Pontus-Mpemba effects

Mpemba effects occur after a sudden quench of control parameters if for ''far'' (or ''hot'') initial states with respect to a final target state, the relaxation time toward the target state is shorter than for ''close'' (or ''cold'') initial states. Following a strategy of fishermen in Pontus described by Aristotle, we introduce the Pontus-Mpemba effect as a two-step protocol which includes the time needed for preparing the system in the ''far'' initial state that can now be an arbitrary nonequilibrium state. Our protocol needs no parameter distance concept and applies to general (classical or quantum) systems. We find that all possible Pontus-Mpemba effects fall into three classes and illustrate the theory for open Markovian two-state quantum systems.