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Advances in High Energy Physics
Volume 2013 (2013), Article ID 967618, 6 pages
Research Article

Two-Dimensional Einstein Manifolds in Geometrothermodynamics

1Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A.P. 70-543, 04510 Mexico, DF, Mexico
2Facultad de Ciencias Básicas, Universidad Tecnológica de Bolívar, Cartagena 13001, Colombia
3Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, A.P. 50-542, 04510 México, DF, Mexico

Received 16 March 2013; Accepted 15 June 2013

Academic Editor: Hernando Quevedo

Copyright © 2013 Antonio C. Gutiérrez-Piñeres et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present a class of thermodynamic systems with constant thermodynamic curvature which, within the context of geometric approaches of thermodynamics, can be interpreted as constant thermodynamic interaction among their components. In particular, for systems constrained by the vanishing of the Hessian curvature we write down the systems of partial differential equations. In such a case it is possible to find a subset of solutions lying on a circumference in an abstract space constructed from the first derivatives of the isothermal coordinates. We conjecture that solutions on the characteristic circumference are of physical relevance, separating them from those of pure mathematical interest. We present the case of a one-parameter family of fundamental relations that—when lying in the circumference—describe a polytropic fluid.