Mpemba effects in nonequilibrium open quantum systems

The Mpemba effect was originally referred to as the faster icing of a higher-temperature system than a lower-temperature system, and was later generalized to anomalous decays of both classical and quantum observables to equilibrium states. Mpemba effect is mostly considered in classical systems and during cooling processes towards equilibrium states. We investigate the emergence of the effect in nonequilibrium quantum systems where the system has no asymptotic equilibrium state to approach. Instead, the system is put in contact with two different baths, and only a nonequilibrium state exists, sustained by constant energy injection from the surrounding thermal baths. Firstly, we show that the nonequilibrium conditions can dramatically enlarge the parameter regimes where the MPE emerges. Secondly, we demonstrate that the anomalous MPEs and inverse MPEs emerge in the evolution of quantum correlations in the two-site fermionic system and that nonequilibrium conditions can expedite or delay the MPEs. Thirdly, we show that the nonequilibrium-induced quantum coherence can have considerable contributions to the emergence of the MPE which the conventional Lindbladian dynamics fails to capture.