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第1,996行：
第1,996行： − + − − 不可逆性 − − − − 第2,008行：
第2,002行： − 热力学过程中的不可逆性是热力学作用不对称特性的结果，而不是物体内部任何不可逆的微观性质<font color = 'blue'>的结果</font>。热力学作用是对参与体施加的宏观外部干预，并非来自其内部属性。由于没有认识到这一点，产生了被称为“悖论”的说法。+ − − − − ===Loschmidt's paradox=== − <font color = 'red'><s>洛斯密特悖论 </s></font><font color = 'blue'>洛施密特悖论</font>+ − − 第2,026行：
第2,014行： − + − <font color = 'red'><s>其目的在于不可能从描述宏观系统微观演化的时间对称动力学中推导出不可逆过程。</s></font><font color = 'blue'> − 它反驳说，从描述宏观系统微观演化的时间对称动力学中，不可能推导出不可逆过程。</font> 第2,036行：
第2,022行： − 薛定谔的认为：“现在很明显，您必须以何种方式重新制定熵定律（亦或者所有其他不可逆陈述）以使它们能够从可逆模型中得出。你不能只谈论一个孤立的系统，而应该至少谈论两个。你可以暂时认为它们与世界其它地方是孤立的，但并不总是相互孤立的。”这两个系统被隔离内壁彼此分开，直到被热力学（由热力学定律设想出来的）作用而拆除。热力学作用是从外部施加的，不受支配系统组成部分的可逆微观动力学定律的制约。这是不可逆转的原因。本文中<font color = 'red'><s>的法律声明</s></font><font color = 'blue'>第二定律的陈述</font>符合薛定谔的的建议。 因果关系在逻辑上先于第二定律，而不是由第二定律推导而来。+ − + − − − 庞加莱始态复现定理 − − 第2,051行：
第2,032行： − 庞加莱始态复现定理<font color = 'red'><s>（又叫递归定理）</s></font>考虑了孤立物理系统的理论微观描述。+ − − --[[用户:嘉树|嘉树]]（[[用户讨论:嘉树|讨论]]）又叫递归定理吗？存疑 − − 经过热力学作用去除隔离内壁之后，便可以认为其是热力学系统的模型。在足够长的时间后，系统将返回到非常接近初始状态的微观定义状态。庞加莱复现时间是指回归前经过的时间长度。它极其漫长，可能比宇宙的寿命还要长，并且<font color = 'red'><s>敏感地依赖于被热力学作用拆除的墙体的几何形状</s></font><font color = 'blue'>对那个被热力学作用拆除的内壁的几何形状敏感</font>。复现定理可能被认为是明显与热力学第二定律相矛盾的。但是，更显而易见的是，它只是通过移除两个系统之间的内壁而形成的隔离系统中热力学平衡的微观模型。<font color = 'red'><s>对于典型的热力学系统而言，重复时间是如此之长（比宇宙的寿命长很多倍），以至于在所有的实际目的中，人们都无法观察到这种重复。</s></font><font color = 'blue'>对所有典型的热力学系统的实际目的，人们无法观察到如此之长的复现时间很长（比宇宙的寿命长很多倍）。</font>尽管如此，还是有人会想像一个机会可以等待庞加莱复现的出现，然后重新插入被热力学作用去除的内壁。 − 然后很明显，不可逆性的出现是由于<font color = 'red'><s>庞加莱递归的完全不可预测性</s></font><font color = 'blue'>庞加莱复现完全不可预测的特性</font>，因为仅仅给出了初始状态<font color = 'red'><s>遵守热力学平衡的条件之一</s></font><font color = 'blue'>是热力学平衡之一</font>，就像宏观热力学的情况一样。 − − '''<font color="#32CD32">然后很明显，不可逆性的出现是由于庞加莱复现完全不可预测的特性，因为仅仅给出了初始状态是热力学平衡之一，就像宏观热力学的情况一样。It is then evident that the appearance of irreversibility is due to the utter unpredictability of the Poincaré recurrence given only that the initial state was one of thermodynamic equilibrium, as is the case in macroscopic thermodynamics.</font>''' （这句话重复上面的，是为了标注疑难句的同时保留审校痕迹。生产修改后可以只保留这句，删掉上面重复部分） + − + − 即使<font color = 'red'><s>可以等待，也没有实际可操作性</s></font><font color = 'blue'>一个人可以等那么长时间，他也没有实际操作的可能性</font>来选择合适的时间重新插入内壁。庞加莱始态复现定理为洛施密特悖论提供了一个解决方案。如果一个孤立的热力学系统能以多倍于平均庞加莱复现时间的长度下<font color = 'red'><s>进行</s></font><font color = 'blue'>被</font>监控，则该系统的热力学行为在时间反转下将变得恒定。 − 第2,073行：
第2,046行： − + − − 麦克斯韦<font color = 'red'><s>的恶魔</s></font><font color = 'blue'>妖</font> − − − − 第2,089行：
第2,056行： − + − − 第2,099行：
第2,064行： − + − − 第2,109行：
第2,072行： − 麦克斯韦的<font color = 'red'><s>“恶魔”不断地</s></font><font color = 'blue'>“妖”重复地</font>改变 A 和 B 之间<font color = 'red'><s>墙体的渗透性</s></font><font color = 'blue'>壁的热透性</font>。因此，它是在微观尺度上执行热力学操作，而不仅仅是观察普通的自发或自然的宏观热力学过程。+
→Irreversibility
==Irreversibility==
==Irreversibility==
==Irreversibility==
