Mpemba Possibility Region

Abstract

Uppdate: The Mpemba effect refers to the counterintuitive observation that, under certain conditions, an initially hotter water sample may freeze earlier than a colder comparison sample. Although the phenomenon has commonly been discussed in terms of evaporation, convection, dissolved gases, supercooling, and experimental geometry, freezing cannot be reduced to bulk cooling alone. Ice formation is an activated and path-dependent transition whose timing may depend strongly on the evolving state of the free surface, the three-phase contact line, wetting conditions, and the history-dependent nucleation barrier. The present study extends the previously published phenomenological framework of interfacial ordering and barrier-controlled nucleation (Schaefer, 2026; DOI: 10.5281/zenodo.19916801). Whereas the earlier formulation described a representative trajectory through interfacial state space, the present work treats unresolved kinetic and constitutive quantities as bounded admissible sets rather than as uniquely determined parameters. Interfacial order, effective nucleation barriers, nucleation hazards, and freezing times are therefore represented by intervals and trajectory corridors. Within this set-valued formulation, Mpemba-type freezing is classified as excluded, possible, or robust, depending on whether the admissible freezing-time regions of the hotter and colder samples remain separated or overlap. The framework does not claim a final microscopic proof of a unique mechanism or an exact prediction for every experimental realization. Its contribution is to formulate a physically constrained and empirically testable possibility region within which the hotter sample’s reduction in nucleation delay can, under specified boundary conditions, exceed its additional bulk-cooling delay.