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Moved page from wikipedia:en:Ludwig Boltzmann (history)
此词条暂由彩云小译翻译，翻译字数共2507，未经人工整理和审校，带来阅读不便，请见谅。
{{redirect|Boltzmann}}
{{Infobox scientist
{{Infobox scientist
{信息盒科学家
| image = Boltzmann2.jpg
| image = Boltzmann2.jpg
2.jpg
| image_size = 225px
| image_size = 225px
225px
| caption = Ludwig Boltzmann
| caption = Ludwig Boltzmann
图片来源: 路德维希·玻尔兹曼
| birth_name = Ludwig Eduard Boltzmann
| birth_name = Ludwig Eduard Boltzmann
出生名字 = 路德维希·玻尔兹曼
| birth_date = {{Birth date|1844|2|20|mf=y}}
| birth_date =
出生日期
| birth_place= [[Vienna]], [[Austrian Empire]]
| birth_place= Vienna, Austrian Empire
出生地: 奥地利帝国维也纳
| death_date = {{death date and age|1906|9|5|1844|2|20|mf=y}}
| death_date =
死亡日期
| death_place= [[Tybein]], [[Triest]], [[Austria-Hungary]]
| death_place= Tybein, Triest, Austria-Hungary
死亡地点: Tybein，Triest，Austria-Hungary
| death_cause = [[Suicide by hanging]]
| death_cause = Suicide by hanging
死因 = 上吊自杀
| nationality = Austrian
| nationality = Austrian
| 国籍: 奥地利
| alma_mater = [[University of Vienna]]
| alma_mater = University of Vienna
维也纳大学
| doctoral_advisor = [[Josef Stefan]]
| doctoral_advisor = Josef Stefan
博士导师约瑟夫 · 斯蒂芬
| academic_advisors = {{plainlist|
| academic_advisors = {{plainlist|
学术顾问 = { plainlist |
*[[Robert Bunsen]]
*[[Leo Königsberger]]
*[[Gustav Kirchhoff]]
*[[Hermann von Helmholtz]]}}
| doctoral_students = {{Plainlist|
| doctoral_students = {{Plainlist|
博士生 = { Plainlist |
* [[Paul Ehrenfest]]
* [[Philipp Frank]]
* [[Gustav Herglotz]]
* [[Franc Hočevar]]
* [[Ignacij Klemenčič]]}}
| notable_students = {{Plainlist|
| notable_students = {{Plainlist|
2012年10月12日
*[[Lise Meitner]]
*[[Stefan Meyer (physicist)|Stefan Meyer]]}}
| known_for = {{Plainlist|
| known_for = {{Plainlist|
已知 | for = {{ Plainlist |
* [[Boltzmann constant]]
* [[Boltzmann equation]]
* [[Boltzmann distribution]]
* [[Detailed balance]]
* [[H-theorem|''H''-theorem]]
* [[Maxwell–Boltzmann distribution]]
* [[Stefan–Boltzmann constant]]
* [[Stefan–Boltzmann law]]
* [[Maxwell-Boltzmann statistics]]
* [[Boltzmann factor]]
* [[Epistemological idealism]]
}}
}}
}}
| signature = Ludwig Boltzmann signature.svg
| signature = Ludwig Boltzmann signature.svg
签名 = 路德维希·玻尔兹曼/签名
| field = [[Physics]]
| field = Physics
| field = 物理
| work_institution = {{Plainlist|
| work_institution = {{Plainlist|
2009年10月11日
* [[University of Graz]]
* [[University of Vienna]]
* [[University of Munich]]
* [[University of Leipzig]]}}
| prizes = [[Fellow of the Royal Society|ForMemRS]] (1899)<ref name=frs/>
| prizes = ForMemRS (1899) Max Planck named the constant, , the Boltzmann constant.
1899年，马克斯 · 普朗克将这个常数命名为波兹曼常数。
}}
Statistical mechanics is one of the pillars of modern physics. It describes how macroscopic observations (such as temperature and pressure) are related to microscopic parameters that fluctuate around an average. It connects thermodynamic quantities (such as heat capacity) to microscopic behavior, whereas, in classical thermodynamics, the only available option would be to measure and tabulate such quantities for various materials.
统计力学是现代物理学的支柱之一。它描述了宏观观察(如温度和压力)如何与围绕平均值波动的微观参数相关。它将热力学量(比如热容)与微观行为联系起来，而在经典热力学中，唯一可行的选择就是测量和列表各种材料的热力学量。
'''Ludwig Eduard Boltzmann''' ({{IPA-de|ˈluːtvɪg ˈbɔlt͡sman}}; February 20, 1844 – September 5, 1906) was an [[Austria]]n [[physicist]] and [[philosopher]]. His greatest achievements were the development of [[statistical mechanics]], and the statistical explanation of the [[second law of thermodynamics]]. In 1877 he provided the current definition of [[entropy]], <math>S = k_{\rm B} \ln \Omega \!</math>, interpreted as a measure of statistical disorder of a system.<ref name="EncycloBritan">{{cite book
|last1= Klein
|first1= Martin
|year= 1970
|orig-year= 1768
Boltzmann was born in Erdberg, a suburb of Vienna. His father, Ludwig Georg Boltzmann, was a revenue official. His grandfather, who had moved to Vienna from Berlin, was a clock manufacturer, and Boltzmann's mother, Katharina Pauernfeind, was originally from Salzburg. He received his primary education at the home of his parents. Boltzmann attended high school in Linz, Upper Austria. When Boltzmann was 15, his father died.
波尔兹曼出生于维也纳的郊区 Erdberg。他的父亲路德维希 · 格奥尔格 · 波尔兹曼是一名税务官员。他的祖父从柏林搬到了维也纳，是一个钟表制造商，而波尔兹曼的母亲卡塔琳娜•保恩芬德(Katharina Pauernfeind)来自萨尔茨堡。他在父母家接受小学教育。玻尔兹曼在上奥地利的林茨上高中。波尔兹曼15岁时，父亲去世了。
|chapter= Boltzmann, Ludwig
|editor1-last= Preece
Starting in 1863, Boltzmann studied mathematics and physics at the University of Vienna. He received his doctorate in 1866 and his venia legendi in 1869. Boltzmann worked closely with Josef Stefan, director of the institute of physics. It was Stefan who introduced Boltzmann to Maxwell's work. Boltzmann was appointed full Professor of Mathematical Physics at the University of Graz in the province of Styria. In 1869 he spent several months in Heidelberg working with Robert Bunsen and Leo Königsberger and in 1871 with Gustav Kirchhoff and Hermann von Helmholtz in Berlin. In 1873 Boltzmann joined the University of Vienna as Professor of Mathematics and there he stayed until 1876.
从1863年开始，玻尔兹曼在维也纳大学学习数学和物理学。他于1866年获得博士学位，于1869年获得法学博士学位。玻尔兹曼与物理研究所所长约瑟夫 · 斯蒂芬密切合作。是斯蒂芬把玻尔兹曼介绍给麦克斯韦尔的工作。被任命为 Styria 卡尔·弗朗岑斯大学数学物理学的正式教授。1869年，他在海德保花了几个月的时间与 Robert Bunsen 和莱奥·柯尼希斯贝格尔一起工作，1871年在柏林与古斯塔夫·基尔霍夫和赫尔曼·冯·亥姆霍兹一起工作。1873年，玻尔兹曼作为数学教授加入了维也纳大学，并在那里一直待到1876年。
|editor1-first= Warren E.
Nernst, Streintz, Arrhenius, Hiecke, (sitting, from the left) Aulinger, Ettingshausen, Boltzmann, Klemenčič, Hausmanninger]]
Nernst, Streintz, Arrhenius, Hiecke, (sitting, from the left) Aulinger, Ettingshausen, Boltzmann, Klemenčič, Hausmanninger]]
|title= Encyclopædia Britannica
In 1872, long before women were admitted to Austrian universities, he met Henriette von Aigentler, an aspiring teacher of mathematics and physics in Graz. She was refused permission to audit lectures unofficially. Boltzmann supported her decision to appeal, which was successful. On July 17, 1876 Ludwig Boltzmann married Henriette; they had three daughters: Henriette (1880), Ida (1884) and Else (1891); and a son, Arthur Ludwig (1881). Boltzmann went back to Graz to take up the chair of Experimental Physics. Among his students in Graz were Svante Arrhenius and Walther Nernst. He spent 14 happy years in Graz and it was there that he developed his statistical concept of nature.
1872年，在女性被奥地利大学录取之前很久，他遇到了 Henriette von Aigentler，一位有抱负的格拉茨数学和物理教师。她被拒绝以非正式的方式旁听课程。波尔兹曼支持她上诉的决定，这个决定很成功。1876年7月17日，路德维希·玻尔兹曼和亨利埃特结婚，他们有3个女儿: 亨利埃特(1880年) ，艾达(1884年)和艾尔斯(1891年) ，和一个儿子，亚瑟路德维希(1881年)。波尔兹曼回到格拉茨担任实验物理学教授。他在格拉茨的学生包括斯万特 · 阿伦尼乌斯和瓦尔特 · 纳恩斯特。他在格拉茨度过了快乐的14年，在那里他发展了自己的自然统计学概念。
|type=hard cover
|language= English
Boltzmann was appointed to the Chair of Theoretical Physics at the University of Munich in Bavaria, Germany in 1890.
1890年，玻尔兹曼被任命为德国巴伐利亚慕尼黑大学的理论物理学教授。
|volume= 3
|edition= Commemorative Edition for Expo 70
In 1894, Boltzmann succeeded his teacher Joseph Stefan as Professor of Theoretical Physics at the University of Vienna.
1894年，玻尔兹曼接替他的老师约瑟夫 · 斯蒂芬成为维也纳大学的理论物理学教授。
|location= Chicago
|publisher= William Benton
|publication-date= 1970
|page= 893a
Boltzmann spent a great deal of effort in his final years defending his theories. He did not get along with some of his colleagues in Vienna, particularly Ernst Mach, who became a professor of philosophy and history of sciences in 1895. That same year Georg Helm and Wilhelm Ostwald presented their position on energetics at a meeting in Lübeck. They saw energy, and not matter, as the chief component of the universe. Boltzmann's position carried the day among other physicists who supported his atomic theories in the debate. In 1900, Boltzmann went to the University of Leipzig, on the invitation of Wilhelm Ostwald. Ostwald offered Boltzmann the professorial chair in physics, which became vacant when Gustav Heinrich Wiedemann died. After Mach retired due to bad health, Boltzmann returned to Vienna in 1902.
玻尔兹曼在晚年花费了大量的精力来捍卫他的理论。他和他在维也纳的一些同事处不来，特别是恩斯特 · 马赫，后者在1895年成为哲学和科学史教授。同年，乔治•赫尔姆(Georg Helm)和威廉•奥斯特瓦尔德(Wilhelm Ostwald)在吕贝克的一次会议上，阐述了他们在能源学方面的立场。他们认为能量而不是物质是宇宙的主要组成部分。玻尔兹曼的立场在辩论中赢得了其他支持他的原子理论的物理学家的支持。1900年，应 Wilhelm Ostwald 的邀请，Boltzmann 去了莱比锡大学。奥斯特瓦尔德给波尔兹曼提供了一个物理学教授的职位，这个职位在古斯塔夫·海因里希·维德曼去世后就空了下来。由于身体不好，马赫退役后，波尔兹曼于1902年返回维也纳。
|isbn= 0852291353
}}
In 1906, Boltzmann's deteriorating mental condition forced him to resign his position, and his symptoms indicate he experienced what would today be diagnosed as bipolar disorder. Four months later he died by suicide on September 5, 1906, by hanging himself while on vacation with his wife and daughter in Duino, near Trieste (then Austria). During the 1890s, Boltzmann attempted to formulate a compromise position which would allow both atomists and anti-atomists to do physics without arguing over atoms. His solution was to use Hertz's theory that atoms were Bilder, that is, models or pictures. Atomists could think the pictures were the real atoms while the anti-atomists could think of the pictures as representing a useful but unreal model, but this did not fully satisfy either group. Furthermore, Ostwald and many defenders of "pure thermodynamics" were trying hard to refute the kinetic theory of gases and statistical mechanics because of Boltzmann's assumptions about atoms and molecules and especially statistical interpretation of the second law of thermodynamics.
1906年，Boltzmann 日益恶化的精神状况迫使他辞职，他的症状表明他经历了今天被诊断为躁郁症。四个月后，他于1906年9月5日与妻子和女儿在杜伊诺度假时上吊自杀身亡，当时他们住在的里雅斯特港/特区附近(当时是奥地利)。在19世纪90年代，玻尔兹曼试图阐明一个妥协的立场，允许原子论者和反原子论者在不争论原子的情况下进行物理研究。他的解决方案是使用赫兹的原子是比尔德的理论，即模型或图片。原子论者可以认为这些图片是真正的原子，而反原子论者可以认为这些图片代表了一个有用但不真实的模型，但这并不能完全满足任何一组。此外，Ostwald 和许多“纯热力学”的捍卫者正在努力驳斥分子运动论和统计力学，因为 Boltzmann 对原子和分子的假设，特别是对热力学第二定律的统计解释。
</ref> [[Max Planck]] named the constant, {{math|''k''<sub>B</sub>}}, the [[Boltzmann constant]].<ref>{{Citation
| last = Partington
Around the turn of the century, Boltzmann's science was being threatened by another philosophical objection. Some physicists, including Mach's student, Gustav Jaumann, interpreted Hertz to mean that all electromagnetic behavior is continuous, as if there were no atoms and molecules, and likewise as if all physical behavior were ultimately electromagnetic. This movement around 1900 deeply depressed Boltzmann since it could mean the end of his kinetic theory and statistical interpretation of the second law of thermodynamics.
