The relation between the distribution of work performed on a classical system
by an external force switched on an arbitrary timescale, and the corresponding
equilibrium free energy difference, is generalized to quantum systems. Using
the adiabatic representation we show that this relation holds for isolated
systems as well as for systems coupled to a bath described by a master
equation. A close formal analogy is established between the present classical
trajectory picture over populations of adiabatic states and phase fluctuations
(dephasing) of a quantum coherence in spectral lineshapes, described by the
stochastic Liouville equation.