  In this article we consider the second law of black holes (and other causal
horizons) in theories where the gravitational action is an arbitrary function
of the Lovelock densities. We show that there exists an entropy which increases
locally, for linearized perturbations to regular Killing horizons. In addition
to a classical increase theorem, we also prove a generalized second law for
semiclassical, minimally-coupled matter fields.
