The thermodynamic limit for fractional exclusion statistics

TL;DR

This paper identifies inconsistencies in Haldane's fractional exclusion statistics when mutual exclusion is considered and proposes new, dimension-dependent parameters to ensure consistent thermodynamic descriptions.

Contribution

It introduces a revised definition of mutual exclusion statistics parameters proportional to Hilbert space dimension, resolving previous inconsistencies in fractional exclusion statistics.

Findings

Inconsistencies in particle distribution calculations are addressed.

New mutual exclusion parameters lead to consistent thermodynamics.

Fractional exclusion statistics in interacting systems are physically consistent with the new parameters.

Abstract

I discuss Haldane's concept of generalised exclusion statistics (Phys. Rev. Lett. {\bf 67}, 937, 1991) and I show that it leads to inconsistencies in the calculation of the particle distribution that maximizes the partition function. These inconsistencies appear when mutual exclusion statistics is manifested between different subspecies of particles in the system. In order to eliminate these inconsistencies, I introduce new mutual exclusion statistics parameters, which are proportional to the dimension of the Hilbert sub-space on which they act. These new definitions lead to properly defined particle distributions and thermodynamic properties. In another paper (arXiv:0710.0728) I show that fractional exclusion statistics manifested in general systems with interaction have these, physically consistent, statistics parameters.