  We consider closed quantum systems (into which baths may be integrated) that
are driven, i.e., subject to time-dependent Hamiltonians. As a starting point
we assume that, for systems initialized in microcanonical states at some
energies, the resulting probability densities of work (work-PDFs) are largely
independent of these specific initial energies. We show analytically that this
assumption of "stiffness", together with the assumption of an exponentially
growing density of energy eigenstates, is sufficient but not necessary for the
validity of the Jarzynski relation (JR) for the above microcanonical initial
states. This holds, even in the absence of microreversibility. To scrutinize
the connection between stiffness and the JR for microcanonical initial states,
we perform numerical analysis on systems comprising random matrices which may
be tuned from stiff to nonstiff. In these examples we find the JR fulfilled in
the presence of stiffness, and violated in its absence, which indicates a very
close connection between stiffness and the JR. Remarkably, in the limit of
large systems, we find the JR fulfilled, even for pure initial energy
eigenstates. As this has no analogue in classical systems, we consider it a
genuine quantum phenomenon.
