ENTROPY BALANCE EQUATION OF SPACE-TIME THERMODYNAMICS IN f(R) GRAVITY

We study space-time thermodynamics for nonequilibrium processes. We first generalize the formulation of space-time thermodynamics by using an observer outside the horizon. Then we construct the entropy balance equation of space-time thermodynamics for nonequilibrium 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.