On a Riemannian metric on contact thermodynamic spaces

It is shown how a new Riemannian metric G may be introduced on the space of thermodynamic parameters. This metric is in a sense compatible with the basic contact structure of thermodynamics. The condition of compatibility was given a simple and intuitive meaning because it is connected with a natural decomposition of tangent vector fields into two parts: vertical and horizontal. 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. It turns out that this metric generalizes the metrics considered previously in thermodynamics.