Kinetic Approach to Fractional Exclusion Statistics

TL;DR

This paper introduces a kinetic approach to fractional exclusion statistics, deriving various interpolating distributions between bosons and fermions using a generalized exclusion-inclusion principle, and discusses their thermodynamic properties.

Contribution

It presents a novel kinetic framework that naturally derives fractional exclusion statistics and unifies different models like Haldane and Haldane-Wu within a single approach.

Findings

Derived a variety of statistical distributions interpolating between bosons and fermions.

Unified Haldane and Haldane-Wu exclusion statistics within the kinetic approach.

Discussed thermodynamic properties of systems obeying the generalized exclusion-inclusion principle.

Abstract

We show that the kinetic approach to statistical mechanics permits an elegant and efficient treatment of fractional exclusion statistics. By using the exclusion-inclusion principle recently proposed [Phys. Rev. E49, 5103 (1994)] as a generalization of the Pauli exclusion principle, which is based on a proper definition of the transition probability between two states, we derive a variety of different statistical distributions interpolating between bosons and fermions. The Haldane exclusion principle and the Haldane-Wu fractional exclusion statistics are obtained in a natural way as particular cases. The thermodynamic properties of the statistical systems obeying the generalized exclusion-inclusion principle are discussed.