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arXiv:2401.14259 · Physical Review Research

Mpemba effects in nonequilibrium open quantum systems

Xuanhua Wang, Jin Wang

Published Sep 24, 2024• 55 citations
arXivHTMLPDF

Abstract

The Mpemba effect was originally referred to as the faster icing of a higher-temperature system than a lower-temperature system, and was later generalized to anomalous decays of both classical and quantum observables to equilibrium states. Mpemba effect is mostly considered in classical systems and during cooling processes toward equilibrium states. We investigate the emergence of the effect in nonequilibrium quantum systems where the system has no asymptotic equilibrium state to approach. Instead, the system is put in contact with two different baths, and only a nonequilibrium state exists, sustained by constant energy injection from the surrounding thermal baths. First, we show that the nonequilibrium conditions can dramatically enlarge the parameter regimes where the MPE emerges. Second, we demonstrate that the anomalous MPEs and inverse MPEs emerge in the evolution of quantum correlations in the two-site fermionic system and that nonequilibrium conditions can expedite or delay the MPEs. Third, we show that the nonequilibrium-induced quantum coherence can have considerable contributions to the emergence of the MPE which the conventional Lindbladian dynamics fails to capture. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.033330

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The Mpemba effect was originally referred to as the faster icing of a higher-temperature system than a lower-temperature system, and was later generalized to anomalous decays of both classical and quantum observables to equilibrium states. Mpemba effect is mostly considered in classical systems and during cooling processes toward equilibrium states. We investigate the emergence of the effect in nonequilibrium quantum systems where the system has no asymptotic equilibrium state to approach. Instead, the system is put in contact with two different baths, and only a nonequilibrium state exists, sustained by constant energy injection from the surrounding thermal baths. First, we show that the nonequilibrium conditions can dramatically enlarge the parameter regimes where the MPE emerges. Second, we demonstrate that the anomalous MPEs and inverse MPEs emerge in the evolution of quantum correlations in the two-site fermionic system and that nonequilibrium conditions can expedite or delay the MPEs. Third, we show that the nonequilibrium-induced quantum coherence can have considerable contributions to the emergence of the MPE which the conventional Lindbladian dynamics fails to capture. Published by the American Physical Society 2024
The Mpemba effect (MpE), where a far-from-equilibrium state of a system relaxes faster compared to a state closer to it, is a well-known counterintuitive phenomenon in classical and quantum systems. Various system-specific theories have been proposed to explain this anomalous behavior in driven systems, though the fundamental mechanism of MpE in undriven systems, where MpE was first observed, remains unresolved. This paper provides a generic model of MpE for a quantum spin-1/21/21/2 system following Markovian relaxation dynamics, regardless of system structure or environment. The key lies in the overlap of initial states with the fast relaxation mode; here, the constituents create a fast decay mode via interaction through the shared environment to show MpE, indicating that MpE happens due to the collective behavior of the system. I also show that a system with anisotropic relaxation naturally exhibits MpE, even without a shared environment among the particles.
In recent years, the quantum Mpemba effect (QME) which occurs when an out-of-equilibrium system reaches equilibrium faster than another that is closer to equilibrium has attracted significant attention from the scientific community as an intriguing and counterintuitive phenomenon. It generalizes its classical counterpart, extending the concept beyond thermal equilibration. This paper approaches the QME for Markovian open quantum systems from different perspectives. Firstly, we propose a physical mechanism based on decoherence-free subspaces. Secondly, we show that a macroscopic enhancement of the decay rate that scales linearly with system size can be obtained, leading to an extreme version of the phenomenon on Markovian open quantum systems. Thirdly, we study the Mpemba effect through the unravelings of Davies maps, revealing subtleties in the figures of merit which are chosen for obtaining the QME. Lastly, we propose a microscopic model for a better understanding of thermal bath dynamics in this context.
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.
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.
We generalize the classical thermal Mpemba effect (where an initially hot system relaxes faster to the final equilibrium state than a cold one) to open quantum systems coupled to several reservoirs. We show that, in general, two different types of quantum Mpemba effects are possible. They may be distinguished by quantum state tomography. However, the existence of a quantum Mpemba effect (without determining the type) can already be established by measuring simpler observables such as currents or energies. We illustrate our general results for the experimentally feasible case of an interacting two-site Kitaev model coupled to two metallic leads.
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 ΛΛΛ-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.