The geometry of thermodynamics

Abstract

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-Nordström black hole, but it is not adequate for the thermodynamic description of Kerr black holes.

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

References in corpus (9)

• Geometrothermodynamics
• Geometrothermodynamics of black holes
• Geometry of Higher-Dimensional Black Hole Thermodynamics
• Information Geometry and Phase Transitions
• Information Geometry, One, Two, Three (and Four)
• Geometrisation of Statistical Mechanics
• Thermodynamic length in a 2-D thermodynamic state space
• Curvature of the Weinhold metric for thermodynamical systems with 2 degrees of freedom
• Weinhold'length in an isentropic Ideal and quasi-Ideal Gas

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• Geometrothermodynamics of five dimensional black holes in Einstein-Gauss-Bonnet-theory
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• Geometrothermodynamics: Comments, critics, and supports
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