Universal canonical entropy for gravitating systems

TL;DR

This paper demonstrates that the canonical entropy of gravitating systems with boundaries universally includes logarithmic corrections to the area law, independent of specific spectral assumptions, highlighting a fundamental aspect of quantum gravity thermodynamics.

Contribution

It establishes a universal form for the canonical entropy with logarithmic corrections, derived from boundary quantum dynamics and quantum spacetime fluctuations, applicable across different spectral assumptions.

Findings

Canonical entropy has universal logarithmic corrections to the area law.

The form of the entropy correction is independent of the spectral index.

The approach relies on boundary quantum dynamics and quantum spacetime fluctuations.

Abstract

The thermodynamics of general relativistic systems with boundary, obeying a Hamiltonian constraint in the bulk, is argued to be determined solely by the boundary quantum dynamics, and hence by the area spectrum. Assuming, for large area of the boundary, (a) an area spectrum as determined by Non-perturbative Canonical Quantum General Relativity (NCQGR), (b) an energy spectrum that bears a power law relation to the area spectrum, (c) an area law for the leading order microcanonicai entropy, leading thermal fluctuation corrections to the canonical entropy are shown to be logarithmic in area with a universal coefficient. Since the microcanonical entropy also has univeral logarithmic corrections to the area law (from quantum spacetime fluctuations, as found earlier) the canonical entropy then has a universal form including logarithmic corrections to the area law. This form is shown to be independent of the index appearing in assumption (b). The index, however, is crucial in ascertaining the domain of validity of our approach based on thermal equilibrium.