Micro-canonical and canonical description for generalised entropy

TL;DR

This paper develops a microscopic thermodynamic framework for generalized entropies, linking phase space volume changes to entropy measures, which could shed light on quantum gravity structures.

Contribution

It introduces a unified microscopic description for various generalized entropies based on phase space volume and measure differences.

Findings

Phase space volume changes relate to generalized entropy.

Canonical measure differences correspond to entropy variations.

Framework applicable to diverse entropy forms like Tsallis and Rényi.

Abstract

Few parameters dependent generalised entropy includes Tsallis entropy, R{\'e}nyi entropy, Sharma-Mittal entropy, Barrow entropy, Kaniadakis entropy, etc as particular representatives. Its relation to physical systems is not always clear. In this paper, we propose the microscopic thermodynamic description for an arbitrary generalised entropy in terms of the particle system. It is shown that the change in the volume of the phase space of the particle system in the micro-canonical description or the difference in the integration measure in the phase space in the canonical description may lead to generalised entropy. Our consideration may help us understand the structure of quantum gravity.