Gibbs vs Boltzmann Entropies

1965/05/01 by E. T. Jaynes · 18 citations
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Statistical Mechanics and Entropy

paper · doi:10.1119/1.1971557

openalex publication_date 1965/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

Abstract

The status of the Gibbs and Boltzmann expressions for entropy has been a matter of some confusion in the literature. We show that: (1) the Gibbs H function yields the correct entropy as defined in phenomenological thermodynamics; (2) the Boltzmann H yields an “entropy” that is in error by a nonnegligible amount whenever interparticle forces affect thermodynamic properties; (3) Boltzmann's other interpretation of entropy, S = k log W, is consistent with the Gibbs H, and derivable from it; (4) the Boltzmann H theorem does not constitute a demonstration of the second law for dilute gases; (5) the dynamical invariance of the Gibbs H gives a simple proof of the second law for arbitrary interparticle forces; (6) the second law is a special case of a general requirement for any macroscopic process to be experimentally reproducible. Finally, the “anthropomorphic” nature of entropy, on both the statistical and phenomenological levels, is stressed.

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