The Mpemba Effect in Small Water Clusters A Toy Model of Kinetic Facilitation via Hydrogen-Bond Rearrangement

This preprint presents a minimal toy model exploring a possible kinetic pathway for the Mpemba effect — the counterintuitive phenomenon where hotter water can freeze faster than colder water under certain conditions. Focusing on small water clusters (~20 molecules), the model couples Newtonian cooling to a thermally activated hydrogen-bond rearrangement rate, augmented with autocatalytic feedback to capture seeding and self-reinforcing crystallization. Results show the effect emerging robustly when rearrangement barriers exhibit sufficient cooperativity and system size is small, with early kinetic facilitation in the hot system triggering rapid growth. Parameter sweeps reveal the effect’s sensitivity to activation energy and cluster size; stochastic trials highlight realistic probabilistic behavior. The work offers a pedagogical illustration of how water’s anomalous hydrogen-bonding network may contribute to this long-standing mystery, particularly in confined or small-volume regimes.