In 1932, John von Neumann argued for the equivalence of the thermodynamic entropy and −Trρlnρ, since known as the von Neumann entropy. Meir Hemmo and Orly R. Shenker recently challenged this argument by pointing out an alleged discrepancy between the two entropies in the single-particle case, concluding that they must be distinct. In this article, their argument is shown to be problematic as it (a) allows for a violation of the second law of thermodynamics and (b) is based on an incorrect calculation of the von Neumann entropy.

中文翻译：

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关于冯诺依曼和热力学熵的等价性

1932 年，约翰·冯·诺依曼 (John von Neumann) 论证了热力学熵和 −Trρlnρ 的等价性，因此称为冯·诺依曼熵。Meir Hemmo 和 Orly R. Shenker 最近通过指出单粒子情况下两个熵之间所谓的差异来挑战这一论点，并得出结论认为它们必须是不同的。在这篇文章中，他们的论点被证明是有问题的，因为它 (a) 允许违反热力学第二定律，并且 (b) 基于对冯诺依曼熵的错误计算。