Thermodynamics of non-abelian exclusion statistics

TL;DR

This paper explores the thermodynamic properties of gases obeying non-abelian exclusion statistics, revealing a linear relationship with abelian-part statistics and extending known factorizability properties.

Contribution

It demonstrates that the thermodynamic potential for non-abelian statistics is linear in the abelian-part statistics matrix, extending previous abelian results to non-abelian cases.

Findings

Thermodynamic potential is linear in the abelian-part statistics matrix.

Factorizability property extends from abelian to non-abelian statistics.

Complete expansion of the thermodynamic potential is provided.

Abstract

The thermodynamic potential of ideal gases described by the simplest non-abelian statistics is investigated. I show that the potential is the linear function of the element of the abelian-part statistics matrix. Thus, the factorizable property in the Haldane (abelian) fractional exclusion shown by the author [W. H. Huang, Phys. Rev. Lett. 81, 2392 (1998)] is now extended to the non-abelian case. The complete expansion of the thermodynamic potential is also given.