Thermodynamics of the System of Distinguishable Particles

TL;DR

This paper examines the thermodynamics of distinguishable particles, addressing the non-extensivity of entropy and proposing a corrected Boltzmann counting to resolve the Gibbs paradox within classical statistical mechanics.

Contribution

It introduces a straightforward correction to Boltzmann counting for distinguishable particles, clarifying the thermodynamics and resolving the Gibbs paradox.

Findings

Entropy of distinguishable particles is not extensive.

Corrected Boltzmann counting justifies the entropy correction.

Resolution of the Gibbs paradox in classical mechanics.

Abstract

The issue of the thermodynamics of a system of distinguishable particles is discussed in this paper. In constructing the statistical mechanics of distinguishable particles from the definition of Boltzmann entropy, it is found that the entropy is not extensive. The inextensivity leads to the so-called Gibbs paradox in which the mixing entropy of two identical classical gases increases. Lots of literature from different points of view were created to resolve the paradox. In this paper, starting from the Boltzmann entropy, we present the thermodynamics of the system of distinguishable particles. A straightforward way to get the corrected Boltzmann counting is shown. The corrected Boltzmann counting factor can be justified in classical statistical mechanics.