Thermodynamics for Fractal Statistics

TL;DR

This paper explores the thermodynamic properties of an anyon gas using fractal statistics, providing exact equations of state in specific temperature regimes, and introduces a novel approach to describe anyonic excitations via fractal parameters.

Contribution

It introduces a new fractal statistical framework for anyon gases and derives exact thermodynamic equations in certain temperature limits.

Findings

Exact equations of state in high- and low-temperature limits.

Description of anyonic excitations using fractal parameters.

Application to gases with constant density of states.

Abstract

We consider for an anyon gas its termodynamics properties taking into account the fractal statistics obtained by us recently. This approach describes the anyonic excitations in terms of equivalence classes labeled by fractal parameter or Hausdorff dimension $h$. An exact equation of state is obtained in the high-temperature and low-temperature limits, for gases with a constant density of states.