Energy exchange statistics and fluctuation theorem for nonthermal asymptotic states

Exchange energy statistics between two bodies at different thermal equilibrium obey the Jarzynski W´ ojcik 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 quan tum dynamics leading the quantum system towards a, possibly non-thermal, asymptotic state. To generalize the Jarzynski-W´ ojcik theorem to non-thermal 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 exchange energy 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