On a Riemannian metric on contact thermodynamic spaces
type: Item
instance of: scholarly article
title: On a Riemannian metric on contact thermodynamic spaces
zbMATH Open document ID: 0885.53026
DOI: 10.1016/S0034-4877(97)84887-2
published in: Reports on Mathematical Physics
publication date: 1998-04-02T00:00:00Z
review text: An almost contact structure \(\Sigma\) on a differentiable manifold \(M\) admits a Riemannian metric \(g\) that is compatible with \(\Sigma\) but is not defined uniquely. There are many examples of Riemannian metrics on contact manifolds, but they do not find any application in physics. In this interesting paper, the author presents a new Riemannian metric \(G\) on a \((2n+1)\)-dimensional contact space (thermodynamic phase space) that may be applied in physics; in particular, it may be used in equilibrium thermodynamics and in nonconservative mechanics. The condition of compatibility of \(G\) with a structure has a simple and intuitive meaning since it is defined by a natural decomposition of the tangent bundle. For thermodynamic systems, the construction of \(G\) was also motivated by statistical considerations which gave a new and deeper insight into \(G\) and its reduction to the Legendre submanifolds of the thermodynamic contact space.
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 80A10
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 53Z05
Mathematics Subject Classification ID: 80A05
Mathematics Subject Classification ID: 82B30
zbMATH DE Number: 1090453
zbMATH Keywords: contact structure
zbMATH Keywords: contact termodynamic space
zbMATH Keywords: Legendre submanifold
zbMATH Keywords: curvature
author: R. Mrugała
reviewed by: Andrew Bucki
MaRDI profile type: Publication
Wikidata QID: Q115339889
cites work: Q4174811
cites work: Q4167627
cites work: Q4772438
cites work: Contact structure in thermodynamic theory
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cites work: Almost contact manifolds with Killing structure tensors
cites work: On differentiable manifolds with certain structures which are closely related to almost contact structure. I
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cites work: Q4891077
full work available at URL: s0034-4877(97)84887-2
OpenAlex ID: W1998665633
description: scientific article; zbMATH DE number 1090453