Nonequilibrium statistical mechanics. I. Mathematical formalism. Theorem of N. S. Krylov

Based on an algebraic formulation of quantum mechanics we introduce concepts playing a fundamental role in the constructionof the statistical mechanics of systems having direct classical analogs. We give the definition of a macrostate, mixing in the quantum version, and also demonstrate the existence of an upper bound to the relaxation time for an isolated system. It is shown that the theory constructed here contains both quantum and classical mechanics as limiting cases, but these two cases are not reducible to each other. The existence of a transition range not describable by the Schrodinger equation is noted.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 11, pp. 42–45, November, 1981.