热平衡和“热力学正态性”的方法--基于Goldstein、Lebowitz、Mastrodonato、Tumulka和Zanghi在2009年以及von Neumann在1929年的工作的观察
The approach to thermal equilibrium and "thermodynamic normality" --- An observation based on the works by Goldstein, Lebowitz, Mastrodonato, Tumulka, and Zanghi in 2009, and by von Neumann in 1929
摘要：
我们处理的问题的办法，热平衡，只有诉诸量子动力学的一个孤立的宏观系统。受2009年和1929年两项重要工作的启发，我们注意到，我们称之为“热力学正态性”的宏观观测条件保证了接近平衡（在这个意义上，在时间$t$上对观测的测量几乎肯定会产生一个结果，接近于足够长和典型的$t$的相应微正则平均值）。关键的一点是，我们对系统的初始状态不做任何假设，只是假设它的能量分布接近于某个宏观值。我们还提出了三个（而不是人工）模型，在其中可以建立热力学常态，从而提供了具体的例子中，平衡的方法是严格合理的。注意，这种对任何初始状态都成立的结果在经典系统中是不可能的。因此，我们正在处理一种量子系统所特有的机制。本说明是以自成一体的方式编写的（希望可读性强）。它只需要量子物理和平衡统计力学的基础知识。
英文摘要：
We treat the problem of the approach to thermal equilibrium by only resorting to quantum dynamics of an isolated macroscopic system. Inspired by the two important works in 2009 and in 1929, we have noted that a condition we call "thermodynamic normality" for a macroscopic observable guarantees the approach to equilibrium (in the sense that a measurement of the observable at time $t$ almost certainly yields a result close to the corresponding microcanonical average for a sufficiently long and typical $t$). A crucial point is that we make no assumptions on the initial state of the system, except that its energy is distributed close to a certain macroscopic value. We also present three (rather artificial) models in which the thermodynamic normality can be established, thus providing concrete examples in which the approach to equilibrium is rigorously justified. Note that this kind of results which hold for ANY initial state are never possible in classical systems. We are thus dealing with a mechanism which is peculiar to quantum systems. The present note is written in a self-contained (and hopefully readable) manner. It only requires basic knowledge in quantum physics and equilibrium statistical mechanics.
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