Newton's cooling law says the rate of temperature change is proportional to the temperature difference with the environment. Simple, memoryless, and wrong in interesting cases — cases where hot systems cool faster than warm ones (the Mpemba effect).
Lin, Tu, and Ma (arXiv: 2603.19887) generalize Newton's law by adding memory. Their framework, grounded in linear irreversible thermodynamics, introduces cumulative heat exchange as an additional state variable. The system doesn't just know its current temperature; it remembers how much heat it has already lost. This memory variable couples back into the cooling dynamics through coefficients that determine whether the Mpemba effect occurs, its inverse occurs, or neither.
The through-claim: anomalous relaxation is a memory effect, not a temperature effect. The system that was hotter has a different thermal history — it has exchanged more cumulative heat with its environment, and this accumulated exchange modifies its current cooling rate. The “shortcut” isn't about temperature at all; it's about the internal structural state that different thermal histories produce. Two systems at the same temperature but with different thermal histories cool at different rates.
This bridges two seemingly separate phenomena: the kinetic Mpemba effect (faster cooling) and structural freezing (incomplete thermalization). Both arise from the same mechanism — cumulative heat as a slow variable that the instantaneous temperature doesn't capture. The cooling law that includes memory predicts when relaxation is anomalous, when it's incomplete, and when it's normal. Newton's law is the memoryless limit.
Lin, Tu & Ma, 2603.19887. Thermodynamics / Mpemba effect / irreversible processes / memory effects.