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<p>The aim of this paper is to comprehensively apply dimensional analysis to classical statistical mechanics. Dimensional analysis reduces the number of independent variables but cannot completely determine the form of the function, so Euler’s theorem for homogeneous functions and the equivalence of Boltzmann entropy and Gibbs entropy are adopted as basic principles. This approach can easily calculate the partition function for the empirical model of the state equation and reduce the arbitrariness in the partition function of classical statistical mechanics.</p>

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Dimensional analysis in classical statistical mechanics. 1. Fundamentals and application to pure substance

  • 期刊论文

  • 发表日期：

    2026年2月4日

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  • Kwang Soo Cho,
  • Jehyeok Choi

摘要

The aim of this paper is to comprehensively apply dimensional analysis to classical statistical mechanics. Dimensional analysis reduces the number of independent variables but cannot completely determine the form of the function, so Euler’s theorem for homogeneous functions and the equivalence of Boltzmann entropy and Gibbs entropy are adopted as basic principles. This approach can easily calculate the partition function for the empirical model of the state equation and reduce the arbitrariness in the partition function of classical statistical mechanics.