Quasi-Homogeneous Thermodynamics and Black Holes

TL;DR

This paper introduces a generalized thermodynamics framework based on quasi-homogeneity, which better describes the thermodynamic behavior of self-gravitating systems like black holes, highlighting non-extensivity and resulting in generalized Gibbs-Duhem relations.

Contribution

It develops a quasi-homogeneous thermodynamic formalism that extends traditional approaches to include self-gravitating systems and black holes, emphasizing non-extensive properties.

Findings

Quasi-homogeneous thermodynamics fits black hole thermodynamics.

Generalized Gibbs-Duhem equations are derived from quasi-homogeneity.

The framework explains non-extensivity in self-gravitating systems.

Abstract

We propose a generalized thermodynamics in which quasi-homogeneity of the thermodynamic potentials plays a fundamental role. This thermodynamic formalism arises from a generalization of the approach presented in paper [1], and it is based on the requirement that quasi-homogeneity is a non-trivial symmetry for the Pfaffian form $\delta Q_{rev}$. It is shown that quasi-homogeneous thermodynamics fits the thermodynamic features of at least some self-gravitating systems. We analyze how quasi-homogeneous thermodynamics is suggested by black hole thermodynamics. Then, some existing results involving self-gravitating systems are also shortly discussed in the light of this thermodynamic framework. The consequences of the lack of extensivity are also recalled. We show that generalized Gibbs-Duhem equations arise as a consequence of quasi-homogeneity of the thermodynamic potentials. An heuristic link between this generalized thermodynamic formalism and the thermodynamic limit is also discussed.