The Gibbs Paradox

TL;DR

This paper addresses the Gibbs Paradox by proposing a unified solution based on particle indistinguishability, applicable to both classical and quantum thermodynamics, clarifying the conceptual confusion surrounding particle distinguishability.

Contribution

It offers a novel interpretation of particle indistinguishability that resolves the Gibbs Paradox in both classical and quantum contexts by focusing on quotient spaces under permutations.

Findings

Clarifies the role of indistinguishability in thermodynamics

Proposes a unified approach applicable to classical and quantum cases

Eliminates the conceptual muddle of classical distinguishability

Abstract

The Gibbs Paradox is essentially a set of open questions as to how sameness of gases or fluids (or masses, more generally) are to be treated in thermodynamics and statistical mechanics. They have a variety of answers, some restricted to quantum theory (there is no classical solution), some to classical theory (the quantum case is different). The solution offered here applies to both in equal measure, and is based on the concept of particle indistinguishability (in the classical case, Gibbs' notion of 'generic phase'). Correctly understood, it is the elimination of sequence position as a labelling device, where sequences enter at the level of the tensor (or Cartesian) product of one-particle state spaces. In both cases it amounts to passing to the quotient space under permutations. 'Distinguishability', in the sense in which it is usually used in classical statistical mechanics, is a mathematically convenient, but physically muddled, fiction.