和 I. Oppenheim 指出,热力学平衡状态可以由一个特殊子类的强度变量来定义,该子类中有一定数量的成员。<br />
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When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium. Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<br />
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当一个物质体从不均匀的非平衡状态或化学非平衡状态开始,然后被孤立,它自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如,在这种演变的许多情况下,内部机械平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是,在这种演变的许多情况下,热平衡的发展要比化学平衡快得多。<br />
<br />
<br />
<br />
If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.<br />
<br />
如果热力学平衡位于一个外力场中,那么通常只有温度在空间上是均匀的。如果外力场非零,温度以外的强度变量通常是不均匀的。在这种情况下,一般需要附加变量来描述空间非均匀性。<br />
<br />
===Stability against small perturbations===<br />
对小扰动的稳定性<br />
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In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
<br />
在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
<br />
As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.<br />
<br />
如上所述,J.R. Partington 指出热力学平衡状态在小的瞬态扰动下是稳定的。如果没有这个条件,一般来说,研究热力学平衡系统的实验就会遇到严重的困难。<br />
<br />
<br />
To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics. But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
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考虑孤立热力学系统中的波动概念,一个方便的例子是由其广泛的状态变量、内能、体积和质量组成指定的系统。根据定义,它们是时不变的。根据定义,它们与它们的共轭状态密集函数的时不变名义值相结合,反向温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广泛的状态变量的值,不足以提供这些名义值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
<br />
===Approach to thermodynamic equilibrium within an isolated system===<br />
孤立系统中的热力学平衡<br />
<br />
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It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.<br />
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可以承认,在重复测量这些共轭强度函数时,发现它们的值随时间略有不同。这种可变性被认为是由于内部波动。不同测量值平均到其名义值。<br />
<br />
When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium.<ref name="Fitts 43">Fitts, D.D. (1962), p. 43.</ref> Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<ref>Denbigh, K.G. (1951), p. 42.</ref><br />
<br />
当一个物质体从不均匀的非平衡状态或化学非平衡状态开始,然后被孤立,它自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如,在这种演变的许多情况下,内部机械平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是,在这种演变的许多情况下,热平衡的发展要比化学平衡快得多。<br />
<br />
If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<br />
<br />
如果这个系统真的像经典热力学所假定的那样是宏观的,那么这个系统的波动太小了,宏观上无法检测到。这就是所谓的热力学极限。实际上,物质的分子性质和动量转移的量子性质由于它们太小而看不见,已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中,平衡的波动概念是没有位置的。”<br />
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===Fluctuations within an isolated system in its own internal thermodynamic equilibrium===<br />
孤立系统内部热力学平衡的波动<br />
<br />
<br />
If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
<br />
如果系统被重复细分,最终产生的系统足够小,可以表现出明显的波动。这是一个介观层面的研究。波动则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
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In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
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在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
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If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
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如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在波动过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,即需要量子统计力学。波动可以变得相对占主导地位,测量问题变得重要。<br />
<br />
To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics.<ref>Tschoegl, N.W. (2000). ''Fundamentals of Equilibrium and Steady-State Thermodynamics'', Elsevier, Amsterdam, {{ISBN|0-444-50426-5}}, p. 21.</ref> But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
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考虑孤立热力学系统中的波动概念,一个方便的例子是由其众多的状态变量,内能、体积和质量组成指定的系统。根据定义,它们是时不变的。根据定义,它们与它们的共轭状态密集函数的时不变名义值相结合,反向温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广泛的状态变量的值,不足以提供这些名义值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
<br />
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The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
<br />
"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有时间趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的标称值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微波动期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。非已知属于平衡状态的标称值,否则根据单一的度量无法进行判断。<br />
<br />
It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.<br />
<br />
可以承认,在重复测量这些共轭强度函数时,发现它们的值随时间略有不同。这种可变性被认为是由于内部波动。不同测量值平均到其名义值。<br />
<br />
<br />
<br />
If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<ref>Buchdahl, H.A. (1966), p. 16.</ref><br />
<br />
如果这个系统真的像经典热力学所假定的那样是宏观的,那么这个系统的波动太小了,宏观上无法检测到。这就是所谓的热力学极限。实际上,物质的分子性质和动量转移的量子性质由于它们太小而看不见,已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中,平衡的波动概念是没有位置的。”<br />
<br />
<br />
If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
<br />
如果系统被重复细分,最终产生的系统足够小,可以表现出明显的波动。这是一个介观层面的研究。波动则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
<br />
An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process." This illustrates the importance for thermodynamics of the concept of temperature.<br />
<br />
热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
<br />
<br />
<br />
If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在波动过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,即需要量子统计力学。波动可以变得相对占主导地位,测量问题变得重要。<br />
<br />
Thermal equilibrium is achieved when two systems in thermal contact with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<br />
<br />
当两个相互热接触的系统不再有净能量交换时,就会产生热平衡。因此,如果两个系统处于热平衡,那么它们的温度是相同的。<br />
<br />
<br />
<br />
The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
<br />
"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有时间趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的标称值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微波动期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。非已知属于平衡状态的标称值,否则根据单一的度量无法进行判断。<br />
<br />
Thermal equilibrium occurs when a system's macroscopic thermal observables have ceased to change with time. For example, an ideal gas whose distribution function has stabilised to a specific Maxwell–Boltzmann distribution would be in thermal equilibrium. This outcome allows a single temperature and pressure to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<br />
<br />
当系统的宏观热观测值不再随着时间变化时,就会出现热平衡。例如,一种分布函数稳定到一个特定的麦克斯韦-波兹曼分布的理想气体即处于热平衡状态。这个结果可以将单一的温度和压力归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是很有可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
<br />
=== Thermal equilibrium ===<br />
热平衡<br />
{{Main|Thermal equilibrium}}<br />
<br />
<br />
<br />
An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process."<ref>Eu, B.C. (2002), page 13.</ref> This illustrates the importance for thermodynamics of the concept of temperature.<br />
<br />
热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
<br />
A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<br />
<br />
一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数。<br />
<br />
<br />
<br />
[[Thermal equilibrium]] is achieved when two systems in [[thermal contact]] with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<ref>[[Raj Pathria|R. K. Pathria]], 1996</ref><br />
<br />
当两个相互'''<font color="#ff8000">热接触 Thermal Contact</font>'''的系统不再有净能量交换时,就会产生'''<font color="#ff8000">热平衡 Thermal Equilibrium</font>'''。因此,如果两个系统处于热平衡,那么它们的温度是相同的<br />
<br />
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
<br />
非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
<br />
<br />
<br />
Thermal equilibrium occurs when a system's [[macroscopic]] thermal observables have ceased to change with time. For example, an [[ideal gas]] whose [[Distribution function (physics)|distribution function]] has stabilised to a specific [[Maxwell–Boltzmann distribution]] would be in thermal equilibrium. This outcome allows a single [[temperature]] and [[pressure]] to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<ref>de Groot, S.R., Mazur, P. (1962), p. 44.</ref><br />
<br />
当一个系统的'''<font color="#ff8000">宏观 Macroscopic</font>'''热观测值不再随时间变化时,就会出现热平衡。例如,一种'''<font color="#ff8000">分布函数 Distribution Function</font>'''稳定到一个特定的'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''的'''<font color="#ff8000">理想气体 Ideal Gas</font>'''即处于热平衡状态。这个结果可以将单一的'''<font color="#ff8000">温度 Temperature</font>'''和'''<font color="#ff8000">压力 Pressure</font>'''归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
<br />
Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle. It states that a non-equilibrium system evolves such as to maximize its entropy production.<br />
<br />
定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
<br />
==Non-equilibrium==<br />
非平衡<br />
{{Main|Non-equilibrium thermodynamics}}<br />
<br />
<br />
<br />
Thermodynamic models <br />
<br />
热力学模型<br />
<br />
A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<ref>de Groot, S.R., Mazur, P. (1962), p. 43.</ref><br />
<br />
一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数<br />
<br />
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
<br />
非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
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<br />
Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle.<ref>{{cite book|last1=Ziegler|first1=H.|title=An Introduction to Thermomechanics.|date=1983|location=North Holland, Amsterdam.}}</ref><ref>{{cite journal|last1=Onsager|first1=Lars|title=Reciprocal Relations in Irreversible Processes|journal=Phys. Rev.|date=1931|volume=37|issue=4|doi=10.1103/PhysRev.37.405|bibcode=1931PhRv...37..405O|pages=405–426|doi-access=free}}</ref> It states that a non-equilibrium system evolves such as to maximize its entropy production.<ref>{{cite book|last1=Kleidon|first1=A.|last2=et.|first2=al.|title=Non-equilibrium Thermodynamics and the Production of Entropy.|date=2005|edition=Heidelberg: Springer.}}</ref><ref>{{cite journal|last1=Belkin|first1=Andrey|last2=et.|first2=al.|title=Self-Assembled Wiggling Nano-Structures and the Principle of Maximum Entropy Production|journal=Sci. Rep.|doi=10.1038/srep08323|bibcode=2015NatSR...5E8323B|pmc=4321171|pmid=25662746|volume=5|year=2015|page=8323}}</ref><br />
<br />
定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
<br />
Topics in control theory<br />
<br />
控制理论主题<br />
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==See also ==<br />
<br />
{{Portal|Chemistry}}<br />
<br />
;Thermodynamic models 热力学模型<br />
<br />
{{colbegin}}<br />
<br />
* [[Non-random two-liquid model]] (NRTL model) - Phase equilibrium calculations 非随机两液模型(NRTL 模型)-相平衡计算<br />
<br />
* [[UNIQUAC]] model - Phase equilibrium calculations UNIQUAC 模型-相平衡计算<br />
<br />
* [[Time crystal]] 时间晶体<br />
<br />
{{colend}}<br />
<br />
;Topics in control theory 控制理论主题<br />
<br />
{{colbegin}}<br />
<br />
* [[Steady state]] 稳态<br />
<br />
* [[Transient state]] 瞬态<br />
<br />
* [[Coefficient diagram method]] 系数图法<br />
<br />
* [[Control reconfiguration]] 控制重构<br />
<br />
* [[Cut-insertion theorem]] 切入定理<br />
<br />
* [[Feedback]] 反馈<br />
<br />
* [[H infinity]] H 无限<br />
<br />
* [[Hankel singular value]] 汉克尔奇异值<br />
<br />
* [[Krener's theorem]] 克雷纳定理<br />
<br />
* [[Lead-lag compensator]] 超前滞后补偿器<br />
<br />
* [[Minor loop feedback]] 小循环反馈<br />
<br />
* [[Minor loop feedback|Multi-loop feedback]] 小循环反馈 | 多循环反馈<br />
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* [[Positive systems]] 正向系统<br />
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* [[Radial basis function]] 径向基底函数<br />
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Other related topics<br />
<br />
其他相关话题<br />
<br />
* [[Root locus]] 根轨迹<br />
<br />
* [[Signal-flow graph]]s 信号流图<br />
<br />
* [[Stable polynomial]] 稳定多项式<br />
<br />
* [[State space representation]] 状态空间<br />
<br />
* [[Underactuation]] 欠驱动<br />
<br />
* [[Youla–Kucera parametrization]] 尤拉-库切拉参数化<br />
<br />
* [[Markov chain approximation method]] 马尔可夫链近似法<br />
<br />
{{colend}}<br />
<br />
;Other related topics<br />
其他相关话题<br />
<br />
{{colbegin}}<br />
<br />
* [[Automation and remote control]] 自动化和远程控制<br />
<br />
* [[Bond graph]] 键合图<br />
<br />
* [[Control engineering]] 控制工程<br />
<br />
* [[Control–feedback–abort loop]] 控制-反馈-中止循环<br />
<br />
* [[Controller (control theory)]] 控制器(控制理论)<br />
<br />
* [[Cybernetics]] 控制论<br />
<br />
* [[Intelligent control]] 智能控制<br />
<br />
* [[Mathematical system theory]] 数学系统论<br />
<br />
* [[Negative feedback amplifier]] 负反馈放大器<br />
<br />
* [[People in systems and control]] 系统和控制中的人<br />
<br />
* [[Perceptual control theory]] 知觉控制理论<br />
<br />
* [[Systems theory]] 系统论<br />
<br />
* [[Time scale calculus]] 时间尺度演算<br />
<br />
{{colend}}<br />
<br />
<br />
<br />
== 编者推荐 ==<br />
===集智文章推荐===<br />
<br />
====[https://swarma.org/?p=21322 什么是非平衡态热力学 | 集智百科]====<br />
非平衡态热力学 Non-equilibrium thermodynamics 是热力学的一个分支,研究某些不处于热力学平衡中的物理系统<br />
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<br />
<br />
<br />
==General references==<br />
<br />
* Cesare Barbieri (2007) ''Fundamentals of Astronomy''. First Edition (QB43.3.B37 2006) CRC Press {{ISBN|0-7503-0886-9}}, {{ISBN|978-0-7503-0886-1}}<br />
<br />
* Hans R. Griem (2005) ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}<br />
<br />
* C. Michael Hogan, Leda C. Patmore and Harry Seidman (1973) ''Statistical Prediction of Dynamic Thermal Equilibrium Temperatures using Standard Meteorological Data Bases'', Second Edition (EPA-660/2-73-003 2006) United States Environmental Protection Agency Office of Research and Development, Washington, D.C. [http://library.wur.nl/WebQuery/catalog/lang/1851848]<br />
<br />
* F. Mandl (1988) ''Statistical Physics'', Second Edition, John Wiley & Sons<br />
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<br />
<br />
==References==<br />
<br />
{{Reflist|colwidth=35em}}<br />
<br />
<br />
<br />
==Cited bibliography==<br />
<br />
<br />
<br />
*Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', third edition, McGraw-Hill, London, {{ISBN|0-521-25445-0}}.<br />
<br />
*Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, {{ISBN|0-88318-797-3}}.<br />
<br />
*Beattie, J.A., Oppenheim, I. (1979). ''Principles of Thermodynamics'', Elsevier Scientific Publishing, Amsterdam, {{ISBN|0-444-41806-7}}.<br />
<br />
*[[Ludwig Boltzmann|Boltzmann, L.]] (1896/1964). ''Lectures on Gas Theory'', translated by S.G. Brush, University of California Press, Berkeley.<br />
<br />
*Buchdahl, H.A. (1966). ''The Concepts of Classical Thermodynamics'', Cambridge University Press, Cambridge UK.<br />
<br />
*[[Herbert Callen|Callen, H.B.]] (1960/1985). ''Thermodynamics and an Introduction to Thermostatistics'', (1st edition 1960) 2nd edition 1985, Wiley, New York, {{ISBN|0-471-86256-8}}.<br />
<br />
*[[Constantin Carathéodory|Carathéodory, C.]] (1909). [https://web.archive.org/web/20160304213645/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0067&DMDID=DMDLOG_0033&L=1 Untersuchungen über die Grundlagen der Thermodynamik], ''[[Mathematische Annalen]]'', '''67''': 355–386. A translation may be found [http://neo-classical-physics.info/uploads/3/0/6/5/3065888/caratheodory_-_thermodynamics.pdf here]. Also a mostly reliable [https://books.google.com/books?id=xwBRAAAAMAAJ&q=Investigation+into+the+foundations translation is to be found] at Kestin, J. (1976). ''The Second Law of Thermodynamics'', Dowden, Hutchinson & Ross, Stroudsburg PA.<br />
<br />
*[[Sydney Chapman (mathematician)|Chapman, S.]], [[Thomas George Cowling|Cowling, T.G.]] (1939/1970). ''The Mathematical Theory of Non-uniform gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases'', third edition 1970, Cambridge University Press, London.<br />
<br />
*Crawford, F.H. (1963). ''Heat, Thermodynamics, and Statistical Physics'', Rupert Hart-Davis, London, Harcourt, Brace & World, Inc.<br />
<br />
*de Groot, S.R., Mazur, P. (1962). ''Non-equilibrium Thermodynamics'', North-Holland, Amsterdam. Reprinted (1984), Dover Publications Inc., New York, {{ISBN|0486647412}}.<br />
<br />
*Denbigh, K.G. (1951). ''Thermodynamics of the Steady State'', Methuen, London.<br />
<br />
*Eu, B.C. (2002). ''Generalized Thermodynamics. The Thermodynamics of Irreversible Processes and Generalized Hydrodynamics'', Kluwer Academic Publishers, Dordrecht, {{ISBN|1-4020-0788-4}}.<br />
<br />
*Fitts, D.D. (1962). ''Nonequilibrium thermodynamics. A Phenomenological Theory of Irreversible Processes in Fluid Systems'', McGraw-Hill, New York.<br />
<br />
*[[Josiah Willard Gibbs|Gibbs, J.W.]] (1876/1878). On the equilibrium of heterogeneous substances, ''Trans. Conn. Acad.'', '''3''': 108–248, 343–524, reprinted in ''The Collected Works of J. Willard Gibbs, Ph.D, LL. D.'', edited by W.R. Longley, R.G. Van Name, Longmans, Green & Co., New York, 1928, volume 1, pp.&nbsp;55–353.<br />
<br />
*Griem, H.R. (2005). ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}.<br />
<br />
*[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', fifth revised edition, North-Holland, Amsterdam.<br />
<br />
*Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of ''Thermodynamics'', pages 1–97 of volume 1, ed. W. Jost, of ''Physical Chemistry. An Advanced Treatise'', ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081.<br />
<br />
*[[John Gamble Kirkwood|Kirkwood, J.G.]], Oppenheim, I. (1961). ''Chemical Thermodynamics'', McGraw-Hill Book Company, New York.<br />
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*Landsberg, P.T. (1961). ''Thermodynamics with Quantum Statistical Illustrations'', Interscience, New York.<br />
<br />
*{{cite journal |last1=Lieb |first1=E. H. |last2=Yngvason |first2=J. |year=1999 |title=The Physics and Mathematics of the Second Law of Thermodynamics |journal=Phys. Rep. |volume=310 |issue= 1|pages=1–96 |doi= 10.1016/S0370-1573(98)00082-9|arxiv = cond-mat/9708200 |bibcode = 1999PhR...310....1L |s2cid=119620408 }}<br />
<br />
*Levine, I.N. (1983), ''Physical Chemistry'', second edition, McGraw-Hill, New York, {{ISBN|978-0072538625}}.<br />
<br />
*{{cite journal | last1 = Maxwell | first1 = J.C. | authorlink = James Clerk Maxwell | year = 1867 | title = On the dynamical theory of gases | url = | journal = Phil. Trans. Roy. Soc. London | volume = 157 | issue = | pages = 49–88 }}<br />
<br />
*[[Philip M. Morse|Morse, P.M.]] (1969). ''Thermal Physics'', second edition, W.A. Benjamin, Inc, New York.<br />
<br />
*Münster, A. (1970). ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London.<br />
<br />
*[[J.R. Partington|Partington, J.R.]] (1949). ''An Advanced Treatise on Physical Chemistry'', volume 1, ''Fundamental Principles. The Properties of Gases'', Longmans, Green and Co., London.<br />
<br />
*[[Brian Pippard|Pippard, A.B.]] (1957/1966). ''The Elements of Classical Thermodynamics'', reprinted with corrections 1966, Cambridge University Press, London.<br />
<br />
* [[Max Planck|Planck. M.]] (1914). [https://archive.org/details/theoryofheatradi00planrich ''The Theory of Heat Radiation''], a translation by Masius, M. of the second German edition, P. Blakiston's Son & Co., Philadelphia.<br />
<br />
*[[Ilya Prigogine|Prigogine, I.]] (1947). ''Étude Thermodynamique des Phénomènes irréversibles'', Dunod, Paris, and Desoers, Liège.<br />
<br />
*[[Ilya Prigogine|Prigogine, I.]], Defay, R. (1950/1954). ''Chemical Thermodynamics'', Longmans, Green & Co, London.<br />
<br />
*Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005). ''Physical Chemistry'', fourth edition, Wiley, Hoboken NJ.<br />
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*[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966). ''Elements of Thermodynamics'', Addison-Wesley Publishing, Reading MA.<br />
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*{{cite journal|last=Thomson|first=W.|author-link=William Thomson, 1st Baron Kelvin|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Transactions of the Royal Society of Edinburgh|date=March 1851|volume=XX|issue=part II|pages=261–268; 289–298}} Also published in {{cite journal|last=Thomson|first=W.|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Phil. Mag. |date=December 1852 |volume=IV |series=4 |issue=22 |pages=8–21 |url=https://archive.org/details/londonedinburghp04maga |accessdate=25 June 2012}}<br />
<br />
*[[László Tisza|Tisza, L.]] (1966). ''Generalized Thermodynamics'', M.I.T Press, Cambridge MA.<br />
<br />
*[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963). ''Lectures in Statistical Mechanics'', American Mathematical Society, Providence RI.<br />
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*Waldram, J.R. (1985). ''The Theory of Thermodynamics'', Cambridge University Press, Cambridge UK, {{ISBN|0-521-24575-3}}.<br />
<br />
*[[Mark Zemansky|Zemansky, M.]] (1937/1968). ''Heat and Thermodynamics. An Intermediate Textbook'', fifth edition 1967, McGraw–Hill Book Company, New York.<br />
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== External links ==<br />
<br />
Category:Equilibrium chemistry<br />
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类别: 平衡化学<br />
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*[http://ads.harvard.edu/books/1989fsa..book/AbookC15.pdf Breakdown of Local Thermodynamic Equilibrium] George W. Collins, The Fundamentals of Stellar Astrophysics, Chapter 15<br />
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Category:Thermodynamic cycles<br />
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类别: 热力循环<br />
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*[http://spiff.rit.edu/classes/phys440/lectures/lte/lte.html Thermodynamic Equilibrium, Local and otherwise] lecture by Michael Richmond<br />
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Category:Thermodynamic processes<br />
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类别: 热力学过程<br />
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*[http://journals.ametsoc.org/doi/abs/10.1175/1520-0469%281970%29027%3C0711:NLTEIC%3E2.0.CO%3B2 Non-Local Thermodynamic Equilibrium in Cloudy Planetary Atmospheres] Paper by R. E. Samueison quantifying the effects due to non-LTE in an atmosphere<br />
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Category:Thermodynamic systems<br />
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类别: 热力学系统<br />
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*[http://scienceworld.wolfram.com/physics/LocalThermodynamicEquilibrium.html Local Thermodynamic Equilibrium]<br />
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Category:Thermodynamics<br />
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分类: 热力学<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Thermodynamic equilibrium]]. Its edit history can be viewed at [[平衡热力学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%B9%B3%E8%A1%A1%E7%83%AD%E5%8A%9B%E5%AD%A6&diff=21463平衡热力学2021-01-30T11:25:58Z<p>Jxzhou:/* Thermodynamic state of internal equilibrium of a system */</p>
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<div>此词条暂由小竹凉翻译,翻译字数共5339,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{short description|State of thermodynamic system(s) where no net macroscopic flow of matter or energy occurs}}<br />
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'''Thermodynamic equilibrium''' is an [[axiomatic]] concept of [[thermodynamics]]. It is an internal [[State variables|state]] of a single [[thermodynamic system]], or a relation between several thermodynamic systems connected by more or less permeable or impermeable [[Thermodynamic system#Walls|walls]]. In thermodynamic equilibrium there are no net [[macroscopic]] [[Flow (mathematics)|flows]] of [[matter]] or of [[energy]], either within a system or between systems. <br />
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Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium there are no net macroscopic flows of matter or of energy, either within a system or between systems. <br />
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'''热力学平衡'''是'''<font color="#ff8000">热力学 Thermodynamics</font>'''的一个'''<font color="#ff8000">不言自明的 Axiomatic</font>'''概念。它是单个'''<font color="#ff8000">热力学系统 Thermodynamic System</font>'''的内部'''<font color="#ff8000">状态 State</font>''',或者是几个热力学系统之间通过或多或少的渗透或不渗透的'''<font color="#ff8000">壁 Wall</font>'''连接的关系。无论是在一个系统内还是在系统之间,在热力学平衡中不存在'''<font color="#ff8000">物质 Matter</font>'''或'''<font color="#ff8000">能量 Energy</font>'''的净'''<font color="#ff8000">宏观 Macroscopic</font>''' '''<font color="#ff8000">流动 Flow</font>'''。<br />
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In a system that is in its own state of internal thermodynamic equilibrium, no [[macroscopic]] change occurs. <br />
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In a system that is in its own state of internal thermodynamic equilibrium, no macroscopic change occurs. <br />
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在一个处于内部热力学平衡状态的系统中,不会发生'''<font color="#ff8000">宏观 Macroscopic</font>'''变化。<br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual [[Thermal equilibrium|thermal]], [[Mechanical equilibrium|mechanical]], [[Chemical equilibrium|chemical]], and [[Radiative equilibrium|radiative]] equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a [[thermodynamic operation]]. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a thermodynamic operation. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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相互热力学平衡的体系同时处于互相之间的'''<font color="#ff8000">热 Thermal</font>'''平衡、'''<font color="#ff8000">力学 Mechanical</font>'''平衡、'''<font color="#ff8000">化学 Chemical</font>'''平衡和'''<font color="#ff8000">辐射 Radiative</font>'''平衡。系统可以处于其中一种相互平衡状态,尽管其他状态未平衡。在热力学平衡中所有的平衡同时并且无限期地保持,直到被'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''打破。在一个宏观平衡中,微观交换是完全或几乎完全平衡的;这是对宏观平衡概念的物理解释。<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform [[temperature]]. Its [[Intensive and extensive properties|intensive properties]], other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform temperature. Its intensive properties, other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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一个处于内部热力学状态平衡的热力学系统具有空间均匀的'''<font color="#ff8000">温度 Temperature</font>'''。除了温度以外,它的'''<font color="#ff8000">强度性质 Intensive Properties</font>'''可以由于周围环境施加的不变的长程力场而导致空间不均匀性。<br />
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In systems that are at a state of [[non-equilibrium]] there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a '''meta-stable equilibrium'''.<br />
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In systems that are at a state of non-equilibrium there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a meta-stable equilibrium.<br />
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相比之下,处于'''<font color="#ff8000">非平衡状态 non-equilibrium</font>'''的系统中有物质或能量的净流动。如果这些变化可以在一个还没有发生的系统中被触发,那么这个系统就被称为处于一个'''亚稳定的平衡状态'''。<br />
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Though not a widely named a "law," it is an [[axiom]] of thermodynamics that there exist states of thermodynamic equilibrium. The [[second law of thermodynamics]] states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the [[entropy|entropies]] of the portions.<br />
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Though not a widely named a "law," it is an axiom of thermodynamics that there exist states of thermodynamic equilibrium. The second law of thermodynamics states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the entropies of the portions.<br />
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虽然不是一个广泛命名的“定律” ,但存在热力学平衡状态是一个热力学'''<font color="#ff8000">公理 Axiom</font>'''。'''<font color="#ff8000">热力学第二定律 second law of thermodynamics</font>'''指出,当一个物质体从一个平衡状态开始,在这个状态中,它的一部分被或多或少渗透或不渗透的分区保持在不同的状态,并且是孤立的,热力学操作移除分区或使分区更具渗透性,然后它会自发地达到自己内部热力学平衡的新状态,并伴随着部分'''<font color="#ff8000">熵 Entropy</font>'''的总和增加。<br />
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== Overview 概览==<br />
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{{Thermodynamics|cTopic=[[Thermodynamic system|Systems]]}}<br />
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Classical thermodynamics deals with states of [[dynamic equilibrium]]. The state of a system at thermodynamic equilibrium is the one for which some [[thermodynamic potential]] is minimized, or for which the [[entropy]] (''S'') is maximized, for specified conditions. One such potential is the [[Helmholtz free energy]] (''A''), for a system with surroundings at controlled constant temperature and volume:<br />
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Classical thermodynamics deals with states of dynamic equilibrium. The state of a system at thermodynamic equilibrium is the one for which some thermodynamic potential is minimized, or for which the entropy (S) is maximized, for specified conditions. One such potential is the Helmholtz free energy (A), for a system with surroundings at controlled constant temperature and volume:<br />
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经典热力学研究'''<font color="#ff8000">动态平衡 Dynamic Equilibrium</font>'''的状态。系统的热力学平衡状态是对于特定的条件,一些'''<font color="#ff8000">热力学势 Thermodynamic Potential</font>'''被最小化,或者'''<font color="#ff8000">熵 Entropy</font>'''(S)被最大化。对于一个周围环境温度和体积恒定的系统,其中一个这样的热力学势是'''<font color="#ff8000">亥姆霍兹自由能 Helmholtz Free Energy</font>'''(A):<br />
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:<math>A = U - TS</math><br />
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<math>A = U - TS</math><br />
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A = U-TS<br />
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Another potential, the [[Gibbs free energy]] (''G''), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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Another potential, the Gibbs free energy (G), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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在恒定温度和压力的系统中,另一个热力学势'''<font color="#ff8000">吉布斯自由能 Gibbs Free Energy</font>'''(G)在热力学平衡状态最小:<br />
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:<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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where ''T'' denotes the absolute thermodynamic temperature, ''P'' the pressure, ''S'' the entropy, ''V'' the volume, and ''U'' the internal energy of the system.<br />
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where T denotes the absolute thermodynamic temperature, P the pressure, S the entropy, V the volume, and U the internal energy of the system.<br />
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其中 T 表示热力学绝对温度,P 表示压强,S 表示熵,V 表示体积,U 表示体系的内能。<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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热力学平衡是一种独特的稳定定态,当系统长时间与周围环境相互作用时,它可以被接近或最终到达。上述势能是数学构造的热力学量,在特定的环境条件下最小化。<br />
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== Conditions 条件==<br />
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* For a completely isolated system, ''S'' is maximum at thermodynamic equilibrium. 对于一个完全孤立的系统,S在热力学平衡中取最大值。<br />
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* For a system with controlled constant temperature and volume, ''A'' is minimum at thermodynamic equilibrium. 对于一个恒定温度和体积的系统来说,A在热力学平衡中取最小值。<br />
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* For a system with controlled constant temperature and pressure, ''G'' is minimum at thermodynamic equilibrium. 对于一个恒温恒压的系统,G在热力学平衡中取最小值。<br />
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The various types of equilibriums are achieved as follows:<br />
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The various types of equilibriums are achieved as follows:<br />
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实现各种类型的平衡的方法如下:<br />
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*Two systems are in ''thermal equilibrium'' when their [[temperature]]s are the same. 当两个系统的'''<font color="#ff8000">温度 Temperature</font>'''相同时,它们就处于''热平衡状态''<br />
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*Two systems are in ''mechanical equilibrium'' when their [[pressure]]s are the same. 当两个体系的'''<font color="#ff8000">压力 Pressure</font>'''相同时,它们就处于''力学平衡''<br />
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*Two systems are in ''diffusive equilibrium'' when their [[chemical potential]]s are the same. 当两个题体系的'''<font color="#ff8000">化学势 Chemical Potential</font>'''相同时,它们就处于''扩散平衡''<br />
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*All [[forces]] are balanced and there is no significant external driving force.<br />
所有的'''<font color="#ff8000">力 Force</font>'''都是平衡的,没有明显的外部驱动力<br />
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==Relation of exchange equilibrium between systems 系统之间的交换均衡关系==<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability.<ref name="Nster_a">Münster, A. (1970), p. 49.</ref> When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability. When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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通常,热力学系统的周围环境也可以被看作是另一个热力学系统。在这种观点中,我们可以把系统及其周围环境看作是相互接触的两个系统,远程作用力也将它们联系在一起。系统的包围物是两个系统之间的接触面或边界。在热力学形式中,该表面被认为具有特定的渗透性质。例如,接触的表面可能被认为只能透热,使能量只能作为热传递。当远程力在时间上不发生变化,两个系统之间的热量传递减慢并最终永久停止时,这两个系统被称为热平衡; 这就是接触平衡的一个例子。其它类型的接触平衡可用其它类型的比渗透率来定义。当两个系统对于某一特定类型的渗透率处于接触平衡时,它们具有属于该特定类型渗透率的强变量的共同值。这种强度变量的例子有温度、压力、化学势。<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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接触平衡也可视为交换平衡。在接触平衡状态下,两系统之间某些量的传递速率存在零平衡。例如,对于只能透热的壁,内能作为热在两个系统之间的扩散速率是相等并反向的。两个系统之间的绝热壁只对作为功传递的能量有渗透作用; 在力学平衡,两个系统之间作为功的能量传递速率相等且相反。如果是一个简单的壁,那么通过它的体积转移率也是相等且相反的; 即它两边的压力是相等的。如果绝热壁比较复杂,有一种杠杆,有一个面积比,那么两个体系在交换平衡中的压力与体积交换比成反比,这使得转移率的零平衡作功。<br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<ref name="Planck 1914 40">[[Max Planck|Planck. M.]] (1914), p. 40.</ref><br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<br />
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辐射交换可以发生在两个不同的系统之间。当两个体系温度相同时,辐射交换平衡占优势。<br />
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==Thermodynamic state of internal equilibrium of a system 系统内部平衡的热力学状态==<br />
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A collection of matter may be entirely [[Isolated system|isolated]] from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium.<ref>Haase, R. (1971), p. 4.</ref><ref>Callen, H.B. (1960/1985), p. 26.</ref> (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics.<ref>{{Cite journal |doi = 10.1119/1.4914528|bibcode = 2015AmJPh..83..628M|title = Time and irreversibility in axiomatic thermodynamics|year = 2015|last1 = Marsland|first1 = Robert|last2 = Brown|first2 = Harvey R.|last3 = Valente|first3 = Giovanni|journal = American Journal of Physics|volume = 83|issue = 7|pages = 628–634}}</ref> One textbook<ref>[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963), p. 5.</ref> calls it the "zeroth law", remarking that the authors think this more befitting that title than its [[Zeroth law of thermodynamics|more customary definition]], which apparently was suggested by [[Ralph H. Fowler|Fowler]].)<br />
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A collection of matter may be entirely isolated from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium. (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics. One textbook calls it the "zeroth law", remarking that the authors think this more befitting that title than its more customary definition, which apparently was suggested by Fowler.)<br />
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物质的集合可能与其周围的环境完全'''<font color="#ff8000">孤立 Isolated</font>'''。如果它在无限长的时间内一直保持不受干扰,按照经典热力学假定,它处于一个没有发生任何变化,没有流动的状态,即内部平衡的热力学状态。(这种假设有时被称为“负第一”热力学定律,但并不常见。有教科书称之为“第零定律” ,作者'''<font color="#ff8000">福勒 Fowler</font>'''认为这个名称是'''<font color="#ff8000">更符合惯例的定义 More Customary Definition</font>'''。)<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a [[thermodynamic operation]] be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a thermodynamic operation be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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这种状态是所谓的经典热力学或平衡态热力学的主要关注点,因为它们是系统中被认为在这门学科中得到很好定义的唯一状态。一个与另一个系统处于接触平衡状态可以被一个'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''隔离,在隔离发生时,其内部不会发生任何变化。因此,一个与另一个系统处于接触平衡状态时也可以被视为处于其自身的内部热力学平衡状态。<br />
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==Multiple contact equilibrium==<br />
多点接触平衡<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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热力学形式论允许一个系统同时与其他多个系统接触,这些系统可能也可能没有相互接触,且这些接触具有不同的渗透性。如果这些系统都与世界其他部分相互隔离,那么它们彼此之间就会达到各自的接触平衡。<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy.<ref name="Caratheodory">Carathéodory, C. (1909).</ref><ref>Prigogine, I. (1947), p. 48.</ref><ref>Landsberg, P. T. (1961), pp. 128–142.</ref><ref>Tisza, L. (1966), p. 108.</ref> Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy. Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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如果几个系统彼此之间没有绝热壁,但是它们与世界其他部分共同隔离,那么它们就会达到多重接触平衡状态,且有共同的温度,内能和熵。在众多变量中,这是温度的一个独特性质。即使在远距离作用力存在的情况下,它也是有效的。(也就是说,没有“力”可以维持温度的差异。)举个例子,在热力学平衡的一个垂直的引力场系统中,顶部壁面的压力比底部壁面的压力小,但是各处的温度都是一样的。<br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural [[thermodynamic process]].<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), § 1.12.</ref> It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings.<ref>Levine, I.N. (1983), p. 40.</ref><ref>Lieb, E.H., Yngvason, J. (1999), pp. 17–18.</ref> The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of [[Second law of thermodynamics#Description#Kelvin statement|"inanimate" agency]]; a system in thermodynamic equilibrium is inanimate.<ref>[[William Thomson, 1st Baron Kelvin|Thomson, W.]] (1851).</ref><br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural thermodynamic process. It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings. The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of "inanimate" agency; a system in thermodynamic equilibrium is inanimate.<br />
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热力运行可能作为一个事件发生在周围环境的壁上,既不直接影响与周围环境联系的壁,也不直接影响其内部,且发生在一个明确的有限的时间内。例如,一个固定的绝热壁可以在环境中被放置或拆除。由于这种操作仅限于周围环境,系统可能会在一段时间内远离自身最初的内部状态---- 热力学平衡。根据热力学第二定律的说法,整体经历了变化并最终与周围环境达到了新的平衡。继Planck之后,这一连串的事件被称为自然'''<font color="#ff8000">热力学过程 Thermodynamic Process</font>'''。即使在这个过程中,当系统和周围环境都不处于明确的内部平衡状态时,存在着暂时偏离热力学平衡的现象,由于初始状态和最终状态都是热力学平衡的,这在平衡热力学中也是允许的。一个自然过程在其主要部分中以有限的速率进行,因此,它从根本上不同于虚构的准静态“过程”;即不在整个过程中无限缓慢地进行而且虚构地“可逆”。经典热力学允许,即使一个过程可能需要很长的时间才能达到热力学平衡,如果主要部分的过程是在一个有限的比率中,那么它被认为是自然的,并受制于热力学第二定律,即不可逆的。工程设计的机器、人工设备和操作是允许在周围环境中进行的。允许在环境中而不是在系统中进行此类操作和设备,是开尔文在他的一个热力学第二定律的陈述中提到'''<font color="#ff8000">无生命机构 Inanimate Agency</font>'''的原因; 在热力学平衡的系统是无生命的。<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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否则,热力运行可能会直接影响系统的壁。<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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通常可以很方便地假设周围的某些子系统比系统大得多,以至于这个过程只能影响周围子系统的强度变量,然后将这些子系统称为相关强度变量的储备库。<br />
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== Local and global equilibrium ==<br />
局部和全局均衡<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by [[intensive quantity|intensive]] parameters. As an example, [[temperature]] controls [[Heat equation|heat exchanges]]. ''Global thermodynamic equilibrium'' (GTE) means that those [[intensive quantity|intensive]] parameters are homogeneous throughout the whole system, while ''local thermodynamic equilibrium'' (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by intensive parameters. As an example, temperature controls heat exchanges. Global thermodynamic equilibrium (GTE) means that those intensive parameters are homogeneous throughout the whole system, while local thermodynamic equilibrium (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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区分全局性和局部性热力学平衡是很有用的。在热力学中,系统内部和系统与外部之间的交换是由'''<font color="#ff8000">强度 Intensive</font>'''参数控制的。例如,'''<font color="#ff8000">温度 Temperature</font>'''控制'''<font color="#ff8000">热交换 Heat Equation</font>'''。全局热力学平衡(GTE)意味着这些'''<font color="#ff8000">强度 Intensive</font>'''参数在整个系统中是均匀的,而局部热力学平衡(LTE)意味着这些强度参数在空间和时间上是变化的,但变化如此缓慢,以至于对于任何一点,人们都可以假设在某个邻近的某个热力学平衡。<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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如果对系统的描述要求强度参数的变化过大,那么这些强度参数的定义所依据的假设本身就会破裂,系统将既不处于全局平衡,也不处于局部平衡。例如,粒子需要一定数量的碰撞来平衡其周围环境。如果在这些碰撞中移动的平均距离使它离开平衡邻域,它将永远不会平衡,也就不会有 LTE。根据定义,温度与平衡邻域的平均内部能量成正比。由于没有达到平衡邻域,温度的概念就不成立,温度也就变得不确定。<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to [[massive]] particles. In a [[radiation|radiating]] gas, the [[photon]]s being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to massive particles. In a radiating gas, the photons being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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值得注意的是,这种局部平衡可能只适用于系统中的某个粒子子集。例如,LTE 通常只适用于'''<font color="#ff8000">大 Massive</font>'''质量粒子。在'''<font color="#ff8000">辐射 Radiation</font>'''气体中,被气体发射和吸收的'''<font color="#ff8000">光子 Photon</font>'''不需要彼此在一个热力学平衡内,或与气体中的大量粒子在一起,LTE 才能存在。在某些情况下,自由电子并不需要与大得多的原子或分子处于平衡状态,LTE 才能存在。<br />
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As an example, LTE will exist in a glass of water that contains a melting [[ice cube]]. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the [[Maxwell–Boltzmann distribution]] for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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As an example, LTE will exist in a glass of water that contains a melting ice cube. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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例如,LTE 将存在于一个装有融化的'''<font color="#ff8000">冰块 Ice Cube</font>'''的水杯中。玻璃杯内的温度可以在任何时候定义,但是离冰块近的地方要比离冰块远的地方冷。如果观察到位于给定点附近的分子的能量,它们将按照麦克斯韦-波兹曼分布在一定温度下的分布。如果观察到位于另一点附近的分子的能量,它们将按照'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''分布到另一个温度。<br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural [[transport phenomena]] may lead a system from local to global thermodynamic equilibrium. Going back to our example, the [[diffusion]] of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<ref>H.R. Griem, 2005</ref><br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural transport phenomena may lead a system from local to global thermodynamic equilibrium. Going back to our example, the diffusion of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<br />
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局部热力学平衡不需要局部或全局的平稳性。换句话说,每一个小区域不需要有一个恒定的温度。然而,它确实要求每个小的局部变化缓慢到足以维持其局部麦克斯韦-波兹曼分布的分子速度。全局非平衡态只有通过系统与外界的交换才能保持稳定。例如,通过在水杯中不断添加细粉冰来补偿熔化,并持续排出融水,可以保持全球稳定的静止状态。自然'''<font color="#ff8000">迁移现象 Transport Phenomena</font>'''可能导致一个从局部到全局的热力学平衡系统。回顾我们的例子,热量的扩散将导致我们的玻璃杯水流向全局热力学平衡,在这种状态下,玻璃杯的温度是完全均匀的。<br />
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==Reservations==<br />
保留意见<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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学识渊博的笔者在热力学领域对热力学平衡描述时,经常对他们的描述附加条件或保留意见。有些笔者含蓄地保留了或多或少的空白,以待说明。<br />
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For example, one widely cited writer, [[Herbert Callen|H. B. Callen]] writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. ''Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!''"<ref>Callen, H.B. (1960/1985), p. 15.</ref><br />
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For example, one widely cited writer, H. B. Callen writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!"<br />
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例如,一位被广泛引用的作家'''<font color="#ff8000">H.B.卡伦 H.B.Callen</font>'''在这里写道: “实际上,很少有系统处于绝对和真正的平衡状态。”他提到了放射性过程,认为它们可能需要“宇宙时间才能完成,因此通常可以忽略”。他补充道: “在实践中,平衡的标准是循环的。在操作上,如果一个系统的性质一致地用热力学理论来描述,那么它就处于平衡状态! ”<br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<ref>Beattie, J.A., Oppenheim, I. (1979), p. 3.</ref><br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<br />
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J.A.贝蒂和 I.奥本海姆写道: “坚持对平衡定义的严格解释,将排除热力学应用于实际系统的所有状态。”<br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment",<ref>Callen, H.B. (1960/1985), p. 485.</ref> and cited by Adkins as having written a "classic text",<ref>Adkins, C.J. (1968/1983), p. ''xiii''.</ref> [[Brian Pippard|A.B. Pippard]] writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<ref>Pippard, A.B. (1957/1966), p. 6.</ref><br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment", and cited by Adkins as having written a "classic text", A.B. Pippard writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<br />
