General proof of (maximum) entropy principle in Lovelock gravity

TL;DR

This paper proves a maximum entropy principle for static perfect fluids in Lovelock gravity, establishing conditions under which the total entropy is extremized, extending thermodynamic principles to higher-order gravity theories.

Contribution

It provides a rigorous proof of the maximum entropy principle in Lovelock gravity and introduces a definition of quasi-local isolation for such systems.

Findings

Total entropy extremum under fixed boundary conditions

Converse theorem confirming the extremum condition

Physical interpretation of boundary conditions in Lovelock gravity

Abstract

We consider a static self-gravitating perfect fluid system in Lovelock gravity theory. For a spacial region on the hypersurface orthogonal to static Killing vector, by the Tolman's law of temperature, the assumption of a fixed total particle number inside the spacial region, and all of the variations (of relevant fields) in which the induced metric and its first derivatives are fixed on the boundary of the spacial region, then with the help of the gravitational equations of the theory, we can prove a theorem says that the total entropy of the fluid in this region takes an extremum value. A converse theorem can also be obtained following the reverse process of our proof. We also propose the definition of isolation quasi-locally for the system and explain the physical meaning of the boundary conditions in the proof of the theorems.