Energy exchange statistics and fluctuation theorem for nonthermal asymptotic states

Energy exchange statistics between two bodies at different thermal equilibria obey the Jarzynski-Wójcik fluctuation theorem. The corresponding energy scale factor is the difference of the inverse temperatures associated to the bodies at equilibrium. In this work, we consider a dissipative quantum dynamics leading the quantum system towards a possibly nonthermal, asymptotic state. To generalize the Jarzynski-Wójcik theorem to nonthermal states, we identify a sufficient condition I for the existence of an energy scale factor η^{*} that is unique, finite, and time independent, such that the characteristic function of the energy exchange distribution becomes identically equal to 1 for any time. This η^{*} plays the role of the difference of inverse temperatures. We discuss the physical interpretation of the condition I, showing that it amounts to an almost complete memory loss of the initial state. The robustness of our results against quantifiable deviations from the validity of I is evaluated by experimental studies on a single nitrogen-vacancy center subjected to a sequence of laser pulses and dissipation.