在世纪之交，玻尔兹曼的科学受到另一种哲学反对意见的威胁。一些物理学家，包括马赫的学生古斯塔夫 · 乔曼，将赫兹解释为所有的电磁行为都是连续的，就好像没有原子和分子，同样，所有的物理行为最终都是电磁行为。1900年前后的这一运动使玻尔兹曼深感沮丧，因为它可能意味着他的动力学理论和热力学第二定律的统计解释的终结。
| first = J.R.
| author-link = J.R. Partington
After Mach's resignation in Vienna in 1901, Boltzmann returned there and decided to become a philosopher himself to refute philosophical objections to his physics, but he soon became discouraged again. In 1904 at a physics conference in St. Louis most physicists seemed to reject atoms and he was not even invited to the physics section. Rather, he was stuck in a section called "applied mathematics", he violently attacked philosophy, especially on allegedly Darwinian grounds but actually in terms of Lamarck's theory of the inheritance of acquired characteristics that people inherited bad philosophy from the past and that it was hard for scientists to overcome such inheritance.
1901年马赫在维也纳辞职后，波尔兹曼回到那里，决定自己成为一名哲学家，驳斥哲学界对他的物理学的反对意见，但他很快又变得灰心丧气。1904年在圣路易斯举行的一次物理学会议上，大多数物理学家似乎都排斥原子，甚至没有邀请他参加物理课。相反，他被困在一个叫做“应用数学”的部分，他猛烈抨击哲学，特别是据称基于达尔文的理由，但实际上是根据拉马克的获得性状遗传理论，人们从过去继承了糟糕的哲学，科学家很难克服这种继承。
| title = An Advanced Treatise on Physical Chemistry
| volume = volume 1, ''Fundamental Principles'', ''The Properties of Gases''
In 1905 Boltzmann corresponded extensively with the Austro-German philosopher Franz Brentano with the hope of gaining a better mastery of philosophy, apparently, so that he could better refute its relevancy in science, but he became discouraged about this approach as well.
1905年，波尔兹曼与德国哲学家弗朗茨 · 布伦塔诺有着广泛的通信往来，显然是希望能够更好地掌握哲学，以便更好地驳斥哲学与科学的关联性，但他也对这种方法感到气馁。
| place = London
| publisher = [[Longman|Longmans, Green and Co.]]
| series =
Boltzmann's most important scientific contributions were in kinetic theory, including for motivating the Maxwell–Boltzmann distribution as a description of molecular speeds in a gas. Maxwell–Boltzmann statistics and the Boltzmann distribution remain central in the foundations of classical statistical mechanics. They are also applicable to other phenomena that do not require quantum statistics and provide insight into the meaning of temperature.
玻尔兹曼最重要的科学贡献是在动力学理论，包括激发麦克斯韦-波兹曼分布，作为一种描述分子在气体中的速度。麦克斯韦-玻耳兹曼统计学和波兹曼分布理论仍然是经典统计力学理论基础的核心。它们也适用于其他不需要量子统计的现象，并提供了对温度含义的深入了解。
| origyear =
| year = 1949
Boltzmann's 1898 I<sub>2</sub> molecule diagram showing atomic "sensitive region" (α, β) overlap.
玻耳兹曼1898 i < 亚 > 2 </亚 > 分子图显示原子“敏感区”(α，β)重叠。
| page = 300}}</ref>
Most chemists, since the discoveries of John Dalton in 1808, and James Clerk Maxwell in Scotland and Josiah Willard Gibbs in the United States, shared Boltzmann's belief in atoms and molecules, but much of the physics establishment did not share this belief until decades later. Boltzmann had a long-running dispute with the editor of the preeminent German physics journal of his day, who refused to let Boltzmann refer to atoms and molecules as anything other than convenient theoretical constructs. Only a couple of years after Boltzmann's death, Perrin's studies of colloidal suspensions (1908–1909), based on Einstein's theoretical studies of 1905, confirmed the values of Avogadro's number and Boltzmann's constant, convincing the world that the tiny particles really exist.
自从1808年 John Dalton，苏格兰的詹姆斯·克拉克·麦克斯韦和美国的约西亚·威拉德·吉布斯发现以来，大多数化学家都认同 Boltzmann 的原子和分子理论，但是大多数物理学家直到几十年后才认同这一理论。玻尔兹曼与他那个时代卓越的德国物理学期刊的编辑有一个长期的争论，他拒绝让玻尔兹曼把原子和分子称为除了方便的理论构造以外的任何东西。玻尔兹曼死后仅仅几年，佩兰对胶体悬浮的研究(1908-1909年) ，以爱因斯坦1905年的理论研究为基础，证实了阿伏加德罗常数和波尔兹曼常数的价值，使世界相信微小粒子确实存在。
Statistical mechanics is one of the pillars of modern [[physics]]. It describes how macroscopic observations (such as [[temperature]] and [[pressure]]) are related to microscopic parameters that fluctuate around an average. It connects thermodynamic quantities (such as [[heat capacity]]) to microscopic behavior, whereas, in [[classical thermodynamics]], the only available option would be to measure and tabulate such quantities for various materials.<ref name="gibbs">{{cite book |last=Gibbs |first=Josiah Willard |author-link=Josiah Willard Gibbs |title=Elementary Principles in Statistical Mechanics |year=1902 |publisher=[[Charles Scribner's Sons]] |location=New York |title-link=Elementary Principles in Statistical Mechanics }}</ref>
To quote Planck, "The logarithmic connection between entropy and probability was first stated by L. Boltzmann in his kinetic theory of gases". This famous formula for entropy S is
引用普朗克的话，“熵和概率之间的对数关系最早是由 l. Boltzmann 在他的分子运动论中提出的”。这个著名的熵公式是
==Biography==
<math> S = k_B \ln W </math>
[ math ] s = k _ b ln w [ math ]
===Childhood and education===
Boltzmann was born in Erdberg, a suburb of [[Vienna]]. His father, Ludwig Georg Boltzmann, was a revenue official. His grandfather, who had moved to Vienna from Berlin, was a clock manufacturer, and Boltzmann's mother, Katharina Pauernfeind, was originally from [[Salzburg]]. He received his primary education at the home of his parents.<ref>{{cite book
where k<sub>B</sub> is Boltzmann's constant, and ln is the natural logarithm. W is Wahrscheinlichkeit, a German word meaning the probability of occurrence of a macrostate or, more precisely, the number of possible microstates corresponding to the macroscopic state of a system — the number of (unobservable) "ways" in the (observable) thermodynamic state of a system that can be realized by assigning different positions and momenta to the various molecules. Boltzmann's paradigm was an ideal gas of N identical particles, of which N<sub>i</sub> are in the ith microscopic condition (range) of position and momentum. W can be counted using the formula for permutations
其中 k < sub > b </sub > 是 Boltzmann 常数，ln 是自然对数。W 是 Wahrscheinlichkeit，一个德语单词，意思是发生宏观状态的可能性，或者更准确地说，是对应于系统宏观状态的可能的微观状态的数量---- 一个系统的可观测的热力学状态中的“方式”的数量，可以通过给各种分子分配不同的位置和动量来实现。玻耳兹曼的范式是全同粒子的理想气体，其中 n < sub > i </sub > 处于位置和动量的微观条件。W 可以用排列的公式来计算
|title=The Scientific 100
|first1=John
<math> W = N! \prod_i \frac{1}{N_i!} </math>
W = n！1} n i数学
|last1=Simmons
|first2=Lynda
where i ranges over all possible molecular conditions, and where <math>!</math> denotes factorial. The "correction" in the denominator account for indistinguishable particles in the same condition.
这里 i 可以覆盖所有可能的分子条件，这里 < math > ! </math > 表示阶乘。在相同条件下，分母中的“修正”解释了不可区分的粒子。
|last2=Simmons
|isbn=9780806536781
Boltzmann could also be considered one of the forerunners of quantum mechanics due to his suggestion in 1877 that the energy levels of a physical system could be discrete.
由于他在1877年提出物理系统的能级可以是离散的，Boltzmann 也可以被认为是量子力学的先驱之一。
|page=123
|publisher=Kensington Publishing Corp.
|year=2000
Boltzmann's bust in the courtyard arcade of the main building, University of Vienna.
在维也纳大学主楼的庭院拱廊中的玻尔兹曼的半身像。
}}</ref> Boltzmann attended high school in [[Linz]], [[Upper Austria]]. When Boltzmann was 15, his father died.<ref name=james2004>{{cite book
|title=Remarkable Physicists: From Galileo to Yukawa
The Boltzmann equation was developed to describe the dynamics of an ideal gas.
玻尔兹曼方程是用来描述理想气体的动力学的。
|url=https://archive.org/details/remarkablephysic00jame
|url-access=limited
<math> \frac{\partial f}{\partial t}+ v \frac{\partial f}{\partial x}+ \frac{F}{m} \frac{\partial f}{\partial v} = \frac{\partial f}{\partial t}\left.{\!\!\frac{}{}}\right|_\mathrm{collision} </math>
{ partial t } + v frac { partial f }{ partial x } + frac { f }{ m } frac { partial f }{{ partial v } = frac { partial f }{ partial t }.{ ! ! frac {}{}}右 | _ mathrm { collision } </math >
|first1=Ioan
|last1=James
where ƒ represents the distribution function of single-particle position and momentum at a given time (see the Maxwell–Boltzmann distribution), F is a force, m is the mass of a particle, t is the time and v is an average velocity of particles.
F 表示一定时间内单个粒子的位置和动量的分布函数(见麦克斯韦-波兹曼分布) ，f 表示一个力，m 表示一个粒子的质量，t 表示时间，v 表示粒子的平均速度。
|isbn=9780521017060
|page=[https://archive.org/details/remarkablephysic00jame/page/n185 169]
This equation describes the temporal and spatial variation of the probability distribution for the position and momentum of a density distribution of a cloud of points in single-particle phase space. (See Hamiltonian mechanics.) The first term on the left-hand side represents the explicit time variation of the distribution function, while the second term gives the spatial variation, and the third term describes the effect of any force acting on the particles. The right-hand side of the equation represents the effect of collisions.
这个方程描述了单粒子相空间中点云密度分布的位置和动量的概率分布的时间和空间变化。(参见哈密顿力学。)左边的第一项表示分布函数的显式时间变化，第二项表示空间变化，第三项描述作用在粒子上的任何力的效应。方程的右边表示碰撞的影响。
|publisher=Cambridge University Press
|year=2004
In principle, the above equation completely describes the dynamics of an ensemble of gas particles, given appropriate boundary conditions. This first-order differential equation has a deceptively simple appearance, since ƒ can represent an arbitrary single-particle distribution function. Also, the force acting on the particles depends directly on the velocity distribution function ƒ. The Boltzmann equation is notoriously difficult to integrate. David Hilbert spent years trying to solve it without any real success.
原则上，上述方程在给定适当的边界条件下，完全描述了气体粒子系综的动力学行为。这个一阶微分方程的外观看似简单，因为它可以表示任意的单粒子分布函数。作用在粒子上的力的大小直接取决于它的速度分布函数。众所周知，玻尔兹曼方程是难以整合的。大卫 · 希尔伯特花了数年时间试图解决这个问题，但没有取得任何真正的成功。
}}</ref>
The form of the collision term assumed by Boltzmann was approximate. However, for an ideal gas the standard Chapman–Enskog solution of the Boltzmann equation is highly accurate. It is expected to lead to incorrect results for an ideal gas only under shock wave conditions.
Boltzmann 采用的碰撞术语的形式是近似的。然而，对于理想气体，玻尔兹曼方程的标准 Chapman-Enskog 解决方案是高度准确的。只有在冲击波条件下，理想气体才有可能得到不正确的结果。
Starting in 1863, Boltzmann studied [[mathematics]] and [[physics]] at the [[University of Vienna]]. He received his doctorate in 1866 and his [[venia legendi]] in 1869. Boltzmann worked closely with [[Josef Stefan]], director of the institute of physics. It was Stefan who introduced Boltzmann to [[James Clerk Maxwell|Maxwell's]] work.<ref name=james2004 />
Boltzmann tried for many years to "prove" the second law of thermodynamics using his gas-dynamical equation — his famous H-theorem. However the key assumption he made in formulating the collision term was "molecular chaos", an assumption which breaks time-reversal symmetry as is necessary for anything which could imply the second law. It was from the probabilistic assumption alone that Boltzmann's apparent success emanated, so his long dispute with Loschmidt and others over Loschmidt's paradox ultimately ended in his failure.
多年来，Boltzmann 一直试图用他的气体动力学方程——著名的 h 定理——来“证明”热力学第二定律。然而，他在构造碰撞术语时所作的关键假设是“分子混沌” ，这个假设破坏了时间反转对称性，这对任何可能暗示第二定律的事物都是必要的。波尔兹曼表面上的成功仅仅来自于概率假设，因此他与洛施密特和其他人就洛施密特悖论的长期争论最终以他的失败而告终。
===Academic career===
Finally, in the 1970s E.G.D. Cohen and J. R. Dorfman proved that a systematic (power series) extension of the Boltzmann equation to high densities is mathematically impossible. Consequently, nonequilibrium statistical mechanics for dense gases and liquids focuses on the Green–Kubo relations, the fluctuation theorem, and other approaches instead.
最终，在20世纪70年代的 e.g.d。和 j. r. Dorfman 证明了系统地(幂级数)将玻尔兹曼方程扩展到高密度在数学上是不可能的。因此，稠密气体和液体的非平衡态统计力学集中在格林-库伯关系、涨落定理和其他方法上。
In 1869 at age 25, thanks to a letter of recommendation written by Stefan,<ref>{{cite journal |url=http://www.kvarkadabra.net/2001/12/ludwig-boltzmann/ |title=Ludwig Boltzmann in prva študentka fizike in matematike slovenskega rodu |language=Slovenian |trans-title=Ludwig Boltzmann and the First Student of Physics and Mathematics of Slovene Descent |date=December 2001 |last=Južnič |first=Stanislav |website=Kvarkadabra.net |issue=12 |accessdate=17 February 2012}}</ref> Boltzmann was appointed full Professor of [[Mathematical Physics]] at the [[University of Graz]] in the province of [[Styria]]. In 1869 he spent several months in [[Heidelberg]] working with [[Robert Bunsen]] and [[Leo Königsberger]] and in 1871 with [[Gustav Kirchhoff]] and [[Hermann von Helmholtz]] in Berlin. In 1873 Boltzmann joined the University of Vienna as Professor of Mathematics and there he stayed until 1876.
