A New Derivation of Classical Gravitational Second Law of Thermodynamics

TL;DR

This paper introduces a new way to define gravitational entropy within the covariant phase space formalism, proving a generalized second law of thermodynamics for Einstein gravity without relying on horizons.

Contribution

It proposes a horizon-independent definition of gravitational entropy and demonstrates its non-decreasing nature along causal paths under the strong energy condition.

Findings

Entropy variations are always non-negative along causal paths.

The new definition generalizes existing notions of gravitational entropy.

The second law holds without horizon dependence in Einstein gravity.

Abstract

It is established that black holes have entropy and behave as thermodynamical systems. Associating entropy to gravitational fields has not remained limited to black holes, necessitating the notion of the second law of thermodynamics in gravitating systems. There have been many ideas and attempts to prove the second law in gravitational systems starting from first principles. Within the covariant phase space formalism, we define gravitational entropy as the charge associated with the local boosts, detaching the gravitational entropy from horizons or trapped surfaces. Our definition encompasses and generalizes the existing notions of entropy. Using this definition for the Einstein gravity case, we compute variations of the entropy along the path of any causal observer and establish that the entropy variations are always non-negative if the matter content satisfies the strong energy condition integrated along any segment of the causal path.