  A generic non-integrable (unitary) out-of-equilibrium quantum process, when
interrogated across many times, is shown to yield the same statistics as an
(non-unitary) equilibrated process. In particular, using the tools of quantum
stochastic processes, we prove that under loose assumptions, quantum processes
equilibrate within finite time intervals. Sufficient conditions for this to
occur are that multitime observables are coarse grained in both space and time,
and that the initial state overlaps with many different energy eigenstates.
These results help bridge the gap between (unitary) quantum and (non-unitary)
statistical physics, i.e., when all multitime properties and correlations are
well approximated by stationary quantities, which includes non-Markovianity and
temporal entanglement. We discuss implications of this result for the emergence
of classical stochastic processes from multitime measurements of an underlying
genuinely quantum system.