[[File:Boltzmann-grp.jpg|thumb|left|280px|Ludwig Boltzmann and co-workers in Graz, 1887: (standing, from the left) [[Walther Nernst|Nernst]], [[Heinrich Streintz|Streintz]], [[Svante Arrhenius|Arrhenius]], Hiecke, (sitting, from the left) Aulinger, [[Albert von Ettingshausen|Ettingshausen]], Boltzmann, [[Ignacij Klemenčič|Klemenčič]], Hausmanninger]]
In 1872, long before women were admitted to Austrian universities, he met Henriette von Aigentler, an aspiring teacher of mathematics and physics in Graz. She was refused permission to audit lectures unofficially. Boltzmann supported her decision to appeal, which was successful. On July 17, 1876 Ludwig Boltzmann married Henriette; they had three daughters: Henriette (1880), Ida (1884) and Else (1891); and a son, Arthur Ludwig (1881).<ref>https://www.boltzmann.com/ludwig-boltzmann/biography/</ref> Boltzmann went back to [[Graz]] to take up the chair of Experimental Physics. Among his students in Graz were [[Svante Arrhenius]] and [[Walther Nernst]].<ref name="springer">{{Cite journal |quote=Paul Ehrenfest (1880–1933) along with Nernst, Arrhenius, and Meitner must be considered among Boltzmann's most outstanding students. |last1=Jäger |first1=Gustav |last2=Nabl |first2=Josef |last3=Meyer |first3=Stephan |date=April 1999 |title=Three Assistants on Boltzmann |journal=Synthese |volume=119 |issue=1–2 |pages=69–84 |doi=10.1023/A:1005239104047|s2cid=30499879 }}</ref><ref name="huji">{{cite web |url=http://chem.ch.huji.ac.il/history/nernst.htm |title=Walther Hermann Nernst |quote=Walther Hermann Nernst visited lectures by Ludwig Boltzmann |archive-url=https://web.archive.org/web/20080612133921/http://chem.ch.huji.ac.il/history/nernst.htm |archive-date=2008-06-12 }}</ref> He spent 14 happy years in Graz and it was there that he developed his statistical concept of nature.
Boltzmann's grave in the [[Zentralfriedhof, Vienna, with bust and entropy formula.]]
玻尔兹曼的坟墓[维也纳中心区弗里德霍夫，胸围和熵公式]
The idea that the second law of thermodynamics or "entropy law" is a law of disorder (or that dynamically ordered states are "infinitely improbable") is due to Boltzmann's view of the second law of thermodynamics.
认为热力学第二定律定律或者“熵定律”是无序定律(或者说动态有序的状态是“无限不可能的”)的观点是由于 Boltzmann 对热力学第二定律的观点。
Boltzmann was appointed to the Chair of Theoretical Physics at the [[University of Munich]] in [[Bavaria]], Germany in 1890.
In particular, it was Boltzmann's attempt to reduce it to a stochastic collision function, or law of probability following from the random collisions of mechanical particles. Following Maxwell, Boltzmann modeled gas molecules as colliding billiard balls in a box, noting that with each collision nonequilibrium velocity distributions (groups of molecules moving at the same speed and in the same direction) would become increasingly disordered leading to a final state of macroscopic uniformity and maximum microscopic disorder or the state of maximum entropy (where the macroscopic uniformity corresponds to the obliteration of all field potentials or gradients). The second law, he argued, was thus simply the result of the fact that in a world of mechanically colliding particles disordered states are the most probable. Because there are so many more possible disordered states than ordered ones, a system will almost always be found either in the state of maximum disorder – the macrostate with the greatest number of accessible microstates such as a gas in a box at equilibrium – or moving towards it. A dynamically ordered state, one with molecules moving "at the same speed and in the same direction", Boltzmann concluded, is thus "the most improbable case conceivable...an infinitely improbable configuration of energy."
尤其是，玻尔兹曼试图把它归结为一个随机碰撞函数，或者机械粒子随机碰撞后的概率定律。继麦克斯韦尔之后，玻尔兹曼将气体分子模拟为在一个盒子里碰撞的台球，指出每次碰撞时，非平衡速度分布(以相同速度和方向运动的分子群)将变得越来越无序，导致最终的宏观均匀和最大微观无序状态或最大熵状态(宏观均匀性对应于所有场势或梯度的消失)。因此，他认为第二定律仅仅是这样一个事实的结果，即在一个机械碰撞的粒子无序状态是最有可能的。因为可能存在的无序状态比有序状态多得多，所以一个系统几乎总是处于最大无序状态——具有最多可达微观状态的宏观状态，例如平衡状态下盒子中的气体——或者向无序状态移动。玻尔兹曼总结说，一个动态有序的状态，即分子以“同样的速度和同样的方向”运动，因此是“最不可能想象的情况... ... 一个无限不可能的能量构型”
In 1894, Boltzmann succeeded his teacher [[Joseph Stefan]] as Professor of Theoretical Physics at the University of Vienna.
Boltzmann accomplished the feat of showing that the second law of thermodynamics is only a statistical fact. The gradual disordering of energy is analogous to the disordering of an initially ordered pack of cards under repeated shuffling, and just as the cards will finally return to their original order if shuffled a gigantic number of times, so the entire universe must some-day regain, by pure chance, the state from which it first set out. (This optimistic coda to the idea of the dying universe becomes somewhat muted when one attempts to estimate the timeline which will probably elapse before it spontaneously occurs.) The tendency for entropy increase seems to cause difficulty to beginners in thermodynamics, but is easy to understand from the standpoint of the theory of probability. Consider two ordinary dice, with both sixes face up. After the dice are shaken, the chance of finding these two sixes face up is small (1 in 36); thus one can say that the random motion (the agitation) of the dice, like the chaotic collisions of molecules because of thermal energy, causes the less probable state to change to one that is more probable. With millions of dice, like the millions of atoms involved in thermodynamic calculations, the probability of their all being sixes becomes so vanishingly small that the system must move to one of the more probable states. However, mathematically the odds of all the dice results not being a pair sixes is also as hard as the ones of all of them being sixes, and since statistically the data tend to balance, one in every 36 pairs of dice will tend to be a pair of sixes, and the cards -when shuffled- will sometimes present a certain temporary sequence order even if in its whole the deck was disordered.
玻尔兹曼完成了一项壮举，证明了热力学第二定律只是一个统计事实。能量的逐渐失序类似于一副最初有序的扑克牌在重复洗牌过程中的失序，就像如果洗牌次数过多，扑克牌最终会恢复到原来的秩序一样，因此，整个宇宙必定会在某一天，纯粹出于偶然，恢复到它最初开始时的状态。(当人们试图估计可能在宇宙自发发生之前就已经过去的时间线时，这种对于正在消亡的宇宙这一观点的乐观结尾就变得有些沉默了。)熵增的趋势似乎给热力学初学者带来了困难，但从概率论的角度来看，熵增的趋势是容易理解的。考虑两个普通的骰子，两个6的面朝上。摇动骰子后，发现这两个六的概率很小(1/36) ，因此可以说，骰子的随机运动(搅动) ，就像分子因热能而产生的混沌碰撞，导致较不可能的状态转变为更可能的状态。数以百万计的骰子，就像热力学计算中所涉及的数以百万计的原子一样，它们都是六的概率变得如此微小，以至于系统必须移动到一个更有可能的状态。然而，从数学上计算出所有骰子不是一对六的概率也和所有骰子都是六的概率一样困难，而且由于统计数据趋于平衡，每36对骰子中就有一对是六，而当洗牌时，有时会呈现出某种暂时的序列顺序，即使整副牌是混乱的。
===Final years and death===
Boltzmann spent a great deal of effort in his final years defending his theories.<ref name ="Carlo">Cercignani, Carlo (1998) Ludwig Boltzmann: The Man Who Trusted Atoms. Oxford University Press. {{ISBN|9780198501541}}</ref> He did not get along with some of his colleagues in Vienna, particularly [[Ernst Mach]], who became a professor of philosophy and history of sciences in 1895. That same year [[Georg Helm]] and [[Wilhelm Ostwald]] presented their position on [[energetics]] at a meeting in [[Lübeck]]. They saw energy, and not matter, as the chief component of the universe. Boltzmann's position carried the day among other physicists who supported his atomic theories in the debate.<ref>{{cite journal|author=Max Planck|title=Gegen die neure Energetik|journal=Annalen der Physik|volume=57|issue=1|year=1896|pages=72–78|doi=10.1002/andp.18962930107 |bibcode = 1896AnP...293...72P |url=https://zenodo.org/record/1423910}}</ref> In 1900, Boltzmann went to the [[University of Leipzig]], on the invitation of [[Wilhelm Ostwald]]. Ostwald offered Boltzmann the professorial chair in physics, which became vacant when [[Gustav Heinrich Wiedemann]] died. After Mach retired due to bad health, Boltzmann returned to Vienna in 1902.<ref name ="Carlo"/> In 1903, Boltzmann, together with [[Gustav von Escherich]] and [[Emil Müller (mathematician)|Emil Müller]], founded the [[Austrian Mathematical Society]]. His students included [[Karl Přibram]], [[Paul Ehrenfest]] and [[Lise Meitner]].<ref name ="Carlo"/>
In 1885 he became a member of the Imperial Austrian Academy of Sciences and in 1887 he became the President of the University of Graz. He was elected a member of the Royal Swedish Academy of Sciences in 1888 and a Foreign Member of the Royal Society (ForMemRS) in 1899. Numerous things are named in his honour.
1885年，他成为奥地利帝国科学院的一员，1887年，他成为卡尔·弗朗岑斯大学的院长。他于1888年被选为瑞典皇家科学院院士，并于1899年被选为皇家学会的外国会员。许多事物都以他的名字命名。
In Vienna, Boltzmann taught physics and also lectured on philosophy. Boltzmann's lectures on [[natural philosophy]] were very popular and received considerable attention. His first lecture was an enormous success. Even though the largest lecture hall had been chosen for it, the people stood all the way down the staircase. Because of the great successes of Boltzmann's philosophical lectures, the Emperor invited him for a reception at the Palace.<ref>The Boltzmann Equation: Theory and Applications, E.G.D. Cohen, W. Thirring, ed., Springer Science & Business Media, 2012</ref>
In 1906, Boltzmann's deteriorating mental condition forced him to resign his position, and his symptoms indicate he experienced what would today be diagnosed as [[bipolar disorder]].<ref name ="Carlo"/><ref name="Paperpile">{{cite web | last = Nina Bausek and Stefan Washietl | title = Tragic deaths in science: Ludwig Boltzmann — a mind in disorder | publisher = [[Paperpile]] | date = February 13, 2018 | url = https://paperpile.com/blog/ludwig-boltzmann/ | accessdate = 2020-04-26 }}</ref> Four months later he died by suicide on September 5, 1906, by hanging himself while on vacation with his wife and daughter in [[Duino]], near [[Trieste]] (then Austria).<ref>"Eureka! Science's greatest thinkers and their key breakthroughs", Hazel Muir, p.152, {{ISBN|1780873255}}</ref><ref>{{cite book|last=Boltzmann|first=Ludwig|editor1-first=John T.|editor1-last=Blackmore|title=Ludwig Boltzmann: His Later Life and Philosophy, 1900-1906|chapter-url=https://books.google.com/books?id=apip-Jm9WuwC&pg=PA207 |volume=2|year=1995|publisher=Springer|isbn=978-0-7923-3464-4|pages=206–207|chapter=Conclusions}}</ref><ref>Upon Boltzmann's death, [[Friedrich Hasenöhrl|Friedrich ("Fritz") Hasenöhrl]] became his successor in the professorial chair of physics at Vienna.</ref><ref name="Paperpile" />
He is buried in the Viennese [[Zentralfriedhof]]. His tombstone bears the inscription of [[Boltzmann's entropy formula]]: <math>S = k \cdot \log W </math><ref name ="Carlo"/>
==Philosophy==
{{Unreferenced section|date=December 2018}}
Boltzmann's [[kinetic theory of gases]] seemed to presuppose the reality of [[atom]]s and [[molecule]]s, but almost all [[German philosophy|German philosophers]] and many scientists like [[Ernst Mach]] and the physical chemist [[Wilhelm Ostwald]] disbelieved their existence.<ref>{{cite book | last=Bronowski | first=Jacob | authorlink=Jacob Bronowski | title=The Ascent Of Man | chapter=World Within World | publisher=Little Brown & Co | year=1974 | isbn=978-0-316-10930-7 | page=265 | chapter-url=https://archive.org/details/ascentofmanbron00bron }}</ref> During the 1890s, Boltzmann attempted to formulate a compromise position which would allow both atomists and anti-atomists to do physics without arguing over atoms. His solution was to use [[Heinrich Hertz|Hertz]]'s theory that atoms were ''Bilder'', that is, models or pictures. Atomists could think the pictures were the real atoms while the anti-atomists could think of the pictures as representing a useful but unreal model, but this did not fully satisfy either group. Furthermore, Ostwald and many defenders of "pure thermodynamics" were trying hard to refute the kinetic theory of gases and statistical mechanics because of Boltzmann's assumptions about atoms and molecules and especially statistical interpretation of the [[second law of thermodynamics]].
Around the turn of the century, Boltzmann's science was being threatened by another philosophical objection. Some physicists, including Mach's student, [[Gustav Jaumann]], interpreted Hertz to mean that all electromagnetic behavior is continuous, as if there were no atoms and molecules, and likewise as if all physical behavior were ultimately electromagnetic. This movement around 1900 deeply depressed Boltzmann since it could mean the end of his kinetic theory and statistical interpretation of the second law of thermodynamics.
