Thermodynamic fluctuation theory originated with Einstein who inverted the
relation S=kBlnΩ 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.Comment: 29 pages, 7 figures (added reference 27