Statistical ensembles and logarithmic corrections to black hole entropy

In this paper, we consider general statistical ensembles and compute logarithmic corrections to the microcanonical entropy resulting due to thermodynamic fluctuations which are controlled by the boundary conditions, i.e. due to choice of ensemble. The framework is applied to the case of non-extremal black holes to give certain logarithmic corrections to the Bekenstein-Hawking entropy. We argue that within the framework of black hole chemistry, where the cosmological constant is identified with bulk pressure, the isoenthalpic-isobaric entropy rather than microcanonical entropy carries a more natural and consistent thermodynamic interpretation as black hole entropy. Logarithmic corrections to both microcanonical and isoenthalpic-isobaric entropies of black holes are computed, and we show that the latter set of corrections in black hole chemistry are of the same form as corrections to the microcanonical entropy in theories where the cosmological constant is not interpreted as a thermodynamic pressure. Finally, we compute logarithmic corrections to entropy in the framework of holographic black hole chemistry. We emphasize upon the choice of statistical ensemble, both in the bulk and on the boundary, in order to have a consistent comparison between them. The corrections studied in this paper are distinct from those obtained from Euclidean quantum gravity.

Automated summary

In this paper, the authors study general statistical ensembles and calculate logarithmic corrections to microcanonical entropy resulting from thermodynamic fluctuations. The framework is applied to non-extremal black holes, resulting in certain corrections to the Bekenstein-Hawking entropy. The authors argue that the isoenthalpic-isobaric entropy has a more natural and consistent interpretation as black hole entropy within the framework of black hole chemistry. Logarithmic corrections to both microcanonical and isoenthalpic-isobaric entropies are computed, and comparisons are made to theories where the cosmological constant is not interpreted as a thermodynamic pressure. Finally, logarithmic corrections to entropy in the holographic black hole chemistry framework are computed, emphasizing the importance of choosing the appropriate statistical ensemble.