After Mach's resignation in Vienna in 1901, Boltzmann returned there and decided to become a philosopher himself to refute philosophical objections to his physics, but he soon became discouraged again. In 1904 at a physics conference in St. Louis most physicists seemed to reject atoms and he was not even invited to the physics section. Rather, he was stuck in a section called "applied mathematics", he violently attacked philosophy, especially on allegedly Darwinian grounds but actually in terms of [[Lamarck]]'s theory of the inheritance of acquired characteristics that people inherited bad philosophy from the past and that it was hard for scientists to overcome such inheritance.
In 1905 Boltzmann corresponded extensively with the Austro-German philosopher [[Franz Brentano]] with the hope of gaining a better mastery of philosophy, apparently, so that he could better refute its relevancy in science, but he became discouraged about this approach as well.
==Physics==
Boltzmann's most important scientific contributions were in [[kinetic theory of gases|kinetic theory]], including for motivating the [[Maxwell–Boltzmann distribution]] as a description of molecular speeds in a gas. [[Maxwell–Boltzmann statistics]] and the [[Boltzmann distribution]] remain central in the foundations of [[classical mechanics|classical]] statistical mechanics. They are also applicable to other [[phenomenon|phenomena]] that do not require [[Maxwell–Boltzmann statistics#Limits of applicability|quantum statistics]] and provide insight into the meaning of [[thermodynamic temperature|temperature]].
[[File:Boltzmanns-molecule.jpg|225px|thumb|right|Boltzmann's 1898 I<sub>2</sub> molecule diagram showing atomic "sensitive region" (α, β) overlap.]]
[[History of chemistry#The dispute about atomism|Most]] [[chemistry|chemists]], since the discoveries of [[John Dalton]] in 1808, and [[James Clerk Maxwell]] in Scotland and [[Josiah Willard Gibbs]] in the United States, shared Boltzmann's belief in [[atom]]s and [[molecule]]s, but much of the [[physics]] establishment did not share this belief until decades later. Boltzmann had a long-running dispute with the editor of the preeminent German physics journal of his day, who refused to let Boltzmann refer to atoms and molecules as anything other than convenient [[Theory#Science|theoretical]] constructs. Only a couple of years after Boltzmann's death, [[Jean Baptiste Perrin|Perrin's]] studies of [[colloid]]al suspensions (1908–1909), based on [[Albert Einstein|Einstein's]] [[Albert Einstein#Thermodynamic fluctuations and statistical physics|theoretical studies]] of 1905, confirmed the values of [[Avogadro's number]] and [[Boltzmann constant|Boltzmann's constant]], convincing the world that the tiny particles [[Atomic theory#History|really exist]].
To quote [[Max Planck|Planck]], "The [[logarithm]]ic connection between [[entropy]] and [[probability]] was first stated by L. Boltzmann in his [[kinetic theory of gases]]".<ref>Max Planck, p. 119.</ref> This famous formula for entropy ''S'' is<ref>The concept of [[entropy]] was introduced by [[Rudolf Clausius]] in 1865. He was the first to enunciate the [[second law of thermodynamics]] by saying that "entropy always increases".</ref><ref>An alternative is the [[Information entropy#Formal definitions|information entropy]] definition introduced in 1948 by [[Claude Elwood Shannon|Claude Shannon]].[https://archive.is/20070503225307/http://cm.bell-labs.com/cm/ms/what/shannonday/paper.html] It was intended for use in communication theory, but is applicable in all areas. It reduces to Boltzmann's expression when all the probabilities are equal, but can, of course, be used when they are not. Its virtue is that it yields immediate results without resorting to [[factorial]]s or [[Stirling's approximation]]. Similar formulas are found, however, as far back as the work of Boltzmann, and explicitly in [[H-theorem#Quantum mechanical H-theorem|Gibbs]] (see reference).</ref>
:<math> S = k_B \ln W </math>
where ''k<sub>B</sub>'' is [[Boltzmann constant|Boltzmann's constant]], and ''ln'' is the [[natural logarithm]]. ''W'' is ''Wahrscheinlichkeit'', a German word meaning the [[probability theory|probability]] of occurrence of a [[macrostate]]<ref>{{cite book|last=Pauli| first=Wolfgang| title=Statistical Mechanics|publisher=MIT Press|location=Cambridge|year=1973|isbn=978-0-262-66035-8}}, p. 21</ref> or, more precisely, the number of possible [[microstate (statistical mechanics)|microstates]] corresponding to the macroscopic state of a system — the number of (unobservable) "ways" in the (observable) [[thermodynamics|thermodynamic]] state of a system that can be realized by assigning different [[coordinate system|positions]] and [[momentum|momenta]] to the various molecules. Boltzmann's [[Paradigm#Paradigm shifts|paradigm]] was an [[ideal gas]] of ''N'' ''identical'' particles, of which ''N''<sub>''i''</sub> are in the ''i''th microscopic condition (range) of position and momentum. ''W'' can be counted using the formula for [[Maxwell–Boltzmann statistics#A derivation of the Maxwell–Boltzmann distribution|permutations]]
:<math> W = N! \prod_i \frac{1}{N_i!} </math>
where ''i'' ranges over all possible molecular conditions, and where <math>!</math> denotes [[factorial]]. The "correction" in the denominator account for [[Identical particles|indistinguishable]] particles in the same condition.
Boltzmann could also be considered one of the forerunners of quantum mechanics due to his suggestion in 1877 that the energy levels of a physical system could be discrete.
==Boltzmann equation==
[[File:Ludwig Boltzmann at U Vienna.JPG|thumb|Boltzmann's bust in the courtyard arcade of the main building, University of Vienna.]]
{{main|Boltzmann equation}}
The Boltzmann equation was developed to describe the dynamics of an ideal gas.
:<math> \frac{\partial f}{\partial t}+ v \frac{\partial f}{\partial x}+ \frac{F}{m} \frac{\partial f}{\partial v} = \frac{\partial f}{\partial t}\left.{\!\!\frac{}{}}\right|_\mathrm{collision} </math>
where ''ƒ'' represents the distribution function of single-particle position and momentum at a given time (see the [[Maxwell–Boltzmann distribution]]), ''F'' is a force, ''m'' is the mass of a particle, ''t'' is the time and ''v'' is an average velocity of particles.
This equation describes the [[time|temporal]] and [[space|spatial]] variation of the probability distribution for the position and momentum of a density distribution of a cloud of points in single-particle [[phase space]]. (See [[Hamiltonian mechanics]].) The first term on the left-hand side represents the explicit time variation of the distribution function, while the second term gives the spatial variation, and the third term describes the effect of any force acting on the particles. The right-hand side of the equation represents the effect of collisions.
In principle, the above equation completely describes the dynamics of an ensemble of gas particles, given appropriate [[boundary conditions]]. This first-order [[differential equation]] has a deceptively simple appearance, since ''ƒ'' can represent an arbitrary single-particle distribution function. Also, the [[force]] acting on the particles depends directly on the velocity distribution function ''ƒ''. The Boltzmann equation is notoriously difficult to [[Integral|integrate]]. [[David Hilbert]] spent years trying to solve it without any real success.
The form of the collision term assumed by Boltzmann was approximate. However, for an ideal gas the standard [[Chapman–Enskog theory|Chapman–Enskog]] solution of the Boltzmann equation is highly accurate. It is expected to lead to incorrect results for an ideal gas only under [[shock wave]] conditions.
Category:1844 births
类别: 1844名出生
Boltzmann tried for many years to "prove" the [[second law of thermodynamics]] using his gas-dynamical equation — his famous [[H-theorem]]. However the key assumption he made in formulating the collision term was "[[molecular chaos]]", an assumption which breaks [[CPT symmetry|time-reversal symmetry]] as is necessary for ''anything'' which could imply the second law. It was from the probabilistic assumption alone that Boltzmann's apparent success emanated, so his long dispute with [[Johann Josef Loschmidt|Loschmidt]] and others over [[Loschmidt's paradox]] ultimately ended in his failure.
Category:1906 deaths
分类: 1906人死亡
Category:Scientists from Vienna
类别: 来自维也纳的科学家
Finally, in the 1970s [[E.G.D. Cohen]] and J. R. Dorfman proved that a systematic (power series) extension of the Boltzmann equation to high densities is mathematically impossible. Consequently, [[non-equilibrium statistical mechanics|nonequilibrium statistical mechanics]] for dense gases and liquids focuses on the [[Green–Kubo relations]], the [[fluctuation theorem]], and other approaches instead.
Category:Austrian physicists
类别: 奥地利物理学家
Category:Thermodynamicists
类别: 热力学家
==Second thermodynamics law as a law of disorder==
Category:Fluid dynamicists
类别: 流体动力学家
[[File:Zentralfriedhof Vienna - Boltzmann.JPG|thumb|right|Boltzmann's grave in the [[Zentralfriedhof]], Vienna, with bust and entropy formula.]]
Category:Physicists who committed suicide
类别: 自杀的物理学家
The idea that the [[second law of thermodynamics]] or "entropy law" is a law of disorder (or that dynamically ordered states are "infinitely improbable") is due to Boltzmann's view of the second law of thermodynamics.
Category:Mathematicians who committed suicide
类别: 自杀的数学家
Category:Burials at the Vienna Central Cemetery
类别: 维也纳中央公墓的葬礼
In particular, it was Boltzmann's attempt to reduce it to a [[stochastic]] collision function, or law of probability following from the random collisions of mechanical particles. Following Maxwell,<ref>Maxwell, J. (1871). Theory of heat. London: Longmans, Green & Co.</ref> Boltzmann modeled gas molecules as colliding billiard balls in a box, noting that with each collision nonequilibrium velocity distributions (groups of molecules moving at the same speed and in the same direction) would become increasingly disordered leading to a final state of macroscopic uniformity and maximum microscopic disorder or the state of maximum entropy (where the macroscopic uniformity corresponds to the obliteration of all field potentials or gradients).<ref>Boltzmann, L. (1974). The second law of thermodynamics. Populare Schriften, Essay 3, address to a formal meeting of the Imperial Academy of Science, 29 May 1886, reprinted in Ludwig Boltzmann, Theoretical physics and philosophical problem, S. G. Brush (Trans.). Boston: Reidel. (Original work published 1886)</ref> The second law, he argued, was thus simply the result of the fact that in a world of mechanically colliding particles disordered states are the most probable. Because there are so many more possible disordered states than ordered ones, a system will almost always be found either in the state of maximum disorder – the macrostate with the greatest number of accessible microstates such as a gas in a box at equilibrium – or moving towards it. A dynamically ordered state, one with molecules moving "at the same speed and in the same direction", Boltzmann concluded, is thus "the most improbable case conceivable...an infinitely improbable configuration of energy."<ref>Boltzmann, L. (1974). The second law of thermodynamics. p. 20</ref>
Category:University of Vienna alumni
类别: 维也纳大学校友
Category:Members of the Royal Swedish Academy of Sciences
类别: 瑞典皇家科学院院士
Boltzmann accomplished the feat of showing that the second law of thermodynamics is only a statistical fact. The gradual disordering of energy is analogous to the disordering of an initially ordered [[pack of cards]] under repeated shuffling, and just as the cards will finally return to their original order if shuffled a gigantic number of times, so the entire universe must some-day regain, by pure chance, the state from which it first set out. (This optimistic coda to the idea of the dying universe becomes somewhat muted when one attempts to estimate the timeline which will probably elapse before it spontaneously occurs.)<ref>"[[Collier's Encyclopedia]]", Volume 19 Phyfe to Reni, "Physics", by David Park, p. 15</ref> The tendency for entropy increase seems to cause difficulty to beginners in thermodynamics, but is easy to understand from the standpoint of the theory of probability. Consider two ordinary [[dice]], with both sixes face up. After the dice are shaken, the chance of finding these two sixes face up is small (1 in 36); thus one can say that the random motion (the agitation) of the dice, like the chaotic collisions of molecules because of thermal energy, causes the less probable state to change to one that is more probable. With millions of dice, like the millions of atoms involved in thermodynamic calculations, the probability of their all being sixes becomes so vanishingly small that the system ''must'' move to one of the more probable states.<ref>"Collier's Encyclopedia", Volume 22 Sylt to Uruguay, Thermodynamics, by Leo Peters, p. 275</ref> However, mathematically the odds of all the dice results not being a pair sixes is also as hard as the ones of all of them being sixes{{Citation needed|date=January 2019}}, and since statistically the [[data]] tend to balance, one in every 36 pairs of dice will tend to be a pair of sixes, and the cards -when shuffled- will sometimes present a certain temporary sequence order even if in its whole the deck was disordered.
Category:Corresponding Members of the St Petersburg Academy of Sciences
类别: 圣彼得堡科学院通讯员
Category:Members of the Bavarian Maximilian Order for Science and Art
分类: 美国巴伐利亚马克西米兰科学与艺术勋章（Bavarian Maximilian Order for Science and the Arts）协会会员
==Awards and honours==
Category:Suicides by hanging in Italy
类别: 意大利上吊自杀
In 1885 he became a member of the Imperial [[Austrian Academy of Sciences]] and in 1887 he became the President of the [[University of Graz]]. He was elected a member of the [[Royal Swedish Academy of Sciences]] in 1888 and a [[List of Fellows of the Royal Society elected in 1899|Foreign Member of the Royal Society (ForMemRS) in 1899]].<ref name=frs>{{cite web|archiveurl=https://web.archive.org/web/20150316060617/https://royalsociety.org/about-us/fellowship/fellows/|archivedate=2015-03-16|url=https://royalsociety.org/about-us/fellowship/fellows/|publisher=[[Royal Society]]|location=London|title=Fellows of the Royal Society}}</ref> [[List of things named after Ludwig Boltzmann|Numerous things]] are named in his honour.