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Callen引用另一位作者的话说,他给出了“学术且严谨的论述” ,Adkins引用他的话说,他写了一本“经典著作”—— '''<font color="#ff8000">A.B.皮帕德 A.B.Pippard</font>'''在文中写道: “只要时间足够长,过冷水蒸汽最终会凝结,... ..。时间可能是漫长的,也许长达10年或者更长。就大多数目的而言,只要这种迅速的变化不是人为地刺激,这些系统就可以被视为处于平衡状态。”<br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster">Münster, A. (1970), p. 53.</ref><br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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另一位作者A.Münster,写道。他观察到热核反应发生的速度非常缓慢,以至于在热力学中可以忽略不计。他评论道: “‘绝对平衡’或‘所有可想象过程的平衡’的概念没有物理意义。”他说: “ ... 我们只能考虑特定过程和确定的实验条件下的平衡。”<br />
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According to [[László Tisza|L. Tisza]]: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<ref>Tisza, L. (1966), p. 119.</ref><br />
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According to L. Tisza: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<br />
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根据'''<font color="#ff8000">L.缇莎 L.Tisza</font>'''的说法: “ ... 在讨论接近绝对零度的现象时。经典理论的绝对预测变得特别模糊,因为在非平衡状态下发生冻结是非常普遍的。”<br />
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==Definitions==<br />
定义<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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一个系统最普遍的热力学平衡是通过与周围环境的接触,允许所有化学物质和各种能量同时通过。热力学平衡中的系统以均匀加速度在空间中运动,但此时不能改变其形状或大小; 因此它是由空间中的刚性体积来定义的。它可能存在于外力场中,由远远大于系统本身的外部因素决定,因此系统内的事件不会对外力场产生相当大的影响。只有当外力场是均匀的,并且确定了它的均匀加速度,或者它处于一个非均匀力场中,但是由于表面的局部力,例如机械压力,使它保持静止时,这个系统才能处于热力学平衡。<br />
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Thermodynamic equilibrium is a [[primitive notion]] of the theory of thermodynamics. According to [[Philip M. Morse|P.M. Morse]]: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are ''not'' conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments."<ref>[[Philip M. Morse|Morse, P.M.]] (1969), p. 7.</ref> This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<ref>Bailyn, M. (1994), p. 20.</ref><br />
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Thermodynamic equilibrium is a primitive notion of the theory of thermodynamics. According to P.M. Morse: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are not conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments." This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<br />
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热力学平衡是热力学理论的一个'''<font color="#ff8000">基本概念 Primitive Notion</font>'''。'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''说: “应该强调的是,存在热力学状态这一事实,以及存在由平衡态唯一指定的热力学变量这一事实,并不是从某些哲学第一原理得出的逻辑结论。这些结论不可避免地来自两个多世纪的实验。”这意味着热力学平衡不能仅仅用热力学的其他理论概念来定义。M.Bailyn提出了一个基本的热力学定律理论,它定义并假设了热力学平衡的存在。<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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热力学平衡的教科书定义通常被仔细说明,并有些保留。<br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<ref>Münster, A. (1970), p. 52.</ref><br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<br />
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例如,A. Münster写道:“当系统中没有以可测量的速度发生状态变化时,隔离系统处于热力学平衡状态。”这里有两项保留:系统是孤立的;任何状态的变化都是不可估量的缓慢。他通过对在室温且没有催化剂的情况下混合氧和氢的说明,讨论了第二个条件。Münster指出,热力学平衡状态所描述的宏观变量比给定系统任何其他状态都少。这是部分,但不完全是,因为系统内和系统内的所有流都是零。<br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in ''equilibrium''.<ref>Haase, R. (1971), pp. 3–4.</ref><br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in equilibrium.<br />
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R. Haase's的热力学演示并不从对热力学平衡的限制开始,因为他打算考虑非平衡态热力学。他考虑一个具有时间不变性质的任意系统。他通过切断除外力场以外的所有外部影响来测试它的热力学平衡。如果在绝缘之后,没有任何变化,他说,系统处于平衡状态。<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness".<ref>Callen, H.B. (1960/1985), p. 13.</ref> This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness". This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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在一个标题为“热力学平衡”的章节中,H.B. Callen在段落定义了平衡状态.他指出,它们“是由系统内部的内在因素决定的”。它们是“终端状态” ,随着时间的推移,系统会以“冰川般缓慢”的速度朝着这个终端状态演化。这个说法并没有明确,对于热力学平衡系统必须是孤立的;;Callen也没有说明他所说的“内在因素”是什么意思。<br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<ref>Adkins, C.J. (1968/1983), p. ''7''.</ref><br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<br />
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另一位教科书作者,C.J.Adkins,明确允许热力学平衡在非孤立的系统中发生。然而,他的系统在物质转移方面是封闭的。他写道: “一般来说,热力学平衡的方法包括热和类似变动与周围环境的相互作用。”他将这种热力学平衡与只有通过热接触才能进行能量传递的热平衡相区别。<br />
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Another textbook author, [[J.R. Partington]], writes: "(i) ''An equilibrium state is one which is independent of time''." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..."<ref>Partington, J.R. (1949), p. 161.</ref> This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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Another textbook author, J.R. Partington, writes: "(i) An equilibrium state is one which is independent of time." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..." This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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另一位教科书作者'''<font color="#ff8000">J.R.帕廷顿 J.R.Partington</font>'''写道: “(i)平衡状态是独立于时间的状态。”但是,在提到“只是明显处于平衡状态”的系统时,他补充说: “这样的系统处于‘虚假平衡’状态。帕廷顿的陈述没有明确指出平衡是指一个孤立的系统。和Münster一样,Partington也指的是氧和氢的混合物。他补充说:“在一个真正的平衡状态,任何影响状态的外部条件的最小变化都会产生一个微小的状态变化... ... ”这个条件意味着热力学平衡必须在小的扰动下保持稳定; 这个要求对于热力学平衡的严格意义是必不可少的。<br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, ''thermodynamic—equilibrium.''"<ref>Crawford, F.H. (1963), p. 5.</ref><br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, thermodynamic—equilibrium."<br />
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在F.H.Crawford的一本学生教科书中,有一个标题为“热力学平衡”的章节。它区分了几种流动的驱动因素,然后说: “这些是孤立系统明显普遍趋向于完全机械、热、化学和电力状态的例子——或者简单地说,热力学平衡状态。”<br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in ''equilibrium''."<ref>Buchdahl, H.A. (1966), p. 8.</ref> Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being ''in equilibrium'' so long as experimental tests show that 'slow' transitions are in effect reversible."<ref>Buchdahl, H.A. (1966), p. 111.</ref> It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<ref>Adkins, C.J. (1968/1983), p. 8.</ref><br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in equilibrium." Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being in equilibrium so long as experimental tests show that 'slow' transitions are in effect reversible." It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<br />
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H.A. Buchdahl的一本关于经典热力学的专著考虑了热力学系统的平衡,而实际上并没有写热力学平衡一词。Buchdahl在提到封闭的物质交换系统时写道: “如果一个系统处于一个适当的静态状态,那么它将被称为处于平衡状态。”出于热力学描述的目的,Buchdahl的专著也讨论了非晶态玻璃。它说: “更准确地说,只要实验测试表明‘慢’跃迁实际上是可逆的,玻璃就可以被认为处于平衡状态。”通常来说不会将这一条件作为热力学平衡定义的一部分,而是假定相反的情况:如果热力学平衡中的一个体受到足够慢的过程的影响,则该过程可被视为足够接近可逆,并且该物体在过程中足够接近热力学平衡。<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of ''contact equilibrium''. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by [[Constantin Carathéodory|C. Carathéodory]], and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster" /> Thermodynamic equilibrium for an open system means that, with respect to every relevant kind of selectively permeable wall, contact equilibrium exists when the respective intensive parameters of the system and surroundings are equal.<ref name="Nster_a" /> This definition does not consider the most general kind of thermodynamic equilibrium, which is through unselective contacts. This definition does not simply state that no current of matter or energy exists in the interior or at the boundaries; but it is compatible with the following definition, which does so state.<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of contact equilibrium. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by C. Carathéodory, and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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通过引入接触平衡的概念,A. Münster仔细地扩展了孤立系统热力学平衡的定义。这指定了在考虑非孤立系统的热力学平衡时允许的特定过程,并特别关心开放系统,这些开放系统可能从周围环境获得或丢失物质。利益系统和周围系统之间的接触平衡,通过一种特殊的壁与利益系统接触,其余的连接系统是孤立的。这种特殊类型的壁也被'''<font color="#ff8000">C.喀喇西奥多里 C.Carathéodory</font>'''考虑过,其他作家也提到过。它们具有选择渗透性。它们可能只对机械工作有渗透性,或者只对热有渗透性,或者只对某种特定的化学物质有渗透性。每个接触平衡定义了一个强度参数; 例如,只能透热的壁定义了一个经验温度。对于感兴趣的体系中每一种化学成分,都可以存在接触平衡。在接触平衡中,尽管有可能通过选择性渗透壁进行交换,感兴趣的系统是不变的,好像它处在孤立的热力学平衡。这个方案遵循的一般规则是: “ ... ... 我们只能考虑特定过程和特定实验条件下的平衡。”<br />
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[[Mark Zemansky|M. Zemansky]] also distinguishes mechanical, chemical, and thermal equilibrium. He then writes: "When the conditions for all three types of equilibrium are satisfied, the system is said to be in a state of thermodynamic equilibrium".<ref>[[Mark Zemansky|Zemansky, M.]] (1937/1968), p. 27.</ref><br />
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'''<font color="#ff8000">M.泽曼斯基 M.Zemansky</font>'''还区分了机械、化学和热平衡。他接着写道: “当这三种均衡的条件都满足时,系统就处于热力学平衡状态。”<br />
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P.M. Morse writes that thermodynamics is concerned with "states of thermodynamic equilibrium". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<br />
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[[Philip M. Morse|P.M. Morse]] writes that thermodynamics is concerned with "''states of thermodynamic equilibrium''". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<ref>[[Philip M. Morse|Morse, P.M.]] (1969), pp. 6, 37.</ref><br />
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'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''写道,热力学关注的是“热力学平衡状态”。在讨论物体与周围热源之间的热量传递时,他也使用了“热平衡”这个短语,尽管没有明确定义一个特殊的术语“热平衡”<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "full thermodynamic equilibrium state".<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "''full'' thermodynamic equilibrium state".<ref>Waldram, J.R. (1985), p. 5.</ref><br />
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J.R. Waldram写到了“一个明确的热力学状态”。他将一个系统定义为“当其观测量随时间停止变化时”的“热平衡”。但是在这个定义之下不久,他写到一块玻璃还没有达到“完全的热力学平衡状态”。<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, thermodynamic equilibrium is said to exist." He is not here considering the presence of an external force field.<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, ''thermodynamic equilibrium'' is said to exist." He is not here considering the presence of an external force field.<ref>Bailyn, M. (1994), p. 21.</ref><br />
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考虑到平衡状态,M.Bailyn写道: “每个强度变量都有自己的平衡类型。”然后他定义了热平衡、机械平衡和物质平衡。因此,他写道: “如果所有的强度变量都是一致的,那么热力学平衡就是存在的。”他在这里没有考虑外力场的存在。<br />
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J.G. Kirkwood and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of thermodynamic equilibrium if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<br />
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[[John Gamble Kirkwood|J.G. Kirkwood]] and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of ''thermodynamic equilibrium'' if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<ref>Kirkwood, J.G., Oppenheim, I. (1961), p. 2</ref><br />
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'''<font color="#ff8000">J.G.柯克伍德 J.G.Kirkwood</font>'''和 I.Oppenheim 将热力学平衡定义为: “一个系统处于热力学平衡状态,如果,在分配给实验的时间内,(a)它强度特性与时间无关,(b)它的内部或与周围环境的边界处没有物质或能量流。”显然,他们没有把定义限制在孤立的或封闭的系统。它们不讨论“缓慢”发生变化的可能性,并且超出了分配给实验的时间范围。他们注意到,对于两个相接触的系统,存在一个强度性质的小子类,如果这个小子类的所有子类都相等,那么所有各自的强度性质都相等。只要满足其他一些条件,热力学平衡状态可以由这个子类定义。<br />
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==Characteristics of a state of internal thermodynamic equilibrium==<br />
内部热力学平衡状态的特征<br />
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A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous. Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface." As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.<br />
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在内部热力学平衡中,没有外力的情况下由单相组成的热力学系统是均匀的。Planck在论文中简要介绍了热量、温度和热平衡,然后宣布: “在下文中,我们将主要讨论任何形式的均匀、各向同性的物体,它们在整个物质中具有相同的温度和密度,并受到到处垂直于表面的均匀压力作用。”和 Carathéodory 一样,Planck 将表面效应、外场和各向异性晶体排除在外。虽然Planck提到了温度,但并没有明确提到热力学平衡的概念。相比之下,Carathéodory 关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ,虽然没有明确地使用短语‘热力学平衡’,也没有明确地假设存在一个温度来定义它。<br />
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===Homogeneity in the absence of external forces===<br />
在没有外力的情况下的同质性<br />
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A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous.<ref name="Planck 1903 3"/> This means that the material in any small volume element of the system can be interchanged with the material of any other geometrically congruent volume element of the system, and the effect is to leave the system thermodynamically unchanged. In general, a strong external force field makes a system of a single phase in its own internal thermodynamic equilibrium inhomogeneous with respect to some [[Intensive and extensive properties|intensive variables]]. For example, a relatively dense component of a mixture can be concentrated by centrifugation.<br />
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在没有外力的情况下,由单一相组成的热力学系统,在其自身的内部热力学平衡中是均匀的。这意味着系统中任何小体积单元中的材料可以与系统中任何其他几何相等的体积单元中的材料互换,其效果是使系统在热力学上保持不变。一般来说,一个强外力场使得一个单相系统在其自身的内部热力学平衡中对于一些'''<font color="#ff8000">强变量 Intensive Variable</font>'''是不均匀的。例如,可以通过离心来浓缩混合物中相对密度较大的组分。<br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform. Considerations of kinetic theory or statistical mechanics also support this statement.<br />
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热力学平衡系统中的温度在空间和时间上是均匀的。在一个系统内部热力学平衡状态下,没有净内部宏观流动。特别是,这意味着系统的所有局部部分处于相互辐射交换平衡状态。这意味着系统的温度在空间上是均匀的。动力学理论或统计力学也支持这种说法。<br />
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===Uniform temperature===<br />
均匀温度<br />
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In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium. As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.<br />
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为了使一个系统处于它自己的内部热力学平衡状态,它处于自己内部的热平衡状态当然是必要的,但不是充分的;系统在达到内部热平衡之前,可以达到内部机械平衡。如上所述,根据 A.Münster的说法,对于给定的孤立系统的任何状态,定义一个热力学平衡所需的变量数是最少的。如上所述,J.G.Kirkwood 和 I.Oppenheim 指出,热力学平衡状态可以由一个特殊的子类的强变量定义,该子类中有一定数量的成员。<br />
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Such equilibrium inhomogeneity, induced by external forces, does not occur for the intensive variable [[temperature]]. According to [[Edward A. Guggenheim|E.A. Guggenheim]], "The most important conception of thermodynamics is temperature."<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), p.5.</ref> Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface."<ref name="Planck 1903 3">[[Max Planck|Planck, M.]] (1897/1927), p.3.</ref> As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.<br />
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这种由外力引起的平衡不均匀性,在强烈变化的'''<font color="#ff8000">温度 Temperature</font>'''下不会发生。'''<font color="#ff8000">E.A.古根海姆 E.A. Guggenheim</font>'''认为,“热力学最重要的概念是温度。“Planck在介绍他的论文时,简要叙述了热、温度和热平衡,然后宣布: ”在下文中,我们将主要讨论任何形式的均匀、各向同性的物体,它们的物质具有相同的温度和密度,并受到到处垂直于表面的均匀压力的作用和Carathéodory 一样,Planck将表面效应、外场和各向异性晶体排除在外。虽然Planck提到了温度,但并没有明确提到热力学平衡的概念。相比之下,Carathéodory关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ,虽然没有明确地使用短语‘热力学平衡’ ,也没有明确地假设存在一个温度来定义它。<br />
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If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.<br />
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如果热力学平衡位于一个外力场中,那么通常只有温度在空间上是均匀的。如果外力场非零,温度以外的强度变量通常是不均匀的。在这种情况下,一般需要附加变量来描述空间非均匀性。<br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform.<ref name="Planck 1914 40"/> This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers.<ref>Gibbs, J.W. (1876/1878), pp. 144-150.</ref><ref>[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966), pp. 127–130.</ref><ref>Münster, A. (1970), pp. 309–310.</ref><ref>Bailyn, M. (1994), pp. 254-256.</ref><ref>{{cite journal | last1 = Verkley | first1 = W.T.M. | last2 = Gerkema | first2 = T. | year = 2004 | title = On maximum entropy profiles | journal = J. Atmos. Sci. | volume = 61 | issue = 8| pages = 931–936 | doi=10.1175/1520-0469(2004)061<0931:omep>2.0.co;2| bibcode = 2004JAtS...61..931V | doi-access = free }}</ref><ref>{{cite journal | last1 = Akmaev | first1 = R.A. | year = 2008 | title = On the energetics of maximum-entropy temperature profiles | url = | journal = Q. J. R. Meteorol. Soc. | volume = 134 | issue = 630| pages = 187–197 | doi=10.1002/qj.209| bibcode = 2008QJRMS.134..187A }}</ref> Considerations of kinetic theory or statistical mechanics also support this statement.<ref>Maxwell, J.C. (1867).</ref><ref>Boltzmann, L. (1896/1964), p. 143.</ref><ref>Chapman, S., Cowling, T.G. (1939/1970), Section 4.14, pp. 75–78.</ref><ref>[[J. R. Partington|Partington, J.R.]] (1949), pp. 275–278.</ref><ref>{{cite journal | last1 = Coombes | first1 = C.A. | last2 = Laue | first2 = H. | year = 1985 | title = A paradox concerning the temperature distribution of a gas in a gravitational field | url = | journal = Am. J. Phys. | volume = 53 | issue = 3| pages = 272–273 | doi=10.1119/1.14138| bibcode = 1985AmJPh..53..272C }}</ref><ref>{{cite journal | last1 = Román | first1 = F.L. | last2 = White | first2 = J.A. | last3 = Velasco | first3 = S. | year = 1995 | title = Microcanonical single-particle distributions for an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 16 | issue = 2| pages = 83–90 | doi=10.1088/0143-0807/16/2/008| bibcode = 1995EJPh...16...83R }}</ref><ref>{{cite journal | last1 = Velasco | first1 = S. | last2 = Román | first2 = F.L. | last3 = White | first3 = J.A. | year = 1996 | title = On a paradox concerning the temperature distribution of an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 17 | issue = | pages = 43–44 | doi=10.1088/0143-0807/17/1/008}}</ref><br />
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热力学平衡系统内的温度在时间和空间上都是均匀的。在一个处于内部热力学平衡的系统中,不存在净的内部宏观流动。特别是,这意味着系统的所有局部都处于相互辐射交换平衡。这意味着系统的温度在空间上是均匀的。这在所有情况下都是如此,包括那些非均匀外力场。对于外部施加的引力场,这可以通过使用朗朗日乘数的方法通过变化的演算在宏观热力学术语中证明。动力学理论或统计力学也支持这种说法。<br />
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In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium.<ref name="Fitts 43"/><br />
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为了使一个系统处于它自己的内部热力学平衡状态,它必须处于它自己的内部热平衡状态是必要不充分的; 一个系统在到达内部热平衡之前到达内部机械平衡是可能的。<br />
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As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.<br />
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如上所述,j.r. Partington 指出热力学平衡状态在小的瞬态扰动下是稳定的。如果没有这个条件,一般来说,研究热力学平衡系统的实验就会遇到巨大的困难。<br />
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===Number of real variables needed for specification===<br />
规范所需的实变量数目<br />
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In his exposition of his scheme of closed system equilibrium thermodynamics, C. Carathéodory initially postulates that experiment reveals that a definite number of real variables define the states that are the points of the manifold of equilibria.<ref name="Caratheodory" /> In the words of Prigogine and Defay (1945): "It is a matter of experience that when we have specified a certain number of macroscopic properties of a system, then all the other properties are fixed."<ref>Prigogine, I., Defay, R. (1950/1954), p. 1.</ref><ref>Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005), p. 4.</ref> As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.<br />
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在他关于封闭系统平衡态热力学方案的论述中,C.Carathéodory 最初假定实验揭示了一定数量的实变量定义了作为平衡态流形点的状态。用 Prigogine 和 Defay (1945)的话说: “这是一个经验问题,当我们确定了一个系统一定数量的宏观属性时,那么所有其他属性都是固定的。如上所述,A. Münster认为,定义热力学平衡所需的变量数量对于给定孤立系统的任何状态来说都是最少的。如上所述,J.G. Kirkwood 和 I. Oppenheim 指出,热力学平衡状态可以由一个特殊子类的强度变量来定义,该子类中有一定数量的成员。<br />
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When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium. Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<br />
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当一个物质体从不均匀的非平衡状态或化学非平衡状态开始,然后被孤立,它自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如,在这种演变的许多情况下,内部机械平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是,在这种演变的许多情况下,热平衡的发展要比化学平衡快得多。<br />
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If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.<br />
<br />
如果热力学平衡位于一个外力场中,那么通常只有温度在空间上是均匀的。如果外力场非零,温度以外的强度变量通常是不均匀的。在这种情况下,一般需要附加变量来描述空间非均匀性。<br />
<br />
===Stability against small perturbations===<br />
对小扰动的稳定性<br />
<br />
In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
<br />
在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
<br />
As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.<br />
<br />
如上所述,J.R. Partington 指出热力学平衡状态在小的瞬态扰动下是稳定的。如果没有这个条件,一般来说,研究热力学平衡系统的实验就会遇到严重的困难。<br />
<br />
<br />
To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics. But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
<br />
考虑孤立热力学系统中的波动概念,一个方便的例子是由其广泛的状态变量、内能、体积和质量组成指定的系统。根据定义,它们是时不变的。根据定义,它们与它们的共轭状态密集函数的时不变名义值相结合,反向温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广泛的状态变量的值,不足以提供这些名义值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
<br />
===Approach to thermodynamic equilibrium within an isolated system===<br />
孤立系统中的热力学平衡<br />
<br />
<br />
It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.<br />
<br />
可以承认,在重复测量这些共轭强度函数时,发现它们的值随时间略有不同。这种可变性被认为是由于内部波动。不同测量值平均到其名义值。<br />
<br />
When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium.<ref name="Fitts 43">Fitts, D.D. (1962), p. 43.</ref> Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<ref>Denbigh, K.G. (1951), p. 42.</ref><br />
<br />
当一个物质体从不均匀的非平衡状态或化学非平衡状态开始,然后被孤立,它自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如,在这种演变的许多情况下,内部机械平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是,在这种演变的许多情况下,热平衡的发展要比化学平衡快得多。<br />
<br />
If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<br />
<br />
如果这个系统真的像经典热力学所假定的那样是宏观的,那么这个系统的波动太小了,宏观上无法检测到。这就是所谓的热力学极限。实际上,物质的分子性质和动量转移的量子性质由于它们太小而看不见,已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中,平衡的波动概念是没有位置的。”<br />
<br />
===Fluctuations within an isolated system in its own internal thermodynamic equilibrium===<br />
孤立系统内部热力学平衡的波动<br />
<br />
<br />
If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
<br />
如果系统被重复细分,最终产生的系统足够小,可以表现出明显的波动。这是一个介观层面的研究。波动则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
<br />
In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
<br />
在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
<br />
<br />
If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
<br />
如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在波动过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,即需要量子统计力学。波动可以变得相对占主导地位,测量问题变得重要。<br />
<br />
To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics.<ref>Tschoegl, N.W. (2000). ''Fundamentals of Equilibrium and Steady-State Thermodynamics'', Elsevier, Amsterdam, {{ISBN|0-444-50426-5}}, p. 21.</ref> But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
<br />
考虑孤立热力学系统中的波动概念,一个方便的例子是由其众多的状态变量,内能、体积和质量组成指定的系统。根据定义,它们是时不变的。根据定义,它们与它们的共轭状态密集函数的时不变名义值相结合,反向温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广泛的状态变量的值,不足以提供这些名义值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
<br />
<br />
The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
<br />
"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有时间趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的标称值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微波动期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。非已知属于平衡状态的标称值,否则根据单一的度量无法进行判断。<br />
<br />
It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.<br />
<br />
可以承认,在重复测量这些共轭强度函数时,发现它们的值随时间略有不同。这种可变性被认为是由于内部波动。不同测量值平均到其名义值。<br />
<br />
<br />
<br />
If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<ref>Buchdahl, H.A. (1966), p. 16.</ref><br />
<br />
如果这个系统真的像经典热力学所假定的那样是宏观的,那么这个系统的波动太小了,宏观上无法检测到。这就是所谓的热力学极限。实际上,物质的分子性质和动量转移的量子性质由于它们太小而看不见,已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中,平衡的波动概念是没有位置的。”<br />
<br />
<br />
If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
<br />
如果系统被重复细分,最终产生的系统足够小,可以表现出明显的波动。这是一个介观层面的研究。波动则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
<br />
An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process." This illustrates the importance for thermodynamics of the concept of temperature.<br />
<br />
热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
<br />
<br />
<br />
If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在波动过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,即需要量子统计力学。波动可以变得相对占主导地位,测量问题变得重要。<br />
<br />
Thermal equilibrium is achieved when two systems in thermal contact with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<br />
<br />
当两个相互热接触的系统不再有净能量交换时,就会产生热平衡。因此,如果两个系统处于热平衡,那么它们的温度是相同的。<br />
<br />
<br />
<br />
The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
<br />
"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有时间趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的标称值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微波动期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。非已知属于平衡状态的标称值,否则根据单一的度量无法进行判断。<br />
<br />
Thermal equilibrium occurs when a system's macroscopic thermal observables have ceased to change with time. For example, an ideal gas whose distribution function has stabilised to a specific Maxwell–Boltzmann distribution would be in thermal equilibrium. This outcome allows a single temperature and pressure to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<br />
<br />
当系统的宏观热观测值不再随着时间变化时,就会出现热平衡。例如,一种分布函数稳定到一个特定的麦克斯韦-波兹曼分布的理想气体即处于热平衡状态。这个结果可以将单一的温度和压力归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是很有可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
<br />
=== Thermal equilibrium ===<br />
热平衡<br />
{{Main|Thermal equilibrium}}<br />
<br />
<br />
<br />
An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process."<ref>Eu, B.C. (2002), page 13.</ref> This illustrates the importance for thermodynamics of the concept of temperature.<br />
<br />
热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
<br />
A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<br />
<br />
一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数。<br />
<br />
<br />
<br />
[[Thermal equilibrium]] is achieved when two systems in [[thermal contact]] with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<ref>[[Raj Pathria|R. K. Pathria]], 1996</ref><br />
<br />
当两个相互'''<font color="#ff8000">热接触 Thermal Contact</font>'''的系统不再有净能量交换时,就会产生'''<font color="#ff8000">热平衡 Thermal Equilibrium</font>'''。因此,如果两个系统处于热平衡,那么它们的温度是相同的<br />
<br />
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
<br />
非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
<br />
<br />
<br />
Thermal equilibrium occurs when a system's [[macroscopic]] thermal observables have ceased to change with time. For example, an [[ideal gas]] whose [[Distribution function (physics)|distribution function]] has stabilised to a specific [[Maxwell–Boltzmann distribution]] would be in thermal equilibrium. This outcome allows a single [[temperature]] and [[pressure]] to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<ref>de Groot, S.R., Mazur, P. (1962), p. 44.</ref><br />
<br />
当一个系统的'''<font color="#ff8000">宏观 Macroscopic</font>'''热观测值不再随时间变化时,就会出现热平衡。例如,一种'''<font color="#ff8000">分布函数 Distribution Function</font>'''稳定到一个特定的'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''的'''<font color="#ff8000">理想气体 Ideal Gas</font>'''即处于热平衡状态。这个结果可以将单一的'''<font color="#ff8000">温度 Temperature</font>'''和'''<font color="#ff8000">压力 Pressure</font>'''归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
<br />
Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle. It states that a non-equilibrium system evolves such as to maximize its entropy production.<br />
<br />
定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
<br />
==Non-equilibrium==<br />
非平衡<br />
{{Main|Non-equilibrium thermodynamics}}<br />
<br />
<br />
<br />
Thermodynamic models <br />
<br />
热力学模型<br />
<br />
A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<ref>de Groot, S.R., Mazur, P. (1962), p. 43.</ref><br />
<br />
一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数<br />
<br />
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
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Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle.<ref>{{cite book|last1=Ziegler|first1=H.|title=An Introduction to Thermomechanics.|date=1983|location=North Holland, Amsterdam.}}</ref><ref>{{cite journal|last1=Onsager|first1=Lars|title=Reciprocal Relations in Irreversible Processes|journal=Phys. Rev.|date=1931|volume=37|issue=4|doi=10.1103/PhysRev.37.405|bibcode=1931PhRv...37..405O|pages=405–426|doi-access=free}}</ref> It states that a non-equilibrium system evolves such as to maximize its entropy production.<ref>{{cite book|last1=Kleidon|first1=A.|last2=et.|first2=al.|title=Non-equilibrium Thermodynamics and the Production of Entropy.|date=2005|edition=Heidelberg: Springer.}}</ref><ref>{{cite journal|last1=Belkin|first1=Andrey|last2=et.|first2=al.|title=Self-Assembled Wiggling Nano-Structures and the Principle of Maximum Entropy Production|journal=Sci. Rep.|doi=10.1038/srep08323|bibcode=2015NatSR...5E8323B|pmc=4321171|pmid=25662746|volume=5|year=2015|page=8323}}</ref><br />
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定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
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Topics in control theory<br />
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控制理论主题<br />
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==See also ==<br />
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{{Portal|Chemistry}}<br />
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;Thermodynamic models 热力学模型<br />
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* [[Non-random two-liquid model]] (NRTL model) - Phase equilibrium calculations 非随机两液模型(NRTL 模型)-相平衡计算<br />
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* [[UNIQUAC]] model - Phase equilibrium calculations UNIQUAC 模型-相平衡计算<br />
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* [[Time crystal]] 时间晶体<br />
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;Topics in control theory 控制理论主题<br />
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* [[Steady state]] 稳态<br />
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* [[Transient state]] 瞬态<br />
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* [[Coefficient diagram method]] 系数图法<br />
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* [[Control reconfiguration]] 控制重构<br />
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* [[Cut-insertion theorem]] 切入定理<br />
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* [[Feedback]] 反馈<br />
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* [[H infinity]] H 无限<br />
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* [[Hankel singular value]] 汉克尔奇异值<br />
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* [[Krener's theorem]] 克雷纳定理<br />
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* [[Lead-lag compensator]] 超前滞后补偿器<br />
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* [[Minor loop feedback]] 小循环反馈<br />
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* [[Minor loop feedback|Multi-loop feedback]] 小循环反馈 | 多循环反馈<br />
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* [[Positive systems]] 正向系统<br />
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* [[Radial basis function]] 径向基底函数<br />
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Other related topics<br />
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其他相关话题<br />
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* [[Root locus]] 根轨迹<br />
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* [[Signal-flow graph]]s 信号流图<br />
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* [[Stable polynomial]] 稳定多项式<br />
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* [[State space representation]] 状态空间<br />
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* [[Underactuation]] 欠驱动<br />
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* [[Youla–Kucera parametrization]] 尤拉-库切拉参数化<br />
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* [[Markov chain approximation method]] 马尔可夫链近似法<br />
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{{colend}}<br />
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;Other related topics<br />
其他相关话题<br />
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* [[Automation and remote control]] 自动化和远程控制<br />
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* [[Bond graph]] 键合图<br />
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* [[Control engineering]] 控制工程<br />
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* [[Control–feedback–abort loop]] 控制-反馈-中止循环<br />
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* [[Controller (control theory)]] 控制器(控制理论)<br />
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* [[Cybernetics]] 控制论<br />
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* [[Intelligent control]] 智能控制<br />
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* [[Mathematical system theory]] 数学系统论<br />
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* [[Negative feedback amplifier]] 负反馈放大器<br />
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* [[People in systems and control]] 系统和控制中的人<br />
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* [[Perceptual control theory]] 知觉控制理论<br />
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* [[Systems theory]] 系统论<br />
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* [[Time scale calculus]] 时间尺度演算<br />
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{{colend}}<br />
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== 编者推荐 ==<br />
===集智文章推荐===<br />
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====[https://swarma.org/?p=21322 什么是非平衡态热力学 | 集智百科]====<br />
非平衡态热力学 Non-equilibrium thermodynamics 是热力学的一个分支,研究某些不处于热力学平衡中的物理系统<br />
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==General references==<br />
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* Cesare Barbieri (2007) ''Fundamentals of Astronomy''. First Edition (QB43.3.B37 2006) CRC Press {{ISBN|0-7503-0886-9}}, {{ISBN|978-0-7503-0886-1}}<br />
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* Hans R. Griem (2005) ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}<br />
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* C. Michael Hogan, Leda C. Patmore and Harry Seidman (1973) ''Statistical Prediction of Dynamic Thermal Equilibrium Temperatures using Standard Meteorological Data Bases'', Second Edition (EPA-660/2-73-003 2006) United States Environmental Protection Agency Office of Research and Development, Washington, D.C. [http://library.wur.nl/WebQuery/catalog/lang/1851848]<br />
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* F. Mandl (1988) ''Statistical Physics'', Second Edition, John Wiley & Sons<br />
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==References==<br />
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{{Reflist|colwidth=35em}}<br />
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==Cited bibliography==<br />
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*Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', third edition, McGraw-Hill, London, {{ISBN|0-521-25445-0}}.<br />
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*Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, {{ISBN|0-88318-797-3}}.<br />
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*Beattie, J.A., Oppenheim, I. (1979). ''Principles of Thermodynamics'', Elsevier Scientific Publishing, Amsterdam, {{ISBN|0-444-41806-7}}.<br />
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*[[Ludwig Boltzmann|Boltzmann, L.]] (1896/1964). ''Lectures on Gas Theory'', translated by S.G. Brush, University of California Press, Berkeley.<br />
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*Buchdahl, H.A. (1966). ''The Concepts of Classical Thermodynamics'', Cambridge University Press, Cambridge UK.<br />
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*[[Herbert Callen|Callen, H.B.]] (1960/1985). ''Thermodynamics and an Introduction to Thermostatistics'', (1st edition 1960) 2nd edition 1985, Wiley, New York, {{ISBN|0-471-86256-8}}.<br />
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*[[Constantin Carathéodory|Carathéodory, C.]] (1909). [https://web.archive.org/web/20160304213645/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0067&DMDID=DMDLOG_0033&L=1 Untersuchungen über die Grundlagen der Thermodynamik], ''[[Mathematische Annalen]]'', '''67''': 355–386. A translation may be found [http://neo-classical-physics.info/uploads/3/0/6/5/3065888/caratheodory_-_thermodynamics.pdf here]. Also a mostly reliable [https://books.google.com/books?id=xwBRAAAAMAAJ&q=Investigation+into+the+foundations translation is to be found] at Kestin, J. (1976). ''The Second Law of Thermodynamics'', Dowden, Hutchinson & Ross, Stroudsburg PA.<br />
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*[[Sydney Chapman (mathematician)|Chapman, S.]], [[Thomas George Cowling|Cowling, T.G.]] (1939/1970). ''The Mathematical Theory of Non-uniform gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases'', third edition 1970, Cambridge University Press, London.<br />
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*Crawford, F.H. (1963). ''Heat, Thermodynamics, and Statistical Physics'', Rupert Hart-Davis, London, Harcourt, Brace & World, Inc.<br />
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*de Groot, S.R., Mazur, P. (1962). ''Non-equilibrium Thermodynamics'', North-Holland, Amsterdam. Reprinted (1984), Dover Publications Inc., New York, {{ISBN|0486647412}}.<br />
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*Denbigh, K.G. (1951). ''Thermodynamics of the Steady State'', Methuen, London.<br />
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*Eu, B.C. (2002). ''Generalized Thermodynamics. The Thermodynamics of Irreversible Processes and Generalized Hydrodynamics'', Kluwer Academic Publishers, Dordrecht, {{ISBN|1-4020-0788-4}}.<br />
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*Fitts, D.D. (1962). ''Nonequilibrium thermodynamics. A Phenomenological Theory of Irreversible Processes in Fluid Systems'', McGraw-Hill, New York.<br />
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*[[Josiah Willard Gibbs|Gibbs, J.W.]] (1876/1878). On the equilibrium of heterogeneous substances, ''Trans. Conn. Acad.'', '''3''': 108–248, 343–524, reprinted in ''The Collected Works of J. Willard Gibbs, Ph.D, LL. D.'', edited by W.R. Longley, R.G. Van Name, Longmans, Green & Co., New York, 1928, volume 1, pp.&nbsp;55–353.<br />
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*Griem, H.R. (2005). ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}.<br />
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*[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', fifth revised edition, North-Holland, Amsterdam.<br />
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*Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of ''Thermodynamics'', pages 1–97 of volume 1, ed. W. Jost, of ''Physical Chemistry. An Advanced Treatise'', ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081.<br />
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*[[John Gamble Kirkwood|Kirkwood, J.G.]], Oppenheim, I. (1961). ''Chemical Thermodynamics'', McGraw-Hill Book Company, New York.<br />
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*Landsberg, P.T. (1961). ''Thermodynamics with Quantum Statistical Illustrations'', Interscience, New York.<br />
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*{{cite journal |last1=Lieb |first1=E. H. |last2=Yngvason |first2=J. |year=1999 |title=The Physics and Mathematics of the Second Law of Thermodynamics |journal=Phys. Rep. |volume=310 |issue= 1|pages=1–96 |doi= 10.1016/S0370-1573(98)00082-9|arxiv = cond-mat/9708200 |bibcode = 1999PhR...310....1L |s2cid=119620408 }}<br />
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*Levine, I.N. (1983), ''Physical Chemistry'', second edition, McGraw-Hill, New York, {{ISBN|978-0072538625}}.<br />
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*{{cite journal | last1 = Maxwell | first1 = J.C. | authorlink = James Clerk Maxwell | year = 1867 | title = On the dynamical theory of gases | url = | journal = Phil. Trans. Roy. Soc. London | volume = 157 | issue = | pages = 49–88 }}<br />
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*[[Philip M. Morse|Morse, P.M.]] (1969). ''Thermal Physics'', second edition, W.A. Benjamin, Inc, New York.<br />
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*Münster, A. (1970). ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London.<br />
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*[[J.R. Partington|Partington, J.R.]] (1949). ''An Advanced Treatise on Physical Chemistry'', volume 1, ''Fundamental Principles. The Properties of Gases'', Longmans, Green and Co., London.<br />
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*[[Brian Pippard|Pippard, A.B.]] (1957/1966). ''The Elements of Classical Thermodynamics'', reprinted with corrections 1966, Cambridge University Press, London.<br />
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* [[Max Planck|Planck. M.]] (1914). [https://archive.org/details/theoryofheatradi00planrich ''The Theory of Heat Radiation''], a translation by Masius, M. of the second German edition, P. Blakiston's Son & Co., Philadelphia.<br />
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*[[Ilya Prigogine|Prigogine, I.]] (1947). ''Étude Thermodynamique des Phénomènes irréversibles'', Dunod, Paris, and Desoers, Liège.<br />
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*[[Ilya Prigogine|Prigogine, I.]], Defay, R. (1950/1954). ''Chemical Thermodynamics'', Longmans, Green & Co, London.<br />
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*Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005). ''Physical Chemistry'', fourth edition, Wiley, Hoboken NJ.<br />
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*[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966). ''Elements of Thermodynamics'', Addison-Wesley Publishing, Reading MA.<br />
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*{{cite journal|last=Thomson|first=W.|author-link=William Thomson, 1st Baron Kelvin|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Transactions of the Royal Society of Edinburgh|date=March 1851|volume=XX|issue=part II|pages=261–268; 289–298}} Also published in {{cite journal|last=Thomson|first=W.|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Phil. Mag. |date=December 1852 |volume=IV |series=4 |issue=22 |pages=8–21 |url=https://archive.org/details/londonedinburghp04maga |accessdate=25 June 2012}}<br />
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*[[László Tisza|Tisza, L.]] (1966). ''Generalized Thermodynamics'', M.I.T Press, Cambridge MA.<br />
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*[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963). ''Lectures in Statistical Mechanics'', American Mathematical Society, Providence RI.<br />
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*Waldram, J.R. (1985). ''The Theory of Thermodynamics'', Cambridge University Press, Cambridge UK, {{ISBN|0-521-24575-3}}.<br />
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*[[Mark Zemansky|Zemansky, M.]] (1937/1968). ''Heat and Thermodynamics. An Intermediate Textbook'', fifth edition 1967, McGraw–Hill Book Company, New York.<br />
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== External links ==<br />
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Category:Equilibrium chemistry<br />
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类别: 平衡化学<br />
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*[http://ads.harvard.edu/books/1989fsa..book/AbookC15.pdf Breakdown of Local Thermodynamic Equilibrium] George W. Collins, The Fundamentals of Stellar Astrophysics, Chapter 15<br />
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Category:Thermodynamic cycles<br />
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类别: 热力循环<br />
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*[http://spiff.rit.edu/classes/phys440/lectures/lte/lte.html Thermodynamic Equilibrium, Local and otherwise] lecture by Michael Richmond<br />
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Category:Thermodynamic processes<br />
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类别: 热力学过程<br />
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*[http://journals.ametsoc.org/doi/abs/10.1175/1520-0469%281970%29027%3C0711:NLTEIC%3E2.0.CO%3B2 Non-Local Thermodynamic Equilibrium in Cloudy Planetary Atmospheres] Paper by R. E. Samueison quantifying the effects due to non-LTE in an atmosphere<br />
