论文标题
吉布斯难题的最佳答案大约$ n！$！
The best answer to the puzzle of Gibbs about $N!$!: A note on the paper by Sasa, Hiura, Nakagawa, and Yoshida
论文作者
论文摘要
在最近的一篇论文[1]中，SASA，Hiura，Nakagawa和Yoshida表明，将最低工作原理的自然扩展到小型系统唯一地决定了连接统计机械功能（例如分区功能）和热力学功能（例如免费能量）的关系的因子$ n！$。我们认为，这为我们提供了可以追溯到吉布斯的经典统计力学中“难题”的最清晰答案。 在这里，我们尝试通过在不同的情况下使用Horowitz和Parrondo [2]讨论的过程来解释SASA，Hiura，Nakagawa和Yoshida [1]的理论。尽管本注释的内容对于任何熟悉[1]和[2]的人都应该很明显，但我们认为，从略有不同的角度出现相同理论的评论是有用的。 目前的说明是以独立的方式编写的。我们仅假设经典统计力学和热力学的基本知识。但是，我们邀请读者参考原始论文[2]，以进行背景，参考和相关讨论以及原始思想。
In a recent paper [1], Sasa, Hiura, Nakagawa, and Yoshida showed that a natural extension of the minimum work principle to small systems uniquely determines the factor $N!$ that arrises in relations connecting statistical mechanical functions (such as the partition function) and thermodynamic functions (such as the free energy). We believe that this provides us with the clearest answer to the "puzzle" in classical statistical mechanics that goes back to Gibbs. Here we attempt at explaining the theory of Sasa, Hiura, Nakagawa, and Yoshida [1] by using a process discussed by Horowitz and Parrondo [2] in a different context. Although the content of the present note should be obvious to anybody familiar with both [1] and [2], we believe it is useful to have a commentary that presents the same theory from a slightly different perspective. The present note is written in a self-contained manner. We only assume basic knowledge of classical statistical mechanics and thermodynamics. We nevertheless invite the reader to refer to the original paper [2] for background, references, and related discussions, as well as the original thoughts.
