Thermodynamic systems as extremal hypersurfaces

Abstract

We apply variational principles in the context of geometrothermodynamics. The thermodynamic phase space $\mathcal{T}$ and the space of equilibrium states $\mathcal{E}$ turn out to be described by Riemannian metrics which are invariant with respect to Legendre transformations and satisfy the differential equations following from the variation of a Nambu-Goto-like action. This implies that the volume element of $\mathcal{E}$ is an extremal and that $\mathcal{E}$ and $\mathcal{T}$ are related by an embedding harmonic map. We explore the physical meaning of geodesic curves in $\mathcal{E}$ as describing quasi-static processes that connect different equilibrium states. We present a Legendre invariant metric which is flat (curved) in the case of an ideal (van der Waals) gas and satisfies Nambu-Goto equations. The method is used to derive some new solutions which could represent particular thermodynamic systems.

References in corpus (6)

• Geometrothermodynamics
• Geometrothermodynamics of black holes
• Geometrothermodynamics of asymptotically anti - de Sitter black holes
• Unified geometric description of black hole thermodynamics
• Geometric description of BTZ black holes thermodynamics
• The geometry of thermodynamics

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