Non-coherent evolution of closed weakly interacting system leads to equidistribution of probabilities of microstates

Abstract: We introduce a concept of non-coherent evolution of macroscopic quantum systems. We show that for weakly interacting systems, such evolution is a Markovian stochastic process. The transition rates between system states, which characterize the process, are determined by Fermi's golden rule. Such evolution is time-irreversible and leads to the equidistribution of probabilities across every state of the system. Furthermore, we investigate the time dependence of the mean numbers of particles in single-particle states and find that, under the given assumptions, it is governed by the Boltzmann collision integral. In this theory, non-coherence is the mechanism that transforms time-reversible unitary evolution into time-irreversible stochastic evolution. Thus, we present a possible solution to the famous arrow-of-time problem.