A non-perturbative second law of black hole mechanics in effective field theory

We describe a method for defining dynamical black hole entropy in gravitational effective field theories (EFTs). The entropy is constructed order by order in derivatives. For any fixed number of derivatives, the entropy satisfies a non-perturbative second law of black hole mechanics if the black hole remains within the regime of validity of EFT. In equilibrium the entropy reduces to the Wald entropy. It reduces to the entropy defined by Hollands et al in theories of vacuum gravity with up to 10 derivatives.