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arXiv:2610.21608

Driving the cooling process of a quantum system via classical noise

B. Militello, A. Napoli

quant-phSubmitted Oct 15, 2026• Announced Oct 16, 2026• 0 citations
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Abstract

It is known that under particular hypotheses anomalous thermalization processes can occur, such as the Mpemba effect, consisting in a faster cooling down when the system is prepared in a hotter initial condition, thus making convenient to warm up the system before the freezing process in order to make it freeze in a shorter time. It is shown here that the action of a Markovian classical noise during the freezing process can accelerate the approach to the zero-temperature thermal state. This prediction is counterintuitive, especially after observing that a classical noise can be considered equivalent to the action of an infinite-temperature reservoir, since both drive the system toward the same state. These facts lead to the statement that warming up the system during the contact with a low-temperature reservoir can accelerate the cooling process.

Comments
6 pages, 3 figures

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It is known that under particular hypotheses anomalous thermalization processes can occur, such as the Mpemba effect, consisting in a faster cooling down when the system is prepared in a hotter initial condition, thus making convenient to warm up the system before the freezing process in order to make it freeze in a shorter time. It is shown here that the action of a Markovian classical noise during the freezing process can accelerate the approach to the zero-temperature thermal state. This prediction is counterintuitive, especially after observing that a classical noise can be considered equivalent to the action of an infinite-temperature reservoir, since both drive the system toward the same state. These facts lead to the statement that warming up the system during the contact with a low-temperature reservoir can accelerate the cooling process.
We study the thermalization dynamics of a quantum system embedded in an incommensurate potential and coupled to a Markovian thermal reservoir. The dephasing induced by the bath drives the system toward an infinite-temperature steady state, erasing all initial information-including signatures of localization. We find that initially localized states can relax to the homogeneous steady state faster than delocalized states. Moreover, low-temperature initial states thermalize to infinite temperature more rapidly than high-temperature states---a phenomenon reminiscent of the Mpemba effect, in which hotter liquids freeze faster than colder ones. The slowest relaxation mode in the Liouvillian spectrum plays a critical role in the expedited thermalization for localized or cold initial states. Our results reveal that the combination of disordered structure and environmental dissipation may lead to nontrivial thermalization behavior, which advances both the conceptual framework of the Mpemba effect and the theoretical understanding of nonequilibrium processes in dissipative disordered systems.
The Mpemba effect, where a hotter system cools faster than a colder one under otherwise identical conditions, has been extensively studied in classical systems. In this work, we present the quantum analogue of the Mpemba effect using a dissipative qubit, which is referred to as the canonical quantum Mpemba effect. We demonstrate that, under the identical conditions, the relaxation dynamics of a qubit initialized in a thermal state with a higher temperature can be exponentially faster than those of a colder thermal state. Strikingly, this acceleration is determined solely by the initial temperature of the system, independent of other parameters. The relaxation is confirmed to be a genuine cooling process via the effective steady state temperature, mirroring its classical counterpart. Last, we propose a practical classical quantum hybrid algorithmic quantum circuit to realize this effect using superconducting qubits experimentally.
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 Mpemba effect refers to the counterintuitive phenomenon that an initially hot system can freeze faster than an initially warm one. Recent years have brought major advances in both classical and quantum realizations, with the asymmetric bistable potential emerging as the paradigmatic classical benchmark because its mechanism is especially transparent and controllable. Yet for precisely this benchmark problem, the impact of quantization remains unexplored. Here we show that quantization shifts Mpemba behavior to qualitatively new regimes, moving it to ultra-cold temperatures that are orders of magnitude lower than those relevant for classical thermal barrier crossing. In addition, quantization produces inverse and double inverse Mpemba effects that are absent in the corresponding classical dynamics. Our results establish quantization as a robust route to quantum-enabled Mpemba effects inaccessible in classical regimes.
The Mpemba effect is a counterintuitive relaxation phenomenon that a system which begins hot can cool down faster than the identical system which is initially cold. Here, we investigate heat and work in a quantum open system with being alternatively driven by hot-cold heat reservoirs, which operates as an Otto cycle in finite time, either with or without the Mpemba effect. Based on the quantum master equation, the time duration of the cooling relaxation process is determined by exploring the distance function which can be used to observe the appearance of the Mpemba effect. We then numerically evaluate and compare the average and variance of the power of two scenarios with and without the Mpemba effect. We demonstrate that, given the efficiency, the Markovian Mpemba effect leads to improved performance by significantly increasing the power without sacrificing the stability.
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