Quasi-Homogeneous Thermodynamics and Black Holes

Details Quasi-Homogeneous Thermodynamics and Black Holes Quasi-Homogeneous Thermodynamics and Black Holes

2002-10-07

arxiv.org/abs/gr-qc/0210021v2

J.Math.Phys. 44 (2003) 1089-1128

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

39 pages, uses RevteX. Published version (minor changes w.r.t. the original one)

Scientific paper

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.

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