A new approach to the thermodynamics of scalar-tensor gravity

TL;DR

This paper develops a thermodynamic framework for scalar-tensor gravity by modeling it as a dissipative fluid, deriving effective thermodynamic quantities, and analyzing its evolution towards Einstein gravity as an equilibrium state.

Contribution

It introduces a novel thermodynamic approach to scalar-tensor gravity, including effective quantities and a diffusion equation towards general relativity.

Findings

Derived explicit expressions for heat flux, temperature, viscosities, and entropy density.

Applied the formalism to exact solutions to illustrate the approach to equilibrium.

Provided physical insights into the gravitational diffusion process.

Abstract

We discuss and expand a new approach to the thermodynamics of scalar-tensor gravity and its diffusion toward general relativity (seen as an equilibrium state) proposed in a previous Letter [Phys. Rev. D 103, L121501 (2021)], upon which we build. We describe scalar-tensor gravity as an effective dissipative fluid and apply Eckart's first order thermodynamics to it, obtaining explicitly effective quantities such as heat flux, "temperature of gravity", viscosities, entropy density, plus an equation describing the "diffusion" to Einstein gravity. These quantities, still missing in the usual thermodynamics of spacetime, are obtained with minimal assumptions. Furthermore, we examine certain exact solutions of scalar-tensor gravity to test the proposed formalism and gain some physical insight on the "approach to equilibrium" for this class of theories.