Quantum and Classical Mpemba Effects: From Theoretical Models to Practical Applications

Dear Colleagues,

The Mpemba effect, named after Tanzanian student Erasto Mpemba, refers to the counterintuitive phenomenon where hot water freezes faster than cold water under certain conditions. First documented by Mpemba and Denis Osborne in 1969, this effect traces back to observations made by Aristotle and has sparked debates for centuries. Explanations for the Mpemba effect vary, including evaporation, convection, supercooling, and dissolved gases. Recent studies suggest it arises from nonequilibrium dynamics, where initial conditions influence relaxation rates. Theoretical frameworks like Markovian dynamics and kinetic theory model this effect, showing that systems can exhibit nonmonotonic relaxation times based on their initial states. Models such as the double-well potential for Brownian particles and mean-field spin systems demonstrate the effect, with some predicting a "strong" version where relaxation is exponentially faster. Quantum analogs have also been explored, linking the effect to entanglement and open-system dynamics. Potential applications include optimizing cooling protocols, enhancing heat engine efficiency, and accelerating chemical reactions. Despite progress, the Mpemba effect remains partially understood, with ongoing research aiming to unify its mechanisms and harness its implications for thermodynamics and material science.

Given the significant role of both classical and quantum Mpemba effects in nonequilibrium statistical physics and quantum physics, this Special Issue of Entropy invites contributions exploring various aspects of the Mpemba effect. Topics of interest include, but are not limited to, the following:

• Theoretical models of the Mpemba effect;
• Physical mechanisms underlying the Mpemba effect;
• Manifestations of the Mpemba effect in diverse physical systems;
• Experimental verification of the Mpemba effect;
• Nonequilibrium simulation methods consistent with the laws of thermodynamics and statistical mechanics;
• Mpemba effect and machine learning;
• Practical applications of the Mpemba effect.

The above list is indicative rather than exhaustive. We welcome original theoretical, computational, experimental, and review articles on the Mpemba effect. Studies covering a broad range of systems—such as water, colloidal systems, spin systems, granular gases, spin glasses, polymer systems, quantum systems, and active matter—are particularly encouraged.

We hope this collection will advance our understanding of anomalous relaxation phenomena across classical and quantum domains. We look forward to receiving your contributions.

Dr. Jixuan Hou
Dr. Zhiyue Lu
Guest Editors

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