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Category:Thermodynamic systems<br />
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类别: 热力学系统<br />
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*[http://scienceworld.wolfram.com/physics/LocalThermodynamicEquilibrium.html Local Thermodynamic Equilibrium]<br />
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Category:Thermodynamics<br />
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分类: 热力学<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Thermodynamic equilibrium]]. Its edit history can be viewed at [[平衡热力学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%B9%B3%E8%A1%A1%E7%83%AD%E5%8A%9B%E5%AD%A6&diff=21462平衡热力学2021-01-30T11:19:30Z<p>Jxzhou:/* Relation of exchange equilibrium between systems */</p>
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<div>此词条暂由小竹凉翻译,翻译字数共5339,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{short description|State of thermodynamic system(s) where no net macroscopic flow of matter or energy occurs}}<br />
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'''Thermodynamic equilibrium''' is an [[axiomatic]] concept of [[thermodynamics]]. It is an internal [[State variables|state]] of a single [[thermodynamic system]], or a relation between several thermodynamic systems connected by more or less permeable or impermeable [[Thermodynamic system#Walls|walls]]. In thermodynamic equilibrium there are no net [[macroscopic]] [[Flow (mathematics)|flows]] of [[matter]] or of [[energy]], either within a system or between systems. <br />
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Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium there are no net macroscopic flows of matter or of energy, either within a system or between systems. <br />
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'''热力学平衡'''是'''<font color="#ff8000">热力学 Thermodynamics</font>'''的一个'''<font color="#ff8000">不言自明的 Axiomatic</font>'''概念。它是单个'''<font color="#ff8000">热力学系统 Thermodynamic System</font>'''的内部'''<font color="#ff8000">状态 State</font>''',或者是几个热力学系统之间通过或多或少的渗透或不渗透的'''<font color="#ff8000">壁 Wall</font>'''连接的关系。无论是在一个系统内还是在系统之间,在热力学平衡中不存在'''<font color="#ff8000">物质 Matter</font>'''或'''<font color="#ff8000">能量 Energy</font>'''的净'''<font color="#ff8000">宏观 Macroscopic</font>''' '''<font color="#ff8000">流动 Flow</font>'''。<br />
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In a system that is in its own state of internal thermodynamic equilibrium, no [[macroscopic]] change occurs. <br />
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In a system that is in its own state of internal thermodynamic equilibrium, no macroscopic change occurs. <br />
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在一个处于内部热力学平衡状态的系统中,不会发生'''<font color="#ff8000">宏观 Macroscopic</font>'''变化。<br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual [[Thermal equilibrium|thermal]], [[Mechanical equilibrium|mechanical]], [[Chemical equilibrium|chemical]], and [[Radiative equilibrium|radiative]] equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a [[thermodynamic operation]]. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a thermodynamic operation. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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相互热力学平衡的体系同时处于互相之间的'''<font color="#ff8000">热 Thermal</font>'''平衡、'''<font color="#ff8000">力学 Mechanical</font>'''平衡、'''<font color="#ff8000">化学 Chemical</font>'''平衡和'''<font color="#ff8000">辐射 Radiative</font>'''平衡。系统可以处于其中一种相互平衡状态,尽管其他状态未平衡。在热力学平衡中所有的平衡同时并且无限期地保持,直到被'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''打破。在一个宏观平衡中,微观交换是完全或几乎完全平衡的;这是对宏观平衡概念的物理解释。<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform [[temperature]]. Its [[Intensive and extensive properties|intensive properties]], other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform temperature. Its intensive properties, other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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一个处于内部热力学状态平衡的热力学系统具有空间均匀的'''<font color="#ff8000">温度 Temperature</font>'''。除了温度以外,它的'''<font color="#ff8000">强度性质 Intensive Properties</font>'''可以由于周围环境施加的不变的长程力场而导致空间不均匀性。<br />
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In systems that are at a state of [[non-equilibrium]] there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a '''meta-stable equilibrium'''.<br />
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In systems that are at a state of non-equilibrium there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a meta-stable equilibrium.<br />
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相比之下,处于'''<font color="#ff8000">非平衡状态 non-equilibrium</font>'''的系统中有物质或能量的净流动。如果这些变化可以在一个还没有发生的系统中被触发,那么这个系统就被称为处于一个'''亚稳定的平衡状态'''。<br />
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Though not a widely named a "law," it is an [[axiom]] of thermodynamics that there exist states of thermodynamic equilibrium. The [[second law of thermodynamics]] states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the [[entropy|entropies]] of the portions.<br />
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Though not a widely named a "law," it is an axiom of thermodynamics that there exist states of thermodynamic equilibrium. The second law of thermodynamics states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the entropies of the portions.<br />
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虽然不是一个广泛命名的“定律” ,但存在热力学平衡状态是一个热力学'''<font color="#ff8000">公理 Axiom</font>'''。'''<font color="#ff8000">热力学第二定律 second law of thermodynamics</font>'''指出,当一个物质体从一个平衡状态开始,在这个状态中,它的一部分被或多或少渗透或不渗透的分区保持在不同的状态,并且是孤立的,热力学操作移除分区或使分区更具渗透性,然后它会自发地达到自己内部热力学平衡的新状态,并伴随着部分'''<font color="#ff8000">熵 Entropy</font>'''的总和增加。<br />
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== Overview 概览==<br />
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{{Thermodynamics|cTopic=[[Thermodynamic system|Systems]]}}<br />
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Classical thermodynamics deals with states of [[dynamic equilibrium]]. The state of a system at thermodynamic equilibrium is the one for which some [[thermodynamic potential]] is minimized, or for which the [[entropy]] (''S'') is maximized, for specified conditions. One such potential is the [[Helmholtz free energy]] (''A''), for a system with surroundings at controlled constant temperature and volume:<br />
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Classical thermodynamics deals with states of dynamic equilibrium. The state of a system at thermodynamic equilibrium is the one for which some thermodynamic potential is minimized, or for which the entropy (S) is maximized, for specified conditions. One such potential is the Helmholtz free energy (A), for a system with surroundings at controlled constant temperature and volume:<br />
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经典热力学研究'''<font color="#ff8000">动态平衡 Dynamic Equilibrium</font>'''的状态。系统的热力学平衡状态是对于特定的条件,一些'''<font color="#ff8000">热力学势 Thermodynamic Potential</font>'''被最小化,或者'''<font color="#ff8000">熵 Entropy</font>'''(S)被最大化。对于一个周围环境温度和体积恒定的系统,其中一个这样的热力学势是'''<font color="#ff8000">亥姆霍兹自由能 Helmholtz Free Energy</font>'''(A):<br />
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:<math>A = U - TS</math><br />
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<math>A = U - TS</math><br />
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A = U-TS<br />
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Another potential, the [[Gibbs free energy]] (''G''), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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Another potential, the Gibbs free energy (G), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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在恒定温度和压力的系统中,另一个热力学势'''<font color="#ff8000">吉布斯自由能 Gibbs Free Energy</font>'''(G)在热力学平衡状态最小:<br />
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:<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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where ''T'' denotes the absolute thermodynamic temperature, ''P'' the pressure, ''S'' the entropy, ''V'' the volume, and ''U'' the internal energy of the system.<br />
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where T denotes the absolute thermodynamic temperature, P the pressure, S the entropy, V the volume, and U the internal energy of the system.<br />
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其中 T 表示热力学绝对温度,P 表示压强,S 表示熵,V 表示体积,U 表示体系的内能。<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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热力学平衡是一种独特的稳定定态,当系统长时间与周围环境相互作用时,它可以被接近或最终到达。上述势能是数学构造的热力学量,在特定的环境条件下最小化。<br />
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== Conditions 条件==<br />
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* For a completely isolated system, ''S'' is maximum at thermodynamic equilibrium. 对于一个完全孤立的系统,S在热力学平衡中取最大值。<br />
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* For a system with controlled constant temperature and volume, ''A'' is minimum at thermodynamic equilibrium. 对于一个恒定温度和体积的系统来说,A在热力学平衡中取最小值。<br />
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* For a system with controlled constant temperature and pressure, ''G'' is minimum at thermodynamic equilibrium. 对于一个恒温恒压的系统,G在热力学平衡中取最小值。<br />
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The various types of equilibriums are achieved as follows:<br />
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The various types of equilibriums are achieved as follows:<br />
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实现各种类型的平衡的方法如下:<br />
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*Two systems are in ''thermal equilibrium'' when their [[temperature]]s are the same. 当两个系统的'''<font color="#ff8000">温度 Temperature</font>'''相同时,它们就处于''热平衡状态''<br />
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*Two systems are in ''mechanical equilibrium'' when their [[pressure]]s are the same. 当两个体系的'''<font color="#ff8000">压力 Pressure</font>'''相同时,它们就处于''力学平衡''<br />
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*Two systems are in ''diffusive equilibrium'' when their [[chemical potential]]s are the same. 当两个题体系的'''<font color="#ff8000">化学势 Chemical Potential</font>'''相同时,它们就处于''扩散平衡''<br />
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*All [[forces]] are balanced and there is no significant external driving force.<br />
所有的'''<font color="#ff8000">力 Force</font>'''都是平衡的,没有明显的外部驱动力<br />
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==Relation of exchange equilibrium between systems 系统之间的交换均衡关系==<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability.<ref name="Nster_a">Münster, A. (1970), p. 49.</ref> When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability. When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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通常,热力学系统的周围环境也可以被看作是另一个热力学系统。在这种观点中,我们可以把系统及其周围环境看作是相互接触的两个系统,远程作用力也将它们联系在一起。系统的包围物是两个系统之间的接触面或边界。在热力学形式中,该表面被认为具有特定的渗透性质。例如,接触的表面可能被认为只能透热,使能量只能作为热传递。当远程力在时间上不发生变化,两个系统之间的热量传递减慢并最终永久停止时,这两个系统被称为热平衡; 这就是接触平衡的一个例子。其它类型的接触平衡可用其它类型的比渗透率来定义。当两个系统对于某一特定类型的渗透率处于接触平衡时,它们具有属于该特定类型渗透率的强变量的共同值。这种强度变量的例子有温度、压力、化学势。<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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接触平衡也可视为交换平衡。在接触平衡状态下,两系统之间某些量的传递速率存在零平衡。例如,对于只能透热的壁,内能作为热在两个系统之间的扩散速率是相等并反向的。两个系统之间的绝热壁只对作为功传递的能量有渗透作用; 在力学平衡,两个系统之间作为功的能量传递速率相等且相反。如果是一个简单的壁,那么通过它的体积转移率也是相等且相反的; 即它两边的压力是相等的。如果绝热壁比较复杂,有一种杠杆,有一个面积比,那么两个体系在交换平衡中的压力与体积交换比成反比,这使得转移率的零平衡作功。<br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<ref name="Planck 1914 40">[[Max Planck|Planck. M.]] (1914), p. 40.</ref><br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<br />
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辐射交换可以发生在两个不同的系统之间。当两个体系温度相同时,辐射交换平衡占优势。<br />
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==Thermodynamic state of internal equilibrium of a system==<br />
系统内部平衡的热力学状态<br />
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A collection of matter may be entirely [[Isolated system|isolated]] from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium.<ref>Haase, R. (1971), p. 4.</ref><ref>Callen, H.B. (1960/1985), p. 26.</ref> (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics.<ref>{{Cite journal |doi = 10.1119/1.4914528|bibcode = 2015AmJPh..83..628M|title = Time and irreversibility in axiomatic thermodynamics|year = 2015|last1 = Marsland|first1 = Robert|last2 = Brown|first2 = Harvey R.|last3 = Valente|first3 = Giovanni|journal = American Journal of Physics|volume = 83|issue = 7|pages = 628–634}}</ref> One textbook<ref>[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963), p. 5.</ref> calls it the "zeroth law", remarking that the authors think this more befitting that title than its [[Zeroth law of thermodynamics|more customary definition]], which apparently was suggested by [[Ralph H. Fowler|Fowler]].)<br />
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A collection of matter may be entirely isolated from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium. (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics. One textbook calls it the "zeroth law", remarking that the authors think this more befitting that title than its more customary definition, which apparently was suggested by Fowler.)<br />
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物质的集合可能与其周围的环境完全'''<font color="#ff8000">孤立 Isolated</font>'''。如果它在无限长的时间内一直保持不受干扰,按照经典热力学假定,它处于一个没有发生任何变化,没有流动的状态,即内部平衡的热力学状态。(这种假设有时被称为“负第一”热力学定律,但并不常见。有教科书称之为“第零定律” ,作者'''<font color="#ff8000">福勒 Fowler</font>'''认为这个名称是'''<font color="#ff8000">更符合惯例的定义 More Customary Definition</font>'''。)<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a [[thermodynamic operation]] be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a thermodynamic operation be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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这种状态是所谓的经典热力学或平衡态热力学的主要关注点,因为它们是系统中被认为在这门学科中得到很好定义的唯一状态。一个与另一个系统处于接触平衡状态可以被一个'''<font color="#ff8000">热力运行 Thermodynamic Operation</font>'''隔离,在隔离发生时,其内部不会发生任何变化。因此,一个与另一个系统处于接触平衡状态时也可以被视为处于其自身的内部热力学平衡状态。<br />
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==Multiple contact equilibrium==<br />
多点接触平衡<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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热力学形式论允许一个系统同时与其他多个系统接触,这些系统可能也可能没有相互接触,且这些接触具有不同的渗透性。如果这些系统都与世界其他部分相互隔离,那么它们彼此之间就会达到各自的接触平衡。<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy.<ref name="Caratheodory">Carathéodory, C. (1909).</ref><ref>Prigogine, I. (1947), p. 48.</ref><ref>Landsberg, P. T. (1961), pp. 128–142.</ref><ref>Tisza, L. (1966), p. 108.</ref> Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy. Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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如果几个系统彼此之间没有绝热壁,但是它们与世界其他部分共同隔离,那么它们就会达到多重接触平衡状态,且有共同的温度,内能和熵。在众多变量中,这是温度的一个独特性质。即使在远距离作用力存在的情况下,它也是有效的。(也就是说,没有“力”可以维持温度的差异。)举个例子,在热力学平衡的一个垂直的引力场系统中,顶部壁面的压力比底部壁面的压力小,但是各处的温度都是一样的。<br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural [[thermodynamic process]].<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), § 1.12.</ref> It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings.<ref>Levine, I.N. (1983), p. 40.</ref><ref>Lieb, E.H., Yngvason, J. (1999), pp. 17–18.</ref> The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of [[Second law of thermodynamics#Description#Kelvin statement|"inanimate" agency]]; a system in thermodynamic equilibrium is inanimate.<ref>[[William Thomson, 1st Baron Kelvin|Thomson, W.]] (1851).</ref><br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural thermodynamic process. It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings. The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of "inanimate" agency; a system in thermodynamic equilibrium is inanimate.<br />
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热力运行可能作为一个事件发生在周围环境的壁上,既不直接影响与周围环境联系的壁,也不直接影响其内部,且发生在一个明确的有限的时间内。例如,一个固定的绝热壁可以在环境中被放置或拆除。由于这种操作仅限于周围环境,系统可能会在一段时间内远离自身最初的内部状态---- 热力学平衡。根据热力学第二定律的说法,整体经历了变化并最终与周围环境达到了新的平衡。继Planck之后,这一连串的事件被称为自然'''<font color="#ff8000">热力学过程 Thermodynamic Process</font>'''。即使在这个过程中,当系统和周围环境都不处于明确的内部平衡状态时,存在着暂时偏离热力学平衡的现象,由于初始状态和最终状态都是热力学平衡的,这在平衡热力学中也是允许的。一个自然过程在其主要部分中以有限的速率进行,因此,它从根本上不同于虚构的准静态“过程”;即不在整个过程中无限缓慢地进行而且虚构地“可逆”。经典热力学允许,即使一个过程可能需要很长的时间才能达到热力学平衡,如果主要部分的过程是在一个有限的比率中,那么它被认为是自然的,并受制于热力学第二定律,即不可逆的。工程设计的机器、人工设备和操作是允许在周围环境中进行的。允许在环境中而不是在系统中进行此类操作和设备,是开尔文在他的一个热力学第二定律的陈述中提到'''<font color="#ff8000">无生命机构 Inanimate Agency</font>'''的原因; 在热力学平衡的系统是无生命的。<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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否则,热力运行可能会直接影响系统的壁。<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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通常可以很方便地假设周围的某些子系统比系统大得多,以至于这个过程只能影响周围子系统的强度变量,然后将这些子系统称为相关强度变量的储备库。<br />
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== Local and global equilibrium ==<br />
局部和全局均衡<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by [[intensive quantity|intensive]] parameters. As an example, [[temperature]] controls [[Heat equation|heat exchanges]]. ''Global thermodynamic equilibrium'' (GTE) means that those [[intensive quantity|intensive]] parameters are homogeneous throughout the whole system, while ''local thermodynamic equilibrium'' (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by intensive parameters. As an example, temperature controls heat exchanges. Global thermodynamic equilibrium (GTE) means that those intensive parameters are homogeneous throughout the whole system, while local thermodynamic equilibrium (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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区分全局性和局部性热力学平衡是很有用的。在热力学中,系统内部和系统与外部之间的交换是由'''<font color="#ff8000">强度 Intensive</font>'''参数控制的。例如,'''<font color="#ff8000">温度 Temperature</font>'''控制'''<font color="#ff8000">热交换 Heat Equation</font>'''。全局热力学平衡(GTE)意味着这些'''<font color="#ff8000">强度 Intensive</font>'''参数在整个系统中是均匀的,而局部热力学平衡(LTE)意味着这些强度参数在空间和时间上是变化的,但变化如此缓慢,以至于对于任何一点,人们都可以假设在某个邻近的某个热力学平衡。<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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如果对系统的描述要求强度参数的变化过大,那么这些强度参数的定义所依据的假设本身就会破裂,系统将既不处于全局平衡,也不处于局部平衡。例如,粒子需要一定数量的碰撞来平衡其周围环境。如果在这些碰撞中移动的平均距离使它离开平衡邻域,它将永远不会平衡,也就不会有 LTE。根据定义,温度与平衡邻域的平均内部能量成正比。由于没有达到平衡邻域,温度的概念就不成立,温度也就变得不确定。<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to [[massive]] particles. In a [[radiation|radiating]] gas, the [[photon]]s being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to massive particles. In a radiating gas, the photons being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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值得注意的是,这种局部平衡可能只适用于系统中的某个粒子子集。例如,LTE 通常只适用于'''<font color="#ff8000">大 Massive</font>'''质量粒子。在'''<font color="#ff8000">辐射 Radiation</font>'''气体中,被气体发射和吸收的'''<font color="#ff8000">光子 Photon</font>'''不需要彼此在一个热力学平衡内,或与气体中的大量粒子在一起,LTE 才能存在。在某些情况下,自由电子并不需要与大得多的原子或分子处于平衡状态,LTE 才能存在。<br />
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As an example, LTE will exist in a glass of water that contains a melting [[ice cube]]. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the [[Maxwell–Boltzmann distribution]] for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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As an example, LTE will exist in a glass of water that contains a melting ice cube. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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例如,LTE 将存在于一个装有融化的'''<font color="#ff8000">冰块 Ice Cube</font>'''的水杯中。玻璃杯内的温度可以在任何时候定义,但是离冰块近的地方要比离冰块远的地方冷。如果观察到位于给定点附近的分子的能量,它们将按照麦克斯韦-波兹曼分布在一定温度下的分布。如果观察到位于另一点附近的分子的能量,它们将按照'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''分布到另一个温度。<br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural [[transport phenomena]] may lead a system from local to global thermodynamic equilibrium. Going back to our example, the [[diffusion]] of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<ref>H.R. Griem, 2005</ref><br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural transport phenomena may lead a system from local to global thermodynamic equilibrium. Going back to our example, the diffusion of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<br />
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局部热力学平衡不需要局部或全局的平稳性。换句话说,每一个小区域不需要有一个恒定的温度。然而,它确实要求每个小的局部变化缓慢到足以维持其局部麦克斯韦-波兹曼分布的分子速度。全局非平衡态只有通过系统与外界的交换才能保持稳定。例如,通过在水杯中不断添加细粉冰来补偿熔化,并持续排出融水,可以保持全球稳定的静止状态。自然'''<font color="#ff8000">迁移现象 Transport Phenomena</font>'''可能导致一个从局部到全局的热力学平衡系统。回顾我们的例子,热量的扩散将导致我们的玻璃杯水流向全局热力学平衡,在这种状态下,玻璃杯的温度是完全均匀的。<br />
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==Reservations==<br />
保留意见<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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学识渊博的笔者在热力学领域对热力学平衡描述时,经常对他们的描述附加条件或保留意见。有些笔者含蓄地保留了或多或少的空白,以待说明。<br />
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For example, one widely cited writer, [[Herbert Callen|H. B. Callen]] writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. ''Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!''"<ref>Callen, H.B. (1960/1985), p. 15.</ref><br />
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For example, one widely cited writer, H. B. Callen writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!"<br />
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例如,一位被广泛引用的作家'''<font color="#ff8000">H.B.卡伦 H.B.Callen</font>'''在这里写道: “实际上,很少有系统处于绝对和真正的平衡状态。”他提到了放射性过程,认为它们可能需要“宇宙时间才能完成,因此通常可以忽略”。他补充道: “在实践中,平衡的标准是循环的。在操作上,如果一个系统的性质一致地用热力学理论来描述,那么它就处于平衡状态! ”<br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<ref>Beattie, J.A., Oppenheim, I. (1979), p. 3.</ref><br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<br />
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J.A.贝蒂和 I.奥本海姆写道: “坚持对平衡定义的严格解释,将排除热力学应用于实际系统的所有状态。”<br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment",<ref>Callen, H.B. (1960/1985), p. 485.</ref> and cited by Adkins as having written a "classic text",<ref>Adkins, C.J. (1968/1983), p. ''xiii''.</ref> [[Brian Pippard|A.B. Pippard]] writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<ref>Pippard, A.B. (1957/1966), p. 6.</ref><br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment", and cited by Adkins as having written a "classic text", A.B. Pippard writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<br />
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Callen引用另一位作者的话说,他给出了“学术且严谨的论述” ,Adkins引用他的话说,他写了一本“经典著作”—— '''<font color="#ff8000">A.B.皮帕德 A.B.Pippard</font>'''在文中写道: “只要时间足够长,过冷水蒸汽最终会凝结,... ..。时间可能是漫长的,也许长达10年或者更长。就大多数目的而言,只要这种迅速的变化不是人为地刺激,这些系统就可以被视为处于平衡状态。”<br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster">Münster, A. (1970), p. 53.</ref><br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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另一位作者A.Münster,写道。他观察到热核反应发生的速度非常缓慢,以至于在热力学中可以忽略不计。他评论道: “‘绝对平衡’或‘所有可想象过程的平衡’的概念没有物理意义。”他说: “ ... 我们只能考虑特定过程和确定的实验条件下的平衡。”<br />
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According to [[László Tisza|L. Tisza]]: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<ref>Tisza, L. (1966), p. 119.</ref><br />
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According to L. Tisza: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<br />
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根据'''<font color="#ff8000">L.缇莎 L.Tisza</font>'''的说法: “ ... 在讨论接近绝对零度的现象时。经典理论的绝对预测变得特别模糊,因为在非平衡状态下发生冻结是非常普遍的。”<br />
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==Definitions==<br />
定义<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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一个系统最普遍的热力学平衡是通过与周围环境的接触,允许所有化学物质和各种能量同时通过。热力学平衡中的系统以均匀加速度在空间中运动,但此时不能改变其形状或大小; 因此它是由空间中的刚性体积来定义的。它可能存在于外力场中,由远远大于系统本身的外部因素决定,因此系统内的事件不会对外力场产生相当大的影响。只有当外力场是均匀的,并且确定了它的均匀加速度,或者它处于一个非均匀力场中,但是由于表面的局部力,例如机械压力,使它保持静止时,这个系统才能处于热力学平衡。<br />
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Thermodynamic equilibrium is a [[primitive notion]] of the theory of thermodynamics. According to [[Philip M. Morse|P.M. Morse]]: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are ''not'' conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments."<ref>[[Philip M. Morse|Morse, P.M.]] (1969), p. 7.</ref> This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<ref>Bailyn, M. (1994), p. 20.</ref><br />
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Thermodynamic equilibrium is a primitive notion of the theory of thermodynamics. According to P.M. Morse: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are not conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments." This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<br />
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热力学平衡是热力学理论的一个'''<font color="#ff8000">基本概念 Primitive Notion</font>'''。'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''说: “应该强调的是,存在热力学状态这一事实,以及存在由平衡态唯一指定的热力学变量这一事实,并不是从某些哲学第一原理得出的逻辑结论。这些结论不可避免地来自两个多世纪的实验。”这意味着热力学平衡不能仅仅用热力学的其他理论概念来定义。M.Bailyn提出了一个基本的热力学定律理论,它定义并假设了热力学平衡的存在。<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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热力学平衡的教科书定义通常被仔细说明,并有些保留。<br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<ref>Münster, A. (1970), p. 52.</ref><br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<br />
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例如,A. Münster写道:“当系统中没有以可测量的速度发生状态变化时,隔离系统处于热力学平衡状态。”这里有两项保留:系统是孤立的;任何状态的变化都是不可估量的缓慢。他通过对在室温且没有催化剂的情况下混合氧和氢的说明,讨论了第二个条件。Münster指出,热力学平衡状态所描述的宏观变量比给定系统任何其他状态都少。这是部分,但不完全是,因为系统内和系统内的所有流都是零。<br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in ''equilibrium''.<ref>Haase, R. (1971), pp. 3–4.</ref><br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in equilibrium.<br />
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R. Haase's的热力学演示并不从对热力学平衡的限制开始,因为他打算考虑非平衡态热力学。他考虑一个具有时间不变性质的任意系统。他通过切断除外力场以外的所有外部影响来测试它的热力学平衡。如果在绝缘之后,没有任何变化,他说,系统处于平衡状态。<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness".<ref>Callen, H.B. (1960/1985), p. 13.</ref> This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness". This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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在一个标题为“热力学平衡”的章节中,H.B. Callen在段落定义了平衡状态.他指出,它们“是由系统内部的内在因素决定的”。它们是“终端状态” ,随着时间的推移,系统会以“冰川般缓慢”的速度朝着这个终端状态演化。这个说法并没有明确,对于热力学平衡系统必须是孤立的;;Callen也没有说明他所说的“内在因素”是什么意思。<br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<ref>Adkins, C.J. (1968/1983), p. ''7''.</ref><br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<br />
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另一位教科书作者,C.J.Adkins,明确允许热力学平衡在非孤立的系统中发生。然而,他的系统在物质转移方面是封闭的。他写道: “一般来说,热力学平衡的方法包括热和类似变动与周围环境的相互作用。”他将这种热力学平衡与只有通过热接触才能进行能量传递的热平衡相区别。<br />
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Another textbook author, [[J.R. Partington]], writes: "(i) ''An equilibrium state is one which is independent of time''." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..."<ref>Partington, J.R. (1949), p. 161.</ref> This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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Another textbook author, J.R. Partington, writes: "(i) An equilibrium state is one which is independent of time." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..." This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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另一位教科书作者'''<font color="#ff8000">J.R.帕廷顿 J.R.Partington</font>'''写道: “(i)平衡状态是独立于时间的状态。”但是,在提到“只是明显处于平衡状态”的系统时,他补充说: “这样的系统处于‘虚假平衡’状态。帕廷顿的陈述没有明确指出平衡是指一个孤立的系统。和Münster一样,Partington也指的是氧和氢的混合物。他补充说:“在一个真正的平衡状态,任何影响状态的外部条件的最小变化都会产生一个微小的状态变化... ... ”这个条件意味着热力学平衡必须在小的扰动下保持稳定; 这个要求对于热力学平衡的严格意义是必不可少的。<br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, ''thermodynamic—equilibrium.''"<ref>Crawford, F.H. (1963), p. 5.</ref><br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, thermodynamic—equilibrium."<br />
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在F.H.Crawford的一本学生教科书中,有一个标题为“热力学平衡”的章节。它区分了几种流动的驱动因素,然后说: “这些是孤立系统明显普遍趋向于完全机械、热、化学和电力状态的例子——或者简单地说,热力学平衡状态。”<br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in ''equilibrium''."<ref>Buchdahl, H.A. (1966), p. 8.</ref> Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being ''in equilibrium'' so long as experimental tests show that 'slow' transitions are in effect reversible."<ref>Buchdahl, H.A. (1966), p. 111.</ref> It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<ref>Adkins, C.J. (1968/1983), p. 8.</ref><br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in equilibrium." Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being in equilibrium so long as experimental tests show that 'slow' transitions are in effect reversible." It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<br />
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H.A. Buchdahl的一本关于经典热力学的专著考虑了热力学系统的平衡,而实际上并没有写热力学平衡一词。Buchdahl在提到封闭的物质交换系统时写道: “如果一个系统处于一个适当的静态状态,那么它将被称为处于平衡状态。”出于热力学描述的目的,Buchdahl的专著也讨论了非晶态玻璃。它说: “更准确地说,只要实验测试表明‘慢’跃迁实际上是可逆的,玻璃就可以被认为处于平衡状态。”通常来说不会将这一条件作为热力学平衡定义的一部分,而是假定相反的情况:如果热力学平衡中的一个体受到足够慢的过程的影响,则该过程可被视为足够接近可逆,并且该物体在过程中足够接近热力学平衡。<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of ''contact equilibrium''. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by [[Constantin Carathéodory|C. Carathéodory]], and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster" /> Thermodynamic equilibrium for an open system means that, with respect to every relevant kind of selectively permeable wall, contact equilibrium exists when the respective intensive parameters of the system and surroundings are equal.<ref name="Nster_a" /> This definition does not consider the most general kind of thermodynamic equilibrium, which is through unselective contacts. This definition does not simply state that no current of matter or energy exists in the interior or at the boundaries; but it is compatible with the following definition, which does so state.<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of contact equilibrium. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by C. Carathéodory, and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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通过引入接触平衡的概念,A. Münster仔细地扩展了孤立系统热力学平衡的定义。这指定了在考虑非孤立系统的热力学平衡时允许的特定过程,并特别关心开放系统,这些开放系统可能从周围环境获得或丢失物质。利益系统和周围系统之间的接触平衡,通过一种特殊的壁与利益系统接触,其余的连接系统是孤立的。这种特殊类型的壁也被'''<font color="#ff8000">C.喀喇西奥多里 C.Carathéodory</font>'''考虑过,其他作家也提到过。它们具有选择渗透性。它们可能只对机械工作有渗透性,或者只对热有渗透性,或者只对某种特定的化学物质有渗透性。每个接触平衡定义了一个强度参数; 例如,只能透热的壁定义了一个经验温度。对于感兴趣的体系中每一种化学成分,都可以存在接触平衡。在接触平衡中,尽管有可能通过选择性渗透壁进行交换,感兴趣的系统是不变的,好像它处在孤立的热力学平衡。这个方案遵循的一般规则是: “ ... ... 我们只能考虑特定过程和特定实验条件下的平衡。”<br />
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[[Mark Zemansky|M. Zemansky]] also distinguishes mechanical, chemical, and thermal equilibrium. He then writes: "When the conditions for all three types of equilibrium are satisfied, the system is said to be in a state of thermodynamic equilibrium".<ref>[[Mark Zemansky|Zemansky, M.]] (1937/1968), p. 27.</ref><br />
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'''<font color="#ff8000">M.泽曼斯基 M.Zemansky</font>'''还区分了机械、化学和热平衡。他接着写道: “当这三种均衡的条件都满足时,系统就处于热力学平衡状态。”<br />
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P.M. Morse writes that thermodynamics is concerned with "states of thermodynamic equilibrium". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<br />
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[[Philip M. Morse|P.M. Morse]] writes that thermodynamics is concerned with "''states of thermodynamic equilibrium''". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<ref>[[Philip M. Morse|Morse, P.M.]] (1969), pp. 6, 37.</ref><br />
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'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''写道,热力学关注的是“热力学平衡状态”。在讨论物体与周围热源之间的热量传递时,他也使用了“热平衡”这个短语,尽管没有明确定义一个特殊的术语“热平衡”<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "full thermodynamic equilibrium state".<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "''full'' thermodynamic equilibrium state".<ref>Waldram, J.R. (1985), p. 5.</ref><br />
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J.R. Waldram写到了“一个明确的热力学状态”。他将一个系统定义为“当其观测量随时间停止变化时”的“热平衡”。但是在这个定义之下不久,他写到一块玻璃还没有达到“完全的热力学平衡状态”。<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, thermodynamic equilibrium is said to exist." He is not here considering the presence of an external force field.<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, ''thermodynamic equilibrium'' is said to exist." He is not here considering the presence of an external force field.<ref>Bailyn, M. (1994), p. 21.</ref><br />
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考虑到平衡状态,M.Bailyn写道: “每个强度变量都有自己的平衡类型。”然后他定义了热平衡、机械平衡和物质平衡。因此,他写道: “如果所有的强度变量都是一致的,那么热力学平衡就是存在的。”他在这里没有考虑外力场的存在。<br />
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J.G. Kirkwood and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of thermodynamic equilibrium if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<br />
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[[John Gamble Kirkwood|J.G. Kirkwood]] and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of ''thermodynamic equilibrium'' if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<ref>Kirkwood, J.G., Oppenheim, I. (1961), p. 2</ref><br />
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'''<font color="#ff8000">J.G.柯克伍德 J.G.Kirkwood</font>'''和 I.Oppenheim 将热力学平衡定义为: “一个系统处于热力学平衡状态,如果,在分配给实验的时间内,(a)它强度特性与时间无关,(b)它的内部或与周围环境的边界处没有物质或能量流。”显然,他们没有把定义限制在孤立的或封闭的系统。它们不讨论“缓慢”发生变化的可能性,并且超出了分配给实验的时间范围。他们注意到,对于两个相接触的系统,存在一个强度性质的小子类,如果这个小子类的所有子类都相等,那么所有各自的强度性质都相等。只要满足其他一些条件,热力学平衡状态可以由这个子类定义。<br />
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==Characteristics of a state of internal thermodynamic equilibrium==<br />
内部热力学平衡状态的特征<br />
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A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous. Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface." As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.<br />
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在内部热力学平衡中,没有外力的情况下由单相组成的热力学系统是均匀的。Planck在论文中简要介绍了热量、温度和热平衡,然后宣布: “在下文中,我们将主要讨论任何形式的均匀、各向同性的物体,它们在整个物质中具有相同的温度和密度,并受到到处垂直于表面的均匀压力作用。”和 Carathéodory 一样,Planck 将表面效应、外场和各向异性晶体排除在外。虽然Planck提到了温度,但并没有明确提到热力学平衡的概念。相比之下,Carathéodory 关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ,虽然没有明确地使用短语‘热力学平衡’,也没有明确地假设存在一个温度来定义它。<br />
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===Homogeneity in the absence of external forces===<br />
在没有外力的情况下的同质性<br />
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A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous.<ref name="Planck 1903 3"/> This means that the material in any small volume element of the system can be interchanged with the material of any other geometrically congruent volume element of the system, and the effect is to leave the system thermodynamically unchanged. In general, a strong external force field makes a system of a single phase in its own internal thermodynamic equilibrium inhomogeneous with respect to some [[Intensive and extensive properties|intensive variables]]. For example, a relatively dense component of a mixture can be concentrated by centrifugation.<br />
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在没有外力的情况下,由单一相组成的热力学系统,在其自身的内部热力学平衡中是均匀的。这意味着系统中任何小体积单元中的材料可以与系统中任何其他几何相等的体积单元中的材料互换,其效果是使系统在热力学上保持不变。一般来说,一个强外力场使得一个单相系统在其自身的内部热力学平衡中对于一些'''<font color="#ff8000">强变量 Intensive Variable</font>'''是不均匀的。例如,可以通过离心来浓缩混合物中相对密度较大的组分。<br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform. Considerations of kinetic theory or statistical mechanics also support this statement.<br />
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热力学平衡系统中的温度在空间和时间上是均匀的。在一个系统内部热力学平衡状态下,没有净内部宏观流动。特别是,这意味着系统的所有局部部分处于相互辐射交换平衡状态。这意味着系统的温度在空间上是均匀的。动力学理论或统计力学也支持这种说法。<br />
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===Uniform temperature===<br />
均匀温度<br />
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In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium. As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.<br />
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为了使一个系统处于它自己的内部热力学平衡状态,它处于自己内部的热平衡状态当然是必要的,但不是充分的;系统在达到内部热平衡之前,可以达到内部机械平衡。如上所述,根据 A.Münster的说法,对于给定的孤立系统的任何状态,定义一个热力学平衡所需的变量数是最少的。如上所述,J.G.Kirkwood 和 I.Oppenheim 指出,热力学平衡状态可以由一个特殊的子类的强变量定义,该子类中有一定数量的成员。<br />
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Such equilibrium inhomogeneity, induced by external forces, does not occur for the intensive variable [[temperature]]. According to [[Edward A. Guggenheim|E.A. Guggenheim]], "The most important conception of thermodynamics is temperature."<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), p.5.</ref> Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface."<ref name="Planck 1903 3">[[Max Planck|Planck, M.]] (1897/1927), p.3.</ref> As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.<br />
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这种由外力引起的平衡不均匀性,在强烈变化的'''<font color="#ff8000">温度 Temperature</font>'''下不会发生。'''<font color="#ff8000">E.A.古根海姆 E.A. Guggenheim</font>'''认为,“热力学最重要的概念是温度。“Planck在介绍他的论文时,简要叙述了热、温度和热平衡,然后宣布: ”在下文中,我们将主要讨论任何形式的均匀、各向同性的物体,它们的物质具有相同的温度和密度,并受到到处垂直于表面的均匀压力的作用和Carathéodory 一样,Planck将表面效应、外场和各向异性晶体排除在外。虽然Planck提到了温度,但并没有明确提到热力学平衡的概念。相比之下,Carathéodory关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ,虽然没有明确地使用短语‘热力学平衡’ ,也没有明确地假设存在一个温度来定义它。<br />
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If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.<br />
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如果热力学平衡位于一个外力场中,那么通常只有温度在空间上是均匀的。如果外力场非零,温度以外的强度变量通常是不均匀的。在这种情况下,一般需要附加变量来描述空间非均匀性。<br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform.<ref name="Planck 1914 40"/> This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers.<ref>Gibbs, J.W. (1876/1878), pp. 144-150.</ref><ref>[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966), pp. 127–130.</ref><ref>Münster, A. (1970), pp. 309–310.</ref><ref>Bailyn, M. (1994), pp. 254-256.</ref><ref>{{cite journal | last1 = Verkley | first1 = W.T.M. | last2 = Gerkema | first2 = T. | year = 2004 | title = On maximum entropy profiles | journal = J. Atmos. Sci. | volume = 61 | issue = 8| pages = 931–936 | doi=10.1175/1520-0469(2004)061<0931:omep>2.0.co;2| bibcode = 2004JAtS...61..931V | doi-access = free }}</ref><ref>{{cite journal | last1 = Akmaev | first1 = R.A. | year = 2008 | title = On the energetics of maximum-entropy temperature profiles | url = | journal = Q. J. R. Meteorol. Soc. | volume = 134 | issue = 630| pages = 187–197 | doi=10.1002/qj.209| bibcode = 2008QJRMS.134..187A }}</ref> Considerations of kinetic theory or statistical mechanics also support this statement.<ref>Maxwell, J.C. (1867).</ref><ref>Boltzmann, L. (1896/1964), p. 143.</ref><ref>Chapman, S., Cowling, T.G. (1939/1970), Section 4.14, pp. 75–78.</ref><ref>[[J. R. Partington|Partington, J.R.]] (1949), pp. 275–278.</ref><ref>{{cite journal | last1 = Coombes | first1 = C.A. | last2 = Laue | first2 = H. | year = 1985 | title = A paradox concerning the temperature distribution of a gas in a gravitational field | url = | journal = Am. J. Phys. | volume = 53 | issue = 3| pages = 272–273 | doi=10.1119/1.14138| bibcode = 1985AmJPh..53..272C }}</ref><ref>{{cite journal | last1 = Román | first1 = F.L. | last2 = White | first2 = J.A. | last3 = Velasco | first3 = S. | year = 1995 | title = Microcanonical single-particle distributions for an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 16 | issue = 2| pages = 83–90 | doi=10.1088/0143-0807/16/2/008| bibcode = 1995EJPh...16...83R }}</ref><ref>{{cite journal | last1 = Velasco | first1 = S. | last2 = Román | first2 = F.L. | last3 = White | first3 = J.A. | year = 1996 | title = On a paradox concerning the temperature distribution of an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 17 | issue = | pages = 43–44 | doi=10.1088/0143-0807/17/1/008}}</ref><br />
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热力学平衡系统内的温度在时间和空间上都是均匀的。在一个处于内部热力学平衡的系统中,不存在净的内部宏观流动。特别是,这意味着系统的所有局部都处于相互辐射交换平衡。这意味着系统的温度在空间上是均匀的。这在所有情况下都是如此,包括那些非均匀外力场。对于外部施加的引力场,这可以通过使用朗朗日乘数的方法通过变化的演算在宏观热力学术语中证明。动力学理论或统计力学也支持这种说法。<br />
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In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium.<ref name="Fitts 43"/><br />
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为了使一个系统处于它自己的内部热力学平衡状态,它必须处于它自己的内部热平衡状态是必要不充分的; 一个系统在到达内部热平衡之前到达内部机械平衡是可能的。<br />
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As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.<br />
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如上所述,j.r. Partington 指出热力学平衡状态在小的瞬态扰动下是稳定的。如果没有这个条件,一般来说,研究热力学平衡系统的实验就会遇到巨大的困难。<br />
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===Number of real variables needed for specification===<br />
规范所需的实变量数目<br />
<br />
<br />
In his exposition of his scheme of closed system equilibrium thermodynamics, C. Carathéodory initially postulates that experiment reveals that a definite number of real variables define the states that are the points of the manifold of equilibria.<ref name="Caratheodory" /> In the words of Prigogine and Defay (1945): "It is a matter of experience that when we have specified a certain number of macroscopic properties of a system, then all the other properties are fixed."<ref>Prigogine, I., Defay, R. (1950/1954), p. 1.</ref><ref>Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005), p. 4.</ref> As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.<br />
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在他关于封闭系统平衡态热力学方案的论述中,C.Carathéodory 最初假定实验揭示了一定数量的实变量定义了作为平衡态流形点的状态。用 Prigogine 和 Defay (1945)的话说: “这是一个经验问题,当我们确定了一个系统一定数量的宏观属性时,那么所有其他属性都是固定的。如上所述,A. Münster认为,定义热力学平衡所需的变量数量对于给定孤立系统的任何状态来说都是最少的。如上所述,J.G. Kirkwood 和 I. Oppenheim 指出,热力学平衡状态可以由一个特殊子类的强度变量来定义,该子类中有一定数量的成员。<br />
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When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium. Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<br />
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当一个物质体从不均匀的非平衡状态或化学非平衡状态开始,然后被孤立,它自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如,在这种演变的许多情况下,内部机械平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是,在这种演变的许多情况下,热平衡的发展要比化学平衡快得多。<br />
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If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.<br />
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如果热力学平衡位于一个外力场中,那么通常只有温度在空间上是均匀的。如果外力场非零,温度以外的强度变量通常是不均匀的。在这种情况下,一般需要附加变量来描述空间非均匀性。<br />
<br />
===Stability against small perturbations===<br />
对小扰动的稳定性<br />
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In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
<br />
在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
<br />
As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.<br />
<br />
如上所述,J.R. Partington 指出热力学平衡状态在小的瞬态扰动下是稳定的。如果没有这个条件,一般来说,研究热力学平衡系统的实验就会遇到严重的困难。<br />
<br />
<br />
To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics. But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
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考虑孤立热力学系统中的波动概念,一个方便的例子是由其广泛的状态变量、内能、体积和质量组成指定的系统。根据定义,它们是时不变的。根据定义,它们与它们的共轭状态密集函数的时不变名义值相结合,反向温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广泛的状态变量的值,不足以提供这些名义值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
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===Approach to thermodynamic equilibrium within an isolated system===<br />
孤立系统中的热力学平衡<br />
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It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.<br />
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可以承认,在重复测量这些共轭强度函数时,发现它们的值随时间略有不同。这种可变性被认为是由于内部波动。不同测量值平均到其名义值。<br />
<br />
When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium.<ref name="Fitts 43">Fitts, D.D. (1962), p. 43.</ref> Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<ref>Denbigh, K.G. (1951), p. 42.</ref><br />
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当一个物质体从不均匀的非平衡状态或化学非平衡状态开始,然后被孤立,它自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如,在这种演变的许多情况下,内部机械平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是,在这种演变的许多情况下,热平衡的发展要比化学平衡快得多。<br />
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If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<br />
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如果这个系统真的像经典热力学所假定的那样是宏观的,那么这个系统的波动太小了,宏观上无法检测到。这就是所谓的热力学极限。实际上,物质的分子性质和动量转移的量子性质由于它们太小而看不见,已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中,平衡的波动概念是没有位置的。”<br />
