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

TL;DR

This paper explores the microscopic origins of the Mpemba effect using quantum resource theories, highlighting the roles of correlations, memory effects, and system parameters in enabling or modulating the phenomenon.

Contribution

It introduces correlations as a new mechanism within a unified resource theory framework and analyzes their impact on the Mpemba effect's occurrence.

Findings

Classical correlations can support the Mpemba effect.

Quantum correlations are relevant only under specific conditions.

Correlations are necessary but not sufficient for the effect.

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.