Quantum extension of the Jarzynski relation: Analogy with stochastic dephasing

The relation between the distribution of work performed on a classical system by an external force switched on an arbitrary time scale 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 line shapes, described by the stochastic Liouville equation.