  Numerous works have shown that under mild assumptions unitary dynamics
inevitably leads to equilibration of physical expectation values if many energy
eigenstates contribute to the initial state. Here, we consider systems driven
by arbitrary time-dependent Hamiltonians as a protocol to prepare systems that
do not equilibrate. We introduce a measure of the resilience against
equilibration of such states and show, under natural assumptions, that in order
to increase the resilience against equilibration of a given system, one needs
to possess a resource system which itself has a large resilience. In this way,
we establish a new link between the theory of equilibration and resource
theories by quantifying the resilience against equilibration and the resources
that are needed to produce it. We connect these findings with insights into
local quantum quenches and investigate the (im-)possibility of formulating a
second law of equilibration, by studying how resilience can be either only
redistributed among subsystems, if these remain completely uncorrelated, or in
turn created in a catalytic process if subsystems are allowed to build up some
correlations.
