The inequivalence of thermodynamic ensembles

Details The inequivalence of thermodynamic ensembles The inequivalence of thermodynamic ensembles

1994-10-13

arxiv.org/abs/gr-qc/9410017v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages, Latex file with 3 figures available on request at parenta@physique.ens.fr

Scientific paper

The inequivalence of thermodynamical ensembles related by a Legendre transformation is manifest in self-gravitating systems and in black hole thermodynamics. Using the Poincare's method of the linear series, we describe the mathematical reasons which lead to this inequivalence which in turn induces a hierarchy of ensembles: the most stable ensemble describes the most isolated system. Moreover, we prove that one can obtain the degree of stability of all equilibrium configurations in any ensensemble related by Legendre transformations to the most stable if one knows the degree of stability in the most stable ensemble.

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