Conventional physical explanations for the Mpemba effect—the counterintuitive phenomenon that hot water freezes faster than cold water—rely on extrinsic macroscopic factors including evaporation, dissolved gas precipitation, and convection, lacking a unified microscopic kinetic framework. In this work, we construct a complete kinetic model incorporating a modified Newton’s law of cooling and a thermodynamically constrained net phase-transition rate equation, grounded on the core axiom of two-dimensional wave theory: local intrinsic time flow is linearly proportional to local temperature. We rigorously derive closed-form mathematical expressions for the two-stage evolutionary process, consisting of a pure cooling stage and a supercooled phase-transition stage. Numerical validation is performed for 80 °C hot water and 10 °C cold water under standard refrigerator freezer conditions (\ (T ₄₍ₕ=253\ K\) ). The results demonstrate that nonlinear cooling drastically compresses the cooling time ratio of hot water relative to cold water from 4. 0 (predicted by classical linear cooling theory) to 3. 67. Furthermore, structural nonequilibrium residual from rapid high-temperature cooling significantly shifts the supercooling onset threshold \ (T ₄₍₃\), enabling total freezing time reversal along the integral evolution path. Under strict mathematical self-consistency, this model delivers a novel first-principles quantitative interpretation of the Mpemba effect.
Jun Yan (Sun,) studied this question.