Two-Dimensional Einstein Manifolds in Geometrothermodynamics

摘要

We present a class of thermodynamic systems with constant thermodynamic curvature which, within the context of geometric approaches of thermodynamics, can be interpreted as constant thermodynamic interaction among their components. In particular, for systems constrained by the vanishing of theHessian curvaturewe write down the systems of partial differential equations. In such a case it is possible to find a subset of solutions lying on a circumference in an abstract space constructed from the first derivatives of the isothermal coordinates.We conjecture that solutions on the characteristic circumference are of physical relevance, separating them fromthose of puremathematical interest.We present the case of a one-parameter family of fundamental relations that—when lying in the circumference—describe a polytropic fluid.