On a Riemannian metric on contact thermodynamic spaces
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.
scientific article; zbMATH DE number 1090453