== Irreversibility 不可逆性 ==
Irreversibility in [[thermodynamic process]]es is a consequence of the asymmetric character of thermodynamic operations, and not of any internally irreversible microscopic properties of the bodies. Thermodynamic operations are macroscopic external interventions imposed on the participating bodies, not derived from their internal properties. There are reputed "paradoxes" that arise from failure to recognize this.
Irreversibility in [[thermodynamic process]]es is a consequence of the asymmetric character of thermodynamic operations, and not of any internally irreversible microscopic properties of the bodies. Thermodynamic operations are macroscopic external interventions imposed on the participating bodies, not derived from their internal properties. There are reputed "paradoxes" that arise from failure to recognize this.
Irreversibility in thermodynamic processes is a consequence of the asymmetric character of thermodynamic operations, and not of any internally irreversible microscopic properties of the bodies. Thermodynamic operations are macroscopic external interventions imposed on the participating bodies, not derived from their internal properties. There are reputed "paradoxes" that arise from failure to recognize this.
Irreversibility in thermodynamic processes is a consequence of the asymmetric character of thermodynamic operations, and not of any internally irreversible microscopic properties of the bodies. Thermodynamic operations are macroscopic external interventions imposed on the participating bodies, not derived from their internal properties. There are reputed "paradoxes" that arise from failure to recognize this.
热力学过程中的不可逆性是热力学作用不对称特性的结果，而不是物体内部任何不可逆的微观性质的结果。热力学作用是对参与体施加的宏观外部干预，并非来自其内部属性。由于没有认识到这一点，产生了被称为“悖论”的说法。
=== Loschmidt's paradox 洛施密特悖论 ===
{{main article|Loschmidt's paradox}}
{{main article|Loschmidt's paradox}}
[[Loschmidt's paradox]], also known as the reversibility paradox, is the objection that it should not be possible to deduce an irreversible process from the time-symmetric dynamics that describe the microscopic evolution of a macroscopic system.
[[Loschmidt's paradox]], also known as the reversibility paradox, is the objection that it should not be possible to deduce an irreversible process from the time-symmetric dynamics that describe the microscopic evolution of a macroscopic system.
Loschmidt's paradox, also known as the reversibility paradox, is the objection that it should not be possible to deduce an irreversible process from the time-symmetric dynamics that describe the microscopic evolution of a macroscopic system.
Loschmidt's paradox, also known as the reversibility paradox, is the objection that it should not be possible to deduce an irreversible process from the time-symmetric dynamics that describe the microscopic evolution of a macroscopic system.
