New approach to the thermodynamics of scalar-tensor gravity

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 paper [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.