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===Fluctuations within an isolated system in its own internal thermodynamic equilibrium===<br />
孤立系统内部热力学平衡的波动<br />
<br />
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If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
<br />
如果系统被重复细分,最终产生的系统足够小,可以表现出明显的波动。这是一个介观层面的研究。波动则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
<br />
In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
<br />
在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
<br />
<br />
If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
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如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在波动过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,即需要量子统计力学。波动可以变得相对占主导地位,测量问题变得重要。<br />
<br />
To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics.<ref>Tschoegl, N.W. (2000). ''Fundamentals of Equilibrium and Steady-State Thermodynamics'', Elsevier, Amsterdam, {{ISBN|0-444-50426-5}}, p. 21.</ref> But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
<br />
考虑孤立热力学系统中的波动概念,一个方便的例子是由其众多的状态变量,内能、体积和质量组成指定的系统。根据定义,它们是时不变的。根据定义,它们与它们的共轭状态密集函数的时不变名义值相结合,反向温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广泛的状态变量的值,不足以提供这些名义值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
<br />
<br />
The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
<br />
"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有时间趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的标称值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微波动期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。非已知属于平衡状态的标称值,否则根据单一的度量无法进行判断。<br />
<br />
It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.<br />
<br />
可以承认,在重复测量这些共轭强度函数时,发现它们的值随时间略有不同。这种可变性被认为是由于内部波动。不同测量值平均到其名义值。<br />
<br />
<br />
<br />
If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<ref>Buchdahl, H.A. (1966), p. 16.</ref><br />
<br />
如果这个系统真的像经典热力学所假定的那样是宏观的,那么这个系统的波动太小了,宏观上无法检测到。这就是所谓的热力学极限。实际上,物质的分子性质和动量转移的量子性质由于它们太小而看不见,已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中,平衡的波动概念是没有位置的。”<br />
<br />
<br />
If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
<br />
如果系统被重复细分,最终产生的系统足够小,可以表现出明显的波动。这是一个介观层面的研究。波动则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
<br />
An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process." This illustrates the importance for thermodynamics of the concept of temperature.<br />
<br />
热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
<br />
<br />
<br />
If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在波动过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,即需要量子统计力学。波动可以变得相对占主导地位,测量问题变得重要。<br />
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Thermal equilibrium is achieved when two systems in thermal contact with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<br />
<br />
当两个相互热接触的系统不再有净能量交换时,就会产生热平衡。因此,如果两个系统处于热平衡,那么它们的温度是相同的。<br />
<br />
<br />
<br />
The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
<br />
"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有时间趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的标称值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微波动期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。非已知属于平衡状态的标称值,否则根据单一的度量无法进行判断。<br />
<br />
Thermal equilibrium occurs when a system's macroscopic thermal observables have ceased to change with time. For example, an ideal gas whose distribution function has stabilised to a specific Maxwell–Boltzmann distribution would be in thermal equilibrium. This outcome allows a single temperature and pressure to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<br />
<br />
当系统的宏观热观测值不再随着时间变化时,就会出现热平衡。例如,一种分布函数稳定到一个特定的麦克斯韦-波兹曼分布的理想气体即处于热平衡状态。这个结果可以将单一的温度和压力归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是很有可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
<br />
=== Thermal equilibrium ===<br />
热平衡<br />
{{Main|Thermal equilibrium}}<br />
<br />
<br />
<br />
An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process."<ref>Eu, B.C. (2002), page 13.</ref> This illustrates the importance for thermodynamics of the concept of temperature.<br />
<br />
热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
<br />
A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<br />
<br />
一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数。<br />
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[[Thermal equilibrium]] is achieved when two systems in [[thermal contact]] with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<ref>[[Raj Pathria|R. K. Pathria]], 1996</ref><br />
<br />
当两个相互'''<font color="#ff8000">热接触 Thermal Contact</font>'''的系统不再有净能量交换时,就会产生'''<font color="#ff8000">热平衡 Thermal Equilibrium</font>'''。因此,如果两个系统处于热平衡,那么它们的温度是相同的<br />
<br />
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
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Thermal equilibrium occurs when a system's [[macroscopic]] thermal observables have ceased to change with time. For example, an [[ideal gas]] whose [[Distribution function (physics)|distribution function]] has stabilised to a specific [[Maxwell–Boltzmann distribution]] would be in thermal equilibrium. This outcome allows a single [[temperature]] and [[pressure]] to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<ref>de Groot, S.R., Mazur, P. (1962), p. 44.</ref><br />
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当一个系统的'''<font color="#ff8000">宏观 Macroscopic</font>'''热观测值不再随时间变化时,就会出现热平衡。例如,一种'''<font color="#ff8000">分布函数 Distribution Function</font>'''稳定到一个特定的'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''的'''<font color="#ff8000">理想气体 Ideal Gas</font>'''即处于热平衡状态。这个结果可以将单一的'''<font color="#ff8000">温度 Temperature</font>'''和'''<font color="#ff8000">压力 Pressure</font>'''归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
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Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle. It states that a non-equilibrium system evolves such as to maximize its entropy production.<br />
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定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
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==Non-equilibrium==<br />
非平衡<br />
{{Main|Non-equilibrium thermodynamics}}<br />
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Thermodynamic models <br />
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热力学模型<br />
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A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<ref>de Groot, S.R., Mazur, P. (1962), p. 43.</ref><br />
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一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数<br />
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Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
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Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle.<ref>{{cite book|last1=Ziegler|first1=H.|title=An Introduction to Thermomechanics.|date=1983|location=North Holland, Amsterdam.}}</ref><ref>{{cite journal|last1=Onsager|first1=Lars|title=Reciprocal Relations in Irreversible Processes|journal=Phys. Rev.|date=1931|volume=37|issue=4|doi=10.1103/PhysRev.37.405|bibcode=1931PhRv...37..405O|pages=405–426|doi-access=free}}</ref> It states that a non-equilibrium system evolves such as to maximize its entropy production.<ref>{{cite book|last1=Kleidon|first1=A.|last2=et.|first2=al.|title=Non-equilibrium Thermodynamics and the Production of Entropy.|date=2005|edition=Heidelberg: Springer.}}</ref><ref>{{cite journal|last1=Belkin|first1=Andrey|last2=et.|first2=al.|title=Self-Assembled Wiggling Nano-Structures and the Principle of Maximum Entropy Production|journal=Sci. Rep.|doi=10.1038/srep08323|bibcode=2015NatSR...5E8323B|pmc=4321171|pmid=25662746|volume=5|year=2015|page=8323}}</ref><br />
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定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
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Topics in control theory<br />
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控制理论主题<br />
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==See also ==<br />
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{{Portal|Chemistry}}<br />
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;Thermodynamic models 热力学模型<br />
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* [[Non-random two-liquid model]] (NRTL model) - Phase equilibrium calculations 非随机两液模型(NRTL 模型)-相平衡计算<br />
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* [[UNIQUAC]] model - Phase equilibrium calculations UNIQUAC 模型-相平衡计算<br />
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* [[Time crystal]] 时间晶体<br />
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;Topics in control theory 控制理论主题<br />
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* [[Steady state]] 稳态<br />
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* [[Transient state]] 瞬态<br />
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* [[Coefficient diagram method]] 系数图法<br />
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* [[Control reconfiguration]] 控制重构<br />
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* [[Cut-insertion theorem]] 切入定理<br />
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* [[Feedback]] 反馈<br />
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* [[H infinity]] H 无限<br />
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* [[Hankel singular value]] 汉克尔奇异值<br />
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* [[Krener's theorem]] 克雷纳定理<br />
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* [[Lead-lag compensator]] 超前滞后补偿器<br />
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* [[Minor loop feedback]] 小循环反馈<br />
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* [[Minor loop feedback|Multi-loop feedback]] 小循环反馈 | 多循环反馈<br />
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* [[Positive systems]] 正向系统<br />
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* [[Radial basis function]] 径向基底函数<br />
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Other related topics<br />
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其他相关话题<br />
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* [[Root locus]] 根轨迹<br />
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* [[Signal-flow graph]]s 信号流图<br />
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* [[Stable polynomial]] 稳定多项式<br />
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* [[State space representation]] 状态空间<br />
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* [[Underactuation]] 欠驱动<br />
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* [[Youla–Kucera parametrization]] 尤拉-库切拉参数化<br />
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* [[Markov chain approximation method]] 马尔可夫链近似法<br />
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{{colend}}<br />
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;Other related topics<br />
其他相关话题<br />
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* [[Automation and remote control]] 自动化和远程控制<br />
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* [[Bond graph]] 键合图<br />
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* [[Control engineering]] 控制工程<br />
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* [[Control–feedback–abort loop]] 控制-反馈-中止循环<br />
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* [[Controller (control theory)]] 控制器(控制理论)<br />
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* [[Cybernetics]] 控制论<br />
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* [[Intelligent control]] 智能控制<br />
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* [[Mathematical system theory]] 数学系统论<br />
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* [[Negative feedback amplifier]] 负反馈放大器<br />
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* [[People in systems and control]] 系统和控制中的人<br />
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* [[Perceptual control theory]] 知觉控制理论<br />
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* [[Systems theory]] 系统论<br />
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* [[Time scale calculus]] 时间尺度演算<br />
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{{colend}}<br />
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== 编者推荐 ==<br />
===集智文章推荐===<br />
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====[https://swarma.org/?p=21322 什么是非平衡态热力学 | 集智百科]====<br />
非平衡态热力学 Non-equilibrium thermodynamics 是热力学的一个分支,研究某些不处于热力学平衡中的物理系统<br />
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==General references==<br />
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* Cesare Barbieri (2007) ''Fundamentals of Astronomy''. First Edition (QB43.3.B37 2006) CRC Press {{ISBN|0-7503-0886-9}}, {{ISBN|978-0-7503-0886-1}}<br />
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* Hans R. Griem (2005) ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}<br />
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* C. Michael Hogan, Leda C. Patmore and Harry Seidman (1973) ''Statistical Prediction of Dynamic Thermal Equilibrium Temperatures using Standard Meteorological Data Bases'', Second Edition (EPA-660/2-73-003 2006) United States Environmental Protection Agency Office of Research and Development, Washington, D.C. [http://library.wur.nl/WebQuery/catalog/lang/1851848]<br />
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* F. Mandl (1988) ''Statistical Physics'', Second Edition, John Wiley & Sons<br />
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==References==<br />
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{{Reflist|colwidth=35em}}<br />
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==Cited bibliography==<br />
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*Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', third edition, McGraw-Hill, London, {{ISBN|0-521-25445-0}}.<br />
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*Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, {{ISBN|0-88318-797-3}}.<br />
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*Beattie, J.A., Oppenheim, I. (1979). ''Principles of Thermodynamics'', Elsevier Scientific Publishing, Amsterdam, {{ISBN|0-444-41806-7}}.<br />
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*[[Ludwig Boltzmann|Boltzmann, L.]] (1896/1964). ''Lectures on Gas Theory'', translated by S.G. Brush, University of California Press, Berkeley.<br />
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*Buchdahl, H.A. (1966). ''The Concepts of Classical Thermodynamics'', Cambridge University Press, Cambridge UK.<br />
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*[[Herbert Callen|Callen, H.B.]] (1960/1985). ''Thermodynamics and an Introduction to Thermostatistics'', (1st edition 1960) 2nd edition 1985, Wiley, New York, {{ISBN|0-471-86256-8}}.<br />
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*[[Constantin Carathéodory|Carathéodory, C.]] (1909). [https://web.archive.org/web/20160304213645/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0067&DMDID=DMDLOG_0033&L=1 Untersuchungen über die Grundlagen der Thermodynamik], ''[[Mathematische Annalen]]'', '''67''': 355–386. A translation may be found [http://neo-classical-physics.info/uploads/3/0/6/5/3065888/caratheodory_-_thermodynamics.pdf here]. Also a mostly reliable [https://books.google.com/books?id=xwBRAAAAMAAJ&q=Investigation+into+the+foundations translation is to be found] at Kestin, J. (1976). ''The Second Law of Thermodynamics'', Dowden, Hutchinson & Ross, Stroudsburg PA.<br />
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*[[Sydney Chapman (mathematician)|Chapman, S.]], [[Thomas George Cowling|Cowling, T.G.]] (1939/1970). ''The Mathematical Theory of Non-uniform gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases'', third edition 1970, Cambridge University Press, London.<br />
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*Crawford, F.H. (1963). ''Heat, Thermodynamics, and Statistical Physics'', Rupert Hart-Davis, London, Harcourt, Brace & World, Inc.<br />
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*de Groot, S.R., Mazur, P. (1962). ''Non-equilibrium Thermodynamics'', North-Holland, Amsterdam. Reprinted (1984), Dover Publications Inc., New York, {{ISBN|0486647412}}.<br />
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*Denbigh, K.G. (1951). ''Thermodynamics of the Steady State'', Methuen, London.<br />
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*Eu, B.C. (2002). ''Generalized Thermodynamics. The Thermodynamics of Irreversible Processes and Generalized Hydrodynamics'', Kluwer Academic Publishers, Dordrecht, {{ISBN|1-4020-0788-4}}.<br />
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*Fitts, D.D. (1962). ''Nonequilibrium thermodynamics. A Phenomenological Theory of Irreversible Processes in Fluid Systems'', McGraw-Hill, New York.<br />
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*[[Josiah Willard Gibbs|Gibbs, J.W.]] (1876/1878). On the equilibrium of heterogeneous substances, ''Trans. Conn. Acad.'', '''3''': 108–248, 343–524, reprinted in ''The Collected Works of J. Willard Gibbs, Ph.D, LL. D.'', edited by W.R. Longley, R.G. Van Name, Longmans, Green & Co., New York, 1928, volume 1, pp.&nbsp;55–353.<br />
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*Griem, H.R. (2005). ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}.<br />
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*[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', fifth revised edition, North-Holland, Amsterdam.<br />
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*Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of ''Thermodynamics'', pages 1–97 of volume 1, ed. W. Jost, of ''Physical Chemistry. An Advanced Treatise'', ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081.<br />
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*[[John Gamble Kirkwood|Kirkwood, J.G.]], Oppenheim, I. (1961). ''Chemical Thermodynamics'', McGraw-Hill Book Company, New York.<br />
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*Landsberg, P.T. (1961). ''Thermodynamics with Quantum Statistical Illustrations'', Interscience, New York.<br />
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*{{cite journal |last1=Lieb |first1=E. H. |last2=Yngvason |first2=J. |year=1999 |title=The Physics and Mathematics of the Second Law of Thermodynamics |journal=Phys. Rep. |volume=310 |issue= 1|pages=1–96 |doi= 10.1016/S0370-1573(98)00082-9|arxiv = cond-mat/9708200 |bibcode = 1999PhR...310....1L |s2cid=119620408 }}<br />
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*Levine, I.N. (1983), ''Physical Chemistry'', second edition, McGraw-Hill, New York, {{ISBN|978-0072538625}}.<br />
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*{{cite journal | last1 = Maxwell | first1 = J.C. | authorlink = James Clerk Maxwell | year = 1867 | title = On the dynamical theory of gases | url = | journal = Phil. Trans. Roy. Soc. London | volume = 157 | issue = | pages = 49–88 }}<br />
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*[[Philip M. Morse|Morse, P.M.]] (1969). ''Thermal Physics'', second edition, W.A. Benjamin, Inc, New York.<br />
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*Münster, A. (1970). ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London.<br />
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*[[J.R. Partington|Partington, J.R.]] (1949). ''An Advanced Treatise on Physical Chemistry'', volume 1, ''Fundamental Principles. The Properties of Gases'', Longmans, Green and Co., London.<br />
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*[[Brian Pippard|Pippard, A.B.]] (1957/1966). ''The Elements of Classical Thermodynamics'', reprinted with corrections 1966, Cambridge University Press, London.<br />
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* [[Max Planck|Planck. M.]] (1914). [https://archive.org/details/theoryofheatradi00planrich ''The Theory of Heat Radiation''], a translation by Masius, M. of the second German edition, P. Blakiston's Son & Co., Philadelphia.<br />
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*[[Ilya Prigogine|Prigogine, I.]] (1947). ''Étude Thermodynamique des Phénomènes irréversibles'', Dunod, Paris, and Desoers, Liège.<br />
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*[[Ilya Prigogine|Prigogine, I.]], Defay, R. (1950/1954). ''Chemical Thermodynamics'', Longmans, Green & Co, London.<br />
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*Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005). ''Physical Chemistry'', fourth edition, Wiley, Hoboken NJ.<br />
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*[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966). ''Elements of Thermodynamics'', Addison-Wesley Publishing, Reading MA.<br />
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*{{cite journal|last=Thomson|first=W.|author-link=William Thomson, 1st Baron Kelvin|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Transactions of the Royal Society of Edinburgh|date=March 1851|volume=XX|issue=part II|pages=261–268; 289–298}} Also published in {{cite journal|last=Thomson|first=W.|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Phil. Mag. |date=December 1852 |volume=IV |series=4 |issue=22 |pages=8–21 |url=https://archive.org/details/londonedinburghp04maga |accessdate=25 June 2012}}<br />
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*[[László Tisza|Tisza, L.]] (1966). ''Generalized Thermodynamics'', M.I.T Press, Cambridge MA.<br />
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*[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963). ''Lectures in Statistical Mechanics'', American Mathematical Society, Providence RI.<br />
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*Waldram, J.R. (1985). ''The Theory of Thermodynamics'', Cambridge University Press, Cambridge UK, {{ISBN|0-521-24575-3}}.<br />
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*[[Mark Zemansky|Zemansky, M.]] (1937/1968). ''Heat and Thermodynamics. An Intermediate Textbook'', fifth edition 1967, McGraw–Hill Book Company, New York.<br />
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== External links ==<br />
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Category:Equilibrium chemistry<br />
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类别: 平衡化学<br />
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*[http://ads.harvard.edu/books/1989fsa..book/AbookC15.pdf Breakdown of Local Thermodynamic Equilibrium] George W. Collins, The Fundamentals of Stellar Astrophysics, Chapter 15<br />
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Category:Thermodynamic cycles<br />
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类别: 热力循环<br />
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*[http://spiff.rit.edu/classes/phys440/lectures/lte/lte.html Thermodynamic Equilibrium, Local and otherwise] lecture by Michael Richmond<br />
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Category:Thermodynamic processes<br />
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类别: 热力学过程<br />
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*[http://journals.ametsoc.org/doi/abs/10.1175/1520-0469%281970%29027%3C0711:NLTEIC%3E2.0.CO%3B2 Non-Local Thermodynamic Equilibrium in Cloudy Planetary Atmospheres] Paper by R. E. Samueison quantifying the effects due to non-LTE in an atmosphere<br />
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Category:Thermodynamic systems<br />
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类别: 热力学系统<br />
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*[http://scienceworld.wolfram.com/physics/LocalThermodynamicEquilibrium.html Local Thermodynamic Equilibrium]<br />
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Category:Thermodynamics<br />
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分类: 热力学<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Thermodynamic equilibrium]]. Its edit history can be viewed at [[平衡热力学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%B9%B3%E8%A1%A1%E7%83%AD%E5%8A%9B%E5%AD%A6&diff=21461平衡热力学2021-01-30T11:18:16Z<p>Jxzhou:/* Relation of exchange equilibrium between systems */</p>
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<div>此词条暂由小竹凉翻译,翻译字数共5339,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{short description|State of thermodynamic system(s) where no net macroscopic flow of matter or energy occurs}}<br />
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'''Thermodynamic equilibrium''' is an [[axiomatic]] concept of [[thermodynamics]]. It is an internal [[State variables|state]] of a single [[thermodynamic system]], or a relation between several thermodynamic systems connected by more or less permeable or impermeable [[Thermodynamic system#Walls|walls]]. In thermodynamic equilibrium there are no net [[macroscopic]] [[Flow (mathematics)|flows]] of [[matter]] or of [[energy]], either within a system or between systems. <br />
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Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium there are no net macroscopic flows of matter or of energy, either within a system or between systems. <br />
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'''热力学平衡'''是'''<font color="#ff8000">热力学 Thermodynamics</font>'''的一个'''<font color="#ff8000">不言自明的 Axiomatic</font>'''概念。它是单个'''<font color="#ff8000">热力学系统 Thermodynamic System</font>'''的内部'''<font color="#ff8000">状态 State</font>''',或者是几个热力学系统之间通过或多或少的渗透或不渗透的'''<font color="#ff8000">壁 Wall</font>'''连接的关系。无论是在一个系统内还是在系统之间,在热力学平衡中不存在'''<font color="#ff8000">物质 Matter</font>'''或'''<font color="#ff8000">能量 Energy</font>'''的净'''<font color="#ff8000">宏观 Macroscopic</font>''' '''<font color="#ff8000">流动 Flow</font>'''。<br />
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In a system that is in its own state of internal thermodynamic equilibrium, no [[macroscopic]] change occurs. <br />
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In a system that is in its own state of internal thermodynamic equilibrium, no macroscopic change occurs. <br />
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在一个处于内部热力学平衡状态的系统中,不会发生'''<font color="#ff8000">宏观 Macroscopic</font>'''变化。<br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual [[Thermal equilibrium|thermal]], [[Mechanical equilibrium|mechanical]], [[Chemical equilibrium|chemical]], and [[Radiative equilibrium|radiative]] equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a [[thermodynamic operation]]. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a thermodynamic operation. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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相互热力学平衡的体系同时处于互相之间的'''<font color="#ff8000">热 Thermal</font>'''平衡、'''<font color="#ff8000">力学 Mechanical</font>'''平衡、'''<font color="#ff8000">化学 Chemical</font>'''平衡和'''<font color="#ff8000">辐射 Radiative</font>'''平衡。系统可以处于其中一种相互平衡状态,尽管其他状态未平衡。在热力学平衡中所有的平衡同时并且无限期地保持,直到被'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''打破。在一个宏观平衡中,微观交换是完全或几乎完全平衡的;这是对宏观平衡概念的物理解释。<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform [[temperature]]. Its [[Intensive and extensive properties|intensive properties]], other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform temperature. Its intensive properties, other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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一个处于内部热力学状态平衡的热力学系统具有空间均匀的'''<font color="#ff8000">温度 Temperature</font>'''。除了温度以外,它的'''<font color="#ff8000">强度性质 Intensive Properties</font>'''可以由于周围环境施加的不变的长程力场而导致空间不均匀性。<br />
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In systems that are at a state of [[non-equilibrium]] there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a '''meta-stable equilibrium'''.<br />
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In systems that are at a state of non-equilibrium there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a meta-stable equilibrium.<br />
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相比之下,处于'''<font color="#ff8000">非平衡状态 non-equilibrium</font>'''的系统中有物质或能量的净流动。如果这些变化可以在一个还没有发生的系统中被触发,那么这个系统就被称为处于一个'''亚稳定的平衡状态'''。<br />
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Though not a widely named a "law," it is an [[axiom]] of thermodynamics that there exist states of thermodynamic equilibrium. The [[second law of thermodynamics]] states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the [[entropy|entropies]] of the portions.<br />
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Though not a widely named a "law," it is an axiom of thermodynamics that there exist states of thermodynamic equilibrium. The second law of thermodynamics states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the entropies of the portions.<br />
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虽然不是一个广泛命名的“定律” ,但存在热力学平衡状态是一个热力学'''<font color="#ff8000">公理 Axiom</font>'''。'''<font color="#ff8000">热力学第二定律 second law of thermodynamics</font>'''指出,当一个物质体从一个平衡状态开始,在这个状态中,它的一部分被或多或少渗透或不渗透的分区保持在不同的状态,并且是孤立的,热力学操作移除分区或使分区更具渗透性,然后它会自发地达到自己内部热力学平衡的新状态,并伴随着部分'''<font color="#ff8000">熵 Entropy</font>'''的总和增加。<br />
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== Overview 概览==<br />
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{{Thermodynamics|cTopic=[[Thermodynamic system|Systems]]}}<br />
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Classical thermodynamics deals with states of [[dynamic equilibrium]]. The state of a system at thermodynamic equilibrium is the one for which some [[thermodynamic potential]] is minimized, or for which the [[entropy]] (''S'') is maximized, for specified conditions. One such potential is the [[Helmholtz free energy]] (''A''), for a system with surroundings at controlled constant temperature and volume:<br />
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Classical thermodynamics deals with states of dynamic equilibrium. The state of a system at thermodynamic equilibrium is the one for which some thermodynamic potential is minimized, or for which the entropy (S) is maximized, for specified conditions. One such potential is the Helmholtz free energy (A), for a system with surroundings at controlled constant temperature and volume:<br />
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经典热力学研究'''<font color="#ff8000">动态平衡 Dynamic Equilibrium</font>'''的状态。系统的热力学平衡状态是对于特定的条件,一些'''<font color="#ff8000">热力学势 Thermodynamic Potential</font>'''被最小化,或者'''<font color="#ff8000">熵 Entropy</font>'''(S)被最大化。对于一个周围环境温度和体积恒定的系统,其中一个这样的热力学势是'''<font color="#ff8000">亥姆霍兹自由能 Helmholtz Free Energy</font>'''(A):<br />
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:<math>A = U - TS</math><br />
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<math>A = U - TS</math><br />
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A = U-TS<br />
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Another potential, the [[Gibbs free energy]] (''G''), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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Another potential, the Gibbs free energy (G), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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在恒定温度和压力的系统中,另一个热力学势'''<font color="#ff8000">吉布斯自由能 Gibbs Free Energy</font>'''(G)在热力学平衡状态最小:<br />
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:<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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where ''T'' denotes the absolute thermodynamic temperature, ''P'' the pressure, ''S'' the entropy, ''V'' the volume, and ''U'' the internal energy of the system.<br />
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where T denotes the absolute thermodynamic temperature, P the pressure, S the entropy, V the volume, and U the internal energy of the system.<br />
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其中 T 表示热力学绝对温度,P 表示压强,S 表示熵,V 表示体积,U 表示体系的内能。<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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热力学平衡是一种独特的稳定定态,当系统长时间与周围环境相互作用时,它可以被接近或最终到达。上述势能是数学构造的热力学量,在特定的环境条件下最小化。<br />
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== Conditions 条件==<br />
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* For a completely isolated system, ''S'' is maximum at thermodynamic equilibrium. 对于一个完全孤立的系统,S在热力学平衡中取最大值。<br />
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* For a system with controlled constant temperature and volume, ''A'' is minimum at thermodynamic equilibrium. 对于一个恒定温度和体积的系统来说,A在热力学平衡中取最小值。<br />
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* For a system with controlled constant temperature and pressure, ''G'' is minimum at thermodynamic equilibrium. 对于一个恒温恒压的系统,G在热力学平衡中取最小值。<br />
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The various types of equilibriums are achieved as follows:<br />
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The various types of equilibriums are achieved as follows:<br />
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实现各种类型的平衡的方法如下:<br />
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*Two systems are in ''thermal equilibrium'' when their [[temperature]]s are the same. 当两个系统的'''<font color="#ff8000">温度 Temperature</font>'''相同时,它们就处于''热平衡状态''<br />
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*Two systems are in ''mechanical equilibrium'' when their [[pressure]]s are the same. 当两个体系的'''<font color="#ff8000">压力 Pressure</font>'''相同时,它们就处于''力学平衡''<br />
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*Two systems are in ''diffusive equilibrium'' when their [[chemical potential]]s are the same. 当两个题体系的'''<font color="#ff8000">化学势 Chemical Potential</font>'''相同时,它们就处于''扩散平衡''<br />
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*All [[forces]] are balanced and there is no significant external driving force.<br />
所有的'''<font color="#ff8000">力 Force</font>'''都是平衡的,没有明显的外部驱动力<br />
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==Relation of exchange equilibrium between systems==<br />
系统之间的交换均衡关系<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability.<ref name="Nster_a">Münster, A. (1970), p. 49.</ref> When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability. When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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通常,热力学系统的周围环境也可以被看作是另一个热力学系统。在这种观点中,我们可以把系统及其周围环境看作是相互接触的两个系统,远程作用力也将它们联系在一起。系统的包围物是两个系统之间的接触面或边界。在热力学形式中,该表面被认为具有特定的渗透性质。例如,接触的表面可能被认为只能透热,使能量只能作为热传递。当远程力在时间上不发生变化,两个系统之间的热量传递减慢并最终永久停止时,这两个系统被称为热平衡; 这就是接触平衡的一个例子。其它类型的接触平衡可用其它类型的比渗透率来定义。当两个系统对于某一特定类型的渗透率处于接触平衡时,它们具有属于该特定类型渗透率的强变量的共同值。这种强度变量的例子有温度、压力、化学势。<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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接触平衡也可视为交换平衡。在接触平衡状态下,两系统之间某些量的传递速率存在零平衡。例如,对于只能透热的壁,内能作为热在两个系统之间的扩散速率是相等并反向的。两个系统之间的绝热壁只对作为功传递的能量有渗透作用; 在力学平衡,两个系统之间作为功的能量传递速率相等且相反。如果是一个简单的壁,那么通过它的体积转移率也是相等且相反的; 即它两边的压力是相等的。如果绝热壁比较复杂,有一种杠杆,有一个面积比,那么两个体系在交换平衡中的压力与体积交换比成反比,这使得转移率的零平衡作功。<br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<ref name="Planck 1914 40">[[Max Planck|Planck. M.]] (1914), p. 40.</ref><br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<br />
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辐射交换可以发生在两个不同的系统之间。当两个体系温度相同时,辐射交换平衡占优势。<br />
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==Thermodynamic state of internal equilibrium of a system==<br />
系统内部平衡的热力学状态<br />
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A collection of matter may be entirely [[Isolated system|isolated]] from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium.<ref>Haase, R. (1971), p. 4.</ref><ref>Callen, H.B. (1960/1985), p. 26.</ref> (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics.<ref>{{Cite journal |doi = 10.1119/1.4914528|bibcode = 2015AmJPh..83..628M|title = Time and irreversibility in axiomatic thermodynamics|year = 2015|last1 = Marsland|first1 = Robert|last2 = Brown|first2 = Harvey R.|last3 = Valente|first3 = Giovanni|journal = American Journal of Physics|volume = 83|issue = 7|pages = 628–634}}</ref> One textbook<ref>[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963), p. 5.</ref> calls it the "zeroth law", remarking that the authors think this more befitting that title than its [[Zeroth law of thermodynamics|more customary definition]], which apparently was suggested by [[Ralph H. Fowler|Fowler]].)<br />
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A collection of matter may be entirely isolated from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium. (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics. One textbook calls it the "zeroth law", remarking that the authors think this more befitting that title than its more customary definition, which apparently was suggested by Fowler.)<br />
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物质的集合可能与其周围的环境完全'''<font color="#ff8000">孤立 Isolated</font>'''。如果它在无限长的时间内一直保持不受干扰,按照经典热力学假定,它处于一个没有发生任何变化,没有流动的状态,即内部平衡的热力学状态。(这种假设有时被称为“负第一”热力学定律,但并不常见。有教科书称之为“第零定律” ,作者'''<font color="#ff8000">福勒 Fowler</font>'''认为这个名称是'''<font color="#ff8000">更符合惯例的定义 More Customary Definition</font>'''。)<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a [[thermodynamic operation]] be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a thermodynamic operation be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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这种状态是所谓的经典热力学或平衡态热力学的主要关注点,因为它们是系统中被认为在这门学科中得到很好定义的唯一状态。一个与另一个系统处于接触平衡状态可以被一个'''<font color="#ff8000">热力运行 Thermodynamic Operation</font>'''隔离,在隔离发生时,其内部不会发生任何变化。因此,一个与另一个系统处于接触平衡状态时也可以被视为处于其自身的内部热力学平衡状态。<br />
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==Multiple contact equilibrium==<br />
多点接触平衡<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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热力学形式论允许一个系统同时与其他多个系统接触,这些系统可能也可能没有相互接触,且这些接触具有不同的渗透性。如果这些系统都与世界其他部分相互隔离,那么它们彼此之间就会达到各自的接触平衡。<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy.<ref name="Caratheodory">Carathéodory, C. (1909).</ref><ref>Prigogine, I. (1947), p. 48.</ref><ref>Landsberg, P. T. (1961), pp. 128–142.</ref><ref>Tisza, L. (1966), p. 108.</ref> Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy. Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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如果几个系统彼此之间没有绝热壁,但是它们与世界其他部分共同隔离,那么它们就会达到多重接触平衡状态,且有共同的温度,内能和熵。在众多变量中,这是温度的一个独特性质。即使在远距离作用力存在的情况下,它也是有效的。(也就是说,没有“力”可以维持温度的差异。)举个例子,在热力学平衡的一个垂直的引力场系统中,顶部壁面的压力比底部壁面的压力小,但是各处的温度都是一样的。<br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural [[thermodynamic process]].<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), § 1.12.</ref> It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings.<ref>Levine, I.N. (1983), p. 40.</ref><ref>Lieb, E.H., Yngvason, J. (1999), pp. 17–18.</ref> The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of [[Second law of thermodynamics#Description#Kelvin statement|"inanimate" agency]]; a system in thermodynamic equilibrium is inanimate.<ref>[[William Thomson, 1st Baron Kelvin|Thomson, W.]] (1851).</ref><br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural thermodynamic process. It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings. The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of "inanimate" agency; a system in thermodynamic equilibrium is inanimate.<br />
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热力运行可能作为一个事件发生在周围环境的壁上,既不直接影响与周围环境联系的壁,也不直接影响其内部,且发生在一个明确的有限的时间内。例如,一个固定的绝热壁可以在环境中被放置或拆除。由于这种操作仅限于周围环境,系统可能会在一段时间内远离自身最初的内部状态---- 热力学平衡。根据热力学第二定律的说法,整体经历了变化并最终与周围环境达到了新的平衡。继Planck之后,这一连串的事件被称为自然'''<font color="#ff8000">热力学过程 Thermodynamic Process</font>'''。即使在这个过程中,当系统和周围环境都不处于明确的内部平衡状态时,存在着暂时偏离热力学平衡的现象,由于初始状态和最终状态都是热力学平衡的,这在平衡热力学中也是允许的。一个自然过程在其主要部分中以有限的速率进行,因此,它从根本上不同于虚构的准静态“过程”;即不在整个过程中无限缓慢地进行而且虚构地“可逆”。经典热力学允许,即使一个过程可能需要很长的时间才能达到热力学平衡,如果主要部分的过程是在一个有限的比率中,那么它被认为是自然的,并受制于热力学第二定律,即不可逆的。工程设计的机器、人工设备和操作是允许在周围环境中进行的。允许在环境中而不是在系统中进行此类操作和设备,是开尔文在他的一个热力学第二定律的陈述中提到'''<font color="#ff8000">无生命机构 Inanimate Agency</font>'''的原因; 在热力学平衡的系统是无生命的。<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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否则,热力运行可能会直接影响系统的壁。<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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通常可以很方便地假设周围的某些子系统比系统大得多,以至于这个过程只能影响周围子系统的强度变量,然后将这些子系统称为相关强度变量的储备库。<br />
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== Local and global equilibrium ==<br />
局部和全局均衡<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by [[intensive quantity|intensive]] parameters. As an example, [[temperature]] controls [[Heat equation|heat exchanges]]. ''Global thermodynamic equilibrium'' (GTE) means that those [[intensive quantity|intensive]] parameters are homogeneous throughout the whole system, while ''local thermodynamic equilibrium'' (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by intensive parameters. As an example, temperature controls heat exchanges. Global thermodynamic equilibrium (GTE) means that those intensive parameters are homogeneous throughout the whole system, while local thermodynamic equilibrium (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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区分全局性和局部性热力学平衡是很有用的。在热力学中,系统内部和系统与外部之间的交换是由'''<font color="#ff8000">强度 Intensive</font>'''参数控制的。例如,'''<font color="#ff8000">温度 Temperature</font>'''控制'''<font color="#ff8000">热交换 Heat Equation</font>'''。全局热力学平衡(GTE)意味着这些'''<font color="#ff8000">强度 Intensive</font>'''参数在整个系统中是均匀的,而局部热力学平衡(LTE)意味着这些强度参数在空间和时间上是变化的,但变化如此缓慢,以至于对于任何一点,人们都可以假设在某个邻近的某个热力学平衡。<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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如果对系统的描述要求强度参数的变化过大,那么这些强度参数的定义所依据的假设本身就会破裂,系统将既不处于全局平衡,也不处于局部平衡。例如,粒子需要一定数量的碰撞来平衡其周围环境。如果在这些碰撞中移动的平均距离使它离开平衡邻域,它将永远不会平衡,也就不会有 LTE。根据定义,温度与平衡邻域的平均内部能量成正比。由于没有达到平衡邻域,温度的概念就不成立,温度也就变得不确定。<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to [[massive]] particles. In a [[radiation|radiating]] gas, the [[photon]]s being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to massive particles. In a radiating gas, the photons being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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值得注意的是,这种局部平衡可能只适用于系统中的某个粒子子集。例如,LTE 通常只适用于'''<font color="#ff8000">大 Massive</font>'''质量粒子。在'''<font color="#ff8000">辐射 Radiation</font>'''气体中,被气体发射和吸收的'''<font color="#ff8000">光子 Photon</font>'''不需要彼此在一个热力学平衡内,或与气体中的大量粒子在一起,LTE 才能存在。在某些情况下,自由电子并不需要与大得多的原子或分子处于平衡状态,LTE 才能存在。<br />
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As an example, LTE will exist in a glass of water that contains a melting [[ice cube]]. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the [[Maxwell–Boltzmann distribution]] for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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As an example, LTE will exist in a glass of water that contains a melting ice cube. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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例如,LTE 将存在于一个装有融化的'''<font color="#ff8000">冰块 Ice Cube</font>'''的水杯中。玻璃杯内的温度可以在任何时候定义,但是离冰块近的地方要比离冰块远的地方冷。如果观察到位于给定点附近的分子的能量,它们将按照麦克斯韦-波兹曼分布在一定温度下的分布。如果观察到位于另一点附近的分子的能量,它们将按照'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''分布到另一个温度。<br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural [[transport phenomena]] may lead a system from local to global thermodynamic equilibrium. Going back to our example, the [[diffusion]] of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<ref>H.R. Griem, 2005</ref><br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural transport phenomena may lead a system from local to global thermodynamic equilibrium. Going back to our example, the diffusion of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<br />
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局部热力学平衡不需要局部或全局的平稳性。换句话说,每一个小区域不需要有一个恒定的温度。然而,它确实要求每个小的局部变化缓慢到足以维持其局部麦克斯韦-波兹曼分布的分子速度。全局非平衡态只有通过系统与外界的交换才能保持稳定。例如,通过在水杯中不断添加细粉冰来补偿熔化,并持续排出融水,可以保持全球稳定的静止状态。自然'''<font color="#ff8000">迁移现象 Transport Phenomena</font>'''可能导致一个从局部到全局的热力学平衡系统。回顾我们的例子,热量的扩散将导致我们的玻璃杯水流向全局热力学平衡,在这种状态下,玻璃杯的温度是完全均匀的。<br />
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==Reservations==<br />
保留意见<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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学识渊博的笔者在热力学领域对热力学平衡描述时,经常对他们的描述附加条件或保留意见。有些笔者含蓄地保留了或多或少的空白,以待说明。<br />
