Thermodynamics of scalar-tensor gravity

Previously, the Einstein equation has been described as an equation of state, general relativity as the equilibrium state of gravity, and f(R) gravity as a nonequilibrium one. We apply Eckart's first order thermodynamics to the effective dissipative fluid describing scalar-tensor gravity. Surprisingly, we obtain simple expressions for the effective heat flux, "temperature of gravity", shear and bulk viscosity, and entropy density, plus a generalized Fourier law in a consistent Eckart thermodynamical picture. Well-defined notions of temperature and approach to equilibrium, missing in the current thermodynamics of spacetime scenarios, naturally emerge.