  We study the quantum Jarzynski relation for driven quantum models embedded in
various environments. We do so by generalizing a proof presented by Mukamel
[Phys. Rev. Lett 90, 170604 (2003)] for closed quantum systems. In this way, we
are able to prove that the Jarzynski relation also holds for a bipartite system
with microcanonical coupling. Furthermore, we show that, under the assumption
that the interaction energy remains constant during the whole process, the
relation is valid even for canonical coupling. The same follows for open
quantum systems at high initial temperatures up to third order of the inverse
temperature. Our analytical study is complemented by a numerical investigation
of a special model system.
