Plea for the use of the exact Stirling formula in statistical mechanics

Abstract

In statistical mechanics, the generally called Stirling approximation is actually an approximation of Stirling's formula. In this article, it is shown that the term that is dropped is in fact the one that takes fluctuations into account. The use of the Stirling's exact formula forces us to reintroduce them into the already proposed solutions of well-know puzzles such as the extensivity paradox or the Gibbs' paradox of joining two volumes of identical gas. This amendment clearly results in a gain in consistency and rigor of these solutions.

References in corpus (4)

• Why Colloidal Systems can be described by Statistical Mechanics: Some not very original comments on the Gibbs paradox
• The Gibbs Paradox and the Distinguishability of Identical Particles
• The Gibbs Paradox
• A short derivation of Boltzmann distribution and Gibbs entropy formula from the fundamental postulate

Cited by in corpus (2)

• The fundamental difference between logical and thermodynamic irreversibilities, or, Why Landauer's result cannot be a physical principle
• Disentangling Brillouin's negentropy law of information and Landauer's law on data erasure