The thermodynamic limit and black hole entropy in the area ensemble

TL;DR

This paper examines the thermodynamic limit in loop quantum gravity's area ensemble to derive a smooth black hole entropy, highlighting differences in subleading corrections that affect entropy concavity.

Contribution

It provides a rigorous analysis of the thermodynamic limit in the area ensemble, clarifying how subleading corrections influence black hole entropy properties.

Findings

Leading behavior of smoothed entropy matches counting entropy for large areas

Subleading corrections differ between smoothed and counting entropy

Corrections impact the concavity or convexity of the entropy function

Abstract

We discuss the thermodynamic limit in the canonical area ensemble used in loop quantum gravity to model quantum black holes. The computation of the thermodynamic limit is the rigorous way to obtain a smooth entropy from the counting entropy given by a direct determination of the number of microstates compatible with macroscopic quantities (the energy in standard statistical mechanics or the area in the framework presented here). As we will show in specific examples the leading behavior of the smoothed entropy for large horizon areas is the same as the counting entropy but the subleading contributions differ. This is important because these corrections determine the concavity or convexity of the entropy as a function of the area.