  Systems that are driven out of thermal equilibrium typically dissipate random
quantities of energy on microscopic scales. Crooks fluctuation theorem relates
the distribution of these random work costs with the corresponding distribution
for the reverse process. By an analysis that explicitly incorporates the energy
reservoir that donates the energy, and the control system that implements the
dynamic, we here obtain a quantum generalization of Crooks theorem that not
only includes the energy changes in the reservoir, but the full description of
its evolution, including coherences. This approach moreover opens up for
generalizations of the concept of fluctuation relations. Here we introduce
`conditional' fluctuation relations that are applicable to non-equilibrium
systems, as well as approximate fluctuation relations that allow for the
analysis of autonomous evolution generated by global time-independent
Hamiltonians. We furthermore extend these notions to Markovian master
equations, implicitly modeling the influence of the heat bath.
