Thermodynamic curvature and black holes

TL;DR

This paper surveys thermodynamic curvature across various systems, including fluids, solids, spin systems, and black holes, highlighting its geometric invariance and significance in understanding microscopic interactions and structures.

Contribution

It provides a systematic overview of thermodynamic curvature in black hole thermodynamics, extending concepts from fluids and solids to gravitational systems.

Findings

$R$ indicates the nature of microscopic interactions.

$|R|$ estimates the size of mesoscopic structures.

Thermodynamic principles may be universally applicable to black holes.

Abstract

I give a relatively broad survey of thermodynamic curvature $R$, one spanning results in fluids and solids, spin systems, and black hole thermodynamics. $R$ results from the thermodynamic information metric giving thermodynamic fluctuations. $R$ has a unique status in thermodynamics as being a geometric invariant, the same for any given thermodynamic state. In fluid and solid systems, the sign of $R$ indicates the character of microscopic interactions, repulsive or attractive. $|R|$ gives the average size of organized mesoscopic fluctuating structures. The broad generality of thermodynamic principles might lead one to believe the same for black hole thermodynamics. This paper explores this issue with a systematic tabulation of results in a number of cases.