The Gibbs paradox revisited from the fluctuation theorem with absolute irreversibility

Is the Boltzmann equation reversible? A large deviation perspective on the irreversibility paradox

We consider the kinetic theory of dilute gases in the Boltzmann--Grad limit. We propose a new perspective based on a large deviation estimate for the probability of the empirical distribution dynamics. Assuming Boltzmann molecular chaos hypothesis (Stosszahlansatz), we derive a large deviation rate function, or action, that describes the stochastic process for the empirical distribution. The quasipotential for this action is the negative of the entropy, as should be expected. While the Boltzmann equation appears as the most probable evolution, corresponding to a law of large numbers, the actio…

摆的不可逆性：从希斯的绝热参数重新审视

Irreversibility of the pendulum revisited from Husimi's adiabaticity parameter

本文重新审视了具有时间依赖角频率的摆的不可逆性，扩展了希斯的论点，探讨了绝热参数对热力学第二定律的影响。

Absolute Irreversibility in Information Thermodynamics

Nonequilibrium equalities have attracted considerable interest in the context of statistical mechanics and information thermodynamics. What is remarkable about nonequilibrium equalities is that they apply to rather general nonequilibrium situations beyond the linear response regime. However, nonequilibrium equalities are known to be inapplicable to some important situations. In this thesis, we introduce a concept of absolute irreversibility as a new class of irreversibility that encompasses the entire range of those irreversible situations to which the conventional nonequilibrium equalities ar…

孤立系的信息守恒、熵增加和统计不可逆性

Information Conservation, Entropy Increase and the Statistical Irreversibility for an Isolated System

我们考虑了统计不可逆性及其与可逆动力学的相容性。详细分析了观测所起的作用。它使我们以前对热力学第二定律的证明更加清楚。在此基础上，强调了热力学第二定律的重要性和广泛适用性。提出了用信息守恒原理代替这一定律的新物理形式。另外，我们还解决了薛定谔猫悖论，证明了宇宙不会自发地走向所谓的热寂。

哈密顿热库、粗粒化与不可逆性：来自经典力学的微观动力学熵

Hamiltonian Heat Baths, Coarse-Graining and Irreversibility: A Microscopic Dynamical Entropy from Classical Mechanics

针对可逆哈密顿动力学与热力学第二定律的矛盾，本文通过忽略热库条件密度的细节，提出可定量对应热力学熵且能在速度反转后正确倒带的微观动力学熵。

吉布斯佯谬的量子热力学解释

Explanation of the Gibbs paradox within the framework of quantum thermodynamics

吉布斯悖论的问题是，当考虑两种气体在经典热力学中的混合时，混合熵似乎是两种气体之间差异的不连续函数：对于任何小的差异，它都是有限的，但对于相同的气体，它为零。在文献中提供的解决方案，在量子混合熵的帮助下，后来被证明是不令人满意的，正是在它试图解决悖论。宏观热力学，无论是经典的还是量子的，都不适合解释这个悖论，因为它没有明确地处理气体之间的差异。正确的方法是使用量子热力学，它处理耦合到大浴和宏观功源的有限量子系统。在量子热力学中，熵通常失去其主导地位，悖论的目标自然转移到混合前后最大可用功的减少（混合各向同性）。与熵相反，这是一个明确的量。对于几乎完全相同的气体，混合各向同性连续地趋于零，从而解决了这个悖论。在这种方法中，“气体之间的差异”的概念得到了与控制所涉及的量子态的可能性有关的明确的操作意义。在熵表述中，阻碍解决悖论的困难在这里并不存在。混合各态历经有几个违反直觉的特征。当允许不太精确的操作时，它可以增加。在量子情形下（与经典情形相反），当降低气体之间的混合程度或降低它们的可混合性时，混合各向同性也会增加。这些观点与物理不可逆性与缺乏信息的直接联系背道而驰。