Revisit to Thermodynamic Relations in the AdS/CMT Models

TL;DR

This paper revisits thermodynamic relations in hairy AdS black holes, improving holographic computations to include hairy contributions and maintaining the universal first law within the AdS/CMT framework.

Contribution

It extends previous results by explicitly incorporating hairy contributions into the thermodynamic and quantum statistical relations of AdS black holes.

Findings

Holographic computation aligns with bulk calculations when hairy contributions are included.

The first law of thermodynamics remains valid in the presence of hair.

The relation between Euclidean action and free energy can be deformed to account for hair.

Abstract

Motivated by the recent unified approach to the Smarr-like relation of AdS planar black holes in conjunction with the quasi-local formalism on conserved charges, we revisit the quantum statistical and thermodynamic relations of hairy AdS planar black holes. By extending the previous results, we identify the hairy contribution in the bulk and show that the holographic computation can be improved so that it is consistent with the bulk computation. We argue that the first law can be retained in its universal form while the relation between the on-shell renormalized Euclidean action and its free energy interpretation in gravity may be deformed to contain the hairy contribution in hairy AdS black holes.