Temperature–Time Flow Coupling Model Based on Two-Dimensional Wave Theory: Quantitative Derivation and Self-Consistent Verification of the Mpemba Effect

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 (\(Tₑₙᵥ=253\ K\)). 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 \(Tend\), 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.