First-order thermodynamics of Horndeski gravity

TL;DR

This paper extends the thermodynamic description of gravity to Horndeski theories, identifying equilibrium and out-of-equilibrium states, and introduces concepts like effective heat current and shear viscosity within this framework.

Contribution

It generalizes the thermodynamic approach to gravity from scalar-tensor theories to the broader class of Horndeski theories, revealing new out-of-equilibrium states.

Findings

General relativity as an equilibrium state

Identification of effective heat current and shear viscosity

Extension of thermodynamic description to Horndeski theories

Abstract

We extend to the Horndeski realm the irreversible thermodynamics description of gravity previously studied in "first generation" scalar-tensor theories. We identify a subclass of Horndeski theories as an out-of--equilibrium state, while general relativity corresponds to an equilibrium state. In this context, we identify an effective heat current, "temperature of gravity", and shear viscosity in the space of theories. The identification is accomplished by recasting the field equations as effective Einstein equations with an effective dissipative fluid, with Einstein gravity as the equilibrium state, following Eckart's first-order thermodynamics.