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For example, one widely cited writer, [[Herbert Callen|H. B. Callen]] writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. ''Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!''"<ref>Callen, H.B. (1960/1985), p. 15.</ref><br />
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For example, one widely cited writer, H. B. Callen writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!"<br />
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例如,一位被广泛引用的作家'''<font color="#ff8000">H.B.卡伦 H.B.Callen</font>'''在这里写道: “实际上,很少有系统处于绝对和真正的平衡状态。”他提到了放射性过程,认为它们可能需要“宇宙时间才能完成,因此通常可以忽略”。他补充道: “在实践中,平衡的标准是循环的。在操作上,如果一个系统的性质一致地用热力学理论来描述,那么它就处于平衡状态! ”<br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<ref>Beattie, J.A., Oppenheim, I. (1979), p. 3.</ref><br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<br />
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J.A.贝蒂和 I.奥本海姆写道: “坚持对平衡定义的严格解释,将排除热力学应用于实际系统的所有状态。”<br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment",<ref>Callen, H.B. (1960/1985), p. 485.</ref> and cited by Adkins as having written a "classic text",<ref>Adkins, C.J. (1968/1983), p. ''xiii''.</ref> [[Brian Pippard|A.B. Pippard]] writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<ref>Pippard, A.B. (1957/1966), p. 6.</ref><br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment", and cited by Adkins as having written a "classic text", A.B. Pippard writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<br />
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Callen引用另一位作者的话说,他给出了“学术且严谨的论述” ,Adkins引用他的话说,他写了一本“经典著作”—— '''<font color="#ff8000">A.B.皮帕德 A.B.Pippard</font>'''在文中写道: “只要时间足够长,过冷水蒸汽最终会凝结,... ..。时间可能是漫长的,也许长达10年或者更长。就大多数目的而言,只要这种迅速的变化不是人为地刺激,这些系统就可以被视为处于平衡状态。”<br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster">Münster, A. (1970), p. 53.</ref><br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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另一位作者A.Münster,写道。他观察到热核反应发生的速度非常缓慢,以至于在热力学中可以忽略不计。他评论道: “‘绝对平衡’或‘所有可想象过程的平衡’的概念没有物理意义。”他说: “ ... 我们只能考虑特定过程和确定的实验条件下的平衡。”<br />
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According to [[László Tisza|L. Tisza]]: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<ref>Tisza, L. (1966), p. 119.</ref><br />
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According to L. Tisza: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<br />
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根据'''<font color="#ff8000">L.缇莎 L.Tisza</font>'''的说法: “ ... 在讨论接近绝对零度的现象时。经典理论的绝对预测变得特别模糊,因为在非平衡状态下发生冻结是非常普遍的。”<br />
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==Definitions==<br />
定义<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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一个系统最普遍的热力学平衡是通过与周围环境的接触,允许所有化学物质和各种能量同时通过。热力学平衡中的系统以均匀加速度在空间中运动,但此时不能改变其形状或大小; 因此它是由空间中的刚性体积来定义的。它可能存在于外力场中,由远远大于系统本身的外部因素决定,因此系统内的事件不会对外力场产生相当大的影响。只有当外力场是均匀的,并且确定了它的均匀加速度,或者它处于一个非均匀力场中,但是由于表面的局部力,例如机械压力,使它保持静止时,这个系统才能处于热力学平衡。<br />
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Thermodynamic equilibrium is a [[primitive notion]] of the theory of thermodynamics. According to [[Philip M. Morse|P.M. Morse]]: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are ''not'' conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments."<ref>[[Philip M. Morse|Morse, P.M.]] (1969), p. 7.</ref> This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<ref>Bailyn, M. (1994), p. 20.</ref><br />
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Thermodynamic equilibrium is a primitive notion of the theory of thermodynamics. According to P.M. Morse: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are not conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments." This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<br />
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热力学平衡是热力学理论的一个'''<font color="#ff8000">基本概念 Primitive Notion</font>'''。'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''说: “应该强调的是,存在热力学状态这一事实,以及存在由平衡态唯一指定的热力学变量这一事实,并不是从某些哲学第一原理得出的逻辑结论。这些结论不可避免地来自两个多世纪的实验。”这意味着热力学平衡不能仅仅用热力学的其他理论概念来定义。M.Bailyn提出了一个基本的热力学定律理论,它定义并假设了热力学平衡的存在。<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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热力学平衡的教科书定义通常被仔细说明,并有些保留。<br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<ref>Münster, A. (1970), p. 52.</ref><br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<br />
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例如,A. Münster写道:“当系统中没有以可测量的速度发生状态变化时,隔离系统处于热力学平衡状态。”这里有两项保留:系统是孤立的;任何状态的变化都是不可估量的缓慢。他通过对在室温且没有催化剂的情况下混合氧和氢的说明,讨论了第二个条件。Münster指出,热力学平衡状态所描述的宏观变量比给定系统任何其他状态都少。这是部分,但不完全是,因为系统内和系统内的所有流都是零。<br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in ''equilibrium''.<ref>Haase, R. (1971), pp. 3–4.</ref><br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in equilibrium.<br />
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R. Haase's的热力学演示并不从对热力学平衡的限制开始,因为他打算考虑非平衡态热力学。他考虑一个具有时间不变性质的任意系统。他通过切断除外力场以外的所有外部影响来测试它的热力学平衡。如果在绝缘之后,没有任何变化,他说,系统处于平衡状态。<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness".<ref>Callen, H.B. (1960/1985), p. 13.</ref> This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness". This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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在一个标题为“热力学平衡”的章节中,H.B. Callen在段落定义了平衡状态.他指出,它们“是由系统内部的内在因素决定的”。它们是“终端状态” ,随着时间的推移,系统会以“冰川般缓慢”的速度朝着这个终端状态演化。这个说法并没有明确,对于热力学平衡系统必须是孤立的;;Callen也没有说明他所说的“内在因素”是什么意思。<br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<ref>Adkins, C.J. (1968/1983), p. ''7''.</ref><br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<br />
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另一位教科书作者,C.J.Adkins,明确允许热力学平衡在非孤立的系统中发生。然而,他的系统在物质转移方面是封闭的。他写道: “一般来说,热力学平衡的方法包括热和类似变动与周围环境的相互作用。”他将这种热力学平衡与只有通过热接触才能进行能量传递的热平衡相区别。<br />
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Another textbook author, [[J.R. Partington]], writes: "(i) ''An equilibrium state is one which is independent of time''." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..."<ref>Partington, J.R. (1949), p. 161.</ref> This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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Another textbook author, J.R. Partington, writes: "(i) An equilibrium state is one which is independent of time." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..." This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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另一位教科书作者'''<font color="#ff8000">J.R.帕廷顿 J.R.Partington</font>'''写道: “(i)平衡状态是独立于时间的状态。”但是,在提到“只是明显处于平衡状态”的系统时,他补充说: “这样的系统处于‘虚假平衡’状态。帕廷顿的陈述没有明确指出平衡是指一个孤立的系统。和Münster一样,Partington也指的是氧和氢的混合物。他补充说:“在一个真正的平衡状态,任何影响状态的外部条件的最小变化都会产生一个微小的状态变化... ... ”这个条件意味着热力学平衡必须在小的扰动下保持稳定; 这个要求对于热力学平衡的严格意义是必不可少的。<br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, ''thermodynamic—equilibrium.''"<ref>Crawford, F.H. (1963), p. 5.</ref><br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, thermodynamic—equilibrium."<br />
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在F.H.Crawford的一本学生教科书中,有一个标题为“热力学平衡”的章节。它区分了几种流动的驱动因素,然后说: “这些是孤立系统明显普遍趋向于完全机械、热、化学和电力状态的例子——或者简单地说,热力学平衡状态。”<br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in ''equilibrium''."<ref>Buchdahl, H.A. (1966), p. 8.</ref> Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being ''in equilibrium'' so long as experimental tests show that 'slow' transitions are in effect reversible."<ref>Buchdahl, H.A. (1966), p. 111.</ref> It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<ref>Adkins, C.J. (1968/1983), p. 8.</ref><br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in equilibrium." Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being in equilibrium so long as experimental tests show that 'slow' transitions are in effect reversible." It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<br />
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H.A. Buchdahl的一本关于经典热力学的专著考虑了热力学系统的平衡,而实际上并没有写热力学平衡一词。Buchdahl在提到封闭的物质交换系统时写道: “如果一个系统处于一个适当的静态状态,那么它将被称为处于平衡状态。”出于热力学描述的目的,Buchdahl的专著也讨论了非晶态玻璃。它说: “更准确地说,只要实验测试表明‘慢’跃迁实际上是可逆的,玻璃就可以被认为处于平衡状态。”通常来说不会将这一条件作为热力学平衡定义的一部分,而是假定相反的情况:如果热力学平衡中的一个体受到足够慢的过程的影响,则该过程可被视为足够接近可逆,并且该物体在过程中足够接近热力学平衡。<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of ''contact equilibrium''. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by [[Constantin Carathéodory|C. Carathéodory]], and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster" /> Thermodynamic equilibrium for an open system means that, with respect to every relevant kind of selectively permeable wall, contact equilibrium exists when the respective intensive parameters of the system and surroundings are equal.<ref name="Nster_a" /> This definition does not consider the most general kind of thermodynamic equilibrium, which is through unselective contacts. This definition does not simply state that no current of matter or energy exists in the interior or at the boundaries; but it is compatible with the following definition, which does so state.<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of contact equilibrium. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by C. Carathéodory, and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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通过引入接触平衡的概念,A. Münster仔细地扩展了孤立系统热力学平衡的定义。这指定了在考虑非孤立系统的热力学平衡时允许的特定过程,并特别关心开放系统,这些开放系统可能从周围环境获得或丢失物质。利益系统和周围系统之间的接触平衡,通过一种特殊的壁与利益系统接触,其余的连接系统是孤立的。这种特殊类型的壁也被'''<font color="#ff8000">C.喀喇西奥多里 C.Carathéodory</font>'''考虑过,其他作家也提到过。它们具有选择渗透性。它们可能只对机械工作有渗透性,或者只对热有渗透性,或者只对某种特定的化学物质有渗透性。每个接触平衡定义了一个强度参数; 例如,只能透热的壁定义了一个经验温度。对于感兴趣的体系中每一种化学成分,都可以存在接触平衡。在接触平衡中,尽管有可能通过选择性渗透壁进行交换,感兴趣的系统是不变的,好像它处在孤立的热力学平衡。这个方案遵循的一般规则是: “ ... ... 我们只能考虑特定过程和特定实验条件下的平衡。”<br />
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[[Mark Zemansky|M. Zemansky]] also distinguishes mechanical, chemical, and thermal equilibrium. He then writes: "When the conditions for all three types of equilibrium are satisfied, the system is said to be in a state of thermodynamic equilibrium".<ref>[[Mark Zemansky|Zemansky, M.]] (1937/1968), p. 27.</ref><br />
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'''<font color="#ff8000">M.泽曼斯基 M.Zemansky</font>'''还区分了机械、化学和热平衡。他接着写道: “当这三种均衡的条件都满足时,系统就处于热力学平衡状态。”<br />
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P.M. Morse writes that thermodynamics is concerned with "states of thermodynamic equilibrium". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<br />
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[[Philip M. Morse|P.M. Morse]] writes that thermodynamics is concerned with "''states of thermodynamic equilibrium''". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<ref>[[Philip M. Morse|Morse, P.M.]] (1969), pp. 6, 37.</ref><br />
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'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''写道,热力学关注的是“热力学平衡状态”。在讨论物体与周围热源之间的热量传递时,他也使用了“热平衡”这个短语,尽管没有明确定义一个特殊的术语“热平衡”<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "full thermodynamic equilibrium state".<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "''full'' thermodynamic equilibrium state".<ref>Waldram, J.R. (1985), p. 5.</ref><br />
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J.R. Waldram写到了“一个明确的热力学状态”。他将一个系统定义为“当其观测量随时间停止变化时”的“热平衡”。但是在这个定义之下不久,他写到一块玻璃还没有达到“完全的热力学平衡状态”。<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, thermodynamic equilibrium is said to exist." He is not here considering the presence of an external force field.<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, ''thermodynamic equilibrium'' is said to exist." He is not here considering the presence of an external force field.<ref>Bailyn, M. (1994), p. 21.</ref><br />
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考虑到平衡状态,M.Bailyn写道: “每个强度变量都有自己的平衡类型。”然后他定义了热平衡、机械平衡和物质平衡。因此,他写道: “如果所有的强度变量都是一致的,那么热力学平衡就是存在的。”他在这里没有考虑外力场的存在。<br />
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J.G. Kirkwood and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of thermodynamic equilibrium if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<br />
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[[John Gamble Kirkwood|J.G. Kirkwood]] and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of ''thermodynamic equilibrium'' if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<ref>Kirkwood, J.G., Oppenheim, I. (1961), p. 2</ref><br />
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'''<font color="#ff8000">J.G.柯克伍德 J.G.Kirkwood</font>'''和 I.Oppenheim 将热力学平衡定义为: “一个系统处于热力学平衡状态,如果,在分配给实验的时间内,(a)它强度特性与时间无关,(b)它的内部或与周围环境的边界处没有物质或能量流。”显然,他们没有把定义限制在孤立的或封闭的系统。它们不讨论“缓慢”发生变化的可能性,并且超出了分配给实验的时间范围。他们注意到,对于两个相接触的系统,存在一个强度性质的小子类,如果这个小子类的所有子类都相等,那么所有各自的强度性质都相等。只要满足其他一些条件,热力学平衡状态可以由这个子类定义。<br />
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==Characteristics of a state of internal thermodynamic equilibrium==<br />
内部热力学平衡状态的特征<br />
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A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous. Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface." As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.<br />
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在内部热力学平衡中,没有外力的情况下由单相组成的热力学系统是均匀的。Planck在论文中简要介绍了热量、温度和热平衡,然后宣布: “在下文中,我们将主要讨论任何形式的均匀、各向同性的物体,它们在整个物质中具有相同的温度和密度,并受到到处垂直于表面的均匀压力作用。”和 Carathéodory 一样,Planck 将表面效应、外场和各向异性晶体排除在外。虽然Planck提到了温度,但并没有明确提到热力学平衡的概念。相比之下,Carathéodory 关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ,虽然没有明确地使用短语‘热力学平衡’,也没有明确地假设存在一个温度来定义它。<br />
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===Homogeneity in the absence of external forces===<br />
在没有外力的情况下的同质性<br />
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A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous.<ref name="Planck 1903 3"/> This means that the material in any small volume element of the system can be interchanged with the material of any other geometrically congruent volume element of the system, and the effect is to leave the system thermodynamically unchanged. In general, a strong external force field makes a system of a single phase in its own internal thermodynamic equilibrium inhomogeneous with respect to some [[Intensive and extensive properties|intensive variables]]. For example, a relatively dense component of a mixture can be concentrated by centrifugation.<br />
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在没有外力的情况下,由单一相组成的热力学系统,在其自身的内部热力学平衡中是均匀的。这意味着系统中任何小体积单元中的材料可以与系统中任何其他几何相等的体积单元中的材料互换,其效果是使系统在热力学上保持不变。一般来说,一个强外力场使得一个单相系统在其自身的内部热力学平衡中对于一些'''<font color="#ff8000">强变量 Intensive Variable</font>'''是不均匀的。例如,可以通过离心来浓缩混合物中相对密度较大的组分。<br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform. Considerations of kinetic theory or statistical mechanics also support this statement.<br />
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热力学平衡系统中的温度在空间和时间上是均匀的。在一个系统内部热力学平衡状态下,没有净内部宏观流动。特别是,这意味着系统的所有局部部分处于相互辐射交换平衡状态。这意味着系统的温度在空间上是均匀的。动力学理论或统计力学也支持这种说法。<br />
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===Uniform temperature===<br />
均匀温度<br />
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In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium. As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.<br />
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为了使一个系统处于它自己的内部热力学平衡状态,它处于自己内部的热平衡状态当然是必要的,但不是充分的;系统在达到内部热平衡之前,可以达到内部机械平衡。如上所述,根据 A.Münster的说法,对于给定的孤立系统的任何状态,定义一个热力学平衡所需的变量数是最少的。如上所述,J.G.Kirkwood 和 I.Oppenheim 指出,热力学平衡状态可以由一个特殊的子类的强变量定义,该子类中有一定数量的成员。<br />
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Such equilibrium inhomogeneity, induced by external forces, does not occur for the intensive variable [[temperature]]. According to [[Edward A. Guggenheim|E.A. Guggenheim]], "The most important conception of thermodynamics is temperature."<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), p.5.</ref> Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface."<ref name="Planck 1903 3">[[Max Planck|Planck, M.]] (1897/1927), p.3.</ref> As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.<br />
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这种由外力引起的平衡不均匀性,在强烈变化的'''<font color="#ff8000">温度 Temperature</font>'''下不会发生。'''<font color="#ff8000">E.A.古根海姆 E.A. Guggenheim</font>'''认为,“热力学最重要的概念是温度。“Planck在介绍他的论文时,简要叙述了热、温度和热平衡,然后宣布: ”在下文中,我们将主要讨论任何形式的均匀、各向同性的物体,它们的物质具有相同的温度和密度,并受到到处垂直于表面的均匀压力的作用和Carathéodory 一样,Planck将表面效应、外场和各向异性晶体排除在外。虽然Planck提到了温度,但并没有明确提到热力学平衡的概念。相比之下,Carathéodory关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ,虽然没有明确地使用短语‘热力学平衡’ ,也没有明确地假设存在一个温度来定义它。<br />
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<br />
If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.<br />
<br />
如果热力学平衡位于一个外力场中,那么通常只有温度在空间上是均匀的。如果外力场非零,温度以外的强度变量通常是不均匀的。在这种情况下,一般需要附加变量来描述空间非均匀性。<br />
<br />
The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform.<ref name="Planck 1914 40"/> This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers.<ref>Gibbs, J.W. (1876/1878), pp. 144-150.</ref><ref>[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966), pp. 127–130.</ref><ref>Münster, A. (1970), pp. 309–310.</ref><ref>Bailyn, M. (1994), pp. 254-256.</ref><ref>{{cite journal | last1 = Verkley | first1 = W.T.M. | last2 = Gerkema | first2 = T. | year = 2004 | title = On maximum entropy profiles | journal = J. Atmos. Sci. | volume = 61 | issue = 8| pages = 931–936 | doi=10.1175/1520-0469(2004)061<0931:omep>2.0.co;2| bibcode = 2004JAtS...61..931V | doi-access = free }}</ref><ref>{{cite journal | last1 = Akmaev | first1 = R.A. | year = 2008 | title = On the energetics of maximum-entropy temperature profiles | url = | journal = Q. J. R. Meteorol. Soc. | volume = 134 | issue = 630| pages = 187–197 | doi=10.1002/qj.209| bibcode = 2008QJRMS.134..187A }}</ref> Considerations of kinetic theory or statistical mechanics also support this statement.<ref>Maxwell, J.C. (1867).</ref><ref>Boltzmann, L. (1896/1964), p. 143.</ref><ref>Chapman, S., Cowling, T.G. (1939/1970), Section 4.14, pp. 75–78.</ref><ref>[[J. R. Partington|Partington, J.R.]] (1949), pp. 275–278.</ref><ref>{{cite journal | last1 = Coombes | first1 = C.A. | last2 = Laue | first2 = H. | year = 1985 | title = A paradox concerning the temperature distribution of a gas in a gravitational field | url = | journal = Am. J. Phys. | volume = 53 | issue = 3| pages = 272–273 | doi=10.1119/1.14138| bibcode = 1985AmJPh..53..272C }}</ref><ref>{{cite journal | last1 = Román | first1 = F.L. | last2 = White | first2 = J.A. | last3 = Velasco | first3 = S. | year = 1995 | title = Microcanonical single-particle distributions for an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 16 | issue = 2| pages = 83–90 | doi=10.1088/0143-0807/16/2/008| bibcode = 1995EJPh...16...83R }}</ref><ref>{{cite journal | last1 = Velasco | first1 = S. | last2 = Román | first2 = F.L. | last3 = White | first3 = J.A. | year = 1996 | title = On a paradox concerning the temperature distribution of an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 17 | issue = | pages = 43–44 | doi=10.1088/0143-0807/17/1/008}}</ref><br />
<br />
热力学平衡系统内的温度在时间和空间上都是均匀的。在一个处于内部热力学平衡的系统中,不存在净的内部宏观流动。特别是,这意味着系统的所有局部都处于相互辐射交换平衡。这意味着系统的温度在空间上是均匀的。这在所有情况下都是如此,包括那些非均匀外力场。对于外部施加的引力场,这可以通过使用朗朗日乘数的方法通过变化的演算在宏观热力学术语中证明。动力学理论或统计力学也支持这种说法。<br />
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<br />
In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium.<ref name="Fitts 43"/><br />
<br />
为了使一个系统处于它自己的内部热力学平衡状态,它必须处于它自己的内部热平衡状态是必要不充分的; 一个系统在到达内部热平衡之前到达内部机械平衡是可能的。<br />
<br />
As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.<br />
<br />
如上所述,j.r. Partington 指出热力学平衡状态在小的瞬态扰动下是稳定的。如果没有这个条件,一般来说,研究热力学平衡系统的实验就会遇到巨大的困难。<br />
<br />
===Number of real variables needed for specification===<br />
规范所需的实变量数目<br />
<br />
<br />
In his exposition of his scheme of closed system equilibrium thermodynamics, C. Carathéodory initially postulates that experiment reveals that a definite number of real variables define the states that are the points of the manifold of equilibria.<ref name="Caratheodory" /> In the words of Prigogine and Defay (1945): "It is a matter of experience that when we have specified a certain number of macroscopic properties of a system, then all the other properties are fixed."<ref>Prigogine, I., Defay, R. (1950/1954), p. 1.</ref><ref>Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005), p. 4.</ref> As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.<br />
<br />
在他关于封闭系统平衡态热力学方案的论述中,C.Carathéodory 最初假定实验揭示了一定数量的实变量定义了作为平衡态流形点的状态。用 Prigogine 和 Defay (1945)的话说: “这是一个经验问题,当我们确定了一个系统一定数量的宏观属性时,那么所有其他属性都是固定的。如上所述,A. Münster认为,定义热力学平衡所需的变量数量对于给定孤立系统的任何状态来说都是最少的。如上所述,J.G. Kirkwood 和 I. Oppenheim 指出,热力学平衡状态可以由一个特殊子类的强度变量来定义,该子类中有一定数量的成员。<br />
<br />
When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium. Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<br />
<br />
当一个物质体从不均匀的非平衡状态或化学非平衡状态开始,然后被孤立,它自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如,在这种演变的许多情况下,内部机械平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是,在这种演变的许多情况下,热平衡的发展要比化学平衡快得多。<br />
<br />
<br />
<br />
If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.<br />
<br />
如果热力学平衡位于一个外力场中,那么通常只有温度在空间上是均匀的。如果外力场非零,温度以外的强度变量通常是不均匀的。在这种情况下,一般需要附加变量来描述空间非均匀性。<br />
<br />
===Stability against small perturbations===<br />
对小扰动的稳定性<br />
<br />
In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
<br />
在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
<br />
As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.<br />
<br />
如上所述,J.R. Partington 指出热力学平衡状态在小的瞬态扰动下是稳定的。如果没有这个条件,一般来说,研究热力学平衡系统的实验就会遇到严重的困难。<br />
<br />
<br />
To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics. But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
<br />
考虑孤立热力学系统中的波动概念,一个方便的例子是由其广泛的状态变量、内能、体积和质量组成指定的系统。根据定义,它们是时不变的。根据定义,它们与它们的共轭状态密集函数的时不变名义值相结合,反向温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广泛的状态变量的值,不足以提供这些名义值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
<br />
===Approach to thermodynamic equilibrium within an isolated system===<br />
孤立系统中的热力学平衡<br />
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It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.<br />
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可以承认,在重复测量这些共轭强度函数时,发现它们的值随时间略有不同。这种可变性被认为是由于内部波动。不同测量值平均到其名义值。<br />
<br />
When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium.<ref name="Fitts 43">Fitts, D.D. (1962), p. 43.</ref> Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<ref>Denbigh, K.G. (1951), p. 42.</ref><br />
<br />
当一个物质体从不均匀的非平衡状态或化学非平衡状态开始,然后被孤立,它自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如,在这种演变的许多情况下,内部机械平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是,在这种演变的许多情况下,热平衡的发展要比化学平衡快得多。<br />
<br />
If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<br />
<br />
如果这个系统真的像经典热力学所假定的那样是宏观的,那么这个系统的波动太小了,宏观上无法检测到。这就是所谓的热力学极限。实际上,物质的分子性质和动量转移的量子性质由于它们太小而看不见,已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中,平衡的波动概念是没有位置的。”<br />
<br />
===Fluctuations within an isolated system in its own internal thermodynamic equilibrium===<br />
孤立系统内部热力学平衡的波动<br />
<br />
<br />
If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
<br />
如果系统被重复细分,最终产生的系统足够小,可以表现出明显的波动。这是一个介观层面的研究。波动则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
<br />
In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
<br />
在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
<br />
<br />
If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
<br />
如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在波动过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,即需要量子统计力学。波动可以变得相对占主导地位,测量问题变得重要。<br />
<br />
To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics.<ref>Tschoegl, N.W. (2000). ''Fundamentals of Equilibrium and Steady-State Thermodynamics'', Elsevier, Amsterdam, {{ISBN|0-444-50426-5}}, p. 21.</ref> But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
<br />
考虑孤立热力学系统中的波动概念,一个方便的例子是由其众多的状态变量,内能、体积和质量组成指定的系统。根据定义,它们是时不变的。根据定义,它们与它们的共轭状态密集函数的时不变名义值相结合,反向温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广泛的状态变量的值,不足以提供这些名义值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
<br />
<br />
The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
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"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有时间趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的标称值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微波动期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。非已知属于平衡状态的标称值,否则根据单一的度量无法进行判断。<br />
<br />
It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.<br />
<br />
可以承认,在重复测量这些共轭强度函数时,发现它们的值随时间略有不同。这种可变性被认为是由于内部波动。不同测量值平均到其名义值。<br />
<br />
<br />
<br />
If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<ref>Buchdahl, H.A. (1966), p. 16.</ref><br />
<br />
如果这个系统真的像经典热力学所假定的那样是宏观的,那么这个系统的波动太小了,宏观上无法检测到。这就是所谓的热力学极限。实际上,物质的分子性质和动量转移的量子性质由于它们太小而看不见,已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中,平衡的波动概念是没有位置的。”<br />
<br />
<br />
If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
<br />
如果系统被重复细分,最终产生的系统足够小,可以表现出明显的波动。这是一个介观层面的研究。波动则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
<br />
An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process." This illustrates the importance for thermodynamics of the concept of temperature.<br />
<br />
热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
<br />
<br />
<br />
If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在波动过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,即需要量子统计力学。波动可以变得相对占主导地位,测量问题变得重要。<br />
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Thermal equilibrium is achieved when two systems in thermal contact with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<br />
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当两个相互热接触的系统不再有净能量交换时,就会产生热平衡。因此,如果两个系统处于热平衡,那么它们的温度是相同的。<br />
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The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
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"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有时间趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的标称值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微波动期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。非已知属于平衡状态的标称值,否则根据单一的度量无法进行判断。<br />
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Thermal equilibrium occurs when a system's macroscopic thermal observables have ceased to change with time. For example, an ideal gas whose distribution function has stabilised to a specific Maxwell–Boltzmann distribution would be in thermal equilibrium. This outcome allows a single temperature and pressure to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<br />
<br />
当系统的宏观热观测值不再随着时间变化时,就会出现热平衡。例如,一种分布函数稳定到一个特定的麦克斯韦-波兹曼分布的理想气体即处于热平衡状态。这个结果可以将单一的温度和压力归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是很有可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
<br />
=== Thermal equilibrium ===<br />
热平衡<br />
{{Main|Thermal equilibrium}}<br />
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<br />
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An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process."<ref>Eu, B.C. (2002), page 13.</ref> This illustrates the importance for thermodynamics of the concept of temperature.<br />
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热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
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A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<br />
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一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数。<br />
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[[Thermal equilibrium]] is achieved when two systems in [[thermal contact]] with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<ref>[[Raj Pathria|R. K. Pathria]], 1996</ref><br />
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当两个相互'''<font color="#ff8000">热接触 Thermal Contact</font>'''的系统不再有净能量交换时,就会产生'''<font color="#ff8000">热平衡 Thermal Equilibrium</font>'''。因此,如果两个系统处于热平衡,那么它们的温度是相同的<br />
<br />
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
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非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
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Thermal equilibrium occurs when a system's [[macroscopic]] thermal observables have ceased to change with time. For example, an [[ideal gas]] whose [[Distribution function (physics)|distribution function]] has stabilised to a specific [[Maxwell–Boltzmann distribution]] would be in thermal equilibrium. This outcome allows a single [[temperature]] and [[pressure]] to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<ref>de Groot, S.R., Mazur, P. (1962), p. 44.</ref><br />
<br />
当一个系统的'''<font color="#ff8000">宏观 Macroscopic</font>'''热观测值不再随时间变化时,就会出现热平衡。例如,一种'''<font color="#ff8000">分布函数 Distribution Function</font>'''稳定到一个特定的'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''的'''<font color="#ff8000">理想气体 Ideal Gas</font>'''即处于热平衡状态。这个结果可以将单一的'''<font color="#ff8000">温度 Temperature</font>'''和'''<font color="#ff8000">压力 Pressure</font>'''归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
<br />
Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle. It states that a non-equilibrium system evolves such as to maximize its entropy production.<br />
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定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
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==Non-equilibrium==<br />
非平衡<br />
{{Main|Non-equilibrium thermodynamics}}<br />
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Thermodynamic models <br />
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热力学模型<br />
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A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<ref>de Groot, S.R., Mazur, P. (1962), p. 43.</ref><br />
<br />
一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数<br />
<br />
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
<br />
非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
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Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle.<ref>{{cite book|last1=Ziegler|first1=H.|title=An Introduction to Thermomechanics.|date=1983|location=North Holland, Amsterdam.}}</ref><ref>{{cite journal|last1=Onsager|first1=Lars|title=Reciprocal Relations in Irreversible Processes|journal=Phys. Rev.|date=1931|volume=37|issue=4|doi=10.1103/PhysRev.37.405|bibcode=1931PhRv...37..405O|pages=405–426|doi-access=free}}</ref> It states that a non-equilibrium system evolves such as to maximize its entropy production.<ref>{{cite book|last1=Kleidon|first1=A.|last2=et.|first2=al.|title=Non-equilibrium Thermodynamics and the Production of Entropy.|date=2005|edition=Heidelberg: Springer.}}</ref><ref>{{cite journal|last1=Belkin|first1=Andrey|last2=et.|first2=al.|title=Self-Assembled Wiggling Nano-Structures and the Principle of Maximum Entropy Production|journal=Sci. Rep.|doi=10.1038/srep08323|bibcode=2015NatSR...5E8323B|pmc=4321171|pmid=25662746|volume=5|year=2015|page=8323}}</ref><br />
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定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
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Topics in control theory<br />
<br />
控制理论主题<br />
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==See also ==<br />
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{{Portal|Chemistry}}<br />
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;Thermodynamic models 热力学模型<br />
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{{colbegin}}<br />
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* [[Non-random two-liquid model]] (NRTL model) - Phase equilibrium calculations 非随机两液模型(NRTL 模型)-相平衡计算<br />
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* [[UNIQUAC]] model - Phase equilibrium calculations UNIQUAC 模型-相平衡计算<br />
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* [[Time crystal]] 时间晶体<br />
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{{colend}}<br />
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;Topics in control theory 控制理论主题<br />
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{{colbegin}}<br />
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* [[Steady state]] 稳态<br />
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* [[Transient state]] 瞬态<br />
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* [[Coefficient diagram method]] 系数图法<br />
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* [[Control reconfiguration]] 控制重构<br />
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* [[Cut-insertion theorem]] 切入定理<br />
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* [[Feedback]] 反馈<br />
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* [[H infinity]] H 无限<br />
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* [[Hankel singular value]] 汉克尔奇异值<br />
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* [[Krener's theorem]] 克雷纳定理<br />
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* [[Lead-lag compensator]] 超前滞后补偿器<br />
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* [[Minor loop feedback]] 小循环反馈<br />
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* [[Minor loop feedback|Multi-loop feedback]] 小循环反馈 | 多循环反馈<br />
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* [[Positive systems]] 正向系统<br />
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* [[Radial basis function]] 径向基底函数<br />
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Other related topics<br />
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其他相关话题<br />
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* [[Root locus]] 根轨迹<br />
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* [[Signal-flow graph]]s 信号流图<br />
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* [[Stable polynomial]] 稳定多项式<br />
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* [[State space representation]] 状态空间<br />
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* [[Underactuation]] 欠驱动<br />
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* [[Youla–Kucera parametrization]] 尤拉-库切拉参数化<br />
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* [[Markov chain approximation method]] 马尔可夫链近似法<br />
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{{colend}}<br />
<br />
;Other related topics<br />
其他相关话题<br />
<br />
{{colbegin}}<br />
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* [[Automation and remote control]] 自动化和远程控制<br />
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* [[Bond graph]] 键合图<br />
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* [[Control engineering]] 控制工程<br />
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* [[Control–feedback–abort loop]] 控制-反馈-中止循环<br />
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* [[Controller (control theory)]] 控制器(控制理论)<br />
<br />
* [[Cybernetics]] 控制论<br />
<br />
* [[Intelligent control]] 智能控制<br />
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* [[Mathematical system theory]] 数学系统论<br />
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* [[Negative feedback amplifier]] 负反馈放大器<br />
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* [[People in systems and control]] 系统和控制中的人<br />
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* [[Perceptual control theory]] 知觉控制理论<br />
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* [[Systems theory]] 系统论<br />
<br />
* [[Time scale calculus]] 时间尺度演算<br />
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{{colend}}<br />
<br />
<br />
<br />
== 编者推荐 ==<br />
===集智文章推荐===<br />
<br />
====[https://swarma.org/?p=21322 什么是非平衡态热力学 | 集智百科]====<br />
非平衡态热力学 Non-equilibrium thermodynamics 是热力学的一个分支,研究某些不处于热力学平衡中的物理系统<br />
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<br />
==General references==<br />
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* Cesare Barbieri (2007) ''Fundamentals of Astronomy''. First Edition (QB43.3.B37 2006) CRC Press {{ISBN|0-7503-0886-9}}, {{ISBN|978-0-7503-0886-1}}<br />
<br />
* Hans R. Griem (2005) ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}<br />
<br />
* C. Michael Hogan, Leda C. Patmore and Harry Seidman (1973) ''Statistical Prediction of Dynamic Thermal Equilibrium Temperatures using Standard Meteorological Data Bases'', Second Edition (EPA-660/2-73-003 2006) United States Environmental Protection Agency Office of Research and Development, Washington, D.C. [http://library.wur.nl/WebQuery/catalog/lang/1851848]<br />
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* F. Mandl (1988) ''Statistical Physics'', Second Edition, John Wiley & Sons<br />
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==References==<br />
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{{Reflist|colwidth=35em}}<br />
<br />
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==Cited bibliography==<br />
<br />
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<br />
*Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', third edition, McGraw-Hill, London, {{ISBN|0-521-25445-0}}.<br />
<br />
*Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, {{ISBN|0-88318-797-3}}.<br />
<br />
*Beattie, J.A., Oppenheim, I. (1979). ''Principles of Thermodynamics'', Elsevier Scientific Publishing, Amsterdam, {{ISBN|0-444-41806-7}}.<br />
<br />
*[[Ludwig Boltzmann|Boltzmann, L.]] (1896/1964). ''Lectures on Gas Theory'', translated by S.G. Brush, University of California Press, Berkeley.<br />
<br />
*Buchdahl, H.A. (1966). ''The Concepts of Classical Thermodynamics'', Cambridge University Press, Cambridge UK.<br />
<br />
*[[Herbert Callen|Callen, H.B.]] (1960/1985). ''Thermodynamics and an Introduction to Thermostatistics'', (1st edition 1960) 2nd edition 1985, Wiley, New York, {{ISBN|0-471-86256-8}}.<br />
<br />
*[[Constantin Carathéodory|Carathéodory, C.]] (1909). [https://web.archive.org/web/20160304213645/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0067&DMDID=DMDLOG_0033&L=1 Untersuchungen über die Grundlagen der Thermodynamik], ''[[Mathematische Annalen]]'', '''67''': 355–386. A translation may be found [http://neo-classical-physics.info/uploads/3/0/6/5/3065888/caratheodory_-_thermodynamics.pdf here]. Also a mostly reliable [https://books.google.com/books?id=xwBRAAAAMAAJ&q=Investigation+into+the+foundations translation is to be found] at Kestin, J. (1976). ''The Second Law of Thermodynamics'', Dowden, Hutchinson & Ross, Stroudsburg PA.<br />
<br />
*[[Sydney Chapman (mathematician)|Chapman, S.]], [[Thomas George Cowling|Cowling, T.G.]] (1939/1970). ''The Mathematical Theory of Non-uniform gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases'', third edition 1970, Cambridge University Press, London.<br />
<br />
*Crawford, F.H. (1963). ''Heat, Thermodynamics, and Statistical Physics'', Rupert Hart-Davis, London, Harcourt, Brace & World, Inc.<br />
<br />
*de Groot, S.R., Mazur, P. (1962). ''Non-equilibrium Thermodynamics'', North-Holland, Amsterdam. Reprinted (1984), Dover Publications Inc., New York, {{ISBN|0486647412}}.<br />
<br />
*Denbigh, K.G. (1951). ''Thermodynamics of the Steady State'', Methuen, London.<br />
<br />
*Eu, B.C. (2002). ''Generalized Thermodynamics. The Thermodynamics of Irreversible Processes and Generalized Hydrodynamics'', Kluwer Academic Publishers, Dordrecht, {{ISBN|1-4020-0788-4}}.<br />
<br />
*Fitts, D.D. (1962). ''Nonequilibrium thermodynamics. A Phenomenological Theory of Irreversible Processes in Fluid Systems'', McGraw-Hill, New York.<br />
<br />
*[[Josiah Willard Gibbs|Gibbs, J.W.]] (1876/1878). On the equilibrium of heterogeneous substances, ''Trans. Conn. Acad.'', '''3''': 108–248, 343–524, reprinted in ''The Collected Works of J. Willard Gibbs, Ph.D, LL. D.'', edited by W.R. Longley, R.G. Van Name, Longmans, Green & Co., New York, 1928, volume 1, pp.&nbsp;55–353.<br />
<br />
*Griem, H.R. (2005). ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}.<br />
<br />
*[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', fifth revised edition, North-Holland, Amsterdam.<br />
<br />
*Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of ''Thermodynamics'', pages 1–97 of volume 1, ed. W. Jost, of ''Physical Chemistry. An Advanced Treatise'', ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081.<br />
<br />
*[[John Gamble Kirkwood|Kirkwood, J.G.]], Oppenheim, I. (1961). ''Chemical Thermodynamics'', McGraw-Hill Book Company, New York.<br />
<br />
*Landsberg, P.T. (1961). ''Thermodynamics with Quantum Statistical Illustrations'', Interscience, New York.<br />
<br />
*{{cite journal |last1=Lieb |first1=E. H. |last2=Yngvason |first2=J. |year=1999 |title=The Physics and Mathematics of the Second Law of Thermodynamics |journal=Phys. Rep. |volume=310 |issue= 1|pages=1–96 |doi= 10.1016/S0370-1573(98)00082-9|arxiv = cond-mat/9708200 |bibcode = 1999PhR...310....1L |s2cid=119620408 }}<br />
<br />
*Levine, I.N. (1983), ''Physical Chemistry'', second edition, McGraw-Hill, New York, {{ISBN|978-0072538625}}.<br />
<br />
*{{cite journal | last1 = Maxwell | first1 = J.C. | authorlink = James Clerk Maxwell | year = 1867 | title = On the dynamical theory of gases | url = | journal = Phil. Trans. Roy. Soc. London | volume = 157 | issue = | pages = 49–88 }}<br />
<br />
*[[Philip M. Morse|Morse, P.M.]] (1969). ''Thermal Physics'', second edition, W.A. Benjamin, Inc, New York.<br />
<br />
*Münster, A. (1970). ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London.<br />
<br />
*[[J.R. Partington|Partington, J.R.]] (1949). ''An Advanced Treatise on Physical Chemistry'', volume 1, ''Fundamental Principles. The Properties of Gases'', Longmans, Green and Co., London.<br />
<br />
*[[Brian Pippard|Pippard, A.B.]] (1957/1966). ''The Elements of Classical Thermodynamics'', reprinted with corrections 1966, Cambridge University Press, London.<br />
<br />
* [[Max Planck|Planck. M.]] (1914). [https://archive.org/details/theoryofheatradi00planrich ''The Theory of Heat Radiation''], a translation by Masius, M. of the second German edition, P. Blakiston's Son & Co., Philadelphia.<br />
<br />
*[[Ilya Prigogine|Prigogine, I.]] (1947). ''Étude Thermodynamique des Phénomènes irréversibles'', Dunod, Paris, and Desoers, Liège.<br />
<br />
*[[Ilya Prigogine|Prigogine, I.]], Defay, R. (1950/1954). ''Chemical Thermodynamics'', Longmans, Green & Co, London.<br />
<br />
*Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005). ''Physical Chemistry'', fourth edition, Wiley, Hoboken NJ.<br />
<br />
*[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966). ''Elements of Thermodynamics'', Addison-Wesley Publishing, Reading MA.<br />
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*{{cite journal|last=Thomson|first=W.|author-link=William Thomson, 1st Baron Kelvin|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Transactions of the Royal Society of Edinburgh|date=March 1851|volume=XX|issue=part II|pages=261–268; 289–298}} Also published in {{cite journal|last=Thomson|first=W.|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Phil. Mag. |date=December 1852 |volume=IV |series=4 |issue=22 |pages=8–21 |url=https://archive.org/details/londonedinburghp04maga |accessdate=25 June 2012}}<br />
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*[[László Tisza|Tisza, L.]] (1966). ''Generalized Thermodynamics'', M.I.T Press, Cambridge MA.<br />
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*[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963). ''Lectures in Statistical Mechanics'', American Mathematical Society, Providence RI.<br />
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*Waldram, J.R. (1985). ''The Theory of Thermodynamics'', Cambridge University Press, Cambridge UK, {{ISBN|0-521-24575-3}}.<br />
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*[[Mark Zemansky|Zemansky, M.]] (1937/1968). ''Heat and Thermodynamics. An Intermediate Textbook'', fifth edition 1967, McGraw–Hill Book Company, New York.<br />
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== External links ==<br />
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Category:Equilibrium chemistry<br />
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类别: 平衡化学<br />
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*[http://ads.harvard.edu/books/1989fsa..book/AbookC15.pdf Breakdown of Local Thermodynamic Equilibrium] George W. Collins, The Fundamentals of Stellar Astrophysics, Chapter 15<br />
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Category:Thermodynamic cycles<br />
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类别: 热力循环<br />
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*[http://spiff.rit.edu/classes/phys440/lectures/lte/lte.html Thermodynamic Equilibrium, Local and otherwise] lecture by Michael Richmond<br />
