Logarithmic corrections to the entropy function of black holes in the open ensemble

TL;DR

This paper derives the precise form of logarithmic corrections to black hole entropy within the open thermodynamic ensemble, accounting for fluctuations in energy, volume, and charge, especially for charged and rotating AdS black holes.

Contribution

It provides the first exact analytic form of logarithmic entropy corrections for black holes in the open ensemble, extending previous results to include charge and rotation.

Findings

Logarithmic corrections depend on fluctuations in energy, volume, and charge.

Exact analytic formulas for corrected entropy of charged and rotating AdS black holes.

Open ensemble is suitable for black hole thermodynamics due to quasi-homogeneity of entropy.

Abstract

An `open' or $(\mu,P,T)$-ensemble describes equilibrium systems whose control parameters are chemical potential $\mu$, pressure $P$ and temperature $T$. Such an unconstrained ensemble is seldom used for applications to standard thermodynamic systems due to the fact that the corresponding free energy identically vanishes as a result of the Euler relation. However, an open ensemble is perfectly regular for the case of black holes, as the entropy is a quasi-homogeneous function of extensive thermodynamic variables with scaling dictated by the Smarr formula. Following a brief discussion on thermodynamics in the open ensemble, we compute the general form of logarithmic corrections to the entropy of a typical system, due to fluctuations in energy, thermodynamic volume and a generic charge $N$. This is then used to obtain the exact analytic form of the logarithmically corrected black hole entropy for charged and rotating black holes in anti-de Sitter spacetimes.