Thermodynamics: A Riemannian geometric model

Abstract

By including the theory of fluctuations in the axioms of thermodynamics it is shown that thermodynamic systems can be represented by Riemannian manifolds. Of special interest is the curvature of these manifolds which, for pure fluids, is associated with effective interparticle interaction strength by means of a general thermodynamic "interaction hypothesis." This interpretation of curvature appears to be consistent with hyperscaling and two-scale-factor universality. The Riemannian geometric model is a new attempt to extract information from the axioms of thermodynamics.