Surface Density of Spacetime Degrees of Freedom from Equipartition Law in theories of Gravity

TL;DR

This paper demonstrates that the equipartition law applied to spacetime surfaces in equilibrium can determine the density of microscopic degrees of freedom, linking entropy with Wald entropy and deriving field equations from entropy extremization.

Contribution

It introduces a method to find the surface density of spacetime degrees of freedom using equipartition, connecting thermodynamics with gravitational field equations in diffeomorphism invariant theories.

Findings

Surface degrees of freedom density matches Wald entropy.

Spacetime entropy resides on boundary when in thermal equilibrium.

Field equations derived from extremizing spacetime entropy.

Abstract

I show that the principle of equipartition, applied to area elements of a surface which are in equilibrium at the local Davies-Unruh temperature, allows one to determine the surface number density of the microscopic spacetime degrees of freedom in any diffeomorphism invariant theory of gravity. The entropy associated with these degrees of freedom matches with the Wald entropy for the theory. This result also allows one to attribute an entropy density to the spacetime in a natural manner. The field equations of the theory can then be obtained by extremising this entropy. Moreover, when the microscopic degrees of freedom are in local thermal equilibrium, the spacetime entropy of a bulk region resides on its boundary.