More on the first-order thermodynamics of scalar-tensor and Horndeski gravity

TL;DR

This paper clarifies the first-order thermodynamics of scalar-tensor and Horndeski gravity, demonstrating its validity in cosmological models and showing it aligns with Eckart's thermodynamics without introducing new physics.

Contribution

It extends the first-order thermodynamics formalism to all Bianchi universes within scalar-tensor and Horndeski gravity, confirming its consistency and applicability.

Findings

Formalism applies to FLRW and Bianchi universes

Constitutive relations of Eckart's thermodynamics are satisfied

Effective Einstein equations with dissipative fluid are equivalent to original physics

Abstract

Two issues in the first-order thermodynamics of scalar-tensor (including ``viable'' Horndeski) gravity are elucidated. The application of this new formalism to FLRW cosmology is shown to be fully legitimate and then extended to all Bianchi universes. It is shown that the formalism holds thanks to the almost miraculous fact that the constitutive relations of Eckart's thermodynamics are satisfied, while writing the field equations as effective Einstein equations with an effective dissipative fluid does not contain new physics.