  By looking for possible violation of the generalized second law, we might be
able to find regions in the space of theories and states that do not allow
holographic dual descriptions. We revisit three proposals for violation of the
generalized second law in the simplest Higgs phase of gravity called ghost
condensate. Two of them, (i) analogue of Penrose process and (ii) semiclassical
heat flow, are based on Lorentz breaking effects, by which particles of
different species can have different limits of speed. We show that processes in
both (i) and (ii) are always slower than accretion of ghost condensate and
cannot decrease the total entropy before the accretion increases the entropy.
The other proposal is to use (iii) negative energy carried by excitations of
ghost condensate. We prove an averaged null energy condition, which we
conjecture prevents the proposal (iii) from violating the generalized second
law in a coarse-grained sense.
