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arXiv:2504.21758 · APL Quantum

Quantum Mpemba effect from initial system–reservoir entanglement

Stefano Longhi

Published Jun 1, 2025• 12 citations

Abstract

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.

DOI: 10.1063/5.0266143

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The quantum Mpemba effect refers to the counterintuitive phenomenon in which a system initially farther from equilibrium relaxes faster than one prepared closer to it. Several mechanisms have been identified in open quantum systems to explain this behavior, including the strong Mpemba effect, non-Markovian memory, and initial system-reservoir entanglement. Here, we unveil a distinct mechanism rooted in the non-normal nature of the Liouvillian superoperator in Markovian dynamics. When the Liouvillian's eigenmodes are non-orthogonal, transient interference between decaying modes can induce anomalous early-time behavior-such as delayed thermalization or transient freezing-even though asymptotic decay rates remain unchanged. This differs fundamentally from strong Mpemba effects, which hinge on suppressed overlap with slow-decaying modes. We demonstrate this mechanism using a waveguide quantum electrodynamics model, where quantum emitters interact with the photonic modes of a one-dimensional waveguide. The directional and radiative nature of these couplings naturally introduces non-normality into the system's dynamics. As a result, certain initial states-despite being closer to equilibrium-can exhibit slower relaxation at short times. This work reveals a previously unexplored and universal source of Mpemba-like behavior in memoryless quantum systems, expanding the theoretical framework for anomalous relaxation and opening new avenues for control in engineered quantum platforms.

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.

We demonstrate the quantum Mpemba effect in a quantum dot coupled to two reservoirs, described by the Anderson model. We show that the system temperatures starting from two different initial values (hot and cold) cross each other at finite time (and thereby reverse their identities; i.e., hot becomes cold and vice versa) to generate thermal quantum Mpemba effect. The slowest relaxation mode believed to play the dominating role in Mpemba effect in Markovian systems does not contribute to such anomalous relaxation in the present model. In this connection, our analytical result provides necessary condition for producing quantum Mpemba effect in the density matrix elements of the quantum dot, as a combined effect of the remaining relaxation modes.

In classical thermodynamics, the Mpemba effect refers to the counterintuitive observation that hot water can freeze faster than cold water, manifesting as an anomalous crossing of dynamical trajectories. While analogues of this phenomenon have been explored in open quantum systems and spin-chain entanglement asymmetry, its connection to the finite-time loss of entanglement remains elusive. In this work, we report a distinct Mpemba effect for quantum entanglement in a dissipative quantum system associated with entanglement sudden death (ESD). By analyzing two qubits interacting with local amplitude damping reservoirs, we demonstrate that a more strongly entangled initial state can experience a faster collapse into a separable state than a more weakly entangled state. This anomalous decay stems from the competition between initial coherence and excited-state population, where the latter acts as a catalyst for ESD. We provide exact analytical derivations for the trajectory crossover and ESD time, and map the phase diagram to precisely identify the parameter regime where the effect occurs. Our results offer a new strategy for controlling the lifetime of quantum resources in dissipative environments.

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We investigate the quantum Mpemba effect, whereby a system initially farther from equilibrium relaxes faster than one initially closer to equilibrium, emerging in a quantum harmonic oscillator linearly coupled to a bosonic environment. Starting from factorized thermal states at different temperatures, we derive exact analytical criteria for the occurrence of the quantum Mpemba effect valid also beyond the typically considered weak-coupling and Markovian approximations. Most importantly, we show that the effect is enabled by the initial-slip dynamics generated by the sudden switch-on of the system-bath interaction. Neglecting this contribution completely suppresses the anomalous relaxation, identifying transient system-bath correlations as the key ingredient underlying the quantum Mpemba effect.