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Originally, the Mpemba effect (MPE) is referred to the faster icing of ahigher-temperature system than a system of a lower temperature. This conceptwas later generalized to anomalous decays of certain system quantities to theequilibrium states. In this study, we investigate the scenario when a systemhas no such equilibrium state to approach. Instead, the system is put incontact 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 enlargethe parameter regimes where the MPE emerges. Secondly, we demonstrate that theanomalous MPEs and inverse MPEs emerge in the evolution of quantum correlationsin the two-site fermionic system and that nonequilibrium conditions canexpedite or delay the MPEs. Thirdly, we show that the nonequilibrium-inducedquantum coherence can have considerable contributions to the emergence of theMPE which the conventional Lindbladian dynamics fails to capture.

Mpemba effects in nonequilibrium open quantum systems