In the article “Quirks of Stirling’s Approximation” published in this Journal, Macrae and Allgeier appear to conclude erroneously that the exactness of Boltzmann’s entropy formula for the microcanonical ensemble depends on the ensemble size. This conclusion seems to originate from the adoption of an unnecessary approximation appearing in Physical Chemistry: A Molecular Approach by McQuarrie and Simon. This letter provides a simple derivation of the entropy of the microcanonical ensemble that leads to the exact Boltzmann expression. In addition, this letter aims to stress that the entropy of a system or an ensemble is truly maximized only when no constraint is imposed on the system or ensemble. In particular, when the entropy of a microcanonical ensemble is to be maximized, it is inappropriate to assume the most probable distribution of the systems in the ensemble because this assumption is an unnecessary and unjustified constraint.

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评论“斯特林近似的怪癖”

在该杂志上发表的文章“斯特林近似测验”中，Macrae和Allgeier似乎错误地得出结论：玻尔兹曼熵公式对微规范集合的精确度取决于集合的大小。该结论似乎源于对《物理化学：分子方法》中出现的不必要近似的采用。麦夸里（McQuarrie）和西蒙（Simon）。这封信提供了微正则合奏的熵的简单推导，可导致确切的玻耳兹曼表达。另外，这封信旨在强调，只有在不对系统或集合施加任何约束的情况下，系统或集合的熵才真正最大化。特别地，当要使微经典合奏的熵最大化时，假设该合奏中系统的最可能分布是不合适的，因为该假设是不必要且不合理的约束。