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Category:Thermodynamic processes<br />
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类别: 热力学过程<br />
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*[http://journals.ametsoc.org/doi/abs/10.1175/1520-0469%281970%29027%3C0711:NLTEIC%3E2.0.CO%3B2 Non-Local Thermodynamic Equilibrium in Cloudy Planetary Atmospheres] Paper by R. E. Samueison quantifying the effects due to non-LTE in an atmosphere<br />
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Category:Thermodynamic systems<br />
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类别: 热力学系统<br />
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*[http://scienceworld.wolfram.com/physics/LocalThermodynamicEquilibrium.html Local Thermodynamic Equilibrium]<br />
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Category:Thermodynamics<br />
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分类: 热力学<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Thermodynamic equilibrium]]. Its edit history can be viewed at [[平衡热力学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%B9%B3%E8%A1%A1%E7%83%AD%E5%8A%9B%E5%AD%A6&diff=21137平衡热力学2021-01-22T08:04:49Z<p>Jxzhou:/* Conditions */</p>
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<div>此词条暂由小竹凉翻译,翻译字数共5339,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{short description|State of thermodynamic system(s) where no net macroscopic flow of matter or energy occurs}}<br />
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'''Thermodynamic equilibrium''' is an [[axiomatic]] concept of [[thermodynamics]]. It is an internal [[State variables|state]] of a single [[thermodynamic system]], or a relation between several thermodynamic systems connected by more or less permeable or impermeable [[Thermodynamic system#Walls|walls]]. In thermodynamic equilibrium there are no net [[macroscopic]] [[Flow (mathematics)|flows]] of [[matter]] or of [[energy]], either within a system or between systems. <br />
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Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium there are no net macroscopic flows of matter or of energy, either within a system or between systems. <br />
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'''热力学平衡'''是'''<font color="#ff8000">热力学 Thermodynamics</font>'''的一个'''<font color="#ff8000">不言自明的 Axiomatic</font>'''概念。它是单个'''<font color="#ff8000">热力学系统 Thermodynamic System</font>'''的内部'''<font color="#ff8000">状态 State</font>''',或者是几个热力学系统之间通过或多或少的渗透或不渗透的'''<font color="#ff8000">壁 Wall</font>'''连接的关系。无论是在一个系统内还是在系统之间,在热力学平衡中不存在'''<font color="#ff8000">物质 Matter</font>'''或'''<font color="#ff8000">能量 Energy</font>'''的净'''<font color="#ff8000">宏观 Macroscopic</font>''' '''<font color="#ff8000">流动 Flow</font>'''。<br />
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In a system that is in its own state of internal thermodynamic equilibrium, no [[macroscopic]] change occurs. <br />
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In a system that is in its own state of internal thermodynamic equilibrium, no macroscopic change occurs. <br />
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在一个处于内部热力学平衡状态的系统中,不会发生'''<font color="#ff8000">宏观 Macroscopic</font>'''变化。<br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual [[Thermal equilibrium|thermal]], [[Mechanical equilibrium|mechanical]], [[Chemical equilibrium|chemical]], and [[Radiative equilibrium|radiative]] equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a [[thermodynamic operation]]. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a thermodynamic operation. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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相互热力学平衡的体系同时处于互相之间的'''<font color="#ff8000">热 Thermal</font>'''平衡、'''<font color="#ff8000">力学 Mechanical</font>'''平衡、'''<font color="#ff8000">化学 Chemical</font>'''平衡和'''<font color="#ff8000">辐射 Radiative</font>'''平衡。系统可以处于其中一种相互平衡状态,尽管其他状态未平衡。在热力学平衡中所有的平衡同时并且无限期地保持,直到被'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''打破。在一个宏观平衡中,微观交换是完全或几乎完全平衡的;这是对宏观平衡概念的物理解释。<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform [[temperature]]. Its [[Intensive and extensive properties|intensive properties]], other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform temperature. Its intensive properties, other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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一个处于内部热力学状态平衡的热力学系统具有空间均匀的'''<font color="#ff8000">温度 Temperature</font>'''。除了温度以外,它的'''<font color="#ff8000">强度性质 Intensive Properties</font>'''可以由于周围环境施加的不变的长程力场而导致空间不均匀性。<br />
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In systems that are at a state of [[non-equilibrium]] there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a '''meta-stable equilibrium'''.<br />
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In systems that are at a state of non-equilibrium there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a meta-stable equilibrium.<br />
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相比之下,处于'''<font color="#ff8000">非平衡状态 non-equilibrium</font>'''的系统中有物质或能量的净流动。如果这些变化可以在一个还没有发生的系统中被触发,那么这个系统就被称为处于一个'''亚稳定的平衡状态'''。<br />
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Though not a widely named a "law," it is an [[axiom]] of thermodynamics that there exist states of thermodynamic equilibrium. The [[second law of thermodynamics]] states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the [[entropy|entropies]] of the portions.<br />
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Though not a widely named a "law," it is an axiom of thermodynamics that there exist states of thermodynamic equilibrium. The second law of thermodynamics states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the entropies of the portions.<br />
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虽然不是一个广泛命名的“定律” ,但存在热力学平衡状态是一个热力学'''<font color="#ff8000">公理 Axiom</font>'''。'''<font color="#ff8000">热力学第二定律 second law of thermodynamics</font>'''指出,当一个物质体从一个平衡状态开始,在这个状态中,它的一部分被或多或少渗透或不渗透的分区保持在不同的状态,并且是孤立的,热力学操作移除分区或使分区更具渗透性,然后它会自发地达到自己内部热力学平衡的新状态,并伴随着部分'''<font color="#ff8000">熵 Entropy</font>'''的总和增加。<br />
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== Overview 概览==<br />
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{{Thermodynamics|cTopic=[[Thermodynamic system|Systems]]}}<br />
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Classical thermodynamics deals with states of [[dynamic equilibrium]]. The state of a system at thermodynamic equilibrium is the one for which some [[thermodynamic potential]] is minimized, or for which the [[entropy]] (''S'') is maximized, for specified conditions. One such potential is the [[Helmholtz free energy]] (''A''), for a system with surroundings at controlled constant temperature and volume:<br />
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Classical thermodynamics deals with states of dynamic equilibrium. The state of a system at thermodynamic equilibrium is the one for which some thermodynamic potential is minimized, or for which the entropy (S) is maximized, for specified conditions. One such potential is the Helmholtz free energy (A), for a system with surroundings at controlled constant temperature and volume:<br />
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经典热力学研究'''<font color="#ff8000">动态平衡 Dynamic Equilibrium</font>'''的状态。系统的热力学平衡状态是对于特定的条件,一些'''<font color="#ff8000">热力学势 Thermodynamic Potential</font>'''被最小化,或者'''<font color="#ff8000">熵 Entropy</font>'''(S)被最大化。对于一个周围环境温度和体积恒定的系统,其中一个这样的热力学势是'''<font color="#ff8000">亥姆霍兹自由能 Helmholtz Free Energy</font>'''(A):<br />
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:<math>A = U - TS</math><br />
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<math>A = U - TS</math><br />
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A = U-TS<br />
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Another potential, the [[Gibbs free energy]] (''G''), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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Another potential, the Gibbs free energy (G), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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在恒定温度和压力的系统中,另一个热力学势'''<font color="#ff8000">吉布斯自由能 Gibbs Free Energy</font>'''(G)在热力学平衡状态最小:<br />
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:<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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where ''T'' denotes the absolute thermodynamic temperature, ''P'' the pressure, ''S'' the entropy, ''V'' the volume, and ''U'' the internal energy of the system.<br />
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where T denotes the absolute thermodynamic temperature, P the pressure, S the entropy, V the volume, and U the internal energy of the system.<br />
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其中 T 表示热力学绝对温度,P 表示压强,S 表示熵,V 表示体积,U 表示体系的内能。<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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热力学平衡是一种独特的稳定定态,当系统长时间与周围环境相互作用时,它可以被接近或最终到达。上述势能是数学构造的热力学量,在特定的环境条件下最小化。<br />
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== Conditions 条件==<br />
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* For a completely isolated system, ''S'' is maximum at thermodynamic equilibrium. 对于一个完全孤立的系统,S在热力学平衡中取最大值。<br />
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* For a system with controlled constant temperature and volume, ''A'' is minimum at thermodynamic equilibrium. 对于一个恒定温度和体积的系统来说,A在热力学平衡中取最小值。<br />
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* For a system with controlled constant temperature and pressure, ''G'' is minimum at thermodynamic equilibrium. 对于一个恒温恒压的系统,G在热力学平衡中取最小值。<br />
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The various types of equilibriums are achieved as follows:<br />
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The various types of equilibriums are achieved as follows:<br />
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实现各种类型的平衡的方法如下:<br />
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*Two systems are in ''thermal equilibrium'' when their [[temperature]]s are the same. 当两个系统的'''<font color="#ff8000">温度 Temperature</font>'''相同时,它们就处于''热平衡状态''<br />
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*Two systems are in ''mechanical equilibrium'' when their [[pressure]]s are the same. 当两个体系的'''<font color="#ff8000">压力 Pressure</font>'''相同时,它们就处于''力学平衡''<br />
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*Two systems are in ''diffusive equilibrium'' when their [[chemical potential]]s are the same. 当两个题体系的'''<font color="#ff8000">化学势 Chemical Potential</font>'''相同时,它们就处于''扩散平衡''<br />
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*All [[forces]] are balanced and there is no significant external driving force.<br />
所有的'''<font color="#ff8000">力 Force</font>'''都是平衡的,没有明显的外部驱动力<br />
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==Relation of exchange equilibrium between systems==<br />
系统之间的交换均衡关系<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability.<ref name="Nster_a">Münster, A. (1970), p. 49.</ref> When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability. When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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通常,热力学系统的周围环境也可以被看作是另一个热力学系统。在这种观点中,我们可以把系统及其周围环境看作是相互接触的两个系统,远程作用力也将它们联系在一起。系统的包围物是两个系统之间的接触面或边界。在热力学公式中,该表面被认为具有特定的渗透性质。例如,接触的表面可能被认为只能透热,使能量只能作为热传递。当远程力在时间上不发生变化,两个系统之间的热量传递减慢并最终永久停止时,这两个系统被称为热平衡; 这就是接触平衡的一个例子。其它类型的接触平衡可用其它类型的比渗透率来定义。当两个系统对于某一特定类型的渗透率处于接触平衡时,它们具有属于该特定类型渗透率的强度变量的共同值。这种强度变量的例子有温度、压力、化学势。<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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接触平衡也可视为交换平衡。在接触平衡状态下,两系统之间某些量的传递速率存在零平衡。例如,对于只能透热的壁,内能作为热在两个系统之间的扩散速率是相等并相反的。两个系统之间的绝热壁只对作为功传递的能量有渗透作用; 在机械平衡,两个系统之间作为功的能量传递速率相等且相反。如果是一个简单的壁,那么通过它的体积转移率也是相等且相反的; 即它两边的压力是相等的。如果绝热壁比较复杂,有一种杠杆,有一个面积比,那么两个体系在交换平衡中的压力与体积交换比成反比,这使得转移率的零平衡作功。<br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<ref name="Planck 1914 40">[[Max Planck|Planck. M.]] (1914), p. 40.</ref><br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<br />
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辐射交换可以发生在两个不同的系统之间。当两个体系温度相同时,辐射交换平衡占优势。<br />
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==Thermodynamic state of internal equilibrium of a system==<br />
系统内部平衡的热力学状态<br />
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A collection of matter may be entirely [[Isolated system|isolated]] from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium.<ref>Haase, R. (1971), p. 4.</ref><ref>Callen, H.B. (1960/1985), p. 26.</ref> (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics.<ref>{{Cite journal |doi = 10.1119/1.4914528|bibcode = 2015AmJPh..83..628M|title = Time and irreversibility in axiomatic thermodynamics|year = 2015|last1 = Marsland|first1 = Robert|last2 = Brown|first2 = Harvey R.|last3 = Valente|first3 = Giovanni|journal = American Journal of Physics|volume = 83|issue = 7|pages = 628–634}}</ref> One textbook<ref>[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963), p. 5.</ref> calls it the "zeroth law", remarking that the authors think this more befitting that title than its [[Zeroth law of thermodynamics|more customary definition]], which apparently was suggested by [[Ralph H. Fowler|Fowler]].)<br />
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A collection of matter may be entirely isolated from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium. (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics. One textbook calls it the "zeroth law", remarking that the authors think this more befitting that title than its more customary definition, which apparently was suggested by Fowler.)<br />
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物质的集合可能与其周围的环境完全'''<font color="#ff8000">孤立 Isolated</font>'''。如果它在无限长的时间内一直保持不受干扰,按照经典热力学假定,它处于一个没有发生任何变化,没有流动的状态,即内部平衡的热力学状态。(这种假设有时被称为“负第一”热力学定律,但并不常见。有教科书称之为“第零定律” ,作者'''<font color="#ff8000">福勒 Fowler</font>'''认为这个名称是'''<font color="#ff8000">更符合惯例的定义 More Customary Definition</font>'''。)<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a [[thermodynamic operation]] be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a thermodynamic operation be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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这种状态是所谓的经典热力学或平衡态热力学的主要关注点,因为它们是系统中被认为在这门学科中得到很好定义的唯一状态。一个与另一个系统处于接触平衡状态可以被一个'''<font color="#ff8000">热力运行 Thermodynamic Operation</font>'''隔离,在隔离发生时,其内部不会发生任何变化。因此,一个与另一个系统处于接触平衡状态时也可以被视为处于其自身的内部热力学平衡状态。<br />
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==Multiple contact equilibrium==<br />
多点接触平衡<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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热力学形式论允许一个系统同时与其他多个系统接触,这些系统可能也可能没有相互接触,且这些接触具有不同的渗透性。如果这些系统都与世界其他部分相互隔离,那么它们彼此之间就会达到各自的接触平衡。<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy.<ref name="Caratheodory">Carathéodory, C. (1909).</ref><ref>Prigogine, I. (1947), p. 48.</ref><ref>Landsberg, P. T. (1961), pp. 128–142.</ref><ref>Tisza, L. (1966), p. 108.</ref> Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy. Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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如果几个系统彼此之间没有绝热壁,但是它们与世界其他部分共同隔离,那么它们就会达到多重接触平衡状态,且有共同的温度,内能和熵。在众多变量中,这是温度的一个独特性质。即使在远距离作用力存在的情况下,它也是有效的。(也就是说,没有“力”可以维持温度的差异。)举个例子,在热力学平衡的一个垂直的引力场系统中,顶部壁面的压力比底部壁面的压力小,但是各处的温度都是一样的。<br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural [[thermodynamic process]].<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), § 1.12.</ref> It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings.<ref>Levine, I.N. (1983), p. 40.</ref><ref>Lieb, E.H., Yngvason, J. (1999), pp. 17–18.</ref> The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of [[Second law of thermodynamics#Description#Kelvin statement|"inanimate" agency]]; a system in thermodynamic equilibrium is inanimate.<ref>[[William Thomson, 1st Baron Kelvin|Thomson, W.]] (1851).</ref><br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural thermodynamic process. It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings. The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of "inanimate" agency; a system in thermodynamic equilibrium is inanimate.<br />
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热力运行可能作为一个事件发生在周围环境的壁上,既不直接影响与周围环境联系的壁,也不直接影响其内部,且发生在一个明确的有限的时间内。例如,一个固定的绝热壁可以在环境中被放置或拆除。由于这种操作仅限于周围环境,系统可能会在一段时间内远离自身最初的内部状态---- 热力学平衡。根据热力学第二定律的说法,整体经历了变化并最终与周围环境达到了新的平衡。继Planck之后,这一连串的事件被称为自然'''<font color="#ff8000">热力学过程 Thermodynamic Process</font>'''。即使在这个过程中,当系统和周围环境都不处于明确的内部平衡状态时,存在着暂时偏离热力学平衡的现象,由于初始状态和最终状态都是热力学平衡的,这在平衡热力学中也是允许的。一个自然过程在其主要部分中以有限的速率进行,因此,它从根本上不同于虚构的准静态“过程”;即不在整个过程中无限缓慢地进行而且虚构地“可逆”。经典热力学允许,即使一个过程可能需要很长的时间才能达到热力学平衡,如果主要部分的过程是在一个有限的比率中,那么它被认为是自然的,并受制于热力学第二定律,即不可逆的。工程设计的机器、人工设备和操作是允许在周围环境中进行的。允许在环境中而不是在系统中进行此类操作和设备,是开尔文在他的一个热力学第二定律的陈述中提到'''<font color="#ff8000">无生命机构 Inanimate Agency</font>'''的原因; 在热力学平衡的系统是无生命的。<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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否则,热力运行可能会直接影响系统的壁。<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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通常可以很方便地假设周围的某些子系统比系统大得多,以至于这个过程只能影响周围子系统的强度变量,然后将这些子系统称为相关强度变量的储备库。<br />
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== Local and global equilibrium ==<br />
局部和全局均衡<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by [[intensive quantity|intensive]] parameters. As an example, [[temperature]] controls [[Heat equation|heat exchanges]]. ''Global thermodynamic equilibrium'' (GTE) means that those [[intensive quantity|intensive]] parameters are homogeneous throughout the whole system, while ''local thermodynamic equilibrium'' (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by intensive parameters. As an example, temperature controls heat exchanges. Global thermodynamic equilibrium (GTE) means that those intensive parameters are homogeneous throughout the whole system, while local thermodynamic equilibrium (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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区分全局性和局部性热力学平衡是很有用的。在热力学中,系统内部和系统与外部之间的交换是由'''<font color="#ff8000">强度 Intensive</font>'''参数控制的。例如,'''<font color="#ff8000">温度 Temperature</font>'''控制'''<font color="#ff8000">热交换 Heat Equation</font>'''。全局热力学平衡(GTE)意味着这些'''<font color="#ff8000">强度 Intensive</font>'''参数在整个系统中是均匀的,而局部热力学平衡(LTE)意味着这些强度参数在空间和时间上是变化的,但变化如此缓慢,以至于对于任何一点,人们都可以假设在某个邻近的某个热力学平衡。<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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如果对系统的描述要求强度参数的变化过大,那么这些强度参数的定义所依据的假设本身就会破裂,系统将既不处于全局平衡,也不处于局部平衡。例如,粒子需要一定数量的碰撞来平衡其周围环境。如果在这些碰撞中移动的平均距离使它离开平衡邻域,它将永远不会平衡,也就不会有 LTE。根据定义,温度与平衡邻域的平均内部能量成正比。由于没有达到平衡邻域,温度的概念就不成立,温度也就变得不确定。<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to [[massive]] particles. In a [[radiation|radiating]] gas, the [[photon]]s being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to massive particles. In a radiating gas, the photons being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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值得注意的是,这种局部平衡可能只适用于系统中的某个粒子子集。例如,LTE 通常只适用于'''<font color="#ff8000">大 Massive</font>'''质量粒子。在'''<font color="#ff8000">辐射 Radiation</font>'''气体中,被气体发射和吸收的'''<font color="#ff8000">光子 Photon</font>'''不需要彼此在一个热力学平衡内,或与气体中的大量粒子在一起,LTE 才能存在。在某些情况下,自由电子并不需要与大得多的原子或分子处于平衡状态,LTE 才能存在。<br />
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As an example, LTE will exist in a glass of water that contains a melting [[ice cube]]. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the [[Maxwell–Boltzmann distribution]] for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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As an example, LTE will exist in a glass of water that contains a melting ice cube. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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例如,LTE 将存在于一个装有融化的'''<font color="#ff8000">冰块 Ice Cube</font>'''的水杯中。玻璃杯内的温度可以在任何时候定义,但是离冰块近的地方要比离冰块远的地方冷。如果观察到位于给定点附近的分子的能量,它们将按照麦克斯韦-波兹曼分布在一定温度下的分布。如果观察到位于另一点附近的分子的能量,它们将按照'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''分布到另一个温度。<br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural [[transport phenomena]] may lead a system from local to global thermodynamic equilibrium. Going back to our example, the [[diffusion]] of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<ref>H.R. Griem, 2005</ref><br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural transport phenomena may lead a system from local to global thermodynamic equilibrium. Going back to our example, the diffusion of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<br />
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局部热力学平衡不需要局部或全局的平稳性。换句话说,每一个小区域不需要有一个恒定的温度。然而,它确实要求每个小的局部变化缓慢到足以维持其局部麦克斯韦-波兹曼分布的分子速度。全局非平衡态只有通过系统与外界的交换才能保持稳定。例如,通过在水杯中不断添加细粉冰来补偿熔化,并持续排出融水,可以保持全球稳定的静止状态。自然'''<font color="#ff8000">迁移现象 Transport Phenomena</font>'''可能导致一个从局部到全局的热力学平衡系统。回顾我们的例子,热量的扩散将导致我们的玻璃杯水流向全局热力学平衡,在这种状态下,玻璃杯的温度是完全均匀的。<br />
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==Reservations==<br />
保留意见<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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学识渊博的笔者在热力学领域对热力学平衡描述时,经常对他们的描述附加条件或保留意见。有些笔者含蓄地保留了或多或少的空白,以待说明。<br />
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For example, one widely cited writer, [[Herbert Callen|H. B. Callen]] writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. ''Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!''"<ref>Callen, H.B. (1960/1985), p. 15.</ref><br />
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For example, one widely cited writer, H. B. Callen writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!"<br />
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例如,一位被广泛引用的作家'''<font color="#ff8000">H.B.卡伦 H.B.Callen</font>'''在这里写道: “实际上,很少有系统处于绝对和真正的平衡状态。”他提到了放射性过程,认为它们可能需要“宇宙时间才能完成,因此通常可以忽略”。他补充道: “在实践中,平衡的标准是循环的。在操作上,如果一个系统的性质一致地用热力学理论来描述,那么它就处于平衡状态! ”<br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<ref>Beattie, J.A., Oppenheim, I. (1979), p. 3.</ref><br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<br />
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J.A.贝蒂和 I.奥本海姆写道: “坚持对平衡定义的严格解释,将排除热力学应用于实际系统的所有状态。”<br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment",<ref>Callen, H.B. (1960/1985), p. 485.</ref> and cited by Adkins as having written a "classic text",<ref>Adkins, C.J. (1968/1983), p. ''xiii''.</ref> [[Brian Pippard|A.B. Pippard]] writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<ref>Pippard, A.B. (1957/1966), p. 6.</ref><br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment", and cited by Adkins as having written a "classic text", A.B. Pippard writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<br />
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Callen引用另一位作者的话说,他给出了“学术且严谨的论述” ,Adkins引用他的话说,他写了一本“经典著作”—— '''<font color="#ff8000">A.B.皮帕德 A.B.Pippard</font>'''在文中写道: “只要时间足够长,过冷水蒸汽最终会凝结,... ..。时间可能是漫长的,也许长达10年或者更长。就大多数目的而言,只要这种迅速的变化不是人为地刺激,这些系统就可以被视为处于平衡状态。”<br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster">Münster, A. (1970), p. 53.</ref><br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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另一位作者A.Münster,写道。他观察到热核反应发生的速度非常缓慢,以至于在热力学中可以忽略不计。他评论道: “‘绝对平衡’或‘所有可想象过程的平衡’的概念没有物理意义。”他说: “ ... 我们只能考虑特定过程和确定的实验条件下的平衡。”<br />
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According to [[László Tisza|L. Tisza]]: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<ref>Tisza, L. (1966), p. 119.</ref><br />
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According to L. Tisza: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<br />
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根据'''<font color="#ff8000">L.缇莎 L.Tisza</font>'''的说法: “ ... 在讨论接近绝对零度的现象时。经典理论的绝对预测变得特别模糊,因为在非平衡状态下发生冻结是非常普遍的。”<br />
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==Definitions==<br />
定义<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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一个系统最普遍的热力学平衡是通过与周围环境的接触,允许所有化学物质和各种能量同时通过。热力学平衡中的系统以均匀加速度在空间中运动,但此时不能改变其形状或大小; 因此它是由空间中的刚性体积来定义的。它可能存在于外力场中,由远远大于系统本身的外部因素决定,因此系统内的事件不会对外力场产生相当大的影响。只有当外力场是均匀的,并且确定了它的均匀加速度,或者它处于一个非均匀力场中,但是由于表面的局部力,例如机械压力,使它保持静止时,这个系统才能处于热力学平衡。<br />
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Thermodynamic equilibrium is a [[primitive notion]] of the theory of thermodynamics. According to [[Philip M. Morse|P.M. Morse]]: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are ''not'' conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments."<ref>[[Philip M. Morse|Morse, P.M.]] (1969), p. 7.</ref> This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<ref>Bailyn, M. (1994), p. 20.</ref><br />
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Thermodynamic equilibrium is a primitive notion of the theory of thermodynamics. According to P.M. Morse: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are not conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments." This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<br />
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热力学平衡是热力学理论的一个'''<font color="#ff8000">基本概念 Primitive Notion</font>'''。'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''说: “应该强调的是,存在热力学状态这一事实,以及存在由平衡态唯一指定的热力学变量这一事实,并不是从某些哲学第一原理得出的逻辑结论。这些结论不可避免地来自两个多世纪的实验。”这意味着热力学平衡不能仅仅用热力学的其他理论概念来定义。M.Bailyn提出了一个基本的热力学定律理论,它定义并假设了热力学平衡的存在。<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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热力学平衡的教科书定义通常被仔细说明,并有些保留。<br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<ref>Münster, A. (1970), p. 52.</ref><br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<br />
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例如,A. Münster写道:“当系统中没有以可测量的速度发生状态变化时,隔离系统处于热力学平衡状态。”这里有两项保留:系统是孤立的;任何状态的变化都是不可估量的缓慢。他通过对在室温且没有催化剂的情况下混合氧和氢的说明,讨论了第二个条件。Münster指出,热力学平衡状态所描述的宏观变量比给定系统任何其他状态都少。这是部分,但不完全是,因为系统内和系统内的所有流都是零。<br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in ''equilibrium''.<ref>Haase, R. (1971), pp. 3–4.</ref><br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in equilibrium.<br />
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R. Haase's的热力学演示并不从对热力学平衡的限制开始,因为他打算考虑非平衡态热力学。他考虑一个具有时间不变性质的任意系统。他通过切断除外力场以外的所有外部影响来测试它的热力学平衡。如果在绝缘之后,没有任何变化,他说,系统处于平衡状态。<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness".<ref>Callen, H.B. (1960/1985), p. 13.</ref> This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness". This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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在一个标题为“热力学平衡”的章节中,H.B. Callen在段落定义了平衡状态.他指出,它们“是由系统内部的内在因素决定的”。它们是“终端状态” ,随着时间的推移,系统会以“冰川般缓慢”的速度朝着这个终端状态演化。这个说法并没有明确,对于热力学平衡系统必须是孤立的;;Callen也没有说明他所说的“内在因素”是什么意思。<br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<ref>Adkins, C.J. (1968/1983), p. ''7''.</ref><br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<br />
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另一位教科书作者,C.J.Adkins,明确允许热力学平衡在非孤立的系统中发生。然而,他的系统在物质转移方面是封闭的。他写道: “一般来说,热力学平衡的方法包括热和类似变动与周围环境的相互作用。”他将这种热力学平衡与只有通过热接触才能进行能量传递的热平衡相区别。<br />
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Another textbook author, [[J.R. Partington]], writes: "(i) ''An equilibrium state is one which is independent of time''." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..."<ref>Partington, J.R. (1949), p. 161.</ref> This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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Another textbook author, J.R. Partington, writes: "(i) An equilibrium state is one which is independent of time." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..." This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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另一位教科书作者'''<font color="#ff8000">J.R.帕廷顿 J.R.Partington</font>'''写道: “(i)平衡状态是独立于时间的状态。”但是,在提到“只是明显处于平衡状态”的系统时,他补充说: “这样的系统处于‘虚假平衡’状态。帕廷顿的陈述没有明确指出平衡是指一个孤立的系统。和Münster一样,Partington也指的是氧和氢的混合物。他补充说:“在一个真正的平衡状态,任何影响状态的外部条件的最小变化都会产生一个微小的状态变化... ... ”这个条件意味着热力学平衡必须在小的扰动下保持稳定; 这个要求对于热力学平衡的严格意义是必不可少的。<br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, ''thermodynamic—equilibrium.''"<ref>Crawford, F.H. (1963), p. 5.</ref><br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, thermodynamic—equilibrium."<br />
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在F.H.Crawford的一本学生教科书中,有一个标题为“热力学平衡”的章节。它区分了几种流动的驱动因素,然后说: “这些是孤立系统明显普遍趋向于完全机械、热、化学和电力状态的例子——或者简单地说,热力学平衡状态。”<br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in ''equilibrium''."<ref>Buchdahl, H.A. (1966), p. 8.</ref> Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being ''in equilibrium'' so long as experimental tests show that 'slow' transitions are in effect reversible."<ref>Buchdahl, H.A. (1966), p. 111.</ref> It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<ref>Adkins, C.J. (1968/1983), p. 8.</ref><br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in equilibrium." Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being in equilibrium so long as experimental tests show that 'slow' transitions are in effect reversible." It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<br />
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H.A. Buchdahl的一本关于经典热力学的专著考虑了热力学系统的平衡,而实际上并没有写热力学平衡一词。Buchdahl在提到封闭的物质交换系统时写道: “如果一个系统处于一个适当的静态状态,那么它将被称为处于平衡状态。”出于热力学描述的目的,Buchdahl的专著也讨论了非晶态玻璃。它说: “更准确地说,只要实验测试表明‘慢’跃迁实际上是可逆的,玻璃就可以被认为处于平衡状态。”通常来说不会将这一条件作为热力学平衡定义的一部分,而是假定相反的情况:如果热力学平衡中的一个体受到足够慢的过程的影响,则该过程可被视为足够接近可逆,并且该物体在过程中足够接近热力学平衡。<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of ''contact equilibrium''. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by [[Constantin Carathéodory|C. Carathéodory]], and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster" /> Thermodynamic equilibrium for an open system means that, with respect to every relevant kind of selectively permeable wall, contact equilibrium exists when the respective intensive parameters of the system and surroundings are equal.<ref name="Nster_a" /> This definition does not consider the most general kind of thermodynamic equilibrium, which is through unselective contacts. This definition does not simply state that no current of matter or energy exists in the interior or at the boundaries; but it is compatible with the following definition, which does so state.<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of contact equilibrium. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by C. Carathéodory, and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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通过引入接触平衡的概念,A. Münster仔细地扩展了孤立系统热力学平衡的定义。这指定了在考虑非孤立系统的热力学平衡时允许的特定过程,并特别关心开放系统,这些开放系统可能从周围环境获得或丢失物质。利益系统和周围系统之间的接触平衡,通过一种特殊的壁与利益系统接触,其余的连接系统是孤立的。这种特殊类型的壁也被'''<font color="#ff8000">C.喀喇西奥多里 C.Carathéodory</font>'''考虑过,其他作家也提到过。它们具有选择渗透性。它们可能只对机械工作有渗透性,或者只对热有渗透性,或者只对某种特定的化学物质有渗透性。每个接触平衡定义了一个强度参数; 例如,只能透热的壁定义了一个经验温度。对于感兴趣的体系中每一种化学成分,都可以存在接触平衡。在接触平衡中,尽管有可能通过选择性渗透壁进行交换,感兴趣的系统是不变的,好像它处在孤立的热力学平衡。这个方案遵循的一般规则是: “ ... ... 我们只能考虑特定过程和特定实验条件下的平衡。”<br />
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[[Mark Zemansky|M. Zemansky]] also distinguishes mechanical, chemical, and thermal equilibrium. He then writes: "When the conditions for all three types of equilibrium are satisfied, the system is said to be in a state of thermodynamic equilibrium".<ref>[[Mark Zemansky|Zemansky, M.]] (1937/1968), p. 27.</ref><br />
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'''<font color="#ff8000">M.泽曼斯基 M.Zemansky</font>'''还区分了机械、化学和热平衡。他接着写道: “当这三种均衡的条件都满足时,系统就处于热力学平衡状态。”<br />
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P.M. Morse writes that thermodynamics is concerned with "states of thermodynamic equilibrium". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<br />
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[[Philip M. Morse|P.M. Morse]] writes that thermodynamics is concerned with "''states of thermodynamic equilibrium''". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<ref>[[Philip M. Morse|Morse, P.M.]] (1969), pp. 6, 37.</ref><br />
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'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''写道,热力学关注的是“热力学平衡状态”。在讨论物体与周围热源之间的热量传递时,他也使用了“热平衡”这个短语,尽管没有明确定义一个特殊的术语“热平衡”<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "full thermodynamic equilibrium state".<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "''full'' thermodynamic equilibrium state".<ref>Waldram, J.R. (1985), p. 5.</ref><br />
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J.R. Waldram写到了“一个明确的热力学状态”。他将一个系统定义为“当其观测量随时间停止变化时”的“热平衡”。但是在这个定义之下不久,他写到一块玻璃还没有达到“完全的热力学平衡状态”。<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, thermodynamic equilibrium is said to exist." He is not here considering the presence of an external force field.<br />
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Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, ''thermodynamic equilibrium'' is said to exist." He is not here considering the presence of an external force field.<ref>Bailyn, M. (1994), p. 21.</ref><br />
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考虑到平衡状态,M.Bailyn写道: “每个强度变量都有自己的平衡类型。”然后他定义了热平衡、机械平衡和物质平衡。因此,他写道: “如果所有的强度变量都是一致的,那么热力学平衡就是存在的。”他在这里没有考虑外力场的存在。<br />
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J.G. Kirkwood and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of thermodynamic equilibrium if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<br />
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[[John Gamble Kirkwood|J.G. Kirkwood]] and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of ''thermodynamic equilibrium'' if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<ref>Kirkwood, J.G., Oppenheim, I. (1961), p. 2</ref><br />
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'''<font color="#ff8000">J.G.柯克伍德 J.G.Kirkwood</font>'''和 I.Oppenheim 将热力学平衡定义为: “一个系统处于热力学平衡状态,如果,在分配给实验的时间内,(a)它强度特性与时间无关,(b)它的内部或与周围环境的边界处没有物质或能量流。”显然,他们没有把定义限制在孤立的或封闭的系统。它们不讨论“缓慢”发生变化的可能性,并且超出了分配给实验的时间范围。他们注意到,对于两个相接触的系统,存在一个强度性质的小子类,如果这个小子类的所有子类都相等,那么所有各自的强度性质都相等。只要满足其他一些条件,热力学平衡状态可以由这个子类定义。<br />
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==Characteristics of a state of internal thermodynamic equilibrium==<br />
内部热力学平衡状态的特征<br />
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A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous. Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface." As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.<br />
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在内部热力学平衡中,没有外力的情况下由单相组成的热力学系统是均匀的。Planck在论文中简要介绍了热量、温度和热平衡,然后宣布: “在下文中,我们将主要讨论任何形式的均匀、各向同性的物体,它们在整个物质中具有相同的温度和密度,并受到到处垂直于表面的均匀压力作用。”和 Carathéodory 一样,Planck 将表面效应、外场和各向异性晶体排除在外。虽然Planck提到了温度,但并没有明确提到热力学平衡的概念。相比之下,Carathéodory 关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ,虽然没有明确地使用短语‘热力学平衡’,也没有明确地假设存在一个温度来定义它。<br />
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===Homogeneity in the absence of external forces===<br />
在没有外力的情况下的同质性<br />
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A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous.<ref name="Planck 1903 3"/> This means that the material in any small volume element of the system can be interchanged with the material of any other geometrically congruent volume element of the system, and the effect is to leave the system thermodynamically unchanged. In general, a strong external force field makes a system of a single phase in its own internal thermodynamic equilibrium inhomogeneous with respect to some [[Intensive and extensive properties|intensive variables]]. For example, a relatively dense component of a mixture can be concentrated by centrifugation.<br />
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在没有外力的情况下,由单一相组成的热力学系统,在其自身的内部热力学平衡中是均匀的。这意味着系统中任何小体积单元中的材料可以与系统中任何其他几何相等的体积单元中的材料互换,其效果是使系统在热力学上保持不变。一般来说,一个强外力场使得一个单相系统在其自身的内部热力学平衡中对于一些'''<font color="#ff8000">强变量 Intensive Variable</font>'''是不均匀的。例如,可以通过离心来浓缩混合物中相对密度较大的组分。<br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform. Considerations of kinetic theory or statistical mechanics also support this statement.<br />
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热力学平衡系统中的温度在空间和时间上是均匀的。在一个系统内部热力学平衡状态下,没有净内部宏观流动。特别是,这意味着系统的所有局部部分处于相互辐射交换平衡状态。这意味着系统的温度在空间上是均匀的。动力学理论或统计力学也支持这种说法。<br />
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===Uniform temperature===<br />
均匀温度<br />
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In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium. As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.<br />
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为了使一个系统处于它自己的内部热力学平衡状态,它处于自己内部的热平衡状态当然是必要的,但不是充分的;系统在达到内部热平衡之前,可以达到内部机械平衡。如上所述,根据 A.Münster的说法,对于给定的孤立系统的任何状态,定义一个热力学平衡所需的变量数是最少的。如上所述,J.G.Kirkwood 和 I.Oppenheim 指出,热力学平衡状态可以由一个特殊的子类的强变量定义,该子类中有一定数量的成员。<br />
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Such equilibrium inhomogeneity, induced by external forces, does not occur for the intensive variable [[temperature]]. According to [[Edward A. Guggenheim|E.A. Guggenheim]], "The most important conception of thermodynamics is temperature."<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), p.5.</ref> Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface."<ref name="Planck 1903 3">[[Max Planck|Planck, M.]] (1897/1927), p.3.</ref> As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.<br />
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这种由外力引起的平衡不均匀性,在强烈变化的'''<font color="#ff8000">温度 Temperature</font>'''下不会发生。'''<font color="#ff8000">E.A.古根海姆 E.A. Guggenheim</font>'''认为,“热力学最重要的概念是温度。“Planck在介绍他的论文时,简要叙述了热、温度和热平衡,然后宣布: ”在下文中,我们将主要讨论任何形式的均匀、各向同性的物体,它们的物质具有相同的温度和密度,并受到到处垂直于表面的均匀压力的作用和Carathéodory 一样,Planck将表面效应、外场和各向异性晶体排除在外。虽然Planck提到了温度,但并没有明确提到热力学平衡的概念。相比之下,Carathéodory关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ,虽然没有明确地使用短语‘热力学平衡’ ,也没有明确地假设存在一个温度来定义它。<br />
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<br />
If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.<br />
<br />
如果热力学平衡位于一个外力场中,那么通常只有温度在空间上是均匀的。如果外力场非零,温度以外的强度变量通常是不均匀的。在这种情况下,一般需要附加变量来描述空间非均匀性。<br />
<br />
The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform.<ref name="Planck 1914 40"/> This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers.<ref>Gibbs, J.W. (1876/1878), pp. 144-150.</ref><ref>[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966), pp. 127–130.</ref><ref>Münster, A. (1970), pp. 309–310.</ref><ref>Bailyn, M. (1994), pp. 254-256.</ref><ref>{{cite journal | last1 = Verkley | first1 = W.T.M. | last2 = Gerkema | first2 = T. | year = 2004 | title = On maximum entropy profiles | journal = J. Atmos. Sci. | volume = 61 | issue = 8| pages = 931–936 | doi=10.1175/1520-0469(2004)061<0931:omep>2.0.co;2| bibcode = 2004JAtS...61..931V | doi-access = free }}</ref><ref>{{cite journal | last1 = Akmaev | first1 = R.A. | year = 2008 | title = On the energetics of maximum-entropy temperature profiles | url = | journal = Q. J. R. Meteorol. Soc. | volume = 134 | issue = 630| pages = 187–197 | doi=10.1002/qj.209| bibcode = 2008QJRMS.134..187A }}</ref> Considerations of kinetic theory or statistical mechanics also support this statement.<ref>Maxwell, J.C. (1867).</ref><ref>Boltzmann, L. (1896/1964), p. 143.</ref><ref>Chapman, S., Cowling, T.G. (1939/1970), Section 4.14, pp. 75–78.</ref><ref>[[J. R. Partington|Partington, J.R.]] (1949), pp. 275–278.</ref><ref>{{cite journal | last1 = Coombes | first1 = C.A. | last2 = Laue | first2 = H. | year = 1985 | title = A paradox concerning the temperature distribution of a gas in a gravitational field | url = | journal = Am. J. Phys. | volume = 53 | issue = 3| pages = 272–273 | doi=10.1119/1.14138| bibcode = 1985AmJPh..53..272C }}</ref><ref>{{cite journal | last1 = Román | first1 = F.L. | last2 = White | first2 = J.A. | last3 = Velasco | first3 = S. | year = 1995 | title = Microcanonical single-particle distributions for an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 16 | issue = 2| pages = 83–90 | doi=10.1088/0143-0807/16/2/008| bibcode = 1995EJPh...16...83R }}</ref><ref>{{cite journal | last1 = Velasco | first1 = S. | last2 = Román | first2 = F.L. | last3 = White | first3 = J.A. | year = 1996 | title = On a paradox concerning the temperature distribution of an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 17 | issue = | pages = 43–44 | doi=10.1088/0143-0807/17/1/008}}</ref><br />
<br />
热力学平衡系统内的温度在时间和空间上都是均匀的。在一个处于内部热力学平衡的系统中,不存在净的内部宏观流动。特别是,这意味着系统的所有局部都处于相互辐射交换平衡。这意味着系统的温度在空间上是均匀的。这在所有情况下都是如此,包括那些非均匀外力场。对于外部施加的引力场,这可以通过使用朗朗日乘数的方法通过变化的演算在宏观热力学术语中证明。动力学理论或统计力学也支持这种说法。<br />
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In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium.<ref name="Fitts 43"/><br />
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为了使一个系统处于它自己的内部热力学平衡状态,它必须处于它自己的内部热平衡状态是必要不充分的; 一个系统在到达内部热平衡之前到达内部机械平衡是可能的。<br />
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As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.<br />
<br />
如上所述,j.r. Partington 指出热力学平衡状态在小的瞬态扰动下是稳定的。如果没有这个条件,一般来说,研究热力学平衡系统的实验就会遇到巨大的困难。<br />
<br />
===Number of real variables needed for specification===<br />
规范所需的实变量数目<br />
<br />
<br />
In his exposition of his scheme of closed system equilibrium thermodynamics, C. Carathéodory initially postulates that experiment reveals that a definite number of real variables define the states that are the points of the manifold of equilibria.<ref name="Caratheodory" /> In the words of Prigogine and Defay (1945): "It is a matter of experience that when we have specified a certain number of macroscopic properties of a system, then all the other properties are fixed."<ref>Prigogine, I., Defay, R. (1950/1954), p. 1.</ref><ref>Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005), p. 4.</ref> As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.<br />
<br />
在他关于封闭系统平衡态热力学方案的论述中,C.Carathéodory 最初假定实验揭示了一定数量的实变量定义了作为平衡态流形点的状态。用 Prigogine 和 Defay (1945)的话说: “这是一个经验问题,当我们确定了一个系统一定数量的宏观属性时,那么所有其他属性都是固定的。如上所述,A. Münster认为,定义热力学平衡所需的变量数量对于给定孤立系统的任何状态来说都是最少的。如上所述,J.G. Kirkwood 和 I. Oppenheim 指出,热力学平衡状态可以由一个特殊子类的强度变量来定义,该子类中有一定数量的成员。<br />
<br />
When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium. Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<br />
<br />
当一个物质体从不均匀的非平衡状态或化学非平衡状态开始,然后被孤立,它自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如,在这种演变的许多情况下,内部机械平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是,在这种演变的许多情况下,热平衡的发展要比化学平衡快得多。<br />
<br />
<br />
<br />
If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.<br />
<br />
如果热力学平衡位于一个外力场中,那么通常只有温度在空间上是均匀的。如果外力场非零,温度以外的强度变量通常是不均匀的。在这种情况下,一般需要附加变量来描述空间非均匀性。<br />
<br />
===Stability against small perturbations===<br />
对小扰动的稳定性<br />
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In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
<br />
在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
<br />
As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.<br />
<br />
如上所述,J.R. Partington 指出热力学平衡状态在小的瞬态扰动下是稳定的。如果没有这个条件,一般来说,研究热力学平衡系统的实验就会遇到严重的困难。<br />
<br />
<br />
To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics. But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
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考虑孤立热力学系统中的波动概念,一个方便的例子是由其广泛的状态变量、内能、体积和质量组成指定的系统。根据定义,它们是时不变的。根据定义,它们与它们的共轭状态密集函数的时不变名义值相结合,反向温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广泛的状态变量的值,不足以提供这些名义值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
<br />
===Approach to thermodynamic equilibrium within an isolated system===<br />
孤立系统中的热力学平衡<br />
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It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.<br />
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可以承认,在重复测量这些共轭强度函数时,发现它们的值随时间略有不同。这种可变性被认为是由于内部波动。不同测量值平均到其名义值。<br />
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When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium.<ref name="Fitts 43">Fitts, D.D. (1962), p. 43.</ref> Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<ref>Denbigh, K.G. (1951), p. 42.</ref><br />
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当一个物质体从不均匀的非平衡状态或化学非平衡状态开始,然后被孤立,它自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如,在这种演变的许多情况下,内部机械平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是,在这种演变的许多情况下,热平衡的发展要比化学平衡快得多。<br />
<br />
If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<br />