'''<font color="#ff8000">洛施密特悖论 Loschmidt's paradox</font>'''，也被称为'''<font color="#ff8000">可逆性悖论reversibility paradox</font>'''，
'''<font color="#ff8000">洛施密特悖论 Loschmidt's paradox</font>'''，也被称为'''<font color="#ff8000">可逆性悖论reversibility paradox</font>'''，它反驳说，从描述宏观系统微观演化的时间对称动力学中，不可能推导出不可逆过程。
In the opinion of Schrödinger, "It is now quite obvious in what manner you have to reformulate the law of entropyor for that matter, all other irreversible statementsso that they be capable of being derived from reversible models. You must not speak of one isolated system but at least of two, which you may for the moment consider isolated from the rest of the world, but not always from each other." The two systems are isolated from each other by the wall, until it is removed by the thermodynamic operation, as envisaged by the law. The thermodynamic operation is externally imposed, not subject to the reversible microscopic dynamical laws that govern the constituents of the systems. It is the cause of the irreversibility. The statement of the law in this present article complies with Schrödinger's advice. The cause–effect relation is logically prior to the second law, not derived from it.
In the opinion of Schrödinger, "It is now quite obvious in what manner you have to reformulate the law of entropyor for that matter, all other irreversible statementsso that they be capable of being derived from reversible models. You must not speak of one isolated system but at least of two, which you may for the moment consider isolated from the rest of the world, but not always from each other." The two systems are isolated from each other by the wall, until it is removed by the thermodynamic operation, as envisaged by the law. The thermodynamic operation is externally imposed, not subject to the reversible microscopic dynamical laws that govern the constituents of the systems. It is the cause of the irreversibility. The statement of the law in this present article complies with Schrödinger's advice. The cause–effect relation is logically prior to the second law, not derived from it.
薛定谔的认为：“现在很明显，您必须以何种方式重新制定熵定律（亦或者所有其他不可逆陈述）以使它们能够从可逆模型中得出。你不能只谈论一个孤立的系统，而应该至少谈论两个。你可以暂时认为它们与世界其它地方是孤立的，但并不总是相互孤立的。”这两个系统被隔离内壁彼此分开，直到被热力学（由热力学定律设想出来的）作用而拆除。热力学作用是从外部施加的，不受支配系统组成部分的可逆微观动力学定律的制约。这是不可逆转的原因。本文中第二定律的陈述符合薛定谔的的建议。 因果关系在逻辑上先于第二定律，而不是由第二定律推导而来。
===Poincaré recurrence theorem===
=== Poincaré recurrence theorem 庞加莱始态复现定理 ===
{{Main article|Poincaré recurrence theorem}}
{{Main article|Poincaré recurrence theorem}}
The [[Poincaré recurrence theorem]] considers a theoretical microscopic description of an isolated physical system. This may be considered as a model of a thermodynamic system after a thermodynamic operation has removed an internal wall. The system will, after a sufficiently long time, return to a microscopically defined state very close to the initial one. The Poincaré recurrence time is the length of time elapsed until the return. It is exceedingly long, likely longer than the life of the universe, and depends sensitively on the geometry of the wall that was removed by the thermodynamic operation. The recurrence theorem may be perceived as apparently contradicting the second law of thermodynamics. More obviously, however, it is simply a microscopic model of thermodynamic equilibrium in an isolated system formed by removal of a wall between two systems. For a typical thermodynamical system, the recurrence time is so large (many many times longer than the lifetime of the universe) that, for all practical purposes, one cannot observe the recurrence. One might wish, nevertheless, to imagine that one could wait for the Poincaré recurrence, and then re-insert the wall that was removed by the thermodynamic operation. It is then evident that the appearance of irreversibility is due to the utter unpredictability of the Poincaré recurrence given only that the initial state was one of thermodynamic equilibrium, as is the case in macroscopic thermodynamics. Even if one could wait for it, one has no practical possibility of picking the right instant at which to re-insert the wall. The Poincaré recurrence theorem provides a solution to Loschmidt's paradox. If an isolated thermodynamic system could be monitored over increasingly many multiples of the average Poincaré recurrence time, the thermodynamic behavior of the system would become invariant under time reversal.
