Thermodynamic curvature: pure fluids to black holes

Abstract

Thermodynamics unavoidably contains fluctuation theory, expressible in terms of a unique thermodynamic information metric. This metric produces an invariant thermodynamic Riemannian curvature scalar R which, in fluid and spin systems, measures interatomic interactions. Specifically, |R| measures the size of organized fluctuating microscopic structures, and the sign of R indicates whether the interactions are effectively attractive or repulsive. R has also been calculated for black hole thermodynamics for which there is no consensus about any underlying microscopic structures. It is hoped that the physical interpretation of R in fluid and spin systems might offer insight into black hole microstructures. I give a brief review of results for R in black holes, including stability, the sign of R, R = 0, diverging |R|, and various claims of "inconsistencies" in thermodynamic metric geometry.