标题： 热力学熵定义的最新进展 显示英文标题

标题： Recent Progress in the Definition of Thermodynamic Entropy

摘要： 热力学熵定义的主要方法被讨论，特别参考了Carathéodory、Keenan学派、Lieb和Yngvason以及本文作者所发展的方法。 然后介绍了后一种方法的改进。 采用了七个基本公理：三个假设，被认为具有广泛的适用性，以及四个假设，用于确定能量（假设1）和熵（假设2、3、4）定义的有效范围。 目前熵定义的有效范围不限于稳定平衡态。 对于简单系统的集合，它与Lieb和Yngvason提出的绝热可及性关系存在性和唯一性证明的范围一致。 然而，我们的处理不需要形成缩放副本，因此不仅适用于简单系统的集合，也适用于处于电场或磁场中的系统以及小系统和少粒子系统。 显示英文摘要

摘要： The principal methods for the definition of thermodynamic entropy are discussed with special reference to those developed by Carath\'eodory, the Keenan School, Lieb and Yngvason, and the present authors. An improvement of the latter method is then presented. Seven basic axioms are employed: three Postulates, which are considered as having a quite general validity, and four Assumptions, which identify the domains of validity of the definitions of energy (Assumption 1) and entropy (Assumptions 2, 3, 4). The domain of validity of the present definition of entropy is not restricted to stable equilibrium states. For collections of simple systems, it coincides with that of the proof of existence and uniqueness of an entropy function which characterizes the relation of adiabatic accessibility proposed by Lieb and Yngvason. However, our treatment does not require the formation of scaled copies so that it applies not only to collections of simple systems, but also to systems contained in electric or magnetic fields and to small and few-particle systems.