The [[Poincaré recurrence theorem]] considers a theoretical microscopic description of an isolated physical system. This may be considered as a model of a thermodynamic system after a thermodynamic operation has removed an internal wall. The system will, after a sufficiently long time, return to a microscopically defined state very close to the initial one. The Poincaré recurrence time is the length of time elapsed until the return. It is exceedingly long, likely longer than the life of the universe, and depends sensitively on the geometry of the wall that was removed by the thermodynamic operation. The recurrence theorem may be perceived as apparently contradicting the second law of thermodynamics. More obviously, however, it is simply a microscopic model of thermodynamic equilibrium in an isolated system formed by removal of a wall between two systems. For a typical thermodynamical system, the recurrence time is so large (many many times longer than the lifetime of the universe) that, for all practical purposes, one cannot observe the recurrence. One might wish, nevertheless, to imagine that one could wait for the Poincaré recurrence, and then re-insert the wall that was removed by the thermodynamic operation. It is then evident that the appearance of irreversibility is due to the utter unpredictability of the Poincaré recurrence given only that the initial state was one of thermodynamic equilibrium, as is the case in macroscopic thermodynamics. Even if one could wait for it, one has no practical possibility of picking the right instant at which to re-insert the wall. The Poincaré recurrence theorem provides a solution to Loschmidt's paradox. If an isolated thermodynamic system could be monitored over increasingly many multiples of the average Poincaré recurrence time, the thermodynamic behavior of the system would become invariant under time reversal.
The Poincaré recurrence theorem considers a theoretical microscopic description of an isolated physical system. This may be considered as a model of a thermodynamic system after a thermodynamic operation has removed an internal wall. The system will, after a sufficiently long time, return to a microscopically defined state very close to the initial one. The Poincaré recurrence time is the length of time elapsed until the return. It is exceedingly long, likely longer than the life of the universe, and depends sensitively on the geometry of the wall that was removed by the thermodynamic operation. The recurrence theorem may be perceived as apparently contradicting the second law of thermodynamics. More obviously, however, it is simply a microscopic model of thermodynamic equilibrium in an isolated system formed by removal of a wall between two systems. For a typical thermodynamical system, the recurrence time is so large (many many times longer than the lifetime of the universe) that, for all practical purposes, one cannot observe the recurrence. One might wish, nevertheless, to imagine that one could wait for the Poincaré recurrence, and then re-insert the wall that was removed by the thermodynamic operation. It is then evident that the appearance of irreversibility is due to the utter unpredictability of the Poincaré recurrence given only that the initial state was one of thermodynamic equilibrium, as is the case in macroscopic thermodynamics.Even if one could wait for it, one has no practical possibility of picking the right instant at which to re-insert the wall. The Poincaré recurrence theorem provides a solution to Loschmidt's paradox. If an isolated thermodynamic system could be monitored over increasingly many multiples of the average Poincaré recurrence time, the thermodynamic behavior of the system would become invariant under time reversal.
The Poincaré recurrence theorem considers a theoretical microscopic description of an isolated physical system. This may be considered as a model of a thermodynamic system after a thermodynamic operation has removed an internal wall. The system will, after a sufficiently long time, return to a microscopically defined state very close to the initial one. The Poincaré recurrence time is the length of time elapsed until the return. It is exceedingly long, likely longer than the life of the universe, and depends sensitively on the geometry of the wall that was removed by the thermodynamic operation. The recurrence theorem may be perceived as apparently contradicting the second law of thermodynamics. More obviously, however, it is simply a microscopic model of thermodynamic equilibrium in an isolated system formed by removal of a wall between two systems. For a typical thermodynamical system, the recurrence time is so large (many many times longer than the lifetime of the universe) that, for all practical purposes, one cannot observe the recurrence. One might wish, nevertheless, to imagine that one could wait for the Poincaré recurrence, and then re-insert the wall that was removed by the thermodynamic operation. It is then evident that the appearance of irreversibility is due to the utter unpredictability of the Poincaré recurrence given only that the initial state was one of thermodynamic equilibrium, as is the case in macroscopic thermodynamics.Even if one could wait for it, one has no practical possibility of picking the right instant at which to re-insert the wall. The Poincaré recurrence theorem provides a solution to Loschmidt's paradox. If an isolated thermodynamic system could be monitored over increasingly many multiples of the average Poincaré recurrence time, the thermodynamic behavior of the system would become invariant under time reversal.
