  Recently, Chandrasekaran, Penington and Witten (CPW) have shown that the
generalized entropy of the Schwarzschild black hole at the bifurcation surface
equals the entropy of an extended von Neumann algebra of quantum observables in
the black hole exterior, in semiclassical Einstein gravity. They also derive a
version of the Generalized Second law. We generalize these results to a static
black hole in an arbitrary diffeomorphism invariant theory of gravity. Thus, a
version of the Generalized second law for an arbitrary diffeomorphism invariant
theory of gravity follows.
