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

2005/05/03 by Manuel Santoro, Santoro, Manuel, Serge Preston +1 · 2 citations
Mathematics · Physics and Astronomy · #80A99 #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary: 53B50 #Quantum chaos and dynamical systems #Secondary: 53B21 #Statistical Mechanics and Entropy #math-ph #math.MP #msc:53B21 #msc:53B50 #msc:80A99

paper · pdf · doi:10.48550/arxiv.math-ph/0505010

arxiv created 2005/05/03 · openalex publication_date 2005/05/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work the curvature of Weinhold (thermodynamical) metric is studied in the case of systems with two thermodynamical degrees of freedom. Conditions for the Gauss curvature R to be zero, positive or negative are worked out. Signature change of the Weinhold metric and the corresponding singular behavior of the curvature at the phase boundaries are studied. Cases of systems with the constant C_v, including Ideal and Van der Waals gases, and that of Berthelot gas are discussed in detail.

Citations

• Riemannian geometry of the Pauli paramagnetic gas

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