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第151行：
第151行： − + 第157行：
第157行： − 有许多不同的平衡系综可以考虑，只有一些对应于热力学。为了说明为什么给定系统的整体应该具有这样或那样的形式，还需要一些额外的假设。+ 第171行：
第171行： − 对于一个具有精确已知能量和精确已知组成的孤立系统，可以在任何与该知识一致的微观状态下以等概率找到该系统。+ 第177行：
第177行： − 因此，等量的先验概率假设为下面描述的微正则系综提供了一个动机。有各种各样的论据支持相等的先验概率假设:+ 第184行：
第184行： + + + + + + 第189行：
第195行： − 其他关于统计力学的基本假设也被提出。+ − −
→Fundamental postulate
A sufficient (but not necessary) condition for statistical equilibrium with an isolated system is that the probability distribution is a function only of conserved properties (total energy, total particle numbers, etc.).
A sufficient (but not necessary) condition for statistical equilibrium with an isolated system is that the probability distribution is a function only of conserved properties (total energy, total particle numbers, etc.).
孤立系统统计平衡的一个充分(但不是必要)条件是概率分布只是守恒性质(总能量、总粒子数等)的函数。).
孤立系统统计平衡的一个充分(但不是必要)条件是，其概率分布只是某些守恒量(总能量、总粒子数等)的函数。
There are many different equilibrium ensembles that can be considered, and only some of them correspond to thermodynamics.<ref name="gibbs" /> Additional postulates are necessary to motivate why the ensemble for a given system should have one form or another.
There are many different equilibrium ensembles that can be considered, and only some of them correspond to thermodynamics.<ref name="gibbs" /> Additional postulates are necessary to motivate why the ensemble for a given system should have one form or another.
There are many different equilibrium ensembles that can be considered, and only some of them correspond to thermodynamics. Additional postulates are necessary to motivate why the ensemble for a given system should have one form or another.
There are many different equilibrium ensembles that can be considered, and only some of them correspond to thermodynamics. Additional postulates are necessary to motivate why the ensemble for a given system should have one form or another.
有许多不同的平衡系综可以考虑，只有一些适用于热力学。为了说明为什么给定系统的系综具有这样或那样的形式，还需要一些额外的假设。
For an isolated system with an exactly known energy and exactly known composition, the system can be found with equal probability in any microstate consistent with that knowledge.
For an isolated system with an exactly known energy and exactly known composition, the system can be found with equal probability in any microstate consistent with that knowledge.
对于一个已知精确能量和组成的孤立系统，可以在任何符合条件的微观状态下以等概率找到该系统。
The equal a priori probability postulate therefore provides a motivation for the [[microcanonical ensemble]] described below. There are various arguments in favour of the equal a priori probability postulate:
The equal a priori probability postulate therefore provides a motivation for the [[microcanonical ensemble]] described below. There are various arguments in favour of the equal a priori probability postulate:
The equal a priori probability postulate therefore provides a motivation for the microcanonical ensemble described below. There are various arguments in favour of the equal a priori probability postulate:
The equal a priori probability postulate therefore provides a motivation for the microcanonical ensemble described below. There are various arguments in favour of the equal a priori probability postulate:
因此，先验概率相等假设为下面描述的微正则系综提供了一个动机。有各种各样的论据支持先验概率相等假设:
* [[Ergodic hypothesis]]: An ergodic system is one that evolves over time to explore "all accessible" states: all those with the same energy and composition. In an ergodic system, the microcanonical ensemble is the only possible equilibrium ensemble with fixed energy. This approach has limited applicability, since most systems are not ergodic.
* [[Ergodic hypothesis]]: An ergodic system is one that evolves over time to explore "all accessible" states: all those with the same energy and composition. In an ergodic system, the microcanonical ensemble is the only possible equilibrium ensemble with fixed energy. This approach has limited applicability, since most systems are not ergodic.
* [[Maximum entropy thermodynamics|Maximum information entropy]]: A more elaborate version of the principle of indifference states that the correct ensemble is the ensemble that is compatible with the known information and that has the largest [[Gibbs entropy]] ([[information entropy]]).<ref>{{cite journal | last = Jaynes | first = E.| author-link = Edwin Thompson Jaynes | title = Information Theory and Statistical Mechanics | doi = 10.1103/PhysRev.106.620 | journal = Physical Review | volume = 106 | issue = 4 | pages = 620–630 | year = 1957 | pmid = | pmc = |bibcode = 1957PhRv..106..620J }}</ref>
* [[Maximum entropy thermodynamics|Maximum information entropy]]: A more elaborate version of the principle of indifference states that the correct ensemble is the ensemble that is compatible with the known information and that has the largest [[Gibbs entropy]] ([[information entropy]]).<ref>{{cite journal | last = Jaynes | first = E.| author-link = Edwin Thompson Jaynes | title = Information Theory and Statistical Mechanics | doi = 10.1103/PhysRev.106.620 | journal = Physical Review | volume = 106 | issue = 4 | pages = 620–630 | year = 1957 | pmid = | pmc = |bibcode = 1957PhRv..106..620J }}</ref>
* [[各态历经假设]]:各态历经系统是一种随着时间的演化而探索“所有可到达”状态的系统:所有具有相同能量和组成的状态。在各态历经系统中，微正则系综是唯一可能的具有固定能量的平衡系综。这种方法的适用性有限，因为大多数系统不是各态历经的。
* [[无差别原则]]: 在没有更多信息的情况下，我们只能对每一个相容的情况分配相等的概率。
* [[最大热力学熵|最大信息熵]]: 无差异原则的一个更详细的版本表明，正确的系综是与已知信息兼容且具有最大[[吉布斯熵]] ([[信息熵]])的系综。<ref>{{cite journal | last = Jaynes | first = E.| author-link = Edwin Thompson Jaynes | title = Information Theory and Statistical Mechanics | doi = 10.1103/PhysRev.106.620 | journal = Physical Review | volume = 106 | issue = 4 | pages = 620–630 | year = 1957 | pmid = | pmc = |bibcode = 1957PhRv..106..620J }}</ref>
Other fundamental postulates for statistical mechanics have also been proposed.<ref name="uffink"/>
Other fundamental postulates for statistical mechanics have also been proposed.<ref name="uffink"/>
Other fundamental postulates for statistical mechanics have also been proposed.
Other fundamental postulates for statistical mechanics have also been proposed.
其他关于统计力学的基本假设也有被提出。
===Three thermodynamic ensembles===
===Three thermodynamic ensembles===