Energy exchange statistics and fluctuation theorem for non-thermal asymptotic states

Abstract

Exchange energy statistics between two bodies at different thermal equilibrium 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 non-thermal, asymptotic state. To generalize the Jarzynski-Wójcik theorem to non-thermal states, we identify a sufficient condition $\mathcal{I}$ for the existence of an energy scale factor ${\eta }^{\ast }$ 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 ${\eta }^{\ast }$ plays the role of the difference of inverse temperatures. We discuss the physical interpretation of the condition $\mathcal{I}$, 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 $\mathcal{I}$ is evaluated by experimental studies on a single nitrogen-vacancy center subjected to a sequence of laser pulses and dissipation.

14 pages, 4 figures. Comments and feedback are welcome

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