Thermodynamic curvature measures interactions

Thermodynamic fluctuation theory originated with Einstein, who inverted the relation S=kB ln Ω to express the number of states in terms of entropy: Ω=exp(S/kB). The theory’s Gaussian approximation is discussed in most statistical mechanics texts. I review work showing how to go beyond the Gaussian approximation by adding covariance, conservation, and consistency. This generalization leads to a fundamentally new object: The thermodynamic Riemannian curvature scalar R, a thermodynamic invariant. I argue that |R| is related to the correlation length and suggest that the sign of R corresponds to whether the interparticle interactions are effectively attractive or repulsive.