  Originally, the Mpemba effect (MPE) is referred to the faster icing of a
higher-temperature system than a system of a lower temperature. This concept
was later generalized to anomalous decays of certain system quantities to the
equilibrium states. In this study, we investigate the scenario when a system
has no such 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.
