The geometry of thermodynamics

Details The geometry of thermodynamics The geometry of thermodynamics

2007-12-06

arxiv.org/abs/0712.0868v1

AIP Conf.Proc.977:165-172,2008

Physics

Mathematical Physics

8 pages, no figures, prepared for Proceedings of the III Mexican Meeting on Mathematical and Experimental Physics

Scientific paper

10.1063/1.2902782

We present a review of the main aspects of geometrothermodynamics, an approach which allows us to associate a specific Riemannian structure to any classical thermodynamic system. In the space of equilibrium states, we consider a Legendre invariant metric, which is given in terms of the fundamental equation of the corresponding thermodynamic system, and analyze its geometric properties in the case of the van der Waals gas, and black holes. We conclude that the geometry of this particular metric reproduces the thermodynamic behavior of the van der Waals gas, and the Reissner-Nordstr\"om black hole, but it is not adequate for the thermodynamic description of Kerr black holes.

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