Varying alpha and black hole entropy

Recently it has been suggested that an increase in the fine structure constant α with time would decrease the entropy of a Reissner-Nordstrom black hole, thereby violating the second law of thermodynamics. In this note we point out that, at least for a class of charged dilaton black hole related to string theory, the entropy does not change under adiabatic variations of α and is expected to increase for non-adiabatic changes.