Category:Foreign Members of the Royal Society
类别: 皇家学会的外国成员
Category:Foreign associates of the National Academy of Sciences
类别: 美国国家科学院的外国合伙人
==See also==
Category:Mathematical physicists
类别: 数学物理学家
Category:Theoretical physicists
类别: 理论物理学家
* [[Energetics]]
Category:Rectors of universities in Austria
类别: 奥地利大学校长
<noinclude>
<small>This page was moved from [[wikipedia:en:Ludwig Boltzmann]]. Its edit history can be viewed at [[玻尔兹曼/edithistory]]</small></noinclude>
[[Category:待整理页面]]
{{redirect|Boltzmann}}
{{Infobox scientist
{{Infobox scientist
{信息盒科学家
| image = Boltzmann2.jpg
| image = Boltzmann2.jpg
2.jpg
| image_size = 225px
| image_size = 225px
225px
| caption = Ludwig Boltzmann
| caption = Ludwig Boltzmann
图片来源: 路德维希·玻尔兹曼
| birth_name = Ludwig Eduard Boltzmann
| birth_name = Ludwig Eduard Boltzmann
出生名字 = 路德维希·玻尔兹曼
| birth_date = {{Birth date|1844|2|20|mf=y}}
| birth_date =
出生日期
| birth_place= [[Vienna]], [[Austrian Empire]]
| birth_place= Vienna, Austrian Empire
出生地: 奥地利帝国维也纳
| death_date = {{death date and age|1906|9|5|1844|2|20|mf=y}}
| death_date =
死亡日期
| death_place= [[Tybein]], [[Triest]], [[Austria-Hungary]]
| death_place= Tybein, Triest, Austria-Hungary
死亡地点: Tybein，Triest，Austria-Hungary
| death_cause = [[Suicide by hanging]]
| death_cause = Suicide by hanging
死因 = 上吊自杀
| nationality = Austrian
| nationality = Austrian
| 国籍: 奥地利
| alma_mater = [[University of Vienna]]
| alma_mater = University of Vienna
维也纳大学
| doctoral_advisor = [[Josef Stefan]]
| doctoral_advisor = Josef Stefan
博士导师约瑟夫 · 斯蒂芬
| academic_advisors = {{plainlist|
| academic_advisors = {{plainlist|
学术顾问 = { plainlist |
*[[Robert Bunsen]]
*[[Leo Königsberger]]
*[[Gustav Kirchhoff]]
*[[Hermann von Helmholtz]]}}
| doctoral_students = {{Plainlist|
| doctoral_students = {{Plainlist|
博士生 = { Plainlist |
* [[Paul Ehrenfest]]
* [[Philipp Frank]]
* [[Gustav Herglotz]]
* [[Franc Hočevar]]
* [[Ignacij Klemenčič]]}}
| notable_students = {{Plainlist|
| notable_students = {{Plainlist|
2012年10月12日
*[[Lise Meitner]]
*[[Stefan Meyer (physicist)|Stefan Meyer]]}}
| known_for = {{Plainlist|
| known_for = {{Plainlist|
已知 | for = {{ Plainlist |
* [[Boltzmann constant]]
* [[Boltzmann equation]]
* [[Boltzmann distribution]]
* [[Detailed balance]]
* [[H-theorem|''H''-theorem]]
* [[Maxwell–Boltzmann distribution]]
* [[Stefan–Boltzmann constant]]
* [[Stefan–Boltzmann law]]
* [[Maxwell-Boltzmann statistics]]
* [[Boltzmann factor]]
* [[Epistemological idealism]]
}}
}}
}}
| signature = Ludwig Boltzmann signature.svg
| signature = Ludwig Boltzmann signature.svg
签名 = 路德维希·玻尔兹曼/签名
| field = [[Physics]]
| field = Physics
| field = 物理
| work_institution = {{Plainlist|
| work_institution = {{Plainlist|
2009年10月11日
* [[University of Graz]]
* [[University of Vienna]]
* [[University of Munich]]
* [[University of Leipzig]]}}
| prizes = [[Fellow of the Royal Society|ForMemRS]] (1899)<ref name=frs/>
| prizes = ForMemRS (1899) Max Planck named the constant, , the Boltzmann constant.
1899年，马克斯 · 普朗克将这个常数命名为波兹曼常数。
}}
Statistical mechanics is one of the pillars of modern physics. It describes how macroscopic observations (such as temperature and pressure) are related to microscopic parameters that fluctuate around an average. It connects thermodynamic quantities (such as heat capacity) to microscopic behavior, whereas, in classical thermodynamics, the only available option would be to measure and tabulate such quantities for various materials.
统计力学是现代物理学的支柱之一。它描述了宏观观察(如温度和压力)如何与围绕平均值波动的微观参数相关。它将热力学量(比如热容)与微观行为联系起来，而在经典热力学中，唯一可行的选择就是测量和列表各种材料的热力学量。
'''Ludwig Eduard Boltzmann''' ({{IPA-de|ˈluːtvɪg ˈbɔlt͡sman}}; February 20, 1844 – September 5, 1906) was an [[Austria]]n [[physicist]] and [[philosopher]]. His greatest achievements were the development of [[statistical mechanics]], and the statistical explanation of the [[second law of thermodynamics]]. In 1877 he provided the current definition of [[entropy]], <math>S = k_{\rm B} \ln \Omega \!</math>, interpreted as a measure of statistical disorder of a system.<ref name="EncycloBritan">{{cite book
|last1= Klein
|first1= Martin
|year= 1970
|orig-year= 1768
Boltzmann was born in Erdberg, a suburb of Vienna. His father, Ludwig Georg Boltzmann, was a revenue official. His grandfather, who had moved to Vienna from Berlin, was a clock manufacturer, and Boltzmann's mother, Katharina Pauernfeind, was originally from Salzburg. He received his primary education at the home of his parents. Boltzmann attended high school in Linz, Upper Austria. When Boltzmann was 15, his father died.
波尔兹曼出生于维也纳的郊区 Erdberg。他的父亲路德维希 · 格奥尔格 · 波尔兹曼是一名税务官员。他的祖父从柏林搬到了维也纳，是一个钟表制造商，而波尔兹曼的母亲卡塔琳娜•保恩芬德(Katharina Pauernfeind)来自萨尔茨堡。他在父母家接受小学教育。玻尔兹曼在上奥地利的林茨上高中。波尔兹曼15岁时，父亲去世了。
|chapter= Boltzmann, Ludwig
|editor1-last= Preece
Starting in 1863, Boltzmann studied mathematics and physics at the University of Vienna. He received his doctorate in 1866 and his venia legendi in 1869. Boltzmann worked closely with Josef Stefan, director of the institute of physics. It was Stefan who introduced Boltzmann to Maxwell's work. Boltzmann was appointed full Professor of Mathematical Physics at the University of Graz in the province of Styria. In 1869 he spent several months in Heidelberg working with Robert Bunsen and Leo Königsberger and in 1871 with Gustav Kirchhoff and Hermann von Helmholtz in Berlin. In 1873 Boltzmann joined the University of Vienna as Professor of Mathematics and there he stayed until 1876.
从1863年开始，玻尔兹曼在维也纳大学学习数学和物理学。他于1866年获得博士学位，于1869年获得法学博士学位。玻尔兹曼与物理研究所所长约瑟夫 · 斯蒂芬密切合作。是斯蒂芬把玻尔兹曼介绍给麦克斯韦尔的工作。被任命为 Styria 卡尔·弗朗岑斯大学数学物理学的正式教授。1869年，他在海德保花了几个月的时间与 Robert Bunsen 和莱奥·柯尼希斯贝格尔一起工作，1871年在柏林与古斯塔夫·基尔霍夫和赫尔曼·冯·亥姆霍兹一起工作。1873年，玻尔兹曼作为数学教授加入了维也纳大学，并在那里一直待到1876年。
|editor1-first= Warren E.
Nernst, Streintz, Arrhenius, Hiecke, (sitting, from the left) Aulinger, Ettingshausen, Boltzmann, Klemenčič, Hausmanninger]]
Nernst, Streintz, Arrhenius, Hiecke, (sitting, from the left) Aulinger, Ettingshausen, Boltzmann, Klemenčič, Hausmanninger]]
|title= Encyclopædia Britannica
In 1872, long before women were admitted to Austrian universities, he met Henriette von Aigentler, an aspiring teacher of mathematics and physics in Graz. She was refused permission to audit lectures unofficially. Boltzmann supported her decision to appeal, which was successful. On July 17, 1876 Ludwig Boltzmann married Henriette; they had three daughters: Henriette (1880), Ida (1884) and Else (1891); and a son, Arthur Ludwig (1881). Boltzmann went back to Graz to take up the chair of Experimental Physics. Among his students in Graz were Svante Arrhenius and Walther Nernst. He spent 14 happy years in Graz and it was there that he developed his statistical concept of nature.
1872年，在女性被奥地利大学录取之前很久，他遇到了 Henriette von Aigentler，一位有抱负的格拉茨数学和物理教师。她被拒绝以非正式的方式旁听课程。波尔兹曼支持她上诉的决定，这个决定很成功。1876年7月17日，路德维希·玻尔兹曼和亨利埃特结婚，他们有3个女儿: 亨利埃特(1880年) ，艾达(1884年)和艾尔斯(1891年) ，和一个儿子，亚瑟路德维希(1881年)。波尔兹曼回到格拉茨担任实验物理学教授。他在格拉茨的学生包括斯万特 · 阿伦尼乌斯和瓦尔特 · 纳恩斯特。他在格拉茨度过了快乐的14年，在那里他发展了自己的自然统计学概念。
|type=hard cover
|language= English
Boltzmann was appointed to the Chair of Theoretical Physics at the University of Munich in Bavaria, Germany in 1890.
1890年，玻尔兹曼被任命为德国巴伐利亚慕尼黑大学的理论物理学教授。
|volume= 3
|edition= Commemorative Edition for Expo 70
In 1894, Boltzmann succeeded his teacher Joseph Stefan as Professor of Theoretical Physics at the University of Vienna.
1894年，玻尔兹曼接替他的老师约瑟夫 · 斯蒂芬成为维也纳大学的理论物理学教授。
|location= Chicago
|publisher= William Benton
|publication-date= 1970
|page= 893a
Boltzmann spent a great deal of effort in his final years defending his theories. He did not get along with some of his colleagues in Vienna, particularly Ernst Mach, who became a professor of philosophy and history of sciences in 1895. That same year Georg Helm and Wilhelm Ostwald presented their position on energetics at a meeting in Lübeck. They saw energy, and not matter, as the chief component of the universe. Boltzmann's position carried the day among other physicists who supported his atomic theories in the debate. In 1900, Boltzmann went to the University of Leipzig, on the invitation of Wilhelm Ostwald. Ostwald offered Boltzmann the professorial chair in physics, which became vacant when Gustav Heinrich Wiedemann died. After Mach retired due to bad health, Boltzmann returned to Vienna in 1902.
玻尔兹曼在晚年花费了大量的精力来捍卫他的理论。他和他在维也纳的一些同事处不来，特别是恩斯特 · 马赫，后者在1895年成为哲学和科学史教授。同年，乔治•赫尔姆(Georg Helm)和威廉•奥斯特瓦尔德(Wilhelm Ostwald)在吕贝克的一次会议上，阐述了他们在能源学方面的立场。他们认为能量而不是物质是宇宙的主要组成部分。玻尔兹曼的立场在辩论中赢得了其他支持他的原子理论的物理学家的支持。1900年，应 Wilhelm Ostwald 的邀请，Boltzmann 去了莱比锡大学。奥斯特瓦尔德给波尔兹曼提供了一个物理学教授的职位，这个职位在古斯塔夫·海因里希·维德曼去世后就空了下来。由于身体不好，马赫退役后，波尔兹曼于1902年返回维也纳。
|isbn= 0852291353
}}
In 1906, Boltzmann's deteriorating mental condition forced him to resign his position, and his symptoms indicate he experienced what would today be diagnosed as bipolar disorder. Four months later he died by suicide on September 5, 1906, by hanging himself while on vacation with his wife and daughter in Duino, near Trieste (then Austria). During the 1890s, Boltzmann attempted to formulate a compromise position which would allow both atomists and anti-atomists to do physics without arguing over atoms. His solution was to use Hertz's theory that atoms were Bilder, that is, models or pictures. Atomists could think the pictures were the real atoms while the anti-atomists could think of the pictures as representing a useful but unreal model, but this did not fully satisfy either group. Furthermore, Ostwald and many defenders of "pure thermodynamics" were trying hard to refute the kinetic theory of gases and statistical mechanics because of Boltzmann's assumptions about atoms and molecules and especially statistical interpretation of the second law of thermodynamics.
1906年，Boltzmann 日益恶化的精神状况迫使他辞职，他的症状表明他经历了今天被诊断为躁郁症。四个月后，他于1906年9月5日与妻子和女儿在杜伊诺度假时上吊自杀身亡，当时他们住在的里雅斯特港/特区附近(当时是奥地利)。在19世纪90年代，玻尔兹曼试图阐明一个妥协的立场，允许原子论者和反原子论者在不争论原子的情况下进行物理研究。他的解决方案是使用赫兹的原子是比尔德的理论，即模型或图片。原子论者可以认为这些图片是真正的原子，而反原子论者可以认为这些图片代表了一个有用但不真实的模型，但这并不能完全满足任何一组。此外，Ostwald 和许多“纯热力学”的捍卫者正在努力驳斥分子运动论和统计力学，因为 Boltzmann 对原子和分子的假设，特别是对热力学第二定律的统计解释。
</ref> [[Max Planck]] named the constant, {{math|''k''<sub>B</sub>}}, the [[Boltzmann constant]].<ref>{{Citation
| last = Partington
Around the turn of the century, Boltzmann's science was being threatened by another philosophical objection. Some physicists, including Mach's student, Gustav Jaumann, interpreted Hertz to mean that all electromagnetic behavior is continuous, as if there were no atoms and molecules, and likewise as if all physical behavior were ultimately electromagnetic. This movement around 1900 deeply depressed Boltzmann since it could mean the end of his kinetic theory and statistical interpretation of the second law of thermodynamics.
