The Markovian Mpemba effect

Under certain conditions it takes a shorter time to cool a hot system than to cool the same system initiated at a lower temperature This phenomenon the Mpemba effect was first observed in water and has recently been reported in other systems Whereas several detail dependent explanations were suggested for some of these observations no common underlying mechanism is known We present two widely applicable mechanism for similar effects the Markovian Mpemba effect derive the sufficient conditions for their appearance and demonstrate them explicitly in the anti ferromagnet Ising model Interestingly the Markovian Mpemba effect can be classified as weak or strong and as direct or inverse In the Ising model we show that the strong direct and inverse effect exists even in the thermodynamic limit