Non-extensive and quasi-homogeneous geometrothermodynamics

TL;DR

This paper explores the thermodynamics of black holes using Rényi entropy, revealing that treating the Rényi parameter as an independent variable can lead to stability in Schwarzschild black holes.

Contribution

It introduces a framework where Rényi entropy is used as the fundamental thermodynamic function, incorporating non-extensivity and quasi-homogeneity into black hole thermodynamics.

Findings

Rényi parameter acts as an independent thermodynamic variable.

Schwarzschild black holes can become thermodynamically stable.

Extended thermodynamics framework is necessary for non-extensive entropy.

Abstract

We study the thermodynamic properties of black holes, taking into account the non-extensive character of their entropy at the thermodynamic and statistical level. To this end, we assume that the R\'enyi entropy determines the fundamental thermodynamic equation of black holes and is represented by a quasi-homogeneous function. As a consequence, the R\'enyi parameter turns out to be an independent thermodynamic variable, which must be treated in the framework of extended thermodynamics. As a particular example, we use the formalism of geometrothermodynamics to show that the Schwarzschild black hole can become stable for certain values of the R\'enyi parameter.