在世纪之交，玻尔兹曼的科学受到另一种哲学反对意见的威胁。一些物理学家，包括马赫的学生古斯塔夫 · 乔曼，将赫兹解释为所有的电磁行为都是连续的，就好像没有原子和分子，同样，所有的物理行为最终都是电磁行为。1900年前后的这一运动使玻尔兹曼深感沮丧，因为它可能意味着他的动力学理论和热力学第二定律的统计解释的终结。
| first = J.R.
| author-link = J.R. Partington
After Mach's resignation in Vienna in 1901, Boltzmann returned there and decided to become a philosopher himself to refute philosophical objections to his physics, but he soon became discouraged again. In 1904 at a physics conference in St. Louis most physicists seemed to reject atoms and he was not even invited to the physics section. Rather, he was stuck in a section called "applied mathematics", he violently attacked philosophy, especially on allegedly Darwinian grounds but actually in terms of Lamarck's theory of the inheritance of acquired characteristics that people inherited bad philosophy from the past and that it was hard for scientists to overcome such inheritance.
1901年马赫在维也纳辞职后，波尔兹曼回到那里，决定自己成为一名哲学家，驳斥哲学界对他的物理学的反对意见，但他很快又变得灰心丧气。1904年在圣路易斯举行的一次物理学会议上，大多数物理学家似乎都排斥原子，甚至没有邀请他参加物理课。相反，他被困在一个叫做“应用数学”的部分，他猛烈抨击哲学，特别是据称基于达尔文的理由，但实际上是根据拉马克的获得性状遗传理论，人们从过去继承了糟糕的哲学，科学家很难克服这种继承。
| title = An Advanced Treatise on Physical Chemistry
| volume = volume 1, ''Fundamental Principles'', ''The Properties of Gases''
In 1905 Boltzmann corresponded extensively with the Austro-German philosopher Franz Brentano with the hope of gaining a better mastery of philosophy, apparently, so that he could better refute its relevancy in science, but he became discouraged about this approach as well.
1905年，波尔兹曼与德国哲学家弗朗茨 · 布伦塔诺有着广泛的通信往来，显然是希望能够更好地掌握哲学，以便更好地驳斥哲学与科学的关联性，但他也对这种方法感到气馁。
| place = London
| publisher = [[Longman|Longmans, Green and Co.]]
| series =
Boltzmann's most important scientific contributions were in kinetic theory, including for motivating the Maxwell–Boltzmann distribution as a description of molecular speeds in a gas. Maxwell–Boltzmann statistics and the Boltzmann distribution remain central in the foundations of classical statistical mechanics. They are also applicable to other phenomena that do not require quantum statistics and provide insight into the meaning of temperature.
玻尔兹曼最重要的科学贡献是在动力学理论，包括激发麦克斯韦-波兹曼分布，作为一种描述分子在气体中的速度。麦克斯韦-玻耳兹曼统计学和波兹曼分布理论仍然是经典统计力学理论基础的核心。它们也适用于其他不需要量子统计的现象，并提供了对温度含义的深入了解。
| origyear =
| year = 1949
Boltzmann's 1898 I<sub>2</sub> molecule diagram showing atomic "sensitive region" (α, β) overlap.
玻耳兹曼1898 i < 亚 > 2 </亚 > 分子图显示原子“敏感区”(α，β)重叠。
| page = 300}}</ref>
Most chemists, since the discoveries of John Dalton in 1808, and James Clerk Maxwell in Scotland and Josiah Willard Gibbs in the United States, shared Boltzmann's belief in atoms and molecules, but much of the physics establishment did not share this belief until decades later. Boltzmann had a long-running dispute with the editor of the preeminent German physics journal of his day, who refused to let Boltzmann refer to atoms and molecules as anything other than convenient theoretical constructs. Only a couple of years after Boltzmann's death, Perrin's studies of colloidal suspensions (1908–1909), based on Einstein's theoretical studies of 1905, confirmed the values of Avogadro's number and Boltzmann's constant, convincing the world that the tiny particles really exist.
自从1808年 John Dalton，苏格兰的詹姆斯·克拉克·麦克斯韦和美国的约西亚·威拉德·吉布斯发现以来，大多数化学家都认同 Boltzmann 的原子和分子理论，但是大多数物理学家直到几十年后才认同这一理论。玻尔兹曼与他那个时代卓越的德国物理学期刊的编辑有一个长期的争论，他拒绝让玻尔兹曼把原子和分子称为除了方便的理论构造以外的任何东西。玻尔兹曼死后仅仅几年，佩兰对胶体悬浮的研究(1908-1909年) ，以爱因斯坦1905年的理论研究为基础，证实了阿伏加德罗常数和波尔兹曼常数的价值，使世界相信微小粒子确实存在。
Statistical mechanics is one of the pillars of modern [[physics]]. It describes how macroscopic observations (such as [[temperature]] and [[pressure]]) are related to microscopic parameters that fluctuate around an average. It connects thermodynamic quantities (such as [[heat capacity]]) to microscopic behavior, whereas, in [[classical thermodynamics]], the only available option would be to measure and tabulate such quantities for various materials.<ref name="gibbs">{{cite book |last=Gibbs |first=Josiah Willard |author-link=Josiah Willard Gibbs |title=Elementary Principles in Statistical Mechanics |year=1902 |publisher=[[Charles Scribner's Sons]] |location=New York |title-link=Elementary Principles in Statistical Mechanics }}</ref>
To quote Planck, "The logarithmic connection between entropy and probability was first stated by L. Boltzmann in his kinetic theory of gases". This famous formula for entropy S is
引用普朗克的话，“熵和概率之间的对数关系最早是由 l. Boltzmann 在他的分子运动论中提出的”。这个著名的熵公式是
==Biography==
<math> S = k_B \ln W </math>
[ math ] s = k _ b ln w [ math ]
===Childhood and education===
Boltzmann was born in Erdberg, a suburb of [[Vienna]]. His father, Ludwig Georg Boltzmann, was a revenue official. His grandfather, who had moved to Vienna from Berlin, was a clock manufacturer, and Boltzmann's mother, Katharina Pauernfeind, was originally from [[Salzburg]]. He received his primary education at the home of his parents.<ref>{{cite book
where k<sub>B</sub> is Boltzmann's constant, and ln is the natural logarithm. W is Wahrscheinlichkeit, a German word meaning the probability of occurrence of a macrostate or, more precisely, the number of possible microstates corresponding to the macroscopic state of a system — the number of (unobservable) "ways" in the (observable) thermodynamic state of a system that can be realized by assigning different positions and momenta to the various molecules. Boltzmann's paradigm was an ideal gas of N identical particles, of which N<sub>i</sub> are in the ith microscopic condition (range) of position and momentum. W can be counted using the formula for permutations
其中 k < sub > b </sub > 是 Boltzmann 常数，ln 是自然对数。W 是 Wahrscheinlichkeit，一个德语单词，意思是发生宏观状态的可能性，或者更准确地说，是对应于系统宏观状态的可能的微观状态的数量---- 一个系统的可观测的热力学状态中的“方式”的数量，可以通过给各种分子分配不同的位置和动量来实现。玻耳兹曼的范式是全同粒子的理想气体，其中 n < sub > i </sub > 处于位置和动量的微观条件。W 可以用排列的公式来计算
|title=The Scientific 100
|first1=John
<math> W = N! \prod_i \frac{1}{N_i!} </math>
W = n！1} n i数学
|last1=Simmons
|first2=Lynda
where i ranges over all possible molecular conditions, and where <math>!</math> denotes factorial. The "correction" in the denominator account for indistinguishable particles in the same condition.
这里 i 可以覆盖所有可能的分子条件，这里 < math > ! </math > 表示阶乘。在相同条件下，分母中的“修正”解释了不可区分的粒子。
|last2=Simmons
|isbn=9780806536781
Boltzmann could also be considered one of the forerunners of quantum mechanics due to his suggestion in 1877 that the energy levels of a physical system could be discrete.
由于他在1877年提出物理系统的能级可以是离散的，Boltzmann 也可以被认为是量子力学的先驱之一。
|page=123
|publisher=Kensington Publishing Corp.
|year=2000
Boltzmann's bust in the courtyard arcade of the main building, University of Vienna.
在维也纳大学主楼的庭院拱廊中的玻尔兹曼的半身像。
}}</ref> Boltzmann attended high school in [[Linz]], [[Upper Austria]]. When Boltzmann was 15, his father died.<ref name=james2004>{{cite book
|title=Remarkable Physicists: From Galileo to Yukawa
The Boltzmann equation was developed to describe the dynamics of an ideal gas.
玻尔兹曼方程是用来描述理想气体的动力学的。
|url=https://archive.org/details/remarkablephysic00jame
|url-access=limited
<math> \frac{\partial f}{\partial t}+ v \frac{\partial f}{\partial x}+ \frac{F}{m} \frac{\partial f}{\partial v} = \frac{\partial f}{\partial t}\left.{\!\!\frac{}{}}\right|_\mathrm{collision} </math>
{ partial t } + v frac { partial f }{ partial x } + frac { f }{ m } frac { partial f }{{ partial v } = frac { partial f }{ partial t }.{ ! ! frac {}{}}右 | _ mathrm { collision } </math >
|first1=Ioan
|last1=James
where ƒ represents the distribution function of single-particle position and momentum at a given time (see the Maxwell–Boltzmann distribution), F is a force, m is the mass of a particle, t is the time and v is an average velocity of particles.
F 表示一定时间内单个粒子的位置和动量的分布函数(见麦克斯韦-波兹曼分布) ，f 表示一个力，m 表示一个粒子的质量，t 表示时间，v 表示粒子的平均速度。
|isbn=9780521017060
|page=[https://archive.org/details/remarkablephysic00jame/page/n185 169]
This equation describes the temporal and spatial variation of the probability distribution for the position and momentum of a density distribution of a cloud of points in single-particle phase space. (See Hamiltonian mechanics.) The first term on the left-hand side represents the explicit time variation of the distribution function, while the second term gives the spatial variation, and the third term describes the effect of any force acting on the particles. The right-hand side of the equation represents the effect of collisions.
这个方程描述了单粒子相空间中点云密度分布的位置和动量的概率分布的时间和空间变化。(参见哈密顿力学。)左边的第一项表示分布函数的显式时间变化，第二项表示空间变化，第三项描述作用在粒子上的任何力的效应。方程的右边表示碰撞的影响。
|publisher=Cambridge University Press
|year=2004
In principle, the above equation completely describes the dynamics of an ensemble of gas particles, given appropriate boundary conditions. This first-order differential equation has a deceptively simple appearance, since ƒ can represent an arbitrary single-particle distribution function. Also, the force acting on the particles depends directly on the velocity distribution function ƒ. The Boltzmann equation is notoriously difficult to integrate. David Hilbert spent years trying to solve it without any real success.
原则上，上述方程在给定适当的边界条件下，完全描述了气体粒子系综的动力学行为。这个一阶微分方程的外观看似简单，因为它可以表示任意的单粒子分布函数。作用在粒子上的力的大小直接取决于它的速度分布函数。众所周知，玻尔兹曼方程是难以整合的。大卫 · 希尔伯特花了数年时间试图解决这个问题，但没有取得任何真正的成功。
}}</ref>
The form of the collision term assumed by Boltzmann was approximate. However, for an ideal gas the standard Chapman–Enskog solution of the Boltzmann equation is highly accurate. It is expected to lead to incorrect results for an ideal gas only under shock wave conditions.
Boltzmann 采用的碰撞术语的形式是近似的。然而，对于理想气体，玻尔兹曼方程的标准 Chapman-Enskog 解决方案是高度准确的。只有在冲击波条件下，理想气体才有可能得到不正确的结果。
Starting in 1863, Boltzmann studied [[mathematics]] and [[physics]] at the [[University of Vienna]]. He received his doctorate in 1866 and his [[venia legendi]] in 1869. Boltzmann worked closely with [[Josef Stefan]], director of the institute of physics. It was Stefan who introduced Boltzmann to [[James Clerk Maxwell|Maxwell's]] work.<ref name=james2004 />
Boltzmann tried for many years to "prove" the second law of thermodynamics using his gas-dynamical equation — his famous H-theorem. However the key assumption he made in formulating the collision term was "molecular chaos", an assumption which breaks time-reversal symmetry as is necessary for anything which could imply the second law. It was from the probabilistic assumption alone that Boltzmann's apparent success emanated, so his long dispute with Loschmidt and others over Loschmidt's paradox ultimately ended in his failure.
多年来，Boltzmann 一直试图用他的气体动力学方程——著名的 h 定理——来“证明”热力学第二定律。然而，他在构造碰撞术语时所作的关键假设是“分子混沌” ，这个假设破坏了时间反转对称性，这对任何可能暗示第二定律的事物都是必要的。波尔兹曼表面上的成功仅仅来自于概率假设，因此他与洛施密特和其他人就洛施密特悖论的长期争论最终以他的失败而告终。
===Academic career===
Finally, in the 1970s E.G.D. Cohen and J. R. Dorfman proved that a systematic (power series) extension of the Boltzmann equation to high densities is mathematically impossible. Consequently, nonequilibrium statistical mechanics for dense gases and liquids focuses on the Green–Kubo relations, the fluctuation theorem, and other approaches instead.
最终，在20世纪70年代的 e.g.d。和 j. r. Dorfman 证明了系统地(幂级数)将玻尔兹曼方程扩展到高密度在数学上是不可能的。因此，稠密气体和液体的非平衡态统计力学集中在格林-库伯关系、涨落定理和其他方法上。
In 1869 at age 25, thanks to a letter of recommendation written by Stefan,<ref>{{cite journal |url=http://www.kvarkadabra.net/2001/12/ludwig-boltzmann/ |title=Ludwig Boltzmann in prva študentka fizike in matematike slovenskega rodu |language=Slovenian |trans-title=Ludwig Boltzmann and the First Student of Physics and Mathematics of Slovene Descent |date=December 2001 |last=Južnič |first=Stanislav |website=Kvarkadabra.net |issue=12 |accessdate=17 February 2012}}</ref> Boltzmann was appointed full Professor of [[Mathematical Physics]] at the [[University of Graz]] in the province of [[Styria]]. In 1869 he spent several months in [[Heidelberg]] working with [[Robert Bunsen]] and [[Leo Königsberger]] and in 1871 with [[Gustav Kirchhoff]] and [[Hermann von Helmholtz]] in Berlin. In 1873 Boltzmann joined the University of Vienna as Professor of Mathematics and there he stayed until 1876.
