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.