Equilibration of Multitime Quantum Processes in Finite Time Intervals

TL;DR

This paper demonstrates that non-integrable quantum processes tend to equilibrate within finite time intervals, making their multitime statistics resemble those of classical stochastic processes under certain conditions.

Contribution

It provides a rigorous proof that quantum processes equilibrate in finite time and identifies conditions under which multitime quantum correlations approximate stationary classical statistics.

Findings

Quantum processes equilibrate within finite time.

Multitime observables become stationary under coarse graining.

Results bridge quantum dynamics and classical statistical physics.

Abstract

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.