[[File:Boltzmann-grp.jpg|thumb|left|280px|Ludwig Boltzmann and co-workers in Graz, 1887: (standing, from the left) [[Walther Nernst|Nernst]], [[Heinrich Streintz|Streintz]], [[Svante Arrhenius|Arrhenius]], Hiecke, (sitting, from the left) Aulinger, [[Albert von Ettingshausen|Ettingshausen]], Boltzmann, [[Ignacij Klemenčič|Klemenčič]], Hausmanninger]]
In 1872, long before women were admitted to Austrian universities, he met Henriette von Aigentler, an aspiring teacher of mathematics and physics in Graz. She was refused permission to audit lectures unofficially. Boltzmann supported her decision to appeal, which was successful. On July 17, 1876 Ludwig Boltzmann married Henriette; they had three daughters: Henriette (1880), Ida (1884) and Else (1891); and a son, Arthur Ludwig (1881).<ref>https://www.boltzmann.com/ludwig-boltzmann/biography/</ref> Boltzmann went back to [[Graz]] to take up the chair of Experimental Physics. Among his students in Graz were [[Svante Arrhenius]] and [[Walther Nernst]].<ref name="springer">{{Cite journal |quote=Paul Ehrenfest (1880–1933) along with Nernst, Arrhenius, and Meitner must be considered among Boltzmann's most outstanding students. |last1=Jäger |first1=Gustav |last2=Nabl |first2=Josef |last3=Meyer |first3=Stephan |date=April 1999 |title=Three Assistants on Boltzmann |journal=Synthese |volume=119 |issue=1–2 |pages=69–84 |doi=10.1023/A:1005239104047|s2cid=30499879 }}</ref><ref name="huji">{{cite web |url=http://chem.ch.huji.ac.il/history/nernst.htm |title=Walther Hermann Nernst |quote=Walther Hermann Nernst visited lectures by Ludwig Boltzmann |archive-url=https://web.archive.org/web/20080612133921/http://chem.ch.huji.ac.il/history/nernst.htm |archive-date=2008-06-12 }}</ref> He spent 14 happy years in Graz and it was there that he developed his statistical concept of nature.
Boltzmann's grave in the [[Zentralfriedhof, Vienna, with bust and entropy formula.]]
玻尔兹曼的坟墓[维也纳中心区弗里德霍夫，胸围和熵公式]
The idea that the second law of thermodynamics or "entropy law" is a law of disorder (or that dynamically ordered states are "infinitely improbable") is due to Boltzmann's view of the second law of thermodynamics.
认为热力学第二定律定律或者“熵定律”是无序定律(或者说动态有序的状态是“无限不可能的”)的观点是由于 Boltzmann 对热力学第二定律的观点。
Boltzmann was appointed to the Chair of Theoretical Physics at the [[University of Munich]] in [[Bavaria]], Germany in 1890.
In particular, it was Boltzmann's attempt to reduce it to a stochastic collision function, or law of probability following from the random collisions of mechanical particles. Following Maxwell, Boltzmann modeled gas molecules as colliding billiard balls in a box, noting that with each collision nonequilibrium velocity distributions (groups of molecules moving at the same speed and in the same direction) would become increasingly disordered leading to a final state of macroscopic uniformity and maximum microscopic disorder or the state of maximum entropy (where the macroscopic uniformity corresponds to the obliteration of all field potentials or gradients). The second law, he argued, was thus simply the result of the fact that in a world of mechanically colliding particles disordered states are the most probable. Because there are so many more possible disordered states than ordered ones, a system will almost always be found either in the state of maximum disorder – the macrostate with the greatest number of accessible microstates such as a gas in a box at equilibrium – or moving towards it. A dynamically ordered state, one with molecules moving "at the same speed and in the same direction", Boltzmann concluded, is thus "the most improbable case conceivable...an infinitely improbable configuration of energy."
尤其是，玻尔兹曼试图把它归结为一个随机碰撞函数，或者机械粒子随机碰撞后的概率定律。继麦克斯韦尔之后，玻尔兹曼将气体分子模拟为在一个盒子里碰撞的台球，指出每次碰撞时，非平衡速度分布(以相同速度和方向运动的分子群)将变得越来越无序，导致最终的宏观均匀和最大微观无序状态或最大熵状态(宏观均匀性对应于所有场势或梯度的消失)。因此，他认为第二定律仅仅是这样一个事实的结果，即在一个机械碰撞的粒子无序状态是最有可能的。因为可能存在的无序状态比有序状态多得多，所以一个系统几乎总是处于最大无序状态——具有最多可达微观状态的宏观状态，例如平衡状态下盒子中的气体——或者向无序状态移动。玻尔兹曼总结说，一个动态有序的状态，即分子以“同样的速度和同样的方向”运动，因此是“最不可能想象的情况... ... 一个无限不可能的能量构型”
In 1894, Boltzmann succeeded his teacher [[Joseph Stefan]] as Professor of Theoretical Physics at the University of Vienna.
Boltzmann accomplished the feat of showing that the second law of thermodynamics is only a statistical fact. The gradual disordering of energy is analogous to the disordering of an initially ordered pack of cards under repeated shuffling, and just as the cards will finally return to their original order if shuffled a gigantic number of times, so the entire universe must some-day regain, by pure chance, the state from which it first set out. (This optimistic coda to the idea of the dying universe becomes somewhat muted when one attempts to estimate the timeline which will probably elapse before it spontaneously occurs.) The tendency for entropy increase seems to cause difficulty to beginners in thermodynamics, but is easy to understand from the standpoint of the theory of probability. Consider two ordinary dice, with both sixes face up. After the dice are shaken, the chance of finding these two sixes face up is small (1 in 36); thus one can say that the random motion (the agitation) of the dice, like the chaotic collisions of molecules because of thermal energy, causes the less probable state to change to one that is more probable. With millions of dice, like the millions of atoms involved in thermodynamic calculations, the probability of their all being sixes becomes so vanishingly small that the system must move to one of the more probable states. However, mathematically the odds of all the dice results not being a pair sixes is also as hard as the ones of all of them being sixes, and since statistically the data tend to balance, one in every 36 pairs of dice will tend to be a pair of sixes, and the cards -when shuffled- will sometimes present a certain temporary sequence order even if in its whole the deck was disordered.
玻尔兹曼完成了一项壮举，证明了热力学第二定律只是一个统计事实。能量的逐渐失序类似于一副最初有序的扑克牌在重复洗牌过程中的失序，就像如果洗牌次数过多，扑克牌最终会恢复到原来的秩序一样，因此，整个宇宙必定会在某一天，纯粹出于偶然，恢复到它最初开始时的状态。(当人们试图估计可能在宇宙自发发生之前就已经过去的时间线时，这种对于正在消亡的宇宙这一观点的乐观结尾就变得有些沉默了。)熵增的趋势似乎给热力学初学者带来了困难，但从概率论的角度来看，熵增的趋势是容易理解的。考虑两个普通的骰子，两个6的面朝上。摇动骰子后，发现这两个六的概率很小(1/36) ，因此可以说，骰子的随机运动(搅动) ，就像分子因热能而产生的混沌碰撞，导致较不可能的状态转变为更可能的状态。数以百万计的骰子，就像热力学计算中所涉及的数以百万计的原子一样，它们都是六的概率变得如此微小，以至于系统必须移动到一个更有可能的状态。然而，从数学上计算出所有骰子不是一对六的概率也和所有骰子都是六的概率一样困难，而且由于统计数据趋于平衡，每36对骰子中就有一对是六，而当洗牌时，有时会呈现出某种暂时的序列顺序，即使整副牌是混乱的。
===Final years and death===
Boltzmann spent a great deal of effort in his final years defending his theories.<ref name ="Carlo">Cercignani, Carlo (1998) Ludwig Boltzmann: The Man Who Trusted Atoms. Oxford University Press. {{ISBN|9780198501541}}</ref> He did not get along with some of his colleagues in Vienna, particularly [[Ernst Mach]], who became a professor of philosophy and history of sciences in 1895. That same year [[Georg Helm]] and [[Wilhelm Ostwald]] presented their position on [[energetics]] at a meeting in [[Lübeck]]. They saw energy, and not matter, as the chief component of the universe. Boltzmann's position carried the day among other physicists who supported his atomic theories in the debate.<ref>{{cite journal|author=Max Planck|title=Gegen die neure Energetik|journal=Annalen der Physik|volume=57|issue=1|year=1896|pages=72–78|doi=10.1002/andp.18962930107 |bibcode = 1896AnP...293...72P |url=https://zenodo.org/record/1423910}}</ref> In 1900, Boltzmann went to the [[University of Leipzig]], on the invitation of [[Wilhelm Ostwald]]. Ostwald offered Boltzmann the professorial chair in physics, which became vacant when [[Gustav Heinrich Wiedemann]] died. After Mach retired due to bad health, Boltzmann returned to Vienna in 1902.<ref name ="Carlo"/> In 1903, Boltzmann, together with [[Gustav von Escherich]] and [[Emil Müller (mathematician)|Emil Müller]], founded the [[Austrian Mathematical Society]]. His students included [[Karl Přibram]], [[Paul Ehrenfest]] and [[Lise Meitner]].<ref name ="Carlo"/>
In 1885 he became a member of the Imperial Austrian Academy of Sciences and in 1887 he became the President of the University of Graz. He was elected a member of the Royal Swedish Academy of Sciences in 1888 and a Foreign Member of the Royal Society (ForMemRS) in 1899. Numerous things are named in his honour.
1885年，他成为奥地利帝国科学院的一员，1887年，他成为卡尔·弗朗岑斯大学的院长。他于1888年被选为瑞典皇家科学院院士，并于1899年被选为皇家学会的外国会员。许多事物都以他的名字命名。
In Vienna, Boltzmann taught physics and also lectured on philosophy. Boltzmann's lectures on [[natural philosophy]] were very popular and received considerable attention. His first lecture was an enormous success. Even though the largest lecture hall had been chosen for it, the people stood all the way down the staircase. Because of the great successes of Boltzmann's philosophical lectures, the Emperor invited him for a reception at the Palace.<ref>The Boltzmann Equation: Theory and Applications, E.G.D. Cohen, W. Thirring, ed., Springer Science & Business Media, 2012</ref>
In 1906, Boltzmann's deteriorating mental condition forced him to resign his position, and his symptoms indicate he experienced what would today be diagnosed as [[bipolar disorder]].<ref name ="Carlo"/><ref name="Paperpile">{{cite web | last = Nina Bausek and Stefan Washietl | title = Tragic deaths in science: Ludwig Boltzmann — a mind in disorder | publisher = [[Paperpile]] | date = February 13, 2018 | url = https://paperpile.com/blog/ludwig-boltzmann/ | accessdate = 2020-04-26 }}</ref> Four months later he died by suicide on September 5, 1906, by hanging himself while on vacation with his wife and daughter in [[Duino]], near [[Trieste]] (then Austria).<ref>"Eureka! Science's greatest thinkers and their key breakthroughs", Hazel Muir, p.152, {{ISBN|1780873255}}</ref><ref>{{cite book|last=Boltzmann|first=Ludwig|editor1-first=John T.|editor1-last=Blackmore|title=Ludwig Boltzmann: His Later Life and Philosophy, 1900-1906|chapter-url=https://books.google.com/books?id=apip-Jm9WuwC&pg=PA207 |volume=2|year=1995|publisher=Springer|isbn=978-0-7923-3464-4|pages=206–207|chapter=Conclusions}}</ref><ref>Upon Boltzmann's death, [[Friedrich Hasenöhrl|Friedrich ("Fritz") Hasenöhrl]] became his successor in the professorial chair of physics at Vienna.</ref><ref name="Paperpile" />
He is buried in the Viennese [[Zentralfriedhof]]. His tombstone bears the inscription of [[Boltzmann's entropy formula]]: <math>S = k \cdot \log W </math><ref name ="Carlo"/>
==Philosophy==
{{Unreferenced section|date=December 2018}}
Boltzmann's [[kinetic theory of gases]] seemed to presuppose the reality of [[atom]]s and [[molecule]]s, but almost all [[German philosophy|German philosophers]] and many scientists like [[Ernst Mach]] and the physical chemist [[Wilhelm Ostwald]] disbelieved their existence.<ref>{{cite book | last=Bronowski | first=Jacob | authorlink=Jacob Bronowski | title=The Ascent Of Man | chapter=World Within World | publisher=Little Brown & Co | year=1974 | isbn=978-0-316-10930-7 | page=265 | chapter-url=https://archive.org/details/ascentofmanbron00bron }}</ref> During the 1890s, Boltzmann attempted to formulate a compromise position which would allow both atomists and anti-atomists to do physics without arguing over atoms. His solution was to use [[Heinrich Hertz|Hertz]]'s theory that atoms were ''Bilder'', that is, models or pictures. Atomists could think the pictures were the real atoms while the anti-atomists could think of the pictures as representing a useful but unreal model, but this did not fully satisfy either group. Furthermore, Ostwald and many defenders of "pure thermodynamics" were trying hard to refute the kinetic theory of gases and statistical mechanics because of Boltzmann's assumptions about atoms and molecules and especially statistical interpretation of the [[second law of thermodynamics]].
Around the turn of the century, Boltzmann's science was being threatened by another philosophical objection. Some physicists, including Mach's student, [[Gustav Jaumann]], interpreted Hertz to mean that all electromagnetic behavior is continuous, as if there were no atoms and molecules, and likewise as if all physical behavior were ultimately electromagnetic. This movement around 1900 deeply depressed Boltzmann since it could mean the end of his kinetic theory and statistical interpretation of the second law of thermodynamics.
After Mach's resignation in Vienna in 1901, Boltzmann returned there and decided to become a philosopher himself to refute philosophical objections to his physics, but he soon became discouraged again. In 1904 at a physics conference in St. Louis most physicists seemed to reject atoms and he was not even invited to the physics section. Rather, he was stuck in a section called "applied mathematics", he violently attacked philosophy, especially on allegedly Darwinian grounds but actually in terms of [[Lamarck]]'s theory of the inheritance of acquired characteristics that people inherited bad philosophy from the past and that it was hard for scientists to overcome such inheritance.
