Anomalous cooling and heating -- the Mpemba effect and its inverse

Under certain conditions, it takes a shorter time to cool a hot object than to cool the same object initiated at a lower temperature. This counter-intuitive phenomenon -- the “Mpemba Effect”, has been observed in a variety of systems. So far, no generic mechanism was suggested to explain this effect. In the theoretical framework of non-equilibrium thermodynamics, we construct a model to describe this effect and illustrates the fundamental principles behind it. In addition, we predict and demonstrate an inverse Mpemba effect: it can take a shorter time to heat a cold object than a warmer one. We derive sufficient conditions for the occurrences of both the forward and the inverse Mpemba effects, and suggest experiments to further study the non-equilibrium nature of these effects.