论文标题

一个人被误解:冯·诺伊曼(Von Neumann)没有声称他的熵对应于现象学热力学熵

A Man Misunderstood: Von Neumann did not claim that his entropy corresponds to the phenomenological thermodynamic entropy

论文作者

Sheridan, Erin

论文摘要

最近,注意到了现在著名的1932年思想实验,其中约翰·冯·诺伊曼(John von Neumann)建立了量子机械机械的von neumann熵的形式-tr $ρ\lnρ$($ s_ {vn} $),据说是通过与现象学热力学熵($ s_ {td dd} $的相应来争论的。 Hemmo and Shenker(2006)重建了冯·诺伊曼(Von Neumann)的思想实验,并认为它无法确定这种期望的对应关系。 Prunkl(2019)和Chua(2019)挑战Hemmo和Shenker的结果反过来。本文旨在通过重新审视原始文本(von Neumann(1996,2018))来为当前的辩论提供新的基础。对冯·诺伊曼(Von Neumann)周期性气体转化的彻底训练以及对文本中的另外两个思想实验的重建。这种近距离的外观表明,冯·诺伊曼的目标不是在当前的辩论中假定,而是在$ s_ {vn} $和$ s_ {td} $之间建立链接,而是建立$ s_ {vn} $之间的对应关系。我以这些理由认为,现有的文献误解和歪曲了他的目标。在冯·诺伊曼(von Neumann)的可逆气体转化成功之前,需要经过修订的理解。

Recently, attention has returned to the now-famous 1932 thought experiment in which John von Neumann establishes the form of the quantum mechanical von Neumann entropy -Tr $ ρ\ln ρ$ ($S_{VN}$), supposedly by arguing for its correspondence with the phenomenological thermodynamic entropy ($S_{TD}$). Hemmo and Shenker (2006) reconstruct von Neumann's thought experiment and argue that it fails to establish this desired correspondence. Prunkl (2019) and Chua (2019) challenge Hemmo and Shenker's result in turn. This paper aims to provide a new foundation for the current debate by revisiting the original text (von Neumann (1996, 2018)). A thorough exegesis of von Neumann's cyclical gas transformation is put forth, along with a reconstruction of two additional thought experiments from the text. This closer look reveals that von Neumann's goal is not to establish a link between $S_{VN}$ and $S_{TD}$, as is assumed throughout the current debate, but rather to establish a correspondence between $S_{VN}$ and the Gibbs statistical mechanical entropy $S_{G}$. On these grounds I argue that the existing literature misunderstands and misrepresents his goals. A revised understanding is required before the success of von Neumann's reversible gas transformation can be definitively granted or denied.

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