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arXiv · 1007.2160

Thermodynamic curvature measures interactions

George Ruppeiner
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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.

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George Ruppeiner. 2010-07-13. Thermodynamic curvature measures interactions. https://doi.org/10.1119/1.3459936

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