Thermodynamics of general scalar-tensor theory with non-minimally derivative coupling

TL;DR

This paper explores the thermodynamics of scalar-tensor gravity theories with non-minimal derivative coupling, demonstrating the equivalence between the first law of thermodynamics at the apparent horizon and the Friedmann equations.

Contribution

It establishes the connection between thermodynamics and cosmological dynamics in a broad class of scalar-tensor theories with derivative couplings.

Findings

First law of thermodynamics is equivalent to Friedmann equations in these models.

A mass-like function matching the Misner-Sharp mass is used to demonstrate this equivalence.

Results support the universal link between horizon thermodynamics and cosmological evolution.

Abstract

With the usual definitions for the entropy and the temperature associated with the apparent horizon, we discuss the first law of the thermodynamics on the apparent in the general scalar-tensor theory of gravity with the kinetic term of the scalar field non-minimally coupling to Einstein tensor. We show the equivalence between the first law of thermodynamics on the apparent horizon and Friedmann equation for the general models, by using a mass-like function which is equal to the Misner-Sharp mass on the apparent horizon. The results further support the universal relationship between the first law of thermodynamics and Friedmann equation.