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如果这个系统真的像经典热力学所假定的那样是宏观的,那么这个系统的波动太小了,宏观上无法检测到。这就是所谓的热力学极限。实际上,物质的分子性质和动量转移的量子性质由于它们太小而看不见,已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中,平衡的波动概念是没有位置的。”<br />
<br />
===Fluctuations within an isolated system in its own internal thermodynamic equilibrium===<br />
孤立系统内部热力学平衡的波动<br />
<br />
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If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
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如果系统被重复细分,最终产生的系统足够小,可以表现出明显的波动。这是一个介观层面的研究。波动则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
<br />
In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
<br />
在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
<br />
<br />
If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
<br />
如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在波动过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,即需要量子统计力学。波动可以变得相对占主导地位,测量问题变得重要。<br />
<br />
To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics.<ref>Tschoegl, N.W. (2000). ''Fundamentals of Equilibrium and Steady-State Thermodynamics'', Elsevier, Amsterdam, {{ISBN|0-444-50426-5}}, p. 21.</ref> But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
<br />
考虑孤立热力学系统中的波动概念,一个方便的例子是由其众多的状态变量,内能、体积和质量组成指定的系统。根据定义,它们是时不变的。根据定义,它们与它们的共轭状态密集函数的时不变名义值相结合,反向温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广泛的状态变量的值,不足以提供这些名义值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
<br />
<br />
The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
<br />
"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有时间趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的标称值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微波动期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。非已知属于平衡状态的标称值,否则根据单一的度量无法进行判断。<br />
<br />
It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.<br />
<br />
可以承认,在重复测量这些共轭强度函数时,发现它们的值随时间略有不同。这种可变性被认为是由于内部波动。不同测量值平均到其名义值。<br />
<br />
<br />
<br />
If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<ref>Buchdahl, H.A. (1966), p. 16.</ref><br />
<br />
如果这个系统真的像经典热力学所假定的那样是宏观的,那么这个系统的波动太小了,宏观上无法检测到。这就是所谓的热力学极限。实际上,物质的分子性质和动量转移的量子性质由于它们太小而看不见,已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中,平衡的波动概念是没有位置的。”<br />
<br />
<br />
If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
<br />
如果系统被重复细分,最终产生的系统足够小,可以表现出明显的波动。这是一个介观层面的研究。波动则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
<br />
An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process." This illustrates the importance for thermodynamics of the concept of temperature.<br />
<br />
热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
<br />
<br />
<br />
If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在波动过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,即需要量子统计力学。波动可以变得相对占主导地位,测量问题变得重要。<br />
<br />
Thermal equilibrium is achieved when two systems in thermal contact with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<br />
<br />
当两个相互热接触的系统不再有净能量交换时,就会产生热平衡。因此,如果两个系统处于热平衡,那么它们的温度是相同的。<br />
<br />
<br />
<br />
The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
<br />
"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有时间趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的标称值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微波动期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。非已知属于平衡状态的标称值,否则根据单一的度量无法进行判断。<br />
<br />
Thermal equilibrium occurs when a system's macroscopic thermal observables have ceased to change with time. For example, an ideal gas whose distribution function has stabilised to a specific Maxwell–Boltzmann distribution would be in thermal equilibrium. This outcome allows a single temperature and pressure to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<br />
<br />
当系统的宏观热观测值不再随着时间变化时,就会出现热平衡。例如,一种分布函数稳定到一个特定的麦克斯韦-波兹曼分布的理想气体即处于热平衡状态。这个结果可以将单一的温度和压力归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是很有可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
<br />
=== Thermal equilibrium ===<br />
热平衡<br />
{{Main|Thermal equilibrium}}<br />
<br />
<br />
<br />
An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process."<ref>Eu, B.C. (2002), page 13.</ref> This illustrates the importance for thermodynamics of the concept of temperature.<br />
<br />
热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
<br />
A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<br />
<br />
一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数。<br />
<br />
<br />
<br />
[[Thermal equilibrium]] is achieved when two systems in [[thermal contact]] with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<ref>[[Raj Pathria|R. K. Pathria]], 1996</ref><br />
<br />
当两个相互'''<font color="#ff8000">热接触 Thermal Contact</font>'''的系统不再有净能量交换时,就会产生'''<font color="#ff8000">热平衡 Thermal Equilibrium</font>'''。因此,如果两个系统处于热平衡,那么它们的温度是相同的<br />
<br />
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
<br />
非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
<br />
<br />
<br />
Thermal equilibrium occurs when a system's [[macroscopic]] thermal observables have ceased to change with time. For example, an [[ideal gas]] whose [[Distribution function (physics)|distribution function]] has stabilised to a specific [[Maxwell–Boltzmann distribution]] would be in thermal equilibrium. This outcome allows a single [[temperature]] and [[pressure]] to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<ref>de Groot, S.R., Mazur, P. (1962), p. 44.</ref><br />
<br />
当一个系统的'''<font color="#ff8000">宏观 Macroscopic</font>'''热观测值不再随时间变化时,就会出现热平衡。例如,一种'''<font color="#ff8000">分布函数 Distribution Function</font>'''稳定到一个特定的'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''的'''<font color="#ff8000">理想气体 Ideal Gas</font>'''即处于热平衡状态。这个结果可以将单一的'''<font color="#ff8000">温度 Temperature</font>'''和'''<font color="#ff8000">压力 Pressure</font>'''归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
<br />
Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle. It states that a non-equilibrium system evolves such as to maximize its entropy production.<br />
<br />
定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
<br />
==Non-equilibrium==<br />
非平衡<br />
{{Main|Non-equilibrium thermodynamics}}<br />
<br />
<br />
<br />
Thermodynamic models <br />
<br />
热力学模型<br />
<br />
A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<ref>de Groot, S.R., Mazur, P. (1962), p. 43.</ref><br />
<br />
一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数<br />
<br />
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
<br />
非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
<br />
<br />
Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle.<ref>{{cite book|last1=Ziegler|first1=H.|title=An Introduction to Thermomechanics.|date=1983|location=North Holland, Amsterdam.}}</ref><ref>{{cite journal|last1=Onsager|first1=Lars|title=Reciprocal Relations in Irreversible Processes|journal=Phys. Rev.|date=1931|volume=37|issue=4|doi=10.1103/PhysRev.37.405|bibcode=1931PhRv...37..405O|pages=405–426|doi-access=free}}</ref> It states that a non-equilibrium system evolves such as to maximize its entropy production.<ref>{{cite book|last1=Kleidon|first1=A.|last2=et.|first2=al.|title=Non-equilibrium Thermodynamics and the Production of Entropy.|date=2005|edition=Heidelberg: Springer.}}</ref><ref>{{cite journal|last1=Belkin|first1=Andrey|last2=et.|first2=al.|title=Self-Assembled Wiggling Nano-Structures and the Principle of Maximum Entropy Production|journal=Sci. Rep.|doi=10.1038/srep08323|bibcode=2015NatSR...5E8323B|pmc=4321171|pmid=25662746|volume=5|year=2015|page=8323}}</ref><br />
<br />
定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
<br />
Topics in control theory<br />
<br />
控制理论主题<br />
<br />
==See also ==<br />
<br />
{{Portal|Chemistry}}<br />
<br />
;Thermodynamic models 热力学模型<br />
<br />
{{colbegin}}<br />
<br />
* [[Non-random two-liquid model]] (NRTL model) - Phase equilibrium calculations 非随机两液模型(NRTL 模型)-相平衡计算<br />
<br />
* [[UNIQUAC]] model - Phase equilibrium calculations UNIQUAC 模型-相平衡计算<br />
<br />
* [[Time crystal]] 时间晶体<br />
<br />
{{colend}}<br />
<br />
;Topics in control theory 控制理论主题<br />
<br />
{{colbegin}}<br />
<br />
* [[Steady state]] 稳态<br />
<br />
* [[Transient state]] 瞬态<br />
<br />
* [[Coefficient diagram method]] 系数图法<br />
<br />
* [[Control reconfiguration]] 控制重构<br />
<br />
* [[Cut-insertion theorem]] 切入定理<br />
<br />
* [[Feedback]] 反馈<br />
<br />
* [[H infinity]] H 无限<br />
<br />
* [[Hankel singular value]] 汉克尔奇异值<br />
<br />
* [[Krener's theorem]] 克雷纳定理<br />
<br />
* [[Lead-lag compensator]] 超前滞后补偿器<br />
<br />
* [[Minor loop feedback]] 小循环反馈<br />
<br />
* [[Minor loop feedback|Multi-loop feedback]] 小循环反馈 | 多循环反馈<br />
<br />
* [[Positive systems]] 正向系统<br />
<br />
* [[Radial basis function]] 径向基底函数<br />
<br />
Other related topics<br />
<br />
其他相关话题<br />
<br />
* [[Root locus]] 根轨迹<br />
<br />
* [[Signal-flow graph]]s 信号流图<br />
<br />
* [[Stable polynomial]] 稳定多项式<br />
<br />
* [[State space representation]] 状态空间<br />
<br />
* [[Underactuation]] 欠驱动<br />
<br />
* [[Youla–Kucera parametrization]] 尤拉-库切拉参数化<br />
<br />
* [[Markov chain approximation method]] 马尔可夫链近似法<br />
<br />
{{colend}}<br />
<br />
;Other related topics<br />
其他相关话题<br />
<br />
{{colbegin}}<br />
<br />
* [[Automation and remote control]] 自动化和远程控制<br />
<br />
* [[Bond graph]] 键合图<br />
<br />
* [[Control engineering]] 控制工程<br />
<br />
* [[Control–feedback–abort loop]] 控制-反馈-中止循环<br />
<br />
* [[Controller (control theory)]] 控制器(控制理论)<br />
<br />
* [[Cybernetics]] 控制论<br />
<br />
* [[Intelligent control]] 智能控制<br />
<br />
* [[Mathematical system theory]] 数学系统论<br />
<br />
* [[Negative feedback amplifier]] 负反馈放大器<br />
<br />
* [[People in systems and control]] 系统和控制中的人<br />
<br />
* [[Perceptual control theory]] 知觉控制理论<br />
<br />
* [[Systems theory]] 系统论<br />
<br />
* [[Time scale calculus]] 时间尺度演算<br />
<br />
{{colend}}<br />
<br />
<br />
<br />
== 编者推荐 ==<br />
===集智文章推荐===<br />
<br />
====[https://swarma.org/?p=21322 什么是非平衡态热力学 | 集智百科]====<br />
非平衡态热力学 Non-equilibrium thermodynamics 是热力学的一个分支,研究某些不处于热力学平衡中的物理系统<br />
<br />
<br />
<br />
<br />
==General references==<br />
<br />
* Cesare Barbieri (2007) ''Fundamentals of Astronomy''. First Edition (QB43.3.B37 2006) CRC Press {{ISBN|0-7503-0886-9}}, {{ISBN|978-0-7503-0886-1}}<br />
<br />
* Hans R. Griem (2005) ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}<br />
<br />
* C. Michael Hogan, Leda C. Patmore and Harry Seidman (1973) ''Statistical Prediction of Dynamic Thermal Equilibrium Temperatures using Standard Meteorological Data Bases'', Second Edition (EPA-660/2-73-003 2006) United States Environmental Protection Agency Office of Research and Development, Washington, D.C. [http://library.wur.nl/WebQuery/catalog/lang/1851848]<br />
<br />
* F. Mandl (1988) ''Statistical Physics'', Second Edition, John Wiley & Sons<br />
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<br />
==References==<br />
<br />
{{Reflist|colwidth=35em}}<br />
<br />
<br />
<br />
==Cited bibliography==<br />
<br />
<br />
<br />
*Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', third edition, McGraw-Hill, London, {{ISBN|0-521-25445-0}}.<br />
<br />
*Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, {{ISBN|0-88318-797-3}}.<br />
<br />
*Beattie, J.A., Oppenheim, I. (1979). ''Principles of Thermodynamics'', Elsevier Scientific Publishing, Amsterdam, {{ISBN|0-444-41806-7}}.<br />
<br />
*[[Ludwig Boltzmann|Boltzmann, L.]] (1896/1964). ''Lectures on Gas Theory'', translated by S.G. Brush, University of California Press, Berkeley.<br />
<br />
*Buchdahl, H.A. (1966). ''The Concepts of Classical Thermodynamics'', Cambridge University Press, Cambridge UK.<br />
<br />
*[[Herbert Callen|Callen, H.B.]] (1960/1985). ''Thermodynamics and an Introduction to Thermostatistics'', (1st edition 1960) 2nd edition 1985, Wiley, New York, {{ISBN|0-471-86256-8}}.<br />
<br />
*[[Constantin Carathéodory|Carathéodory, C.]] (1909). [https://web.archive.org/web/20160304213645/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0067&DMDID=DMDLOG_0033&L=1 Untersuchungen über die Grundlagen der Thermodynamik], ''[[Mathematische Annalen]]'', '''67''': 355–386. A translation may be found [http://neo-classical-physics.info/uploads/3/0/6/5/3065888/caratheodory_-_thermodynamics.pdf here]. Also a mostly reliable [https://books.google.com/books?id=xwBRAAAAMAAJ&q=Investigation+into+the+foundations translation is to be found] at Kestin, J. (1976). ''The Second Law of Thermodynamics'', Dowden, Hutchinson & Ross, Stroudsburg PA.<br />
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*[[Sydney Chapman (mathematician)|Chapman, S.]], [[Thomas George Cowling|Cowling, T.G.]] (1939/1970). ''The Mathematical Theory of Non-uniform gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases'', third edition 1970, Cambridge University Press, London.<br />
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*Crawford, F.H. (1963). ''Heat, Thermodynamics, and Statistical Physics'', Rupert Hart-Davis, London, Harcourt, Brace & World, Inc.<br />
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*de Groot, S.R., Mazur, P. (1962). ''Non-equilibrium Thermodynamics'', North-Holland, Amsterdam. Reprinted (1984), Dover Publications Inc., New York, {{ISBN|0486647412}}.<br />
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*Denbigh, K.G. (1951). ''Thermodynamics of the Steady State'', Methuen, London.<br />
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*Eu, B.C. (2002). ''Generalized Thermodynamics. The Thermodynamics of Irreversible Processes and Generalized Hydrodynamics'', Kluwer Academic Publishers, Dordrecht, {{ISBN|1-4020-0788-4}}.<br />
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*Fitts, D.D. (1962). ''Nonequilibrium thermodynamics. A Phenomenological Theory of Irreversible Processes in Fluid Systems'', McGraw-Hill, New York.<br />
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*[[Josiah Willard Gibbs|Gibbs, J.W.]] (1876/1878). On the equilibrium of heterogeneous substances, ''Trans. Conn. Acad.'', '''3''': 108–248, 343–524, reprinted in ''The Collected Works of J. Willard Gibbs, Ph.D, LL. D.'', edited by W.R. Longley, R.G. Van Name, Longmans, Green & Co., New York, 1928, volume 1, pp.&nbsp;55–353.<br />
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*Griem, H.R. (2005). ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}.<br />
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*[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', fifth revised edition, North-Holland, Amsterdam.<br />
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*Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of ''Thermodynamics'', pages 1–97 of volume 1, ed. W. Jost, of ''Physical Chemistry. An Advanced Treatise'', ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081.<br />
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*[[John Gamble Kirkwood|Kirkwood, J.G.]], Oppenheim, I. (1961). ''Chemical Thermodynamics'', McGraw-Hill Book Company, New York.<br />
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*Landsberg, P.T. (1961). ''Thermodynamics with Quantum Statistical Illustrations'', Interscience, New York.<br />
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*{{cite journal |last1=Lieb |first1=E. H. |last2=Yngvason |first2=J. |year=1999 |title=The Physics and Mathematics of the Second Law of Thermodynamics |journal=Phys. Rep. |volume=310 |issue= 1|pages=1–96 |doi= 10.1016/S0370-1573(98)00082-9|arxiv = cond-mat/9708200 |bibcode = 1999PhR...310....1L |s2cid=119620408 }}<br />
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*Levine, I.N. (1983), ''Physical Chemistry'', second edition, McGraw-Hill, New York, {{ISBN|978-0072538625}}.<br />
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*{{cite journal | last1 = Maxwell | first1 = J.C. | authorlink = James Clerk Maxwell | year = 1867 | title = On the dynamical theory of gases | url = | journal = Phil. Trans. Roy. Soc. London | volume = 157 | issue = | pages = 49–88 }}<br />
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*[[Philip M. Morse|Morse, P.M.]] (1969). ''Thermal Physics'', second edition, W.A. Benjamin, Inc, New York.<br />
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*Münster, A. (1970). ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London.<br />
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*[[J.R. Partington|Partington, J.R.]] (1949). ''An Advanced Treatise on Physical Chemistry'', volume 1, ''Fundamental Principles. The Properties of Gases'', Longmans, Green and Co., London.<br />
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*[[Brian Pippard|Pippard, A.B.]] (1957/1966). ''The Elements of Classical Thermodynamics'', reprinted with corrections 1966, Cambridge University Press, London.<br />
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* [[Max Planck|Planck. M.]] (1914). [https://archive.org/details/theoryofheatradi00planrich ''The Theory of Heat Radiation''], a translation by Masius, M. of the second German edition, P. Blakiston's Son & Co., Philadelphia.<br />
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*[[Ilya Prigogine|Prigogine, I.]] (1947). ''Étude Thermodynamique des Phénomènes irréversibles'', Dunod, Paris, and Desoers, Liège.<br />
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*[[Ilya Prigogine|Prigogine, I.]], Defay, R. (1950/1954). ''Chemical Thermodynamics'', Longmans, Green & Co, London.<br />
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*Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005). ''Physical Chemistry'', fourth edition, Wiley, Hoboken NJ.<br />
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*[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966). ''Elements of Thermodynamics'', Addison-Wesley Publishing, Reading MA.<br />
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*{{cite journal|last=Thomson|first=W.|author-link=William Thomson, 1st Baron Kelvin|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Transactions of the Royal Society of Edinburgh|date=March 1851|volume=XX|issue=part II|pages=261–268; 289–298}} Also published in {{cite journal|last=Thomson|first=W.|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Phil. Mag. |date=December 1852 |volume=IV |series=4 |issue=22 |pages=8–21 |url=https://archive.org/details/londonedinburghp04maga |accessdate=25 June 2012}}<br />
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*[[László Tisza|Tisza, L.]] (1966). ''Generalized Thermodynamics'', M.I.T Press, Cambridge MA.<br />
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*[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963). ''Lectures in Statistical Mechanics'', American Mathematical Society, Providence RI.<br />
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*Waldram, J.R. (1985). ''The Theory of Thermodynamics'', Cambridge University Press, Cambridge UK, {{ISBN|0-521-24575-3}}.<br />
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*[[Mark Zemansky|Zemansky, M.]] (1937/1968). ''Heat and Thermodynamics. An Intermediate Textbook'', fifth edition 1967, McGraw–Hill Book Company, New York.<br />
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== External links ==<br />
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Category:Equilibrium chemistry<br />
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类别: 平衡化学<br />
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*[http://ads.harvard.edu/books/1989fsa..book/AbookC15.pdf Breakdown of Local Thermodynamic Equilibrium] George W. Collins, The Fundamentals of Stellar Astrophysics, Chapter 15<br />
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Category:Thermodynamic cycles<br />
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类别: 热力循环<br />
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*[http://spiff.rit.edu/classes/phys440/lectures/lte/lte.html Thermodynamic Equilibrium, Local and otherwise] lecture by Michael Richmond<br />
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Category:Thermodynamic processes<br />
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类别: 热力学过程<br />
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*[http://journals.ametsoc.org/doi/abs/10.1175/1520-0469%281970%29027%3C0711:NLTEIC%3E2.0.CO%3B2 Non-Local Thermodynamic Equilibrium in Cloudy Planetary Atmospheres] Paper by R. E. Samueison quantifying the effects due to non-LTE in an atmosphere<br />
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Category:Thermodynamic systems<br />
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类别: 热力学系统<br />
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*[http://scienceworld.wolfram.com/physics/LocalThermodynamicEquilibrium.html Local Thermodynamic Equilibrium]<br />
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Category:Thermodynamics<br />
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分类: 热力学<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Thermodynamic equilibrium]]. Its edit history can be viewed at [[平衡热力学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Jxzhouhttps://wiki.swarma.org/index.php?title=%E5%B9%B3%E8%A1%A1%E7%83%AD%E5%8A%9B%E5%AD%A6&diff=21136平衡热力学2021-01-22T07:59:18Z<p>Jxzhou:/* Overview 概览 */</p>
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<div>此词条暂由小竹凉翻译,翻译字数共5339,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{short description|State of thermodynamic system(s) where no net macroscopic flow of matter or energy occurs}}<br />
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'''Thermodynamic equilibrium''' is an [[axiomatic]] concept of [[thermodynamics]]. It is an internal [[State variables|state]] of a single [[thermodynamic system]], or a relation between several thermodynamic systems connected by more or less permeable or impermeable [[Thermodynamic system#Walls|walls]]. In thermodynamic equilibrium there are no net [[macroscopic]] [[Flow (mathematics)|flows]] of [[matter]] or of [[energy]], either within a system or between systems. <br />
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Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium there are no net macroscopic flows of matter or of energy, either within a system or between systems. <br />
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'''热力学平衡'''是'''<font color="#ff8000">热力学 Thermodynamics</font>'''的一个'''<font color="#ff8000">不言自明的 Axiomatic</font>'''概念。它是单个'''<font color="#ff8000">热力学系统 Thermodynamic System</font>'''的内部'''<font color="#ff8000">状态 State</font>''',或者是几个热力学系统之间通过或多或少的渗透或不渗透的'''<font color="#ff8000">壁 Wall</font>'''连接的关系。无论是在一个系统内还是在系统之间,在热力学平衡中不存在'''<font color="#ff8000">物质 Matter</font>'''或'''<font color="#ff8000">能量 Energy</font>'''的净'''<font color="#ff8000">宏观 Macroscopic</font>''' '''<font color="#ff8000">流动 Flow</font>'''。<br />
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In a system that is in its own state of internal thermodynamic equilibrium, no [[macroscopic]] change occurs. <br />
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In a system that is in its own state of internal thermodynamic equilibrium, no macroscopic change occurs. <br />
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在一个处于内部热力学平衡状态的系统中,不会发生'''<font color="#ff8000">宏观 Macroscopic</font>'''变化。<br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual [[Thermal equilibrium|thermal]], [[Mechanical equilibrium|mechanical]], [[Chemical equilibrium|chemical]], and [[Radiative equilibrium|radiative]] equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a [[thermodynamic operation]]. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a thermodynamic operation. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. <br />
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相互热力学平衡的体系同时处于互相之间的'''<font color="#ff8000">热 Thermal</font>'''平衡、'''<font color="#ff8000">力学 Mechanical</font>'''平衡、'''<font color="#ff8000">化学 Chemical</font>'''平衡和'''<font color="#ff8000">辐射 Radiative</font>'''平衡。系统可以处于其中一种相互平衡状态,尽管其他状态未平衡。在热力学平衡中所有的平衡同时并且无限期地保持,直到被'''<font color="#ff8000">热力学操作 Thermodynamic Operation</font>'''打破。在一个宏观平衡中,微观交换是完全或几乎完全平衡的;这是对宏观平衡概念的物理解释。<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform [[temperature]]. Its [[Intensive and extensive properties|intensive properties]], other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform temperature. Its intensive properties, other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.<br />
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一个处于内部热力学状态平衡的热力学系统具有空间均匀的'''<font color="#ff8000">温度 Temperature</font>'''。除了温度以外,它的'''<font color="#ff8000">强度性质 Intensive Properties</font>'''可以由于周围环境施加的不变的长程力场而导致空间不均匀性。<br />
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In systems that are at a state of [[non-equilibrium]] there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a '''meta-stable equilibrium'''.<br />
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In systems that are at a state of non-equilibrium there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a meta-stable equilibrium.<br />
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相比之下,处于'''<font color="#ff8000">非平衡状态 non-equilibrium</font>'''的系统中有物质或能量的净流动。如果这些变化可以在一个还没有发生的系统中被触发,那么这个系统就被称为处于一个'''亚稳定的平衡状态'''。<br />
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Though not a widely named a "law," it is an [[axiom]] of thermodynamics that there exist states of thermodynamic equilibrium. The [[second law of thermodynamics]] states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the [[entropy|entropies]] of the portions.<br />
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Though not a widely named a "law," it is an axiom of thermodynamics that there exist states of thermodynamic equilibrium. The second law of thermodynamics states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the entropies of the portions.<br />
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虽然不是一个广泛命名的“定律” ,但存在热力学平衡状态是一个热力学'''<font color="#ff8000">公理 Axiom</font>'''。'''<font color="#ff8000">热力学第二定律 second law of thermodynamics</font>'''指出,当一个物质体从一个平衡状态开始,在这个状态中,它的一部分被或多或少渗透或不渗透的分区保持在不同的状态,并且是孤立的,热力学操作移除分区或使分区更具渗透性,然后它会自发地达到自己内部热力学平衡的新状态,并伴随着部分'''<font color="#ff8000">熵 Entropy</font>'''的总和增加。<br />
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== Overview 概览==<br />
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{{Thermodynamics|cTopic=[[Thermodynamic system|Systems]]}}<br />
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Classical thermodynamics deals with states of [[dynamic equilibrium]]. The state of a system at thermodynamic equilibrium is the one for which some [[thermodynamic potential]] is minimized, or for which the [[entropy]] (''S'') is maximized, for specified conditions. One such potential is the [[Helmholtz free energy]] (''A''), for a system with surroundings at controlled constant temperature and volume:<br />
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Classical thermodynamics deals with states of dynamic equilibrium. The state of a system at thermodynamic equilibrium is the one for which some thermodynamic potential is minimized, or for which the entropy (S) is maximized, for specified conditions. One such potential is the Helmholtz free energy (A), for a system with surroundings at controlled constant temperature and volume:<br />
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经典热力学研究'''<font color="#ff8000">动态平衡 Dynamic Equilibrium</font>'''的状态。系统的热力学平衡状态是对于特定的条件,一些'''<font color="#ff8000">热力学势 Thermodynamic Potential</font>'''被最小化,或者'''<font color="#ff8000">熵 Entropy</font>'''(S)被最大化。对于一个周围环境温度和体积恒定的系统,其中一个这样的热力学势是'''<font color="#ff8000">亥姆霍兹自由能 Helmholtz Free Energy</font>'''(A):<br />
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:<math>A = U - TS</math><br />
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<math>A = U - TS</math><br />
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A = U-TS<br />
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Another potential, the [[Gibbs free energy]] (''G''), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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Another potential, the Gibbs free energy (G), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:<br />
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在恒定温度和压力的系统中,另一个热力学势'''<font color="#ff8000">吉布斯自由能 Gibbs Free Energy</font>'''(G)在热力学平衡状态最小:<br />
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:<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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<math>G = U - TS + PV</math><br />
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where ''T'' denotes the absolute thermodynamic temperature, ''P'' the pressure, ''S'' the entropy, ''V'' the volume, and ''U'' the internal energy of the system.<br />
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where T denotes the absolute thermodynamic temperature, P the pressure, S the entropy, V the volume, and U the internal energy of the system.<br />
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其中 T 表示热力学绝对温度,P 表示压强,S 表示熵,V 表示体积,U 表示体系的内能。<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.<br />
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热力学平衡是一种独特的稳定定态,当系统长时间与周围环境相互作用时,它可以被接近或最终到达。上述势能是数学构造的热力学量,在特定的环境条件下最小化。<br />
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== Conditions ==<br />
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* For a completely isolated system, ''S'' is maximum at thermodynamic equilibrium. 对于一个完全孤立的系统,S是热力学平衡中最大值。<br />
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* For a system with controlled constant temperature and volume, ''A'' is minimum at thermodynamic equilibrium. 对于一个温度和体积可控的系统来说,A是热力学平衡的最小值。<br />
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* For a system with controlled constant temperature and pressure, ''G'' is minimum at thermodynamic equilibrium. 对于一个恒温恒压的系统,G是热力学平衡的最小值。<br />
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The various types of equilibriums are achieved as follows:<br />
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The various types of equilibriums are achieved as follows:<br />
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实现各种类型的平衡的方法如下:<br />
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*Two systems are in ''thermal equilibrium'' when their [[temperature]]s are the same. 当两个系统的'''<font color="#ff8000">温度 Temperature</font>'''相同时,它们就处于''热平衡状态''<br />
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*Two systems are in ''mechanical equilibrium'' when their [[pressure]]s are the same. 当两个体系的'''<font color="#ff8000">压力 Pressure</font>'''相同时,它们就处于''机械平衡''<br />
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*Two systems are in ''diffusive equilibrium'' when their [[chemical potential]]s are the same. 当两个题体系的'''<font color="#ff8000">化学势 Chemical Potential</font>'''相同时,它们就处于''扩散平衡''<br />
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*All [[forces]] are balanced and there is no significant external driving force.<br />
所有的'''<font color="#ff8000">力 Force</font>'''都是平衡的,没有明显的外部驱动力<br />
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==Relation of exchange equilibrium between systems==<br />
系统之间的交换均衡关系<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability.<ref name="Nster_a">Münster, A. (1970), p. 49.</ref> When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability. When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.<br />
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通常,热力学系统的周围环境也可以被看作是另一个热力学系统。在这种观点中,我们可以把系统及其周围环境看作是相互接触的两个系统,远程作用力也将它们联系在一起。系统的包围物是两个系统之间的接触面或边界。在热力学公式中,该表面被认为具有特定的渗透性质。例如,接触的表面可能被认为只能透热,使能量只能作为热传递。当远程力在时间上不发生变化,两个系统之间的热量传递减慢并最终永久停止时,这两个系统被称为热平衡; 这就是接触平衡的一个例子。其它类型的接触平衡可用其它类型的比渗透率来定义。当两个系统对于某一特定类型的渗透率处于接触平衡时,它们具有属于该特定类型渗透率的强度变量的共同值。这种强度变量的例子有温度、压力、化学势。<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.<br />
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接触平衡也可视为交换平衡。在接触平衡状态下,两系统之间某些量的传递速率存在零平衡。例如,对于只能透热的壁,内能作为热在两个系统之间的扩散速率是相等并相反的。两个系统之间的绝热壁只对作为功传递的能量有渗透作用; 在机械平衡,两个系统之间作为功的能量传递速率相等且相反。如果是一个简单的壁,那么通过它的体积转移率也是相等且相反的; 即它两边的压力是相等的。如果绝热壁比较复杂,有一种杠杆,有一个面积比,那么两个体系在交换平衡中的压力与体积交换比成反比,这使得转移率的零平衡作功。<br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<ref name="Planck 1914 40">[[Max Planck|Planck. M.]] (1914), p. 40.</ref><br />
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A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<br />
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辐射交换可以发生在两个不同的系统之间。当两个体系温度相同时,辐射交换平衡占优势。<br />
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==Thermodynamic state of internal equilibrium of a system==<br />
系统内部平衡的热力学状态<br />
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A collection of matter may be entirely [[Isolated system|isolated]] from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium.<ref>Haase, R. (1971), p. 4.</ref><ref>Callen, H.B. (1960/1985), p. 26.</ref> (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics.<ref>{{Cite journal |doi = 10.1119/1.4914528|bibcode = 2015AmJPh..83..628M|title = Time and irreversibility in axiomatic thermodynamics|year = 2015|last1 = Marsland|first1 = Robert|last2 = Brown|first2 = Harvey R.|last3 = Valente|first3 = Giovanni|journal = American Journal of Physics|volume = 83|issue = 7|pages = 628–634}}</ref> One textbook<ref>[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963), p. 5.</ref> calls it the "zeroth law", remarking that the authors think this more befitting that title than its [[Zeroth law of thermodynamics|more customary definition]], which apparently was suggested by [[Ralph H. Fowler|Fowler]].)<br />
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A collection of matter may be entirely isolated from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium. (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics. One textbook calls it the "zeroth law", remarking that the authors think this more befitting that title than its more customary definition, which apparently was suggested by Fowler.)<br />
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物质的集合可能与其周围的环境完全'''<font color="#ff8000">孤立 Isolated</font>'''。如果它在无限长的时间内一直保持不受干扰,按照经典热力学假定,它处于一个没有发生任何变化,没有流动的状态,即内部平衡的热力学状态。(这种假设有时被称为“负第一”热力学定律,但并不常见。有教科书称之为“第零定律” ,作者'''<font color="#ff8000">福勒 Fowler</font>'''认为这个名称是'''<font color="#ff8000">更符合惯例的定义 More Customary Definition</font>'''。)<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a [[thermodynamic operation]] be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a thermodynamic operation be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.<br />
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这种状态是所谓的经典热力学或平衡态热力学的主要关注点,因为它们是系统中被认为在这门学科中得到很好定义的唯一状态。一个与另一个系统处于接触平衡状态可以被一个'''<font color="#ff8000">热力运行 Thermodynamic Operation</font>'''隔离,在隔离发生时,其内部不会发生任何变化。因此,一个与另一个系统处于接触平衡状态时也可以被视为处于其自身的内部热力学平衡状态。<br />
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==Multiple contact equilibrium==<br />
多点接触平衡<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.<br />
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热力学形式论允许一个系统同时与其他多个系统接触,这些系统可能也可能没有相互接触,且这些接触具有不同的渗透性。如果这些系统都与世界其他部分相互隔离,那么它们彼此之间就会达到各自的接触平衡。<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy.<ref name="Caratheodory">Carathéodory, C. (1909).</ref><ref>Prigogine, I. (1947), p. 48.</ref><ref>Landsberg, P. T. (1961), pp. 128–142.</ref><ref>Tisza, L. (1966), p. 108.</ref> Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy. Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.<br />
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如果几个系统彼此之间没有绝热壁,但是它们与世界其他部分共同隔离,那么它们就会达到多重接触平衡状态,且有共同的温度,内能和熵。在众多变量中,这是温度的一个独特性质。即使在远距离作用力存在的情况下,它也是有效的。(也就是说,没有“力”可以维持温度的差异。)举个例子,在热力学平衡的一个垂直的引力场系统中,顶部壁面的压力比底部壁面的压力小,但是各处的温度都是一样的。<br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural [[thermodynamic process]].<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), § 1.12.</ref> It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings.<ref>Levine, I.N. (1983), p. 40.</ref><ref>Lieb, E.H., Yngvason, J. (1999), pp. 17–18.</ref> The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of [[Second law of thermodynamics#Description#Kelvin statement|"inanimate" agency]]; a system in thermodynamic equilibrium is inanimate.<ref>[[William Thomson, 1st Baron Kelvin|Thomson, W.]] (1851).</ref><br />
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A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural thermodynamic process. It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings. The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of "inanimate" agency; a system in thermodynamic equilibrium is inanimate.<br />
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热力运行可能作为一个事件发生在周围环境的壁上,既不直接影响与周围环境联系的壁,也不直接影响其内部,且发生在一个明确的有限的时间内。例如,一个固定的绝热壁可以在环境中被放置或拆除。由于这种操作仅限于周围环境,系统可能会在一段时间内远离自身最初的内部状态---- 热力学平衡。根据热力学第二定律的说法,整体经历了变化并最终与周围环境达到了新的平衡。继Planck之后,这一连串的事件被称为自然'''<font color="#ff8000">热力学过程 Thermodynamic Process</font>'''。即使在这个过程中,当系统和周围环境都不处于明确的内部平衡状态时,存在着暂时偏离热力学平衡的现象,由于初始状态和最终状态都是热力学平衡的,这在平衡热力学中也是允许的。一个自然过程在其主要部分中以有限的速率进行,因此,它从根本上不同于虚构的准静态“过程”;即不在整个过程中无限缓慢地进行而且虚构地“可逆”。经典热力学允许,即使一个过程可能需要很长的时间才能达到热力学平衡,如果主要部分的过程是在一个有限的比率中,那么它被认为是自然的,并受制于热力学第二定律,即不可逆的。工程设计的机器、人工设备和操作是允许在周围环境中进行的。允许在环境中而不是在系统中进行此类操作和设备,是开尔文在他的一个热力学第二定律的陈述中提到'''<font color="#ff8000">无生命机构 Inanimate Agency</font>'''的原因; 在热力学平衡的系统是无生命的。<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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Otherwise, a thermodynamic operation may directly affect a wall of the system.<br />
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否则,热力运行可能会直接影响系统的壁。<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.<br />
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通常可以很方便地假设周围的某些子系统比系统大得多,以至于这个过程只能影响周围子系统的强度变量,然后将这些子系统称为相关强度变量的储备库。<br />
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== Local and global equilibrium ==<br />
局部和全局均衡<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by [[intensive quantity|intensive]] parameters. As an example, [[temperature]] controls [[Heat equation|heat exchanges]]. ''Global thermodynamic equilibrium'' (GTE) means that those [[intensive quantity|intensive]] parameters are homogeneous throughout the whole system, while ''local thermodynamic equilibrium'' (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by intensive parameters. As an example, temperature controls heat exchanges. Global thermodynamic equilibrium (GTE) means that those intensive parameters are homogeneous throughout the whole system, while local thermodynamic equilibrium (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.<br />
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区分全局性和局部性热力学平衡是很有用的。在热力学中,系统内部和系统与外部之间的交换是由'''<font color="#ff8000">强度 Intensive</font>'''参数控制的。例如,'''<font color="#ff8000">温度 Temperature</font>'''控制'''<font color="#ff8000">热交换 Heat Equation</font>'''。全局热力学平衡(GTE)意味着这些'''<font color="#ff8000">强度 Intensive</font>'''参数在整个系统中是均匀的,而局部热力学平衡(LTE)意味着这些强度参数在空间和时间上是变化的,但变化如此缓慢,以至于对于任何一点,人们都可以假设在某个邻近的某个热力学平衡。<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.<br />
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如果对系统的描述要求强度参数的变化过大,那么这些强度参数的定义所依据的假设本身就会破裂,系统将既不处于全局平衡,也不处于局部平衡。例如,粒子需要一定数量的碰撞来平衡其周围环境。如果在这些碰撞中移动的平均距离使它离开平衡邻域,它将永远不会平衡,也就不会有 LTE。根据定义,温度与平衡邻域的平均内部能量成正比。由于没有达到平衡邻域,温度的概念就不成立,温度也就变得不确定。<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to [[massive]] particles. In a [[radiation|radiating]] gas, the [[photon]]s being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to massive particles. In a radiating gas, the photons being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.<br />
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值得注意的是,这种局部平衡可能只适用于系统中的某个粒子子集。例如,LTE 通常只适用于'''<font color="#ff8000">大 Massive</font>'''质量粒子。在'''<font color="#ff8000">辐射 Radiation</font>'''气体中,被气体发射和吸收的'''<font color="#ff8000">光子 Photon</font>'''不需要彼此在一个热力学平衡内,或与气体中的大量粒子在一起,LTE 才能存在。在某些情况下,自由电子并不需要与大得多的原子或分子处于平衡状态,LTE 才能存在。<br />
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As an example, LTE will exist in a glass of water that contains a melting [[ice cube]]. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the [[Maxwell–Boltzmann distribution]] for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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As an example, LTE will exist in a glass of water that contains a melting ice cube. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.<br />
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例如,LTE 将存在于一个装有融化的'''<font color="#ff8000">冰块 Ice Cube</font>'''的水杯中。玻璃杯内的温度可以在任何时候定义,但是离冰块近的地方要比离冰块远的地方冷。如果观察到位于给定点附近的分子的能量,它们将按照麦克斯韦-波兹曼分布在一定温度下的分布。如果观察到位于另一点附近的分子的能量,它们将按照'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''分布到另一个温度。<br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural [[transport phenomena]] may lead a system from local to global thermodynamic equilibrium. Going back to our example, the [[diffusion]] of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<ref>H.R. Griem, 2005</ref><br />
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Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural transport phenomena may lead a system from local to global thermodynamic equilibrium. Going back to our example, the diffusion of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.<br />
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局部热力学平衡不需要局部或全局的平稳性。换句话说,每一个小区域不需要有一个恒定的温度。然而,它确实要求每个小的局部变化缓慢到足以维持其局部麦克斯韦-波兹曼分布的分子速度。全局非平衡态只有通过系统与外界的交换才能保持稳定。例如,通过在水杯中不断添加细粉冰来补偿熔化,并持续排出融水,可以保持全球稳定的静止状态。自然'''<font color="#ff8000">迁移现象 Transport Phenomena</font>'''可能导致一个从局部到全局的热力学平衡系统。回顾我们的例子,热量的扩散将导致我们的玻璃杯水流向全局热力学平衡,在这种状态下,玻璃杯的温度是完全均匀的。<br />
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==Reservations==<br />
保留意见<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.<br />
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学识渊博的笔者在热力学领域对热力学平衡描述时,经常对他们的描述附加条件或保留意见。有些笔者含蓄地保留了或多或少的空白,以待说明。<br />
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For example, one widely cited writer, [[Herbert Callen|H. B. Callen]] writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. ''Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!''"<ref>Callen, H.B. (1960/1985), p. 15.</ref><br />
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For example, one widely cited writer, H. B. Callen writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!"<br />
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例如,一位被广泛引用的作家'''<font color="#ff8000">H.B.卡伦 H.B.Callen</font>'''在这里写道: “实际上,很少有系统处于绝对和真正的平衡状态。”他提到了放射性过程,认为它们可能需要“宇宙时间才能完成,因此通常可以忽略”。他补充道: “在实践中,平衡的标准是循环的。在操作上,如果一个系统的性质一致地用热力学理论来描述,那么它就处于平衡状态! ”<br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<ref>Beattie, J.A., Oppenheim, I. (1979), p. 3.</ref><br />
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J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."<br />
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J.A.贝蒂和 I.奥本海姆写道: “坚持对平衡定义的严格解释,将排除热力学应用于实际系统的所有状态。”<br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment",<ref>Callen, H.B. (1960/1985), p. 485.</ref> and cited by Adkins as having written a "classic text",<ref>Adkins, C.J. (1968/1983), p. ''xiii''.</ref> [[Brian Pippard|A.B. Pippard]] writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<ref>Pippard, A.B. (1957/1966), p. 6.</ref><br />
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Another author, cited by Callen as giving a "scholarly and rigorous treatment", and cited by Adkins as having written a "classic text", A.B. Pippard writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10<sup>100</sup> years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."<br />
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Callen引用另一位作者的话说,他给出了“学术且严谨的论述” ,Adkins引用他的话说,他写了一本“经典著作”—— '''<font color="#ff8000">A.B.皮帕德 A.B.Pippard</font>'''在文中写道: “只要时间足够长,过冷水蒸汽最终会凝结,... ..。时间可能是漫长的,也许长达10年或者更长。就大多数目的而言,只要这种迅速的变化不是人为地刺激,这些系统就可以被视为处于平衡状态。”<br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster">Münster, A. (1970), p. 53.</ref><br />
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Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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另一位作者A.Münster,写道。他观察到热核反应发生的速度非常缓慢,以至于在热力学中可以忽略不计。他评论道: “‘绝对平衡’或‘所有可想象过程的平衡’的概念没有物理意义。”他说: “ ... 我们只能考虑特定过程和确定的实验条件下的平衡。”<br />
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According to [[László Tisza|L. Tisza]]: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<ref>Tisza, L. (1966), p. 119.</ref><br />
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According to L. Tisza: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."<br />
