Thermodynamic curvature measures interactions

Abstract

Thermodynamic fluctuation theory originated with Einstein who inverted the relation $S=k_B\ln \Omega$ to express the number of states in terms of entropy: $\Omega =\exp (S/k_B)$. 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.

29 pages, 7 figures (added reference 27)

References in corpus (3)

• Thermodynamic curvature and phase transitions in Kerr-Newman black holes
• Nonperturbative Thermodynamic Geometry of Anyon Gas
• Ruppeiner theory of black hole thermodynamics

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