  The topological contribution to black hole entropy of a Gauss-Bonnet term in
four dimensions opens up the possibility of a violation of the second law of
thermodynamics in black hole mergers. We show, however, that the second law is
not violated in the regime where Einstein-Gauss-Bonnet holds as an effective
theory and black holes can be treated thermodynamically. For mergers of AdS
black holes, the second law appears to be violated even in Einstein gravity; we
argue, however, that the second law holds when gravitational potential energy
is taken into account.
