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

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.

v2: 24 pages,4 figures, major revision, erroneous discussion on critical points in earlier version corrected and figures replotted, new appendix added, key conclusions and results unchanged, matches published version

References in corpus (8)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume
• Microstates of a Neutral Black Hole in M Theory
• A Rotating Holographic Superconductor
• A scalar field condensation instability of rotating anti-de Sitter black holes
• Counting black hole microscopic states in loop quantum gravity
• Quasi-homogeneous black hole thermodynamics
• Novel logarithmic corrections to black hole entropy

Cited by in corpus (7)

• Non-perturbative correction on the black hole geometry
• Thermal fluctuations of black holes with non-linear electrodynamics and charged Renyi entropy
• Novel logarithmic corrections to black hole entropy
• Topological dyonic black holes of massive gravity with generalized quasitopological electromagnetism
• Relativistic Correction to Black Hole Entropy
• Statistical ensembles and logarithmic corrections to black hole entropy
• Black hole thermodynamic free energy as $A$-discriminants