2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/16984Recently Allahverdyan and Nieuwenhuizen (cond-mat/0006404) argued that the second law of thermodynamics may be violated in a quantum system as a "consequence of quantum coherence in the presence of the slightly off-equilibrium nature of the bath." By using a standard result about relative entropy, we prove rigorously that the second law is never violated (and, in particular, a perpetual motion of the second kind can never be realized) in quantum systems no matter how strong ``quantum coherence'' is or no matter how far one goes from equilibrium.3 pages, made minor changes to make the points of the Comment clearerStatistical Mechanicstext