Thermodynamic limits of the Mpemba effect: A unified resource theory analysis of correlation-enabled mechanisms

Abstract

The Mpemba effect, in which a hotter system cools faster than a colder one, remains one of the most intriguing anomalies in thermodynamics. Here, we investigate its microscopic origin within the framework of quantum resource theories and introduce correlations as a new enabling mechanism: classical correlations can support the effect, whereas quantum correlations become relevant only under specific energy-degeneracy conditions. Importantly, correlations are necessary but not sufficient. Whether they induce the effect depends on their distribution across subsystems and on system parameters. Other resources, such as non-Markovian memory effects and Hilbert space dimensionality, primarily modulate the temperature window in which the effect can occur. Finally, by analyzing both didactic multi-qubit instances and a phenomenological single-molecule model of water, we demonstrate that the insufficiency of correlations helps explain the sporadic and sometimes contradictory observations of the Mpemba effect in experiments.