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

TL;DR

This paper demonstrates that in scalar-tensor theories with non-minimal derivative coupling, the thermodynamic laws on the apparent horizon are consistent with gravitational dynamics, highlighting a fundamental link between gravity and thermodynamics.

Contribution

It establishes the equivalence between the unified first law and Friedmann equations in this specific scalar-tensor theory, extending thermodynamic principles to more complex gravitational models.

Findings

Unified first law is equivalent to Friedmann equations

Second law of thermodynamics holds on the apparent horizon

Supports deep connection between gravity and thermodynamics

Abstract

With the usual definitions for the entropy and the temperature associated with the apparent horizon, we show that the unified first law on the apparent horizon is equivalent to the Friedmann equation for the scalar--tensor theory with non-minimally derivative coupling. The second law of thermodynamics on the apparent horizon is also satisfied. The results support a deep and fundamental connection between gravitation, thermodynamics, and quantum theory.