Entropy Functionals and Second Law in Curvature Squared Gravity Theories

Standard methods for calculating the black hole entropy beyond general relativity are ambiguous when the horizon is non-stationary. We fix these ambiguities in all quadratic curvature gravity theories, by demanding that the entropy be increasing at every time, for linear perturbations to a stationary black hole. Our result matches with the entropy formula found previously in holographic entanglement entropy calculations. We also derive bounds on the higher curvature couplings demanding the validity of the second law for higher order perturbations.