Geometrothermodynamics

2006/04/20 by Hernando Quevedo · 1 voice · 12 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Geometric Analysis and Curvature Flows #Statistical Mechanics and Entropy #gr-qc #math-ph #math.MP #physics.chem-ph

paper · pdf · doi:10.1063/1.2409524

published as J.Math.Phys. 48 (2007) 013506 · Revised version, to be published in Jour. Math. Phys

arxiv published 2006/04/20 · arxiv created 2006/12/05 · arxiv updated 2006/12/05 · openalex publication_date 2007/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We present the fundamentals of geometrothermodynamics, an approach to study the properties of thermodynamic systems in terms of differential geometric concepts. It is based, on the one hand, upon the well-known contact structure of the thermodynamic phase space and, on the other hand, on the metric structure of the space of thermodynamic equilibrium states. In order to make these two structures compatible we introduce a Legendre invariant set of metrics in the phase space, and demand that their pullback generates metrics on the space of equilibrium states. We show that Weinhold's metric, which was introduced \it ad hoc, is not contained within this invariant set. We propose alternative metrics which allow us to redefine the concept of thermodynamic length in an invariant manner and to study phase transitions in terms of curvature singularities.

Citations

• Curvature of the Weinhold metric for thermodynamical systems with 2 degrees of freedom

Cited by

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Discussions

• I'm basically writing a report on the possibility of formulating Thermodynamics in terms of Manifolds, Differential forms and Exterior Algebra. In my search I came across the formalism of Geometrother [stackexchange, 0 points]