Thermodynamics of scalar-tensor gravity

TL;DR

This paper applies Eckart's thermodynamics to scalar-tensor gravity, deriving simple expressions for thermodynamic quantities and providing a consistent thermodynamic framework for gravity theories beyond general relativity.

Contribution

It introduces a novel thermodynamic description of scalar-tensor gravity using Eckart's first order thermodynamics, revealing well-defined temperature and equilibrium concepts.

Findings

Derived effective heat flux and temperature of gravity.

Obtained shear and bulk viscosity expressions.

Presented a generalized Fourier law for scalar-tensor gravity.

Abstract

Previously, the Einstein equation has been described as an equation of state, general relativity as the equilibrium state of gravity, and $f({\cal R})$ gravity as a non-equilibrium one. We apply Eckart's first order thermodynamics to the effective dissipative fluid describing scalar-tensor gravity. Surprisingly, we obtain simple expressions for the effective heat flux, "temperature of gravity", shear and bulk viscosity, and entropy density, plus a generalized Fourier law in a consistent Eckart thermodynamical picture. Well-defined notions of temperature and approach to equilibrium, missing in the current thermodynamics of spacetime scenarios, naturally emerge.