2008/05/30 by H. Quevedo, Hernando Quevedo, Quevedo, H. +6 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.0805.4819
New references, comments and corrections added
openalex publication_date 2008/05/30 · arxiv created 2009/09/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We apply variational principles in the context of geometrothermodynamics. The thermodynamic phase space \cal T and the space of equilibrium states \cal 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 \cal E is an extremal and that \cal E and \cal T are related by an embedding harmonic map. We explore the physical meaning of geodesic curves in \cal 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.