Generalized thermodynamic identity and new Maxwell's law for charged AdS black hole

TL;DR

This paper develops a generalized thermodynamic identity for charged AdS black holes, extending Maxwell's law for phase transitions, and explores thermodynamic relations across different ensembles.

Contribution

It introduces a new generalized thermodynamic identity and extends Maxwell's equal area law for RN-AdS black holes during phase transitions.

Findings

Derived a generalized thermodynamic identity for RN-AdS black holes.

Established relations of thermodynamic coefficients between ensembles.

Extended Maxwell's law for first order phase transitions in black holes.

Abstract

We study the thermodynamic properties of the RN-AdS black hole in full phase space and propose a generalized thermodynamic identity. As an example, we use it to find relations of thermodynamical coefficients between the grand canonical and canonical ensembles. We also show, for the first order phase transition, that the usual Maxwell's equal area law should be extended to a new form for the RN-AdS black hole.