  We characterize the conditions under which a multi-time quantum process with
a finite temporal resolution can be approximately described by an equilibrium
one. By providing a generalization of the notion of equilibration on average,
where a system remains closed to a fixed equilibrium for most times, to one
which can be operationally assessed at multiple times, we place an upper-bound
on a new observable distinguishability measure comparing a multi-time process
with a finite temporal resolution against a fixed equilibrium one. While the
same conditions on single-time equilibration, such as a large occupation of
energy levels in the initial state remain necessary, we obtain genuine
multi-time contributions depending on the temporal resolution of the process
and the amount of disturbance of the observer's operations on it.
