Thermodynamic curvature: pure fluids to black holes

TL;DR

This paper reviews the thermodynamic curvature scalar R, which measures microscopic interactions in fluids and black holes, exploring its implications for understanding black hole microstructures and thermodynamic stability.

Contribution

It provides a comparative review of thermodynamic curvature R in black holes, highlighting its potential to reveal microscopic structures and clarify thermodynamic properties.

Findings

R measures interatomic and black hole microstructures

Sign of R indicates attractive or repulsive interactions

Divergences in R relate to phase transitions or instabilities

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.