庞加莱始态复现定理考虑了孤立物理系统的理论微观描述。
--[[用户:嘉树|嘉树]]（[[用户讨论:嘉树|讨论]]）又叫递归定理吗？存疑
经过热力学作用去除隔离内壁之后，便可以认为其是热力学系统的模型。在足够长的时间后，系统将返回到非常接近初始状态的微观定义状态。庞加莱复现时间是指回归前经过的时间长度。它极其漫长，可能比宇宙的寿命还要长，并且对那个被热力学作用拆除的内壁的几何形状敏感。复现定理可能被认为是明显与热力学第二定律相矛盾的。但是，更显而易见的是，它只是通过移除两个系统之间的内壁而形成的隔离系统中热力学平衡的微观模型。对所有典型的热力学系统的实际目的，人们无法观察到如此之长的复现时间很长（比宇宙的寿命长很多倍）。尽管如此，还是有人会想像一个机会可以等待庞加莱复现的出现，然后重新插入被热力学作用去除的内壁。然后很明显，不可逆性的出现是由于庞加莱复现完全不可预测的特性，因为仅仅给出了初始状态是热力学平衡之一，就像宏观热力学的情况一样。即使一个人可以等那么长时间，他也没有实际操作的可能性来选择合适的时间重新插入内壁。庞加莱始态复现定理为洛施密特悖论提供了一个解决方案。如果一个孤立的热力学系统能以多倍于平均庞加莱复现时间的长度下被监控，则该系统的热力学行为在时间反转下将变得恒定。
詹姆斯·克拉克·麦克斯韦
詹姆斯·克拉克·麦克斯韦
===Maxwell's demon===
=== Maxwell's demon 麦克斯韦妖 ===
{{unreferenced|section|date=August 2018}}
{{unreferenced|section|date=August 2018}}
{{main article|Maxwell's demon}}
{{main article|Maxwell's demon}}
[[James Clerk Maxwell]] imagined one container divided into two parts, ''A'' and ''B''. Both parts are filled with the same [[gas]] at equal temperatures and placed next to each other, separated by a wall. Observing the [[molecule]]s on both sides, an imaginary [[demon]] guards a microscopic trapdoor in the wall. When a faster-than-average molecule from ''A'' flies towards the trapdoor, the demon opens it, and the molecule will fly from ''A'' to ''B''. The average [[speed]] of the molecules in ''B'' will have increased while in ''A'' they will have slowed down on average. Since average molecular speed corresponds to temperature, the temperature decreases in ''A'' and increases in ''B'', contrary to the second law of thermodynamics.
[[James Clerk Maxwell]] imagined one container divided into two parts, ''A'' and ''B''. Both parts are filled with the same [[gas]] at equal temperatures and placed next to each other, separated by a wall. Observing the [[molecule]]s on both sides, an imaginary [[demon]] guards a microscopic trapdoor in the wall. When a faster-than-average molecule from ''A'' flies towards the trapdoor, the demon opens it, and the molecule will fly from ''A'' to ''B''. The average [[speed]] of the molecules in ''B'' will have increased while in ''A'' they will have slowed down on average. Since average molecular speed corresponds to temperature, the temperature decreases in ''A'' and increases in ''B'', contrary to the second law of thermodynamics.
