Nonequilibrium Thermodynamics of Spacetime

It has previously been shown that the Einstein equation can be derived from the requirement that the Clausius relation dS=δQ/T hold for all local acceleration horizons through each spacetime point, where dS is one-quarter the horizon area change in Planck units and δQ and T are the energy flux across the horizon and the Unruh temperature seen by an accelerating observer just inside the horizon. Here we show that a curvature correction to the entropy that is polynomial in the Ricci scalar requires a nonequilibrium treatment. The corresponding field equation is derived from the entropy balance relation dS=δQ/T+d_iS, where d_iS is a bulk viscosity entropy production term that we determine by imposing energy-momentum conservation. Entropy production can also be included in pure Einstein theory by allowing for shear viscosity of the horizon.