  Closed quantum systems obey the Schroedinger equation whereas nonequilibrium
behavior of many of systems is routinely described in terms of classical,
Markovian stochastic processes. Evidently, there are fundamental differences
between those two types of behavior. We discuss the conditions under which the
unitary dynamics may be mapped onto pertinent classical stochastic processes.
This is first principally addressed based on the notions of "consistency" and
"Markovianity." Numerical data are presented that show that the above
conditions are to good approximation fulfilled for Heisenberg-type spin models
comprising 12-20 spins. The accuracy to which these conditions are met
increases with system size.
