Thermodynamic Geometry of Fractional Statistics

TL;DR

This paper explores the thermodynamic geometry of various fractional statistics in different dimensions, revealing stability properties, interaction characteristics, and a condensation phenomenon akin to Bose-Einstein condensation.

Contribution

It extends the analysis of fractional exclusion statistics to higher dimensions and compares different fractional statistics, providing new insights into their thermodynamic stability and phase transitions.

Findings

Two-dimensional Haldane gas is more stable than higher dimensions.

Complete characterization of attractive and repulsive interactions in fractional statistics.

Identification of a condensation phenomenon similar to Bose-Einstein condensation.

Abstract

We extend our earlier study about the fractional exclusion statistics to higher dimensions in full physical range and in the non-relativistic and ultra-relativistic limits. Also, two other fractional statistics, namely Gentile and Polychronakos fractional statistics, will be considered and similarities and differences between these statistics will be explored. Thermodynamic geometry suggests that a two dimensional Haldane fractional exclusion gas is more stable than higher dimensional gases. Also, a complete picture of attractive and repulsive statistical interaction of fractional statistics is given. For a special kind of fractional statistics, by considering the singular points of thermodynamic curvature, we find a condensation for a non-pure bosonic system which is similar to the Bose-Einstein condensation and the phase transition temperature will be worked out.