The Mpemba Effect in Pure Water Has a Stochastic Origin. Experimental and Theoretical Resolution of the Paradox

Abstract

The "Mpemba effect" is the name given to the assertion that hot water freezes quicker than cold water1 or, in a modern and more general form, that the system that is initially more distant from its equilibrium state comes to this state earlier2. This counterintuitive statement seems to breach fundamental thermodynamic and kinetic laws; however, numerous experiments3-10 with classical and quantum systems demonstrate this paradoxical Mpemba effect, leading to extensive discssions in prominent scientific jornals2,5,9,12-14. However, the fundamental physical mechanisms behind this effect have remained elusive14. Here we performed the water freezing experiments under carefully controlled conditions, and found that the Mpemba effect only occurred when the freezer temperature was very close to the temperature of ice nucleation. In this case, the range of freezing times for both hot and cold water was so great that it exceeded the delayed cooling of the initially hotter liquid, and therefore sometimes the hot water froze before the cold water. Our theoretical analysis of this fact shows that the Mpemba paradox associated with water freezing is rooted in the stochastic nature of ice nucleation, typical of first-order phase transitions. We anticipate our assay to be a starting point for reconsidering the famous Mpemba paradox in water and other systems undergoing similar phase transitions.