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 {\it preparation parameters} related to times T≤t′≤t0. Relation with Zubarev's non-equilibrium 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.Comment: 13 pages, latex, romp31 style, no figures, to appear in the
Proceedings of the XXXI Symposium on Mathematical Physics (Torun, Poland), to
be published in Rep. Math. Phy