Description of isolated macroscopic systems inside quantum mechanics

For an isolated macrosystem classical state parameters ζ(t) are introduced inside a quantum mechanical treatment. By a suitable mathematical representation of the actual preparation procedure in the time interval [T, t0] a statistical operator is constructed as a solution of the Liouville—von Neumann equation, exhibiting at time t the state parameters ζ(t′), t0 ≤ t′ ≤ t, and preparation parameters related to times T ≤ t′ ≤ t0. Relation with Zubarevʹs nonequilibrium statistical operator is discussed. A mechanism for memory loss is investigated and time evolution by a semigroup is obtained for a restricted set of relevant observables, slowly varying on a suitable time scale.