Closed quantum systems obey the Schrödinger equation, whereas nonequilibrium behavior of many 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.

• Received 22 July 2015
• Revised 16 December 2015

DOI:https://doi.org/10.1103/PhysRevE.93.012125