The Mpemba effect as a far from equilibrium phenomenon*

The Mpemba effect is the process in which two identical beakers of water, initially at two different temperatures, put in contact with a thermal reservoir at subzero (on the Celsius scale) temperature, evolve in a counter-intuitive manner. While one may expect that the initially cooler sample would freeze first, it has been observed that this is not always the case. In this talk, I will present recent results that show that a Mpemba-like effect appears not only in water but also in some prototypical examples of nonequilibrium systems, namely, granular fluids, Ising model water and spin glasses. Firstly, we will show the Mpemba effect is present in models of granular fluids, both in uniformly heated and in freely cooling systems. Secondly, using the custom built supercomputer Janus II, we were able to find the Mpemba effect in spin glasses and show that it is a non-equilibrium process, governed by the coherence length ξ of the system. The effect occurs when the bath temperature lies in the glassy phase. Finally, we have found a possible origin of the effect in solid and liquid water using well known computational models. The appearance of the Mpemba-like effect in those systems shares some similarities that will be outlined during this presentation.