Black Hole Statistical Mechanics and The Angular Velocity Ensemble

TL;DR

This paper introduces the angular velocity ensemble, a new statistical mechanics framework for black holes, highlighting challenges in deriving entropy and thermodynamics laws due to the absence of external parameters in general relativity.

Contribution

It proposes the angular velocity ensemble derived via Jaynes' entropy maximization, addressing issues in black hole thermodynamics related to external parameters.

Findings

The ensemble is relevant to black holes and their thermodynamics.

Difficulty in deriving entropy as a function of state.

Challenges in recovering the first law of thermodynamics.

Abstract

An new ensemble - the angular velocity ensemble - is derived using Jaynes' method of maximising entropy subject to prior information constraints. The relevance of the ensemble to black holes is motivated by a discussion of external parameters in statistical mechanics and their absence from the Hamiltonian of general relativity. It is shown how this leads to difficulty in deriving entropy as a function of state and recovering the first law of thermodynamics from the microcanonical and canonical ensembles applied to black holes.