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. For Markovian (classical or quantum) systems coupled to multiple reservoirs, all possible Pontus-Mpemba effects fall into three classes. The theory is applied to open two-state systems where all three classes can be realized.