# Quasi-homogeneous black hole thermodynamics

## TL;DR

This paper argues that black hole thermodynamics should be described by quasi-homogeneous functions rather than homogeneous ones, affecting the treatment of coupling constants as thermodynamic variables in generalized gravity theories.

## Contribution

It introduces the concept of quasi-homogeneous functions for black hole thermodynamics and demonstrates the necessity of considering coupling constants as thermodynamic variables.

## Key findings

- Homogeneous functions lead to contradictions in black hole thermodynamics.
- Black holes are better described by quasi-homogeneous functions of different degrees.
- Coupling constants like the cosmological constant should be treated as thermodynamic variables.

## Abstract

Although the fundamental equations of ordinary thermodynamic systems are known to correspond to first-degree homogeneous functions, in the case of non-ordinary systems like black holes the corresponding fundamental equations are not homogeneous. We present several arguments, indicating that black holes should be described by means of quasi-homogeneous functions of degree different from one. In particular, we show that imposing the first-degree condition leads to contradictory results in thermodynamics and geometrothermodynamics of black holes. As a consequence, we show that in generalized gravity theories the coupling constants like the cosmological constant, the Born-Infeld parameter or the Gauss-Bonnet constant must be considered as thermodynamic variables.