In 1905 Boltzmann corresponded extensively with the Austro-German philosopher [[Franz Brentano]] with the hope of gaining a better mastery of philosophy, apparently, so that he could better refute its relevancy in science, but he became discouraged about this approach as well.
==Physics==
Boltzmann's most important scientific contributions were in [[kinetic theory of gases|kinetic theory]], including for motivating the [[Maxwell–Boltzmann distribution]] as a description of molecular speeds in a gas. [[Maxwell–Boltzmann statistics]] and the [[Boltzmann distribution]] remain central in the foundations of [[classical mechanics|classical]] statistical mechanics. They are also applicable to other [[phenomenon|phenomena]] that do not require [[Maxwell–Boltzmann statistics#Limits of applicability|quantum statistics]] and provide insight into the meaning of [[thermodynamic temperature|temperature]].
[[File:Boltzmanns-molecule.jpg|225px|thumb|right|Boltzmann's 1898 I<sub>2</sub> molecule diagram showing atomic "sensitive region" (α, β) overlap.]]
[[History of chemistry#The dispute about atomism|Most]] [[chemistry|chemists]], since the discoveries of [[John Dalton]] in 1808, and [[James Clerk Maxwell]] in Scotland and [[Josiah Willard Gibbs]] in the United States, shared Boltzmann's belief in [[atom]]s and [[molecule]]s, but much of the [[physics]] establishment did not share this belief until decades later. Boltzmann had a long-running dispute with the editor of the preeminent German physics journal of his day, who refused to let Boltzmann refer to atoms and molecules as anything other than convenient [[Theory#Science|theoretical]] constructs. Only a couple of years after Boltzmann's death, [[Jean Baptiste Perrin|Perrin's]] studies of [[colloid]]al suspensions (1908–1909), based on [[Albert Einstein|Einstein's]] [[Albert Einstein#Thermodynamic fluctuations and statistical physics|theoretical studies]] of 1905, confirmed the values of [[Avogadro's number]] and [[Boltzmann constant|Boltzmann's constant]], convincing the world that the tiny particles [[Atomic theory#History|really exist]].
To quote [[Max Planck|Planck]], "The [[logarithm]]ic connection between [[entropy]] and [[probability]] was first stated by L. Boltzmann in his [[kinetic theory of gases]]".<ref>Max Planck, p. 119.</ref> This famous formula for entropy ''S'' is<ref>The concept of [[entropy]] was introduced by [[Rudolf Clausius]] in 1865. He was the first to enunciate the [[second law of thermodynamics]] by saying that "entropy always increases".</ref><ref>An alternative is the [[Information entropy#Formal definitions|information entropy]] definition introduced in 1948 by [[Claude Elwood Shannon|Claude Shannon]].[https://archive.is/20070503225307/http://cm.bell-labs.com/cm/ms/what/shannonday/paper.html] It was intended for use in communication theory, but is applicable in all areas. It reduces to Boltzmann's expression when all the probabilities are equal, but can, of course, be used when they are not. Its virtue is that it yields immediate results without resorting to [[factorial]]s or [[Stirling's approximation]]. Similar formulas are found, however, as far back as the work of Boltzmann, and explicitly in [[H-theorem#Quantum mechanical H-theorem|Gibbs]] (see reference).</ref>
:<math> S = k_B \ln W </math>
where ''k<sub>B</sub>'' is [[Boltzmann constant|Boltzmann's constant]], and ''ln'' is the [[natural logarithm]]. ''W'' is ''Wahrscheinlichkeit'', a German word meaning the [[probability theory|probability]] of occurrence of a [[macrostate]]<ref>{{cite book|last=Pauli| first=Wolfgang| title=Statistical Mechanics|publisher=MIT Press|location=Cambridge|year=1973|isbn=978-0-262-66035-8}}, p. 21</ref> or, more precisely, the number of possible [[microstate (statistical mechanics)|microstates]] corresponding to the macroscopic state of a system — the number of (unobservable) "ways" in the (observable) [[thermodynamics|thermodynamic]] state of a system that can be realized by assigning different [[coordinate system|positions]] and [[momentum|momenta]] to the various molecules. Boltzmann's [[Paradigm#Paradigm shifts|paradigm]] was an [[ideal gas]] of ''N'' ''identical'' particles, of which ''N''<sub>''i''</sub> are in the ''i''th microscopic condition (range) of position and momentum. ''W'' can be counted using the formula for [[Maxwell–Boltzmann statistics#A derivation of the Maxwell–Boltzmann distribution|permutations]]
:<math> W = N! \prod_i \frac{1}{N_i!} </math>
where ''i'' ranges over all possible molecular conditions, and where <math>!</math> denotes [[factorial]]. The "correction" in the denominator account for [[Identical particles|indistinguishable]] particles in the same condition.
Boltzmann could also be considered one of the forerunners of quantum mechanics due to his suggestion in 1877 that the energy levels of a physical system could be discrete.
==Boltzmann equation==
[[File:Ludwig Boltzmann at U Vienna.JPG|thumb|Boltzmann's bust in the courtyard arcade of the main building, University of Vienna.]]
{{main|Boltzmann equation}}
The Boltzmann equation was developed to describe the dynamics of an ideal gas.
:<math> \frac{\partial f}{\partial t}+ v \frac{\partial f}{\partial x}+ \frac{F}{m} \frac{\partial f}{\partial v} = \frac{\partial f}{\partial t}\left.{\!\!\frac{}{}}\right|_\mathrm{collision} </math>
where ''ƒ'' represents the distribution function of single-particle position and momentum at a given time (see the [[Maxwell–Boltzmann distribution]]), ''F'' is a force, ''m'' is the mass of a particle, ''t'' is the time and ''v'' is an average velocity of particles.
This equation describes the [[time|temporal]] and [[space|spatial]] variation of the probability distribution for the position and momentum of a density distribution of a cloud of points in single-particle [[phase space]]. (See [[Hamiltonian mechanics]].) The first term on the left-hand side represents the explicit time variation of the distribution function, while the second term gives the spatial variation, and the third term describes the effect of any force acting on the particles. The right-hand side of the equation represents the effect of collisions.
In principle, the above equation completely describes the dynamics of an ensemble of gas particles, given appropriate [[boundary conditions]]. This first-order [[differential equation]] has a deceptively simple appearance, since ''ƒ'' can represent an arbitrary single-particle distribution function. Also, the [[force]] acting on the particles depends directly on the velocity distribution function ''ƒ''. The Boltzmann equation is notoriously difficult to [[Integral|integrate]]. [[David Hilbert]] spent years trying to solve it without any real success.
The form of the collision term assumed by Boltzmann was approximate. However, for an ideal gas the standard [[Chapman–Enskog theory|Chapman–Enskog]] solution of the Boltzmann equation is highly accurate. It is expected to lead to incorrect results for an ideal gas only under [[shock wave]] conditions.
Category:1844 births
类别: 1844名出生
Boltzmann tried for many years to "prove" the [[second law of thermodynamics]] using his gas-dynamical equation — his famous [[H-theorem]]. However the key assumption he made in formulating the collision term was "[[molecular chaos]]", an assumption which breaks [[CPT symmetry|time-reversal symmetry]] as is necessary for ''anything'' which could imply the second law. It was from the probabilistic assumption alone that Boltzmann's apparent success emanated, so his long dispute with [[Johann Josef Loschmidt|Loschmidt]] and others over [[Loschmidt's paradox]] ultimately ended in his failure.
Category:1906 deaths
分类: 1906人死亡
Category:Scientists from Vienna
类别: 来自维也纳的科学家
Finally, in the 1970s [[E.G.D. Cohen]] and J. R. Dorfman proved that a systematic (power series) extension of the Boltzmann equation to high densities is mathematically impossible. Consequently, [[non-equilibrium statistical mechanics|nonequilibrium statistical mechanics]] for dense gases and liquids focuses on the [[Green–Kubo relations]], the [[fluctuation theorem]], and other approaches instead.
Category:Austrian physicists
类别: 奥地利物理学家
Category:Thermodynamicists
类别: 热力学家
==Second thermodynamics law as a law of disorder==
Category:Fluid dynamicists
类别: 流体动力学家
[[File:Zentralfriedhof Vienna - Boltzmann.JPG|thumb|right|Boltzmann's grave in the [[Zentralfriedhof]], Vienna, with bust and entropy formula.]]
Category:Physicists who committed suicide
类别: 自杀的物理学家
The idea that the [[second law of thermodynamics]] or "entropy law" is a law of disorder (or that dynamically ordered states are "infinitely improbable") is due to Boltzmann's view of the second law of thermodynamics.
Category:Mathematicians who committed suicide
类别: 自杀的数学家
Category:Burials at the Vienna Central Cemetery
类别: 维也纳中央公墓的葬礼
In particular, it was Boltzmann's attempt to reduce it to a [[stochastic]] collision function, or law of probability following from the random collisions of mechanical particles. Following Maxwell,<ref>Maxwell, J. (1871). Theory of heat. London: Longmans, Green & Co.</ref> Boltzmann modeled gas molecules as colliding billiard balls in a box, noting that with each collision nonequilibrium velocity distributions (groups of molecules moving at the same speed and in the same direction) would become increasingly disordered leading to a final state of macroscopic uniformity and maximum microscopic disorder or the state of maximum entropy (where the macroscopic uniformity corresponds to the obliteration of all field potentials or gradients).<ref>Boltzmann, L. (1974). The second law of thermodynamics. Populare Schriften, Essay 3, address to a formal meeting of the Imperial Academy of Science, 29 May 1886, reprinted in Ludwig Boltzmann, Theoretical physics and philosophical problem, S. G. Brush (Trans.). Boston: Reidel. (Original work published 1886)</ref> The second law, he argued, was thus simply the result of the fact that in a world of mechanically colliding particles disordered states are the most probable. Because there are so many more possible disordered states than ordered ones, a system will almost always be found either in the state of maximum disorder – the macrostate with the greatest number of accessible microstates such as a gas in a box at equilibrium – or moving towards it. A dynamically ordered state, one with molecules moving "at the same speed and in the same direction", Boltzmann concluded, is thus "the most improbable case conceivable...an infinitely improbable configuration of energy."<ref>Boltzmann, L. (1974). The second law of thermodynamics. p. 20</ref>
Category:University of Vienna alumni
类别: 维也纳大学校友
Category:Members of the Royal Swedish Academy of Sciences
类别: 瑞典皇家科学院院士
Boltzmann accomplished the feat of showing that the second law of thermodynamics is only a statistical fact. The gradual disordering of energy is analogous to the disordering of an initially ordered [[pack of cards]] under repeated shuffling, and just as the cards will finally return to their original order if shuffled a gigantic number of times, so the entire universe must some-day regain, by pure chance, the state from which it first set out. (This optimistic coda to the idea of the dying universe becomes somewhat muted when one attempts to estimate the timeline which will probably elapse before it spontaneously occurs.)<ref>"[[Collier's Encyclopedia]]", Volume 19 Phyfe to Reni, "Physics", by David Park, p. 15</ref> The tendency for entropy increase seems to cause difficulty to beginners in thermodynamics, but is easy to understand from the standpoint of the theory of probability. Consider two ordinary [[dice]], with both sixes face up. After the dice are shaken, the chance of finding these two sixes face up is small (1 in 36); thus one can say that the random motion (the agitation) of the dice, like the chaotic collisions of molecules because of thermal energy, causes the less probable state to change to one that is more probable. With millions of dice, like the millions of atoms involved in thermodynamic calculations, the probability of their all being sixes becomes so vanishingly small that the system ''must'' move to one of the more probable states.<ref>"Collier's Encyclopedia", Volume 22 Sylt to Uruguay, Thermodynamics, by Leo Peters, p. 275</ref> However, mathematically the odds of all the dice results not being a pair sixes is also as hard as the ones of all of them being sixes{{Citation needed|date=January 2019}}, and since statistically the [[data]] tend to balance, one in every 36 pairs of dice will tend to be a pair of sixes, and the cards -when shuffled- will sometimes present a certain temporary sequence order even if in its whole the deck was disordered.
Category:Corresponding Members of the St Petersburg Academy of Sciences
类别: 圣彼得堡科学院通讯员
Category:Members of the Bavarian Maximilian Order for Science and Art
分类: 美国巴伐利亚马克西米兰科学与艺术勋章（Bavarian Maximilian Order for Science and the Arts）协会会员
==Awards and honours==
Category:Suicides by hanging in Italy
类别: 意大利上吊自杀
In 1885 he became a member of the Imperial [[Austrian Academy of Sciences]] and in 1887 he became the President of the [[University of Graz]]. He was elected a member of the [[Royal Swedish Academy of Sciences]] in 1888 and a [[List of Fellows of the Royal Society elected in 1899|Foreign Member of the Royal Society (ForMemRS) in 1899]].<ref name=frs>{{cite web|archiveurl=https://web.archive.org/web/20150316060617/https://royalsociety.org/about-us/fellowship/fellows/|archivedate=2015-03-16|url=https://royalsociety.org/about-us/fellowship/fellows/|publisher=[[Royal Society]]|location=London|title=Fellows of the Royal Society}}</ref> [[List of things named after Ludwig Boltzmann|Numerous things]] are named in his honour.
Category:Foreign Members of the Royal Society
类别: 皇家学会的外国成员
Category:Foreign associates of the National Academy of Sciences
类别: 美国国家科学院的外国合伙人
==See also==
Category:Mathematical physicists
类别: 数学物理学家
Category:Theoretical physicists
类别: 理论物理学家
* [[Energetics]]
Category:Rectors of universities in Austria
类别: 奥地利大学校长
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<small>This page was moved from [[wikipedia:en:Ludwig Boltzmann]]. Its edit history can be viewed at [[玻尔兹曼/edithistory]]</small></noinclude>
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