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.
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.
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 (ME)—where hot systems cool faster than colder ones—has intrigued both classical and quantum thermodynamics. Compared to classical systems, quantum systems add complexity due to quantum correlations. Recent works have explored anomalous relaxation and Mpemba-like effects in several quantum systems, considering isolated systems at zero temperature or open systems in contact with reservoirs under Markovian or non-Markovian dynamics. However, these models typically assume an initial unentangled system–bath state, overlooking the role of initial system–environment correlations. Here we propose a type of quantum ME, distinct from the strong ME, originating solely from initial system–bath entanglement. It is shown that the degree of initial entanglement significantly influences the early relaxation dynamics, with certain conditions causing backflow and retarded thermalization. As an example, we investigate the spontaneous emission of a two-level atom in a photonic waveguide at zero temperature, where an initial atom-photon entangled state results in delayed relaxation and a pronounced ME. These findings highlight the crucial role of quantum correlations in thermalization processes and open new avenues for identifying and engineering quantum Mpemba phenomena. Controlling relaxation dynamics through system–environment entanglement may have potential applications in quantum thermal machines, state initialization protocols, and quantum information processing, where precise control over thermalization is essential.
The counterintuitive Mpemba effect, wherein a hotter system cools faster, critically lacks a general macroscopic theory. Here, starting from linear irreversible thermodynamics, we formulate a generalized Newton's cooling law, dT/dt=−[γ0+MQ(t)](T−Tr), for a system at temperature T relaxing in a thermal reservoir at Tr, where the bare relaxation rate γ0 is modified by an initial-state memory term, Q(t)∝T(0)−Tr. Arising from the interplay between heat flux and structural evolution, the coefficient M governs anomalous relaxation behaviors, where M>0 (M<0) induces the (inverse) Mpemba effect. This universal thermodynamic framework maps out phase diagram to provide general criteria for the Mpemba effect in complex systems, offering a macroscopic picture that bridges disparate microscopic approaches.
Quantum thermometry provides a key capability for nanoscale devices and quantum technologies, but most existing strategies rely on probes initialized near equilibrium. This equilibrium paradigm imposes intrinsic limitations: sensitivity is tied to long-time thermalization and often cannot be improved in fast, noisy, or nonstationary settings. In contrast, the \textit{Mpemba effect}, the counterintuitive phenomenon where hotter states relax faster than colder ones, has mostly been viewed as a thermodynamic anomaly. Here, we bridge this gap by proving that Mpemba-type inversions generically yield a finite-time enhancement of the quantum Fisher information (QFI) for temperature estimation, thereby converting an anomalous relaxation effect into a concrete metrological resource. Through explicit analyses of two-level and Λ-level probes coupled to bosonic baths, we show that nonequilibrium initializations can transiently outperform both equilibrium strategies and colder states, realizing a \emph{metrological Mpemba effect}. Our results establish anomalous relaxation as a general design principle for nonequilibrium quantum thermometry, enabling ultrafast and nanoscale sensing protocols that exploit, rather than avoid, transient dynamics.
The Mpemba effect originally referred to the observation that, under certain thermalizing dynamics, initially hotter samples can cool faster than colder ones. This effect has since been generalized to other anomalous relaxation behaviors even beyond classical domains, such as symmetry restoration in quantum systems. This work demonstrates that resource theories, widely employed in information theory, provide a unified organizing principle to frame Mpemba physics. We show how the conventional thermal Mpemba effect arises naturally from the resource theory of athermality, while its symmetry-restoring counterpart is fully captured by the resource theories of asymmetry. Leveraging the framework of modes of asymmetry, we demonstrate that the Mpemba effect due to symmetry restoration is governed by the initial overlap with the slowest symmetry-restoring mode, mirroring the role of the slowest Liouvillian eigenmode in thermal Mpemba dynamics. Through this resource-theoretical formalism, we uncover the connection between these seemingly disparate effects and show that the dynamics of thermalization naturally splits into a symmetry-respecting and a symmetry-breaking term.
In classical settings, the Mpemba effect occurs when a hotter system cools faster than an initially colder one. In quantum systems, this effect can be reinterpreted exploiting the concept of symmetries, with the asymmetry of a subsystem playing the role of temperature. A quantum Mpemba effect arises when a more asymmetric state restores the symmetry faster than a less asymmetric one. Previous work mainly focuses on closed systems characterized by thermal equilibration and Hamiltonian symmetries. In this paper, we analyze the dynamics of asymmetry in an open quantum many-body system featuring symmetry breaking and uncover dynamical behavior that appears to be unique to these settings. In the symmetric phase, we demonstrate the existence of a quantum Mpemba effect, which emerges as a direct consequence of a non-monotonic evolution of the asymmetry. In the broken-symmetry phase, we analyze the imbalance between the system's ability to increase or to decrease its asymmetry. Our results extend the notion of quantum Mpemba effects to open quantum many-body systems exhibiting symmetry-breaking phase transitions and establish them as a platform for observing and controlling anomalous relaxation phenomena.