Comment on "A mathematical theorem as a basis for the second law:   Thomson's formulation applied to equilibruim"
  A.E. Allahverdyan and Th. M. Nieuwenhuizen [1] in their paper "A mathematical theorem as a basis for the second law: Thomson's formulation applied to equilibriium" present a proof of the second law of thermodynamics based on quantum mechanics. In this comment on their paper I offer a counterexample to their proof. 
Dan Solomon