  One of the main questions of research on quantum many-body systems following
unitary out of equilibrium dynamics is to find out how local expectation values
equilibrate in time. For non-interacting models, this question is rather well
understood. However, the best known bounds for general quantum systems are
vastly crude, scaling unfavorable with the system size. Nevertheless, empirical
and numerical evidence suggests that for generic interacting many-body systems,
generic local observables, and sufficiently well-behaved states, the
equilibration time does not depend strongly on the system size, but only the
precision with which this occurs does. In this discussion paper, we aim at
giving very simple and plausible arguments for why this happens. While our
discussion does not yield rigorous results about equilibration time scales, we
believe that it helps to clarify the essential underlying mechanisms, the
intuition and important figure of merits behind equilibration. We then connect
our arguments to common assumptions and numerical results in the field of
equilibration and thermalization of closed quantum systems, such as the
eigenstate thermalization hypothesis as well as rigorous results on interacting
quantum many-body systems. Finally, we complement our discussions with
numerical results - both in the case of examples and counter-examples of
equilibrating systems.
