The Mpemba effect is a thermodynamic anomaly in which a system farther away in temperature from equilibrium thermalizes before one that is initially closer. The effect has been experimentally observed across a wide range of systems, including water, colloids, and trapped ions. It has recently been the focus of numerous studies aimed at understanding its mechanisms and developing multiple applications. Despite extensive work in the field, clearly determining which types of systems exhibit the Mpemba effect remains an open question. To address this, we derive simple necessary conditions on the transition rates for the Mpemba effect in a Markovian 3-level system and show that they can be applied to study the Mpemba effect in an N-level system. Multiple time scales govern thermalization in these systems. This allows the evolution to occur more quickly across larger temperature differences, explaining the Mpemba effect. We apply our protocol to evaluate which types of systems exhibit the Mpemba effect and, in doing so, explain why the Mpemba effect in Markovian systems remains a thermodynamic anomaly. In particular, due to the maximum entropy principle, our conditions allow us to discard the sub-Ohmic and Ohmic spectra. The latter describes a wide range of physical and chemical phenomena, which will not exhibit the Mpemba effect. Moreover, our results provide a clear path to determine the minimal physical requirements for the Mpemba effect, and we apply them to understand its underlying mechanisms better. Finally, our protocol could help identify relevant parameters for experiments, numerical simulations and diverse applications.The Mpemba effect is a thermodynamic anomaly in which a system farther away in temperature from equilibrium thermalizes before one that is initially closer. The effect has been experimentally observed across a wide range of systems, including water, colloids, and trapped ions. It has recently been the focus of numerous studies aimed at understanding its mechanisms and developing multiple applications. Despite extensive work in the field, clearly determining which types of systems exhibit the Mpemba effect remains an open question. To address this, we derive simple necessary conditions on the transition rates for the Mpemba effect in a Markovian 3-level system and show that they can be applied to study the Mpemba effect in an N-level system. Multiple time scales govern thermalization in these systems. This allows the evolution to occur more quickly across larger temperature differences, explaining the Mpemba effect. We apply our protocol to evaluate which types of systems exhibit the Mpemba effect and, in doing so, explain why the Mpemba effect in Markovian systems remains a thermodynamic anomaly. In particular, due to the maximum entropy principle, our conditions allow us to discard the sub-Ohmic and Ohmic spectra. The latter describes a wide range of physical and chemical phenomena, which will not exhibit the Mpemba effect. Moreover, our results provide a clear path to determine the minimal physical requirements for the Mpemba effect, and we apply them to understand its underlying mechanisms better. Finally, our protocol could help identify relevant parameters for experiments, numerical simulations and diverse applications.

cond-mat.stat-mechCross-listedarXiv:2603.04567Mar 6, 2026

Quantum tunneling Mpemba effect

Hisao Hayakawa, Satoshi Takada

Jan 1, 20260 citations

Role of electron–electron interaction in the Mpemba effect in quantum dots

Juliane Graf, Janine Splettstoesser, Juliette Monsel

The Mpemba effect has initially been noticed in macroscopic systems-namely that hot water can freeze faster than cold water-but recently its extension to open quantum systems has attracted significant attention. This phenomenon can be explained in the context of nonequilibrium thermodynamics of Markovian systems, relying on the amplitudes of different decay modes of the system dynamics. Here, we study the Mpemba effect in a single-level quantum dot coupled to a thermal bath, highlighting the role of the sign and magnitude of the electron-electron interaction in the occurrence of the Mpemba effect. We gain physical insights into the decay modes from a dissipative symmetry of this system called fermionic duality. Based on this analysis of the relaxation to equilibrium of the dot, we derive criteria for the occurrence of the Mpemba effect using two thermodynamically relevant measures of the distance to equilibrium, the nonequilibrium free energy and the dot energy. We furthermore compare this effect to a possible exponential speedup of the relaxation. Finally, we propose experimentally relevant schemes for the state preparation and explore different ways of observing the Mpemba effect in quantum dots in experiments.The Mpemba effect has initially been noticed in macroscopic systems-namely that hot water can freeze faster than cold water-but recently its extension to open quantum systems has attracted significant attention. This phenomenon can be explained in the context of nonequilibrium thermodynamics of Markovian systems, relying on the amplitudes of different decay modes of the system dynamics. Here, we study the Mpemba effect in a single-level quantum dot coupled to a thermal bath, highlighting the role of the sign and magnitude of the electron-electron interaction in the occurrence of the Mpemba effect. We gain physical insights into the decay modes from a dissipative symmetry of this system called fermionic duality. Based on this analysis of the relaxation to equilibrium of the dot, we derive criteria for the occurrence of the Mpemba effect using two thermodynamically relevant measures of the distance to equilibrium, the nonequilibrium free energy and the dot energy. We furthermore compare this effect to a possible exponential speedup of the relaxation. Finally, we propose experimentally relevant schemes for the state preparation and explore different ways of observing the Mpemba effect in quantum dots in experiments.

arXiv:2412.18456Journal of Physics Condensed MatterMar 21, 20259 citations

Efficient protocol for the Markovian Mpemba effect in $N$ -level systemsEfficient protocol for the Markovian Mpemba effect in $N$-level systems

David Gelbwaser-Klimovsky

The Mpemba effect is an anomalous phenomenon in which the time to thermalize does not depend monotonically on the distance from equilibrium, allowing systems with an initially larger temperature difference to thermalize before those with a smaller one. The rarity of the effect makes it hard to find parameters that produce it, complicating the design of experiments and the development of applications. Here, we find necessary and sufficient conditions for the Markovian Mpemba effect in three-level systems and explain its underlying physical mechanisms. Based on our understanding of the three-level case, we develop an efficient algorithm to determine the parameters for the effect in $N$ -level systems. This protocol could open the door for the realization of Mpemba experiments and related applications in large systems.The Mpemba effect is an anomalous phenomenon in which the time to thermalize does not depend monotonically on the distance from equilibrium, allowing systems with an initially larger temperature difference to thermalize before those with a smaller one. The rarity of the effect makes it hard to find parameters that produce it, complicating the design of experiments and the development of applications. Here, we find necessary and sufficient conditions for the Markovian Mpemba effect in three-level systems and explain its underlying physical mechanisms. Based on our understanding of the three-level case, we develop an efficient algorithm to determine the parameters for the effect in $N$-level systems. This protocol could open the door for the realization of Mpemba experiments and related applications in large systems.

arXiv:2609.09988Sep 9, 20260 citations

Efficient protocol for the Markovian Mpemba effect in

N

-level systems

N

-level systems. This protocol could open the door for the realization of Mpemba experiments and related applications in large systems.