Partition Functions, the Bekenstein Bound and Temperature Inversion in Anti-de Sitter Space and its Conformal Boundary

TL;DR

This paper explores the thermodynamic properties of quantum fields in anti-de Sitter space, reformulating the Bekenstein bound and revealing its limitations for free quantum fields despite its validity for black holes.

Contribution

It reformulates the Bekenstein bound in terms of Helmholtz free energy and demonstrates its failure for free quantum fields in AdS, contrasting with black hole cases.

Findings

Bekenstein bound holds for all known AdS black holes.

Bound is not valid for free quantum fields in AdS.

Thermodynamics in AdS exhibits unique features.

Abstract

We reformulate the Bekenstein bound as the requirement of positivity of the Helmholtz free energy at the minimum value of the function L=E- S/(2\pi R), where R is some measure of the size of the system. The minimum of L occurs at the temperature T=1/(2\pi R). In the case of n-dimensional anti-de Sitter spacetime, the rather poorly defined size R acquires a precise definition in terms of the AdS radius l, with R=l/(n-2). We previously found that the Bekenstein bound holds for all known black holes in AdS. However, in this paper we show that the Bekenstein bound is not generally valid for free quantum fields in AdS, even if one includes the Casimir energy. Some other aspects of thermodynamics in anti-de Sitter spacetime are briefly touched upon.