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根据'''<font color="#ff8000">L.缇莎 L.Tisza</font>'''的说法: “ ... 在讨论接近绝对零度的现象时。经典理论的绝对预测变得特别模糊,因为在非平衡状态下发生冻结是非常普遍的。”<br />
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==Definitions==<br />
定义<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.<br />
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一个系统最普遍的热力学平衡是通过与周围环境的接触,允许所有化学物质和各种能量同时通过。热力学平衡中的系统以均匀加速度在空间中运动,但此时不能改变其形状或大小; 因此它是由空间中的刚性体积来定义的。它可能存在于外力场中,由远远大于系统本身的外部因素决定,因此系统内的事件不会对外力场产生相当大的影响。只有当外力场是均匀的,并且确定了它的均匀加速度,或者它处于一个非均匀力场中,但是由于表面的局部力,例如机械压力,使它保持静止时,这个系统才能处于热力学平衡。<br />
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Thermodynamic equilibrium is a [[primitive notion]] of the theory of thermodynamics. According to [[Philip M. Morse|P.M. Morse]]: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are ''not'' conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments."<ref>[[Philip M. Morse|Morse, P.M.]] (1969), p. 7.</ref> This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<ref>Bailyn, M. (1994), p. 20.</ref><br />
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Thermodynamic equilibrium is a primitive notion of the theory of thermodynamics. According to P.M. Morse: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are not conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments." This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.<br />
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热力学平衡是热力学理论的一个'''<font color="#ff8000">基本概念 Primitive Notion</font>'''。'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''说: “应该强调的是,存在热力学状态这一事实,以及存在由平衡态唯一指定的热力学变量这一事实,并不是从某些哲学第一原理得出的逻辑结论。这些结论不可避免地来自两个多世纪的实验。”这意味着热力学平衡不能仅仅用热力学的其他理论概念来定义。M.Bailyn提出了一个基本的热力学定律理论,它定义并假设了热力学平衡的存在。<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.<br />
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热力学平衡的教科书定义通常被仔细说明,并有些保留。<br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<ref>Münster, A. (1970), p. 52.</ref><br />
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For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.<br />
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例如,A. Münster写道:“当系统中没有以可测量的速度发生状态变化时,隔离系统处于热力学平衡状态。”这里有两项保留:系统是孤立的;任何状态的变化都是不可估量的缓慢。他通过对在室温且没有催化剂的情况下混合氧和氢的说明,讨论了第二个条件。Münster指出,热力学平衡状态所描述的宏观变量比给定系统任何其他状态都少。这是部分,但不完全是,因为系统内和系统内的所有流都是零。<br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in ''equilibrium''.<ref>Haase, R. (1971), pp. 3–4.</ref><br />
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R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in equilibrium.<br />
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R. Haase's的热力学演示并不从对热力学平衡的限制开始,因为他打算考虑非平衡态热力学。他考虑一个具有时间不变性质的任意系统。他通过切断除外力场以外的所有外部影响来测试它的热力学平衡。如果在绝缘之后,没有任何变化,他说,系统处于平衡状态。<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness".<ref>Callen, H.B. (1960/1985), p. 13.</ref> This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness". This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".<br />
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在一个标题为“热力学平衡”的章节中,H.B. Callen在段落定义了平衡状态.他指出,它们“是由系统内部的内在因素决定的”。它们是“终端状态” ,随着时间的推移,系统会以“冰川般缓慢”的速度朝着这个终端状态演化。这个说法并没有明确,对于热力学平衡系统必须是孤立的;;Callen也没有说明他所说的“内在因素”是什么意思。<br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<ref>Adkins, C.J. (1968/1983), p. ''7''.</ref><br />
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Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.<br />
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另一位教科书作者,C.J.Adkins,明确允许热力学平衡在非孤立的系统中发生。然而,他的系统在物质转移方面是封闭的。他写道: “一般来说,热力学平衡的方法包括热和类似变动与周围环境的相互作用。”他将这种热力学平衡与只有通过热接触才能进行能量传递的热平衡相区别。<br />
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Another textbook author, [[J.R. Partington]], writes: "(i) ''An equilibrium state is one which is independent of time''." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..."<ref>Partington, J.R. (1949), p. 161.</ref> This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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Another textbook author, J.R. Partington, writes: "(i) An equilibrium state is one which is independent of time." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..." This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.<br />
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另一位教科书作者'''<font color="#ff8000">J.R.帕廷顿 J.R.Partington</font>'''写道: “(i)平衡状态是独立于时间的状态。”但是,在提到“只是明显处于平衡状态”的系统时,他补充说: “这样的系统处于‘虚假平衡’状态。帕廷顿的陈述没有明确指出平衡是指一个孤立的系统。和Münster一样,Partington也指的是氧和氢的混合物。他补充说:“在一个真正的平衡状态,任何影响状态的外部条件的最小变化都会产生一个微小的状态变化... ... ”这个条件意味着热力学平衡必须在小的扰动下保持稳定; 这个要求对于热力学平衡的严格意义是必不可少的。<br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, ''thermodynamic—equilibrium.''"<ref>Crawford, F.H. (1963), p. 5.</ref><br />
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A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, thermodynamic—equilibrium."<br />
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在F.H.Crawford的一本学生教科书中,有一个标题为“热力学平衡”的章节。它区分了几种流动的驱动因素,然后说: “这些是孤立系统明显普遍趋向于完全机械、热、化学和电力状态的例子——或者简单地说,热力学平衡状态。”<br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in ''equilibrium''."<ref>Buchdahl, H.A. (1966), p. 8.</ref> Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being ''in equilibrium'' so long as experimental tests show that 'slow' transitions are in effect reversible."<ref>Buchdahl, H.A. (1966), p. 111.</ref> It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<ref>Adkins, C.J. (1968/1983), p. 8.</ref><br />
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A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in equilibrium." Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being in equilibrium so long as experimental tests show that 'slow' transitions are in effect reversible." It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.<br />
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H.A. Buchdahl的一本关于经典热力学的专著考虑了热力学系统的平衡,而实际上并没有写热力学平衡一词。Buchdahl在提到封闭的物质交换系统时写道: “如果一个系统处于一个适当的静态状态,那么它将被称为处于平衡状态。”出于热力学描述的目的,Buchdahl的专著也讨论了非晶态玻璃。它说: “更准确地说,只要实验测试表明‘慢’跃迁实际上是可逆的,玻璃就可以被认为处于平衡状态。”通常来说不会将这一条件作为热力学平衡定义的一部分,而是假定相反的情况:如果热力学平衡中的一个体受到足够慢的过程的影响,则该过程可被视为足够接近可逆,并且该物体在过程中足够接近热力学平衡。<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of ''contact equilibrium''. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by [[Constantin Carathéodory|C. Carathéodory]], and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <ref name="Nster" /> Thermodynamic equilibrium for an open system means that, with respect to every relevant kind of selectively permeable wall, contact equilibrium exists when the respective intensive parameters of the system and surroundings are equal.<ref name="Nster_a" /> This definition does not consider the most general kind of thermodynamic equilibrium, which is through unselective contacts. This definition does not simply state that no current of matter or energy exists in the interior or at the boundaries; but it is compatible with the following definition, which does so state.<br />
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A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of contact equilibrium. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by C. Carathéodory, and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." <br />
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通过引入接触平衡的概念,A. Münster仔细地扩展了孤立系统热力学平衡的定义。这指定了在考虑非孤立系统的热力学平衡时允许的特定过程,并特别关心开放系统,这些开放系统可能从周围环境获得或丢失物质。利益系统和周围系统之间的接触平衡,通过一种特殊的壁与利益系统接触,其余的连接系统是孤立的。这种特殊类型的壁也被'''<font color="#ff8000">C.喀喇西奥多里 C.Carathéodory</font>'''考虑过,其他作家也提到过。它们具有选择渗透性。它们可能只对机械工作有渗透性,或者只对热有渗透性,或者只对某种特定的化学物质有渗透性。每个接触平衡定义了一个强度参数; 例如,只能透热的壁定义了一个经验温度。对于感兴趣的体系中每一种化学成分,都可以存在接触平衡。在接触平衡中,尽管有可能通过选择性渗透壁进行交换,感兴趣的系统是不变的,好像它处在孤立的热力学平衡。这个方案遵循的一般规则是: “ ... ... 我们只能考虑特定过程和特定实验条件下的平衡。”<br />
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[[Mark Zemansky|M. Zemansky]] also distinguishes mechanical, chemical, and thermal equilibrium. He then writes: "When the conditions for all three types of equilibrium are satisfied, the system is said to be in a state of thermodynamic equilibrium".<ref>[[Mark Zemansky|Zemansky, M.]] (1937/1968), p. 27.</ref><br />
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'''<font color="#ff8000">M.泽曼斯基 M.Zemansky</font>'''还区分了机械、化学和热平衡。他接着写道: “当这三种均衡的条件都满足时,系统就处于热力学平衡状态。”<br />
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P.M. Morse writes that thermodynamics is concerned with "states of thermodynamic equilibrium". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<br />
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[[Philip M. Morse|P.M. Morse]] writes that thermodynamics is concerned with "''states of thermodynamic equilibrium''". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.<ref>[[Philip M. Morse|Morse, P.M.]] (1969), pp. 6, 37.</ref><br />
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'''<font color="#ff8000">P.M.莫尔斯 P.M.Morse</font>'''写道,热力学关注的是“热力学平衡状态”。在讨论物体与周围热源之间的热量传递时,他也使用了“热平衡”这个短语,尽管没有明确定义一个特殊的术语“热平衡”<br />
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<br />
J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "full thermodynamic equilibrium state".<br />
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J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "''full'' thermodynamic equilibrium state".<ref>Waldram, J.R. (1985), p. 5.</ref><br />
<br />
J.R. Waldram写到了“一个明确的热力学状态”。他将一个系统定义为“当其观测量随时间停止变化时”的“热平衡”。但是在这个定义之下不久,他写到一块玻璃还没有达到“完全的热力学平衡状态”。<br />
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<br />
Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, thermodynamic equilibrium is said to exist." He is not here considering the presence of an external force field.<br />
<br />
Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, ''thermodynamic equilibrium'' is said to exist." He is not here considering the presence of an external force field.<ref>Bailyn, M. (1994), p. 21.</ref><br />
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考虑到平衡状态,M.Bailyn写道: “每个强度变量都有自己的平衡类型。”然后他定义了热平衡、机械平衡和物质平衡。因此,他写道: “如果所有的强度变量都是一致的,那么热力学平衡就是存在的。”他在这里没有考虑外力场的存在。<br />
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<br />
J.G. Kirkwood and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of thermodynamic equilibrium if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<br />
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[[John Gamble Kirkwood|J.G. Kirkwood]] and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of ''thermodynamic equilibrium'' if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<ref>Kirkwood, J.G., Oppenheim, I. (1961), p. 2</ref><br />
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'''<font color="#ff8000">J.G.柯克伍德 J.G.Kirkwood</font>'''和 I.Oppenheim 将热力学平衡定义为: “一个系统处于热力学平衡状态,如果,在分配给实验的时间内,(a)它强度特性与时间无关,(b)它的内部或与周围环境的边界处没有物质或能量流。”显然,他们没有把定义限制在孤立的或封闭的系统。它们不讨论“缓慢”发生变化的可能性,并且超出了分配给实验的时间范围。他们注意到,对于两个相接触的系统,存在一个强度性质的小子类,如果这个小子类的所有子类都相等,那么所有各自的强度性质都相等。只要满足其他一些条件,热力学平衡状态可以由这个子类定义。<br />
<br />
==Characteristics of a state of internal thermodynamic equilibrium==<br />
内部热力学平衡状态的特征<br />
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<br />
A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous. Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface." As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.<br />
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在内部热力学平衡中,没有外力的情况下由单相组成的热力学系统是均匀的。Planck在论文中简要介绍了热量、温度和热平衡,然后宣布: “在下文中,我们将主要讨论任何形式的均匀、各向同性的物体,它们在整个物质中具有相同的温度和密度,并受到到处垂直于表面的均匀压力作用。”和 Carathéodory 一样,Planck 将表面效应、外场和各向异性晶体排除在外。虽然Planck提到了温度,但并没有明确提到热力学平衡的概念。相比之下,Carathéodory 关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ,虽然没有明确地使用短语‘热力学平衡’,也没有明确地假设存在一个温度来定义它。<br />
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===Homogeneity in the absence of external forces===<br />
在没有外力的情况下的同质性<br />
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A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous.<ref name="Planck 1903 3"/> This means that the material in any small volume element of the system can be interchanged with the material of any other geometrically congruent volume element of the system, and the effect is to leave the system thermodynamically unchanged. In general, a strong external force field makes a system of a single phase in its own internal thermodynamic equilibrium inhomogeneous with respect to some [[Intensive and extensive properties|intensive variables]]. For example, a relatively dense component of a mixture can be concentrated by centrifugation.<br />
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在没有外力的情况下,由单一相组成的热力学系统,在其自身的内部热力学平衡中是均匀的。这意味着系统中任何小体积单元中的材料可以与系统中任何其他几何相等的体积单元中的材料互换,其效果是使系统在热力学上保持不变。一般来说,一个强外力场使得一个单相系统在其自身的内部热力学平衡中对于一些'''<font color="#ff8000">强变量 Intensive Variable</font>'''是不均匀的。例如,可以通过离心来浓缩混合物中相对密度较大的组分。<br />
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The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform. Considerations of kinetic theory or statistical mechanics also support this statement.<br />
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热力学平衡系统中的温度在空间和时间上是均匀的。在一个系统内部热力学平衡状态下,没有净内部宏观流动。特别是,这意味着系统的所有局部部分处于相互辐射交换平衡状态。这意味着系统的温度在空间上是均匀的。动力学理论或统计力学也支持这种说法。<br />
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===Uniform temperature===<br />
均匀温度<br />
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In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium. As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.<br />
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为了使一个系统处于它自己的内部热力学平衡状态,它处于自己内部的热平衡状态当然是必要的,但不是充分的;系统在达到内部热平衡之前,可以达到内部机械平衡。如上所述,根据 A.Münster的说法,对于给定的孤立系统的任何状态,定义一个热力学平衡所需的变量数是最少的。如上所述,J.G.Kirkwood 和 I.Oppenheim 指出,热力学平衡状态可以由一个特殊的子类的强变量定义,该子类中有一定数量的成员。<br />
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Such equilibrium inhomogeneity, induced by external forces, does not occur for the intensive variable [[temperature]]. According to [[Edward A. Guggenheim|E.A. Guggenheim]], "The most important conception of thermodynamics is temperature."<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), p.5.</ref> Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface."<ref name="Planck 1903 3">[[Max Planck|Planck, M.]] (1897/1927), p.3.</ref> As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.<br />
<br />
这种由外力引起的平衡不均匀性,在强烈变化的'''<font color="#ff8000">温度 Temperature</font>'''下不会发生。'''<font color="#ff8000">E.A.古根海姆 E.A. Guggenheim</font>'''认为,“热力学最重要的概念是温度。“Planck在介绍他的论文时,简要叙述了热、温度和热平衡,然后宣布: ”在下文中,我们将主要讨论任何形式的均匀、各向同性的物体,它们的物质具有相同的温度和密度,并受到到处垂直于表面的均匀压力的作用和Carathéodory 一样,Planck将表面效应、外场和各向异性晶体排除在外。虽然Planck提到了温度,但并没有明确提到热力学平衡的概念。相比之下,Carathéodory关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ,虽然没有明确地使用短语‘热力学平衡’ ,也没有明确地假设存在一个温度来定义它。<br />
<br />
<br />
If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.<br />
<br />
如果热力学平衡位于一个外力场中,那么通常只有温度在空间上是均匀的。如果外力场非零,温度以外的强度变量通常是不均匀的。在这种情况下,一般需要附加变量来描述空间非均匀性。<br />
<br />
The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform.<ref name="Planck 1914 40"/> This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers.<ref>Gibbs, J.W. (1876/1878), pp. 144-150.</ref><ref>[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966), pp. 127–130.</ref><ref>Münster, A. (1970), pp. 309–310.</ref><ref>Bailyn, M. (1994), pp. 254-256.</ref><ref>{{cite journal | last1 = Verkley | first1 = W.T.M. | last2 = Gerkema | first2 = T. | year = 2004 | title = On maximum entropy profiles | journal = J. Atmos. Sci. | volume = 61 | issue = 8| pages = 931–936 | doi=10.1175/1520-0469(2004)061<0931:omep>2.0.co;2| bibcode = 2004JAtS...61..931V | doi-access = free }}</ref><ref>{{cite journal | last1 = Akmaev | first1 = R.A. | year = 2008 | title = On the energetics of maximum-entropy temperature profiles | url = | journal = Q. J. R. Meteorol. Soc. | volume = 134 | issue = 630| pages = 187–197 | doi=10.1002/qj.209| bibcode = 2008QJRMS.134..187A }}</ref> Considerations of kinetic theory or statistical mechanics also support this statement.<ref>Maxwell, J.C. (1867).</ref><ref>Boltzmann, L. (1896/1964), p. 143.</ref><ref>Chapman, S., Cowling, T.G. (1939/1970), Section 4.14, pp. 75–78.</ref><ref>[[J. R. Partington|Partington, J.R.]] (1949), pp. 275–278.</ref><ref>{{cite journal | last1 = Coombes | first1 = C.A. | last2 = Laue | first2 = H. | year = 1985 | title = A paradox concerning the temperature distribution of a gas in a gravitational field | url = | journal = Am. J. Phys. | volume = 53 | issue = 3| pages = 272–273 | doi=10.1119/1.14138| bibcode = 1985AmJPh..53..272C }}</ref><ref>{{cite journal | last1 = Román | first1 = F.L. | last2 = White | first2 = J.A. | last3 = Velasco | first3 = S. | year = 1995 | title = Microcanonical single-particle distributions for an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 16 | issue = 2| pages = 83–90 | doi=10.1088/0143-0807/16/2/008| bibcode = 1995EJPh...16...83R }}</ref><ref>{{cite journal | last1 = Velasco | first1 = S. | last2 = Román | first2 = F.L. | last3 = White | first3 = J.A. | year = 1996 | title = On a paradox concerning the temperature distribution of an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 17 | issue = | pages = 43–44 | doi=10.1088/0143-0807/17/1/008}}</ref><br />
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热力学平衡系统内的温度在时间和空间上都是均匀的。在一个处于内部热力学平衡的系统中,不存在净的内部宏观流动。特别是,这意味着系统的所有局部都处于相互辐射交换平衡。这意味着系统的温度在空间上是均匀的。这在所有情况下都是如此,包括那些非均匀外力场。对于外部施加的引力场,这可以通过使用朗朗日乘数的方法通过变化的演算在宏观热力学术语中证明。动力学理论或统计力学也支持这种说法。<br />
<br />
<br />
In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium.<ref name="Fitts 43"/><br />
<br />
为了使一个系统处于它自己的内部热力学平衡状态,它必须处于它自己的内部热平衡状态是必要不充分的; 一个系统在到达内部热平衡之前到达内部机械平衡是可能的。<br />
<br />
As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.<br />
<br />
如上所述,j.r. Partington 指出热力学平衡状态在小的瞬态扰动下是稳定的。如果没有这个条件,一般来说,研究热力学平衡系统的实验就会遇到巨大的困难。<br />
<br />
===Number of real variables needed for specification===<br />
规范所需的实变量数目<br />
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<br />
In his exposition of his scheme of closed system equilibrium thermodynamics, C. Carathéodory initially postulates that experiment reveals that a definite number of real variables define the states that are the points of the manifold of equilibria.<ref name="Caratheodory" /> In the words of Prigogine and Defay (1945): "It is a matter of experience that when we have specified a certain number of macroscopic properties of a system, then all the other properties are fixed."<ref>Prigogine, I., Defay, R. (1950/1954), p. 1.</ref><ref>Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005), p. 4.</ref> As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.<br />
<br />
在他关于封闭系统平衡态热力学方案的论述中,C.Carathéodory 最初假定实验揭示了一定数量的实变量定义了作为平衡态流形点的状态。用 Prigogine 和 Defay (1945)的话说: “这是一个经验问题,当我们确定了一个系统一定数量的宏观属性时,那么所有其他属性都是固定的。如上所述,A. Münster认为,定义热力学平衡所需的变量数量对于给定孤立系统的任何状态来说都是最少的。如上所述,J.G. Kirkwood 和 I. Oppenheim 指出,热力学平衡状态可以由一个特殊子类的强度变量来定义,该子类中有一定数量的成员。<br />
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When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium. Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<br />
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当一个物质体从不均匀的非平衡状态或化学非平衡状态开始,然后被孤立,它自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如,在这种演变的许多情况下,内部机械平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是,在这种演变的许多情况下,热平衡的发展要比化学平衡快得多。<br />
<br />
<br />
<br />
If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.<br />
<br />
如果热力学平衡位于一个外力场中,那么通常只有温度在空间上是均匀的。如果外力场非零,温度以外的强度变量通常是不均匀的。在这种情况下,一般需要附加变量来描述空间非均匀性。<br />
<br />
===Stability against small perturbations===<br />
对小扰动的稳定性<br />
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In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
<br />
在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
<br />
As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.<br />
<br />
如上所述,J.R. Partington 指出热力学平衡状态在小的瞬态扰动下是稳定的。如果没有这个条件,一般来说,研究热力学平衡系统的实验就会遇到严重的困难。<br />
<br />
<br />
To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics. But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
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考虑孤立热力学系统中的波动概念,一个方便的例子是由其广泛的状态变量、内能、体积和质量组成指定的系统。根据定义,它们是时不变的。根据定义,它们与它们的共轭状态密集函数的时不变名义值相结合,反向温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广泛的状态变量的值,不足以提供这些名义值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
<br />
===Approach to thermodynamic equilibrium within an isolated system===<br />
孤立系统中的热力学平衡<br />
<br />
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It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.<br />
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可以承认,在重复测量这些共轭强度函数时,发现它们的值随时间略有不同。这种可变性被认为是由于内部波动。不同测量值平均到其名义值。<br />
<br />
When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium.<ref name="Fitts 43">Fitts, D.D. (1962), p. 43.</ref> Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.<ref>Denbigh, K.G. (1951), p. 42.</ref><br />
<br />
当一个物质体从不均匀的非平衡状态或化学非平衡状态开始,然后被孤立,它自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如,在这种演变的许多情况下,内部机械平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是,在这种演变的许多情况下,热平衡的发展要比化学平衡快得多。<br />
<br />
If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<br />
<br />
如果这个系统真的像经典热力学所假定的那样是宏观的,那么这个系统的波动太小了,宏观上无法检测到。这就是所谓的热力学极限。实际上,物质的分子性质和动量转移的量子性质由于它们太小而看不见,已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中,平衡的波动概念是没有位置的。”<br />
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===Fluctuations within an isolated system in its own internal thermodynamic equilibrium===<br />
孤立系统内部热力学平衡的波动<br />
<br />
<br />
If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
<br />
如果系统被重复细分,最终产生的系统足够小,可以表现出明显的波动。这是一个介观层面的研究。波动则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
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In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.<br />
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在一个孤立的系统中,根据定义,热力学平衡可以持续无限长的时间。在经典物理学中,忽略测量的影响通常是很方便的,现在我们假设这一点。<br />
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If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
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如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在波动过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,即需要量子统计力学。波动可以变得相对占主导地位,测量问题变得重要。<br />
<br />
To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics.<ref>Tschoegl, N.W. (2000). ''Fundamentals of Equilibrium and Steady-State Thermodynamics'', Elsevier, Amsterdam, {{ISBN|0-444-50426-5}}, p. 21.</ref> But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.<br />
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考虑孤立热力学系统中的波动概念,一个方便的例子是由其众多的状态变量,内能、体积和质量组成指定的系统。根据定义,它们是时不变的。根据定义,它们与它们的共轭状态密集函数的时不变名义值相结合,反向温度,压力除以温度,化学势除以温度,以便准确地服从热力学定律。但是热力学定律加上指定广泛的状态变量的值,不足以提供这些名义值的知识。我们需要进一步的信息,即关于该系统的构成特性的信息。<br />
<br />
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The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
<br />
"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有时间趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的标称值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微波动期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。非已知属于平衡状态的标称值,否则根据单一的度量无法进行判断。<br />
<br />
It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.<br />
<br />
可以承认,在重复测量这些共轭强度函数时,发现它们的值随时间略有不同。这种可变性被认为是由于内部波动。不同测量值平均到其名义值。<br />
<br />
<br />
<br />
If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."<ref>Buchdahl, H.A. (1966), p. 16.</ref><br />
<br />
如果这个系统真的像经典热力学所假定的那样是宏观的,那么这个系统的波动太小了,宏观上无法检测到。这就是所谓的热力学极限。实际上,物质的分子性质和动量转移的量子性质由于它们太小而看不见,已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中,平衡的波动概念是没有位置的。”<br />
<br />
<br />
If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.<br />
<br />
如果系统被重复细分,最终产生的系统足够小,可以表现出明显的波动。这是一个介观层面的研究。波动则直接取决于系统各壁的性质。因此,精确地选择独立状态变量是很重要的。在这个阶段,热力学定律的统计特征变得明显。<br />
<br />
An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process." This illustrates the importance for thermodynamics of the concept of temperature.<br />
<br />
热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
<br />
<br />
<br />
If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.<br />
如果介观系统进一步重复分裂,最终产生一个微观系统。物质的分子性质和动量传递的量子性质在波动过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域,即需要量子统计力学。波动可以变得相对占主导地位,测量问题变得重要。<br />
<br />
Thermal equilibrium is achieved when two systems in thermal contact with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<br />
<br />
当两个相互热接触的系统不再有净能量交换时,就会产生热平衡。因此,如果两个系统处于热平衡,那么它们的温度是相同的。<br />
<br />
<br />
<br />
The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.<br />
<br />
"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地,许多这样的测量是不时进行的,在各种测量值中没有时间趋势"。因此,一个系统处于它自己的内部热力学平衡,它的状态变量与它状态变量共轭函数的标称值相对应,这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微波动期间进行的,而不是由于未知和不同的构成属性而导致的,即远离那些共轭的状态密集函数的另一组名义值。非已知属于平衡状态的标称值,否则根据单一的度量无法进行判断。<br />
<br />
Thermal equilibrium occurs when a system's macroscopic thermal observables have ceased to change with time. For example, an ideal gas whose distribution function has stabilised to a specific Maxwell–Boltzmann distribution would be in thermal equilibrium. This outcome allows a single temperature and pressure to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<br />
<br />
当系统的宏观热观测值不再随着时间变化时,就会出现热平衡。例如,一种分布函数稳定到一个特定的麦克斯韦-波兹曼分布的理想气体即处于热平衡状态。这个结果可以将单一的温度和压力归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是很有可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
<br />
=== Thermal equilibrium ===<br />
热平衡<br />
{{Main|Thermal equilibrium}}<br />
<br />
<br />
<br />
An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process."<ref>Eu, B.C. (2002), page 13.</ref> This illustrates the importance for thermodynamics of the concept of temperature.<br />
<br />
热平衡和热力学平衡之间的明确区分是由 B.C.Eu 提出的。他认为两个系统在热接触,一个是温度计,另一个是一个系统,其中有几个不可逆过程,产生非零通量; 这两个系统被一个只透热的壁隔开。他考虑了这样一种情况,在有兴趣的时间尺度上,温度计读数和不可逆过程都是稳定的。然后是没有热平衡的热力学平衡。因此,Eu提出,即使在没有热力学第零定律的情况下,也可以考虑应用热力学平衡; 他还提出,如果变化发生得太快,以至于无法确定一个稳定的温度,那么“用热力学形式主义来描述这一过程就不再可能了。换句话说,热力学对这样一个过程没有意义。”这说明了温度概念对热力学的重要性。<br />
<br />
A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<br />
<br />
一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数。<br />
<br />
<br />
<br />
[[Thermal equilibrium]] is achieved when two systems in [[thermal contact]] with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.<ref>[[Raj Pathria|R. K. Pathria]], 1996</ref><br />
<br />
当两个相互'''<font color="#ff8000">热接触 Thermal Contact</font>'''的系统不再有净能量交换时,就会产生'''<font color="#ff8000">热平衡 Thermal Equilibrium</font>'''。因此,如果两个系统处于热平衡,那么它们的温度是相同的<br />
<br />
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
<br />
非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
<br />
<br />
<br />
Thermal equilibrium occurs when a system's [[macroscopic]] thermal observables have ceased to change with time. For example, an [[ideal gas]] whose [[Distribution function (physics)|distribution function]] has stabilised to a specific [[Maxwell–Boltzmann distribution]] would be in thermal equilibrium. This outcome allows a single [[temperature]] and [[pressure]] to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.<ref>de Groot, S.R., Mazur, P. (1962), p. 44.</ref><br />
<br />
当一个系统的'''<font color="#ff8000">宏观 Macroscopic</font>'''热观测值不再随时间变化时,就会出现热平衡。例如,一种'''<font color="#ff8000">分布函数 Distribution Function</font>'''稳定到一个特定的'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''的'''<font color="#ff8000">理想气体 Ideal Gas</font>'''即处于热平衡状态。这个结果可以将单一的'''<font color="#ff8000">温度 Temperature</font>'''和'''<font color="#ff8000">压力 Pressure</font>'''归因于整个系统。对于一个孤立的物体来说,在达到热平衡之前达到机械平衡是可能的,但是最终,所有方面的平衡,包括热平衡,对于热力学平衡来说都是必要的。<br />
<br />
Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle. It states that a non-equilibrium system evolves such as to maximize its entropy production.<br />
<br />
定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
<br />
==Non-equilibrium==<br />
非平衡<br />
{{Main|Non-equilibrium thermodynamics}}<br />
<br />
<br />
<br />
Thermodynamic models <br />
<br />
热力学模型<br />
<br />
A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.<ref>de Groot, S.R., Mazur, P. (1962), p. 43.</ref><br />
<br />
一个不孤立的系统的热力学平衡内部状态应该区别于一个在时间上不变的热力学参数的“定态”,因此在系统内外有非零的宏观流动,这些流动在时间上是常数<br />
<br />
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.<br />
<br />
非平衡热力学是热力学的一个分支,研究的是非热力学平衡系统。大多数在自然界中发现的系统并不处于热力学平衡状态,因为它们正在变化或者可能随着时间而发生变化,并且不断地和不连续地受到来自其他系统的物质和能量流动的影响。非平衡系统的热力学研究比平衡态热力学研究需要更多的一般概念。许多自然系统今天仍然超出了目前已知的宏观热力学方法的范围。<br />
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<br />
Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle.<ref>{{cite book|last1=Ziegler|first1=H.|title=An Introduction to Thermomechanics.|date=1983|location=North Holland, Amsterdam.}}</ref><ref>{{cite journal|last1=Onsager|first1=Lars|title=Reciprocal Relations in Irreversible Processes|journal=Phys. Rev.|date=1931|volume=37|issue=4|doi=10.1103/PhysRev.37.405|bibcode=1931PhRv...37..405O|pages=405–426|doi-access=free}}</ref> It states that a non-equilibrium system evolves such as to maximize its entropy production.<ref>{{cite book|last1=Kleidon|first1=A.|last2=et.|first2=al.|title=Non-equilibrium Thermodynamics and the Production of Entropy.|date=2005|edition=Heidelberg: Springer.}}</ref><ref>{{cite journal|last1=Belkin|first1=Andrey|last2=et.|first2=al.|title=Self-Assembled Wiggling Nano-Structures and the Principle of Maximum Entropy Production|journal=Sci. Rep.|doi=10.1038/srep08323|bibcode=2015NatSR...5E8323B|pmc=4321171|pmid=25662746|volume=5|year=2015|page=8323}}</ref><br />
<br />
定律规定远离平衡的系统也是有争议的。这些系统的指导原则之一就是最大产生熵原则。它指出,非平衡系统可以最大化其产生熵进行演化。<br />
<br />
Topics in control theory<br />
<br />
控制理论主题<br />
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==See also ==<br />
<br />
{{Portal|Chemistry}}<br />
<br />
;Thermodynamic models 热力学模型<br />
<br />
{{colbegin}}<br />
<br />
* [[Non-random two-liquid model]] (NRTL model) - Phase equilibrium calculations 非随机两液模型(NRTL 模型)-相平衡计算<br />
<br />
* [[UNIQUAC]] model - Phase equilibrium calculations UNIQUAC 模型-相平衡计算<br />
<br />
* [[Time crystal]] 时间晶体<br />
<br />
{{colend}}<br />
<br />
;Topics in control theory 控制理论主题<br />
<br />
{{colbegin}}<br />
<br />
* [[Steady state]] 稳态<br />
<br />
* [[Transient state]] 瞬态<br />
<br />
* [[Coefficient diagram method]] 系数图法<br />
<br />
* [[Control reconfiguration]] 控制重构<br />
<br />
* [[Cut-insertion theorem]] 切入定理<br />
<br />
* [[Feedback]] 反馈<br />
<br />
* [[H infinity]] H 无限<br />
<br />
* [[Hankel singular value]] 汉克尔奇异值<br />
<br />
* [[Krener's theorem]] 克雷纳定理<br />
<br />
* [[Lead-lag compensator]] 超前滞后补偿器<br />
<br />
* [[Minor loop feedback]] 小循环反馈<br />
<br />
* [[Minor loop feedback|Multi-loop feedback]] 小循环反馈 | 多循环反馈<br />
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* [[Positive systems]] 正向系统<br />
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* [[Radial basis function]] 径向基底函数<br />
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Other related topics<br />
<br />
其他相关话题<br />
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* [[Root locus]] 根轨迹<br />
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* [[Signal-flow graph]]s 信号流图<br />
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* [[Stable polynomial]] 稳定多项式<br />
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* [[State space representation]] 状态空间<br />
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* [[Underactuation]] 欠驱动<br />
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* [[Youla–Kucera parametrization]] 尤拉-库切拉参数化<br />
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* [[Markov chain approximation method]] 马尔可夫链近似法<br />
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;Other related topics<br />
其他相关话题<br />
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{{colbegin}}<br />
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* [[Automation and remote control]] 自动化和远程控制<br />
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* [[Bond graph]] 键合图<br />
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* [[Control engineering]] 控制工程<br />
<br />
* [[Control–feedback–abort loop]] 控制-反馈-中止循环<br />
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* [[Controller (control theory)]] 控制器(控制理论)<br />
<br />
* [[Cybernetics]] 控制论<br />
<br />
* [[Intelligent control]] 智能控制<br />
<br />
* [[Mathematical system theory]] 数学系统论<br />
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* [[Negative feedback amplifier]] 负反馈放大器<br />
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* [[People in systems and control]] 系统和控制中的人<br />
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* [[Perceptual control theory]] 知觉控制理论<br />
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* [[Systems theory]] 系统论<br />
<br />
* [[Time scale calculus]] 时间尺度演算<br />
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{{colend}}<br />
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<br />
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== 编者推荐 ==<br />
===集智文章推荐===<br />
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====[https://swarma.org/?p=21322 什么是非平衡态热力学 | 集智百科]====<br />
非平衡态热力学 Non-equilibrium thermodynamics 是热力学的一个分支,研究某些不处于热力学平衡中的物理系统<br />
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==General references==<br />
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* Cesare Barbieri (2007) ''Fundamentals of Astronomy''. First Edition (QB43.3.B37 2006) CRC Press {{ISBN|0-7503-0886-9}}, {{ISBN|978-0-7503-0886-1}}<br />
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* Hans R. Griem (2005) ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}<br />
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* C. Michael Hogan, Leda C. Patmore and Harry Seidman (1973) ''Statistical Prediction of Dynamic Thermal Equilibrium Temperatures using Standard Meteorological Data Bases'', Second Edition (EPA-660/2-73-003 2006) United States Environmental Protection Agency Office of Research and Development, Washington, D.C. [http://library.wur.nl/WebQuery/catalog/lang/1851848]<br />
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* F. Mandl (1988) ''Statistical Physics'', Second Edition, John Wiley & Sons<br />
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==References==<br />
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{{Reflist|colwidth=35em}}<br />
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==Cited bibliography==<br />
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*Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', third edition, McGraw-Hill, London, {{ISBN|0-521-25445-0}}.<br />
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*Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, {{ISBN|0-88318-797-3}}.<br />
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*Beattie, J.A., Oppenheim, I. (1979). ''Principles of Thermodynamics'', Elsevier Scientific Publishing, Amsterdam, {{ISBN|0-444-41806-7}}.<br />
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*[[Ludwig Boltzmann|Boltzmann, L.]] (1896/1964). ''Lectures on Gas Theory'', translated by S.G. Brush, University of California Press, Berkeley.<br />
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*Buchdahl, H.A. (1966). ''The Concepts of Classical Thermodynamics'', Cambridge University Press, Cambridge UK.<br />
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*[[Herbert Callen|Callen, H.B.]] (1960/1985). ''Thermodynamics and an Introduction to Thermostatistics'', (1st edition 1960) 2nd edition 1985, Wiley, New York, {{ISBN|0-471-86256-8}}.<br />
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*[[Constantin Carathéodory|Carathéodory, C.]] (1909). [https://web.archive.org/web/20160304213645/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0067&DMDID=DMDLOG_0033&L=1 Untersuchungen über die Grundlagen der Thermodynamik], ''[[Mathematische Annalen]]'', '''67''': 355–386. A translation may be found [http://neo-classical-physics.info/uploads/3/0/6/5/3065888/caratheodory_-_thermodynamics.pdf here]. Also a mostly reliable [https://books.google.com/books?id=xwBRAAAAMAAJ&q=Investigation+into+the+foundations translation is to be found] at Kestin, J. (1976). ''The Second Law of Thermodynamics'', Dowden, Hutchinson & Ross, Stroudsburg PA.<br />
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*[[Sydney Chapman (mathematician)|Chapman, S.]], [[Thomas George Cowling|Cowling, T.G.]] (1939/1970). ''The Mathematical Theory of Non-uniform gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases'', third edition 1970, Cambridge University Press, London.<br />
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*Crawford, F.H. (1963). ''Heat, Thermodynamics, and Statistical Physics'', Rupert Hart-Davis, London, Harcourt, Brace & World, Inc.<br />
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*de Groot, S.R., Mazur, P. (1962). ''Non-equilibrium Thermodynamics'', North-Holland, Amsterdam. Reprinted (1984), Dover Publications Inc., New York, {{ISBN|0486647412}}.<br />
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*Denbigh, K.G. (1951). ''Thermodynamics of the Steady State'', Methuen, London.<br />
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*Eu, B.C. (2002). ''Generalized Thermodynamics. The Thermodynamics of Irreversible Processes and Generalized Hydrodynamics'', Kluwer Academic Publishers, Dordrecht, {{ISBN|1-4020-0788-4}}.<br />
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*Fitts, D.D. (1962). ''Nonequilibrium thermodynamics. A Phenomenological Theory of Irreversible Processes in Fluid Systems'', McGraw-Hill, New York.<br />
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*[[Josiah Willard Gibbs|Gibbs, J.W.]] (1876/1878). On the equilibrium of heterogeneous substances, ''Trans. Conn. Acad.'', '''3''': 108–248, 343–524, reprinted in ''The Collected Works of J. Willard Gibbs, Ph.D, LL. D.'', edited by W.R. Longley, R.G. Van Name, Longmans, Green & Co., New York, 1928, volume 1, pp.&nbsp;55–353.<br />
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*Griem, H.R. (2005). ''Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)'', Cambridge University Press, New York {{ISBN|0-521-61941-6}}.<br />
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*[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', fifth revised edition, North-Holland, Amsterdam.<br />
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*Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of ''Thermodynamics'', pages 1–97 of volume 1, ed. W. Jost, of ''Physical Chemistry. An Advanced Treatise'', ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081.<br />
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*[[John Gamble Kirkwood|Kirkwood, J.G.]], Oppenheim, I. (1961). ''Chemical Thermodynamics'', McGraw-Hill Book Company, New York.<br />
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*Landsberg, P.T. (1961). ''Thermodynamics with Quantum Statistical Illustrations'', Interscience, New York.<br />
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*{{cite journal |last1=Lieb |first1=E. H. |last2=Yngvason |first2=J. |year=1999 |title=The Physics and Mathematics of the Second Law of Thermodynamics |journal=Phys. Rep. |volume=310 |issue= 1|pages=1–96 |doi= 10.1016/S0370-1573(98)00082-9|arxiv = cond-mat/9708200 |bibcode = 1999PhR...310....1L |s2cid=119620408 }}<br />
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*Levine, I.N. (1983), ''Physical Chemistry'', second edition, McGraw-Hill, New York, {{ISBN|978-0072538625}}.<br />
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*{{cite journal | last1 = Maxwell | first1 = J.C. | authorlink = James Clerk Maxwell | year = 1867 | title = On the dynamical theory of gases | url = | journal = Phil. Trans. Roy. Soc. London | volume = 157 | issue = | pages = 49–88 }}<br />
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*[[Philip M. Morse|Morse, P.M.]] (1969). ''Thermal Physics'', second edition, W.A. Benjamin, Inc, New York.<br />
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*Münster, A. (1970). ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London.<br />
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*[[J.R. Partington|Partington, J.R.]] (1949). ''An Advanced Treatise on Physical Chemistry'', volume 1, ''Fundamental Principles. The Properties of Gases'', Longmans, Green and Co., London.<br />
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*[[Brian Pippard|Pippard, A.B.]] (1957/1966). ''The Elements of Classical Thermodynamics'', reprinted with corrections 1966, Cambridge University Press, London.<br />
<br />
* [[Max Planck|Planck. M.]] (1914). [https://archive.org/details/theoryofheatradi00planrich ''The Theory of Heat Radiation''], a translation by Masius, M. of the second German edition, P. Blakiston's Son & Co., Philadelphia.<br />
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*[[Ilya Prigogine|Prigogine, I.]] (1947). ''Étude Thermodynamique des Phénomènes irréversibles'', Dunod, Paris, and Desoers, Liège.<br />
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*[[Ilya Prigogine|Prigogine, I.]], Defay, R. (1950/1954). ''Chemical Thermodynamics'', Longmans, Green & Co, London.<br />
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*Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005). ''Physical Chemistry'', fourth edition, Wiley, Hoboken NJ.<br />
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*[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966). ''Elements of Thermodynamics'', Addison-Wesley Publishing, Reading MA.<br />
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*{{cite journal|last=Thomson|first=W.|author-link=William Thomson, 1st Baron Kelvin|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Transactions of the Royal Society of Edinburgh|date=March 1851|volume=XX|issue=part II|pages=261–268; 289–298}} Also published in {{cite journal|last=Thomson|first=W.|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam|journal=Phil. Mag. |date=December 1852 |volume=IV |series=4 |issue=22 |pages=8–21 |url=https://archive.org/details/londonedinburghp04maga |accessdate=25 June 2012}}<br />
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*[[László Tisza|Tisza, L.]] (1966). ''Generalized Thermodynamics'', M.I.T Press, Cambridge MA.<br />
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*[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963). ''Lectures in Statistical Mechanics'', American Mathematical Society, Providence RI.<br />
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*Waldram, J.R. (1985). ''The Theory of Thermodynamics'', Cambridge University Press, Cambridge UK, {{ISBN|0-521-24575-3}}.<br />
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*[[Mark Zemansky|Zemansky, M.]] (1937/1968). ''Heat and Thermodynamics. An Intermediate Textbook'', fifth edition 1967, McGraw–Hill Book Company, New York.<br />
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== External links ==<br />
<br />
Category:Equilibrium chemistry<br />
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类别: 平衡化学<br />
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*[http://ads.harvard.edu/books/1989fsa..book/AbookC15.pdf Breakdown of Local Thermodynamic Equilibrium] George W. Collins, The Fundamentals of Stellar Astrophysics, Chapter 15<br />
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Category:Thermodynamic cycles<br />
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类别: 热力循环<br />
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*[http://spiff.rit.edu/classes/phys440/lectures/lte/lte.html Thermodynamic Equilibrium, Local and otherwise] lecture by Michael Richmond<br />
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Category:Thermodynamic processes<br />
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类别: 热力学过程<br />
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*[http://journals.ametsoc.org/doi/abs/10.1175/1520-0469%281970%29027%3C0711:NLTEIC%3E2.0.CO%3B2 Non-Local Thermodynamic Equilibrium in Cloudy Planetary Atmospheres] Paper by R. E. Samueison quantifying the effects due to non-LTE in an atmosphere<br />
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Category:Thermodynamic systems<br />
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类别: 热力学系统<br />
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*[http://scienceworld.wolfram.com/physics/LocalThermodynamicEquilibrium.html Local Thermodynamic Equilibrium]<br />
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Category:Thermodynamics<br />
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分类: 热力学<br />
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<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Thermodynamic equilibrium]]. Its edit history can be viewed at [[平衡热力学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Jxzhou