Entropy Balance Equation of Spacetime Thermodynamics in f(R) Gravity

TL;DR

This paper extends the framework of spacetime thermodynamics to non-equilibrium processes in f(R) gravity, deriving an entropy balance equation that includes new entropy production terms and relates viscosities to black hole membrane paradigm coefficients.

Contribution

It generalizes spacetime thermodynamics to non-equilibrium in f(R) gravity and introduces a new entropy production term.

Findings

Derived the entropy balance equation for non-equilibrium f(R) gravity.

Identified viscosities as coefficients of expansion and shear.

Discovered a new entropy production term in the thermodynamic formulation.

Abstract

We study spacetime thermodynamics for non-equilibrium processes. We first generalize the formulation of spacetime thermodynamics by using an observer outside the horizon. Then we construct the entropy balance equation of spacetime thermodynamics for non-equilibrium processes in f(R) gravity. The coefficients of the expansion and shear terms are equal to the viscosities of the black hole membrane paradigm, and a new entropy production term appears.