Comment on "Statistical Distribution for Generalized Ideal Gas of Fractional-Statistics Particles", Phys. Rev. Lett. {\bf 73}, 922 (1994)

TL;DR

This paper critiques a previous influential work on fractional exclusion statistics, highlighting overlooked properties that lead to inconsistencies in the thermodynamics of such systems and providing a corrected interpretation.

Contribution

It identifies and corrects a long-standing error in the thermodynamic description of fractional exclusion statistics, clarifying the proper statistical mechanics framework.

Findings

Highlights overlooked properties of exclusion statistics parameters

Shows the inconsistency in previous thermodynamic formulations

Provides a corrected interpretation of fractional exclusion statistics

Abstract

In Phys. Rev. Lett. 67, 937 (1991) [1], Haldane introduced the fruitful concept of fractional exclusion statistics (FES). One of the most influential papers in which the thermodynamics of FES systems was deduced is Y.-S. Wu, Phys. Rev. Lett. 73, 922 (1994). Unfortunately, some important, but eventually subtle, properties of the exclusion statistics parameters were overlooked in the original paper [1] and in all the papers after that, including [2]. This omission makes the thermodynamics of FES systems inconsistent when mutual exclusion statistics is manifesting in the system. By this Comment I want to point-out this error--an error that persisted for such a long time--and to give the correct statistical mechanics interpretation of FES.