Alternative formulations of the thermodynamics of scalar-tensor theories

TL;DR

This paper investigates alternative thermodynamic formulations of scalar-tensor theories, particularly Horndeski gravity, by mapping their effective stress-energy tensors onto Eckart's thermodynamics and analyzing the impact of different couplings.

Contribution

It introduces new identifications of the scalar field stress-energy tensor that align with Eckart's thermodynamics and examines how various couplings influence the thermodynamic formalism.

Findings

Certain identifications yield constitutive relations matching Eckart's theory.

Different couplings significantly alter the thermodynamic structure.

A specific coupling simplifies the formalism for traditional scalar-tensor theories.

Abstract

We explore alternative formulations of the analogy between viable Horndeski gravity and Eckart's first-order thermodynamics. We single out a class of identifications for the effective stress-energy tensor of the scalar field fluid that, upon performing the imperfect fluid decomposition, yields constitutive relations that can be mapped onto Eckart's theory. We then investigate how different couplings to Einstein's gravity, at the level of the field equations, can affect the thermodynamic formalism overall. Last, we specialize the discussion to the case of ``traditional'' scalar-tensor theories and identify a specific choice of the coupling function that leads to a significant simplification of the formalism.