James Clerk Maxwell imagined one container divided into two parts, A and B. Both parts are filled with the same gas at equal temperatures and placed next to each other, separated by a wall. Observing the molecules on both sides, an imaginary demon guards a microscopic trapdoor in the wall. When a faster-than-average molecule from A flies towards the trapdoor, the demon opens it, and the molecule will fly from A to B. The average speed of the molecules in B will have increased while in A they will have slowed down on average. Since average molecular speed corresponds to temperature, the temperature decreases in A and increases in B, contrary to the second law of thermodynamics.
James Clerk Maxwell imagined one container divided into two parts, A and B. Both parts are filled with the same gas at equal temperatures and placed next to each other, separated by a wall. Observing the molecules on both sides, an imaginary demon guards a microscopic trapdoor in the wall. When a faster-than-average molecule from A flies towards the trapdoor, the demon opens it, and the molecule will fly from A to B. The average speed of the molecules in B will have increased while in A they will have slowed down on average. Since average molecular speed corresponds to temperature, the temperature decreases in A and increases in B, contrary to the second law of thermodynamics.
'''麦克斯韦 James Clerk Maxwell'''设想一个容器分为A和B两部分。两部分均在相同温度下充满相同的气体，并彼此相邻由内壁隔开。<font color = 'red'><s>观察到两侧的分子，一个虚构的恶魔在墙上守着一个微观活板门</s></font><font color = 'blue'>一个虚构的妖精看守着一个内壁上的微型陷门，并观察者内壁两边的分子</font>。当来自A的速度快于平均水平的分子飞向<font color = 'red'><s>活板</s></font>门时，<font color = 'red'><s>恶魔将其打开</s></font><font color = 'blue'>妖精将门打开</font>，该分子将从A飞向B。B中分子的平均速度将增加，而A中分子的平均速度将<font color = 'red'><s>平均</s></font>降低。由于平均分子速度与温度相对应，因此与热力学第二定律相反，温度在A中降低，在B中升高。
'''麦克斯韦 James Clerk Maxwell'''设想一个容器分为A和B两部分。两部分均在相同温度下充满相同的气体，并彼此相邻由内壁隔开。一个虚构的妖精看守着一个内壁上的微型陷门，并观察者内壁两边的分子。当来自A的速度快于平均水平的分子飞向门时，妖精将门打开，该分子将从A飞向B。B中分子的平均速度将增加，而A中分子的平均速度将降低。由于平均分子速度与温度相对应，因此与热力学第二定律相反，温度在A中降低，在B中升高。
One response to this question was suggested in 1929 by Leó Szilárd and later by Léon Brillouin. Szilárd pointed out that a real-life Maxwell's demon would need to have some means of measuring molecular speed, and that the act of acquiring information would require an expenditure of energy.
One response to this question was suggested in 1929 by Leó Szilárd and later by Léon Brillouin. Szilárd pointed out that a real-life Maxwell's demon would need to have some means of measuring molecular speed, and that the act of acquiring information would require an expenditure of energy.
1929年，Leó Szilárd和后来的 Léon Brillouin 对这个问题提出了一个答案。Szilárd指出，现实生活中的麦克斯韦<font color = 'red'><s>恶魔</s></font><font color = 'blue'>妖</font>需要一些测量分子速度的方法，而获取信息<font color = 'blue'>的过程</font>需要消耗<font color = 'red'><s>大量</s></font>能量。
1929年，Leó Szilárd和后来的 Léon Brillouin 对这个问题提出了一个答案。Szilárd指出，现实生活中的麦克斯韦妖需要一些测量分子速度的方法，而获取信息的过程需要消耗能量。
Maxwell's 'demon' repeatedly alters the permeability of the wall between A and B. It is therefore performing thermodynamic operations on a microscopic scale, not just observing ordinary spontaneous or natural macroscopic thermodynamic processes.
Maxwell's 'demon' repeatedly alters the permeability of the wall between A and B. It is therefore performing thermodynamic operations on a microscopic scale, not just observing ordinary spontaneous or natural macroscopic thermodynamic processes.
麦克斯韦的“妖”重复地改变 A 和 B 之间壁的热透性。因此，它是在微观尺度上执行热力学操作，而不仅仅是观察普通的自发或自然的宏观热力学过程。
==Quotations==
==Quotations==