  A hot Markovian system can cool down faster than a colder one: this is known
as the Mpemba effect. Here, we show that a non-equilibrium driving via
stochastic reset can induce this phenomenon, when absent. Moreover, we derive
an optimal driving protocol simultaneously optimizing the appearance time of
the Mpemba effect, and the total energy dissipation into the environment,
revealing the existence of a Pareto front. Building upon previous experimental
results, our findings open up the avenue of possible experimental realizations
of optimal cooling protocols in Markovian systems.
