  Since it's rediscovery in the twentieth century, the Mpemba effect, where a
far-from-equilibrium state may relax faster than a state closer to equilibrium,
has been extensively studied in classical systems and has recently received
significant attention in quantum systems. Many theories explaining this
counter-intuitive behavior in classical systems rely on memory effects.
However, in quantum systems, the relation between the Mpemba effect and memory
has remained unexplored. In this work, we consider a general non-Markovian open
quantum setting and reveal new classes of quantum Mpemba effects, with no
analog in Markovian quantum dynamics. Generically, open quantum dynamics
possess a finite memory time and a unique steady state. Due to non-Markovian
dynamics, even if the system is initialized in the steady state it can take a
long time to relax back. We find other initial states that reach the steady
state much faster. Most notably, we demonstrate that there can be an initial
state in which the system reaches the steady state within the finite memory
time itself, therefore giving the fastest possible relaxation to stationarity.
We verify the effect for quantum dot systems coupled to electronic reservoirs
in equilibrium and non-equilibrium setups at weak, intermediate and strong
coupling, and both with and without interactions. Our work provides new
insights into the rich physics underlying accelerated relaxation in quantum
systems.
