The Canonical Partition Function for Quons

TL;DR

This paper derives the canonical partition function for quon particles, showing it is q-independent and behaves like an ideal gas, with energy and heat capacity identical to classical particles, despite Gibbs paradox issues.

Contribution

It provides a simple counting derivation of the partition function for quon particles and reveals their thermodynamic equivalence to classical particles.

Findings

Partition function $Z_N$ is q-independent.

System obeys ideal gas law.

Internal energy matches Maxwell-Boltzmann particles.

Abstract

We calculate the canonical partition function $Z_N$ for a system of $N$ free particles obeying so-called `quon' statistics where $q$ is real and satisfies $|q|<1$ by using simple counting arguments. We observe that this system is afflicted by the Gibbs paradox and that $Z_N$ is independent of $q$. We demonstrate that such a system of particles obeys the ideal gas law and that the internal energy $U$ ( and hence the specific heat capacity $C_V$ ) is identical to that of a system of $N$ free particles obeying Maxwell-Boltzmann statistics.