Alternative derivation of the classical second law of thermodynamics

Abstract

One of the classical statements of the second law of thermodynamics is derived from an assumption about the behavior of an isolated heat reservoir, together with a further assumption, which seems to be a rather weak one, about initial states. The derivation is otherwise based on the unitary property of time evolution in quantum mechanics. An analogous derivation, within the framework of classical mechanics, is also given; in this case Liouville's theorem substitutes for unitarity.