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

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Quantum Information".

Deadline for manuscript submissions: 20 September 2026 | Viewed by 2709

Special Issue Editors

Dr. Jixuan Hou

E-Mail Website
Guest Editor
School of Physics, Southeast University, Nanjing 211189, China
Interests: equilibrium statistical physics; nonequilibrium statistical physics; thermodynamics of long-range interacting systems; polymer physics; dynamics of polymer liquids; polymer rheology
Dr. Zhiyue Lu

E-Mail Website
Guest Editor
Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3290, USA
Interests: nonequilibrium thermodynamics; theoretical and computational statistical mechanics; molecular machines; chemical physics of living systems

Special Issue Information

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

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Mpemba effect
  • nonequilibrium dynamics
  • anomalous relaxation
  • cooling protocols
  • quantum Mpemba effect
  • quantum thermal quench
  • Markovian dynamics
  • strong Mpemba effect
  • open quantum systems
  • non-equilibrium quantum dynamics
  • non-Markovian quantum dynamics

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Published Papers (3 papers)

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19 pages, 1002 KB  
Article
Giant Mpemba Effect via Weak Interactions in Open Quantum Systems
by Stefano Longhi
Entropy 2026, 28(4), 427; https://doi.org/10.3390/e28040427 - 10 Apr 2026
Viewed by 380
Abstract
The Mpemba effect refers to the counterintuitive situation in which a system initially farther from equilibrium can relax faster than one that starts closer to it. In quantum systems, the effect is enriched by the presence of coherent dynamics, dissipation, and metastable manifolds [...] Read more.
The Mpemba effect refers to the counterintuitive situation in which a system initially farther from equilibrium can relax faster than one that starts closer to it. In quantum systems, the effect is enriched by the presence of coherent dynamics, dissipation, and metastable manifolds associated with long-lived Liouvillian modes. Here we demonstrate a giant Mpemba effect in open quantum systems, where relaxation can be either hyper-accelerated or dramatically slowed depending on the initial state. We focus on weakly-coupled particle-conserving bosonic networks, each of which independently relaxes rapidly to a unique stationary state. When a weak coherent interaction is introduced, the composite system typically develops slow metastable modes and a hierarchy of relaxation timescales. We show that by tailoring the interaction Hamiltonian, these slow modes can be effectively suppressed for a broad class of initial states satisfying a minimal global requirement, enabling ultrafast relaxation even when the system starts far from equilibrium. Conversely, other initial states—sometimes arbitrarily close to the stationary state—may remain trapped in the metastable manifold and decay anomalously slowly. This mechanism provides a general route to engineer giant Mpemba effects, offering new possibilities for controlling dissipative dynamics, accelerating state preparation, and manipulating relaxation processes in complex quantum devices. Full article
(This article belongs to the Special Issue Quantum and Classical Mpemba Effects: From Theoretical Models to Practical Applications)
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17 pages, 1950 KB  
Article
Stark Many-Body Localization-Induced Quantum Mpemba Effect
by Yi-Rui Zhang, Han-Ze Li, Xu-Yang Huang, Yu-Jun Zhao and Jian-Xin Zhong
Entropy 2026, 28(3), 348; https://doi.org/10.3390/e28030348 - 19 Mar 2026
Viewed by 525
Abstract
The quantum Mpemba effect (QME) describes the counterintuitive phenomenon where a system initially further from equilibrium relaxes faster than one closer to it. Specifically, the QME associated with symmetry restoration has been extensively investigated across integrable, ergodic, and disordered localized systems. However, its [...] Read more.
The quantum Mpemba effect (QME) describes the counterintuitive phenomenon where a system initially further from equilibrium relaxes faster than one closer to it. Specifically, the QME associated with symmetry restoration has been extensively investigated across integrable, ergodic, and disordered localized systems. However, its fate in disorder-free ergodicity-breaking settings, such as the Stark many-body localized (Stark-MBL) phase, remains an open question. Here, we explore the dynamics of local U(1) symmetry restoration in a Stark-MBL XXZ spin-12 chain, using the Rényi-2 entanglement asymmetry (EA) as a probe. Using an analytical operator-string expansion supported by numerical simulations, we demonstrate that the QME transitions from an initial-state-dependent anomaly in the ergodic phase to a universal feature in the Stark-MBL regime. Moreover, the Mpemba time scales exponentially with the subsystem size, even in the absence of global transport, and is governed by high-order off-resonant processes. We attribute this robust inversion to a Stark-induced hierarchy of relaxation channels that fundamentally constrains the effective Hilbert space dimension. The findings pave the way for utilizing tunable potentials to engineer and control anomalous relaxation timescales in quantum technologies without reliance on quenched disorder. Full article
(This article belongs to the Special Issue Quantum and Classical Mpemba Effects: From Theoretical Models to Practical Applications)
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11 pages, 1126 KB  
Article
A Minimal Mechanism for the Phase Transition-Driven Mpemba Effect in Systems with a Single Order Parameter
by Li Li and Ji-Xuan Hou
Entropy 2026, 28(1), 100; https://doi.org/10.3390/e28010100 - 14 Jan 2026
Cited by 1 | Viewed by 930
Abstract
The Mpemba effect, where a hotter system can enter a cold phase faster than a cooler one, remains a counterintuitive phenomenon whose origins are still being unraveled. In this work, we propose and demonstrate a simple and general mechanism for the genuine, phase [...] Read more.
The Mpemba effect, where a hotter system can enter a cold phase faster than a cooler one, remains a counterintuitive phenomenon whose origins are still being unraveled. In this work, we propose and demonstrate a simple and general mechanism for the genuine, phase transition-driven Mpemba effect. Our mechanism requires only a single order parameter to describe the system’s state and operates within a standard Markovian framework, distinguishing it from previous models that necessitate multiple order parameters or non-Markovian dynamics. The core of the effect lies in the distinct relaxation pathways following a sudden quench: a system prepared at a higher initial temperature may be projected onto a region of the final free-energy landscape that requires it to cross fewer energy barriers to reach the stable low-temperature phase, whereas a system prepared at an intermediate temperature may be trapped in a metastable state, requiring the crossing of multiple barriers. We concretely illustrate this mechanism using the extended spin-1 Nagle–Kardar model, where an appropriate choice of parameters yields the requisite free-energy topography. Through extensive Monte Carlo simulations, we confirm that the initially hot system consistently reaches the final ferromagnetic phase in less time than its initially warm counterpart, thereby exhibiting a robust Mpemba effect. Our findings provide a minimal and clear explanation for how the initial state’s position in order parameter space can dictate the kinetics of a first-order phase transition, leading to this anomalous acceleration of cooling. Full article
(This article belongs to the Special Issue Quantum and Classical Mpemba Effects: From Theoretical Models to Practical Applications)
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