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{{Use American English|date=January 2019}}

{{Use American English|date=January 2019}}

This device can trap fruit flies, but if it trapped atoms when placed in gas that already uniformly fills the available [[phase space, then both Liouville's theorem and the second law of thermodynamics would be violated.]]

This device can trap fruit flies, but if it trapped atoms when placed in gas that already uniformly fills the available [[phase space, then both Liouville's theorem and the second law of thermodynamics would be violated.]]

这个装置可以捕捉果蝇，但是如果把它放在已经均匀地充满可用相空间的气体中，就会捕捉到原子[[那么 Liouville 定理和热力学第二定律定理都会被违反]。]

这个装置可以捕捉果蝇，但是如果把它放在已经均匀地充满可用相空间的气体中，就会捕捉到原子[[那么 Liouville 定理和热力学第二定律就会被破坏]。]

In [[physics]] and [[thermodynamics]], the '''ergodic hypothesis'''<ref>Originally due to L. Boltzmann. See part 2 of {{cite book|title=Vorlesungen über Gastheorie|year= 1898 |location=Leipzig|publisher=J. A. Barth|url=https://archive.org/details/vorlesungenberg02boltgoog |oclc=01712811}} ('Ergoden' on p.89 in the 1923 reprint.) It was used to prove equipartition of energy in the kinetic theory of gases</ref> says that, over long periods of time, the time spent by a system in some region of the [[phase space]] of [[Microstate (statistical mechanics)|microstates]] with the same energy is proportional to the volume of this region, i.e., that all accessible microstates are [[equiprobable]] over a long period of time.

In [[physics]] and [[thermodynamics]], the '''ergodic hypothesis'''<ref>Originally due to L. Boltzmann. See part 2 of {{cite book|title=Vorlesungen über Gastheorie|year= 1898 |location=Leipzig|publisher=J. A. Barth|url=https://archive.org/details/vorlesungenberg02boltgoog |oclc=01712811}} ('Ergoden' on p.89 in the 1923 reprint.) It was used to prove equipartition of energy in the kinetic theory of gases</ref> says that, over long periods of time, the time spent by a system in some region of the [[phase space]] of [[Microstate (statistical mechanics)|microstates]] with the same energy is proportional to the volume of this region, i.e., that all accessible microstates are [[equiprobable]] over a long period of time.

The ergodic hypothesis is often assumed in the statistical analysis of computational physics. The analyst would assume that the average of a process parameter over time and the average over the statistical ensemble are the same. This assumption—that it is as good to simulate a system over a long time as it is to make many independent realizations of the same system—is not always correct. (See, for example, the Fermi–Pasta–Ulam–Tsingou experiment of 1953.)

The ergodic hypothesis is often assumed in the statistical analysis of computational physics. The analyst would assume that the average of a process parameter over time and the average over the statistical ensemble are the same. This assumption—that it is as good to simulate a system over a long time as it is to make many independent realizations of the same system—is not always correct. (See, for example, the Fermi–Pasta–Ulam–Tsingou experiment of 1953.)

遍历假设通常被认为是计算物理学的统计分析。分析师会假设一个过程参数随时间的平均值和系综的平均值是相同的。这种假设——长时间模拟一个系统和对同一个系统进行许多独立实现一样好——并不总是正确的。(例如，参见1953年的 Fermi-Pasta-Ulam-Tsingou 实验。)

遍历假设通常被认为是计算物理学的统计分析。分析师会假设一个过程参数随时间的平均值和系综的平均值是相同的。这种假设——长时间模拟一个系统和对同一个系统进行许多独立实现一样好——并不总是正确的。(例如，参见1953年的费米-通心粉-乌拉姆-青岛实验。)

Assumption of the ergodic hypothesis allows proof that certain types of perpetual motion machines of the second kind are impossible.

Assumption of the ergodic hypothesis allows proof that certain types of perpetual motion machines of the second kind are impossible.

However, complex disordered systems such as a spin glass show an even more complicated form of ergodicity breaking where the properties of the thermodynamic equilibrium state seen in practice are much more difficult to predict purely by symmetry arguments. Also conventional glasses (e.g. window glasses) violate ergodicity in a complicated manner. In practice this means that on sufficiently short time scales (e.g. those of parts of seconds, minutes, or a few hours) the systems may behave as solids, i.e. with a positive shear modulus, but on extremely long scales, e.g. over millennia or eons, as liquids, or with two or more time scales and plateaux  in between.

However, complex disordered systems such as a spin glass show an even more complicated form of ergodicity breaking where the properties of the thermodynamic equilibrium state seen in practice are much more difficult to predict purely by symmetry arguments. Also conventional glasses (e.g. window glasses) violate ergodicity in a complicated manner. In practice this means that on sufficiently short time scales (e.g. those of parts of seconds, minutes, or a few hours) the systems may behave as solids, i.e. with a positive shear modulus, but on extremely long scales, e.g. over millennia or eons, as liquids, or with two or more time scales and plateaux  in between.

然而，复杂的无序系统，如自旋玻璃表现出一种更加复杂的遍历性破坏形式，在实践中看到的热力学平衡态的性质更加难以纯粹通过对称性论证来预测。还有传统的眼镜(例如:。窗玻璃)以复杂的方式违反遍历性。在实践中，这意味着在足够短的时间范围内(例如:。这些系统可以表现为固体，也就是说，它们可以表现为固体。具有正剪切模量，但是在极长的尺度上，例如:。几千年或者几千年，或者几千年，或者几千年，或者几千年，或者几千年，或者几千年。

然而，复杂的无序系统，如自旋玻璃表现出一种更加复杂的遍历性破坏形式，在实践中看到的热力学平衡态的性质更加难以纯粹通过对称性论证来预测。还有传统的眼镜(例如:。窗玻璃)以复杂的方式违反遍历性。在实践中，这意味着在足够短的时间范围内(例如:。这些系统可以表现为固体，例如:。具有正剪切模量，但是在极长的尺度上，例如:。数千年或数亿年，或是液体，或是两个或两个以上的时间尺度和高原之间。