Ruppeiner Geometry of Anyon Gas

TL;DR

This paper derives the thermodynamic curvature of a two-dimensional ideal anyon gas, revealing how fractional statistics influence stability and interactions, with curvature sign indicating attractive or repulsive behavior.

Contribution

It introduces a novel analysis of thermodynamic curvature in anyon gases, linking fractional statistics to stability and interaction characteristics.

Findings

Attractive interactions yield positive curvature

Repulsive interactions yield negative curvature

Zero curvature indicates a special non-interacting case

Abstract

We derive the thermodynamic curvature of a two dimensional ideal anyon gas of particles obeying fractional statistics. The statistical interactions of anyon gas can be attractive or repulsive. For attractive statistical interactions, thermodynamic curvature is positive and for repulsive statistical interactions, it is negative, which indicates a more stable anyon gas. There is a special case between the two where the thermodynamic curvature is zero. Small deviations from the classical limit will also be explored.