Thermodynamics of Black Holes, far from Equilibrium

Abstract: As in thermodynamics, the celebrated first law of black hole mechanics relates infinitesimal changes in the properties of nearby equilibrium states of black holes (without reference to any physical process that causes the transition). The second law is a qualitative statement that the area of an event horizon cannot decrease under appropriate physical assumptions. These laws are generalized. The new first law applies to black holes in general relativity that can be arbitrarily far from equilibrium and refers to \emph{finite} changes that occur due to \emph{physical processes}. The new second law is a \emph{quantitative} statement that relates the change in the dynamical horizon area with the flux of energy falling into the black hole in a physical process.6