ABSTRACT The Mpemba effect is the counterintuitive phenomenon, where some states relax faster than others despite being initially farther from equilibrium. In quantum systems, realizing this effect typically requires fine‐tuned dissipation or carefully engineered initial states, making it fragile to disorder. Here, we uncover a robust statistical quantum Mpemba effect arising from Griffiths rare‐region physics in a one‐dimensional dissipative lattice. Sparse local losses fragment the system into random loss‐free regions that host long‐lived quasi‐bound modes with broadly distributed lifetimes. We show that simple extended Bloch states, although having identical density profiles, couple very differently to these modes: a uniform state predominantly excites slowly decaying modes, while a phase‐modulated state couples more strongly to rapidly decaying ones. This mismatch produces a disorder‐robust inversion of relaxation times, where the initially “farther” state relaxes faster. Our results identify Griffiths rare‐region physics as a robust mechanism for quantum Mpemba dynamics in disordered quadratic open quantum systems.
ABSTRACT The Mpemba effect is the counterintuitive phenomenon, where some states relax faster than others despite being initially farther from equilibrium. In quantum systems, realizing this effect typically requires fine‐tuned dissipation or carefully engineered initial states, making it fragile to disorder. Here, we uncover a robust statistical quantum Mpemba effect arising from Griffiths rare‐region physics in a one‐dimensional dissipative lattice. Sparse local losses fragment the system into random loss‐free regions that host long‐lived quasi‐bound modes with broadly distributed lifetimes. We show that simple extended Bloch states, although having identical density profiles, couple very differently to these modes: a uniform state predominantly excites slowly decaying modes, while a phase‐modulated state couples more strongly to rapidly decaying ones. This mismatch produces a disorder‐robust inversion of relaxation times, where the initially “farther” state relaxes faster. Our results identify Griffiths rare‐region physics as a robust mechanism for quantum Mpemba dynamics in disordered quadratic open quantum systems.
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 state farther from equilibrium relaxes faster than one closer to it, is a striking phenomenon in both classical and quantum systems. In open quantum systems, however, the quantum Mpemba effect (QME) typically occurs only for specifically chosen initial states, which limits its universality. Here we present a general and experimentally feasible strategy to realize both QME and anti-QME. By applying a temporary bond-dissipation quench, we selectively suppresses or enhances slow relaxation modes, thereby reshaping relaxation pathways independently of both the system and the initial state. We demonstrate this mechanism in systems with dephasing and boundary dissipation, and outline feasible cold-atom implementations. Our results establish controllable dissipation as a versatile tool for quantum control, accelerated relaxation, and efficient nonequilibrium protocols.
The Mpemba effect refers to the counterintuitive situation in which a system initially farther from equilibrium can relax faster than one that starts closer to it. In quantum systems, the effect is enriched by the presence of coherent dynamics, dissipation, and metastable manifolds associated with long-lived Liouvillian modes. Here we demonstrate a giant Mpemba effect in open quantum systems, where relaxation can be either hyper-accelerated or dramatically slowed depending on the initial state. We focus on weakly-coupled particle-conserving bosonic networks, each of which independently relaxes rapidly to a unique stationary state. When a weak coherent interaction is introduced, the composite system typically develops slow metastable modes and a hierarchy of relaxation timescales. We show that by tailoring the interaction Hamiltonian, these slow modes can be effectively suppressed for a broad class of initial states satisfying a minimal global requirement, enabling ultrafast relaxation even when the system starts far from equilibrium. Conversely, other initial states-sometimes arbitrarily close to the stationary state-may remain trapped in the metastable manifold and decay anomalously slowly. This mechanism provides a general route to engineer giant Mpemba effects, offering new possibilities for controlling dissipative dynamics, accelerating state preparation, and manipulating relaxation processes in complex quantum devices.
The quantum Mpemba effect is the counterintuitive phenomenon whereby a quantum state initially farther from equilibrium relaxes faster than one initially closer to it. We demonstrate this effect in random Clifford circuits with a conserved U(1) charge, using the entanglement asymmetry to characterize relaxation through dynamical symmetry restoration. Exact numerical simulations show that an initially more asymmetric state can become locally more symmetric than an initially less asymmetric one. We explain this behavior by mapping the dynamics onto a charge-conserving quantum automaton, in which the decay of the entanglement asymmetry is controlled by the statistics of encounters between two particle species evolving according to a symmetric simple exclusion process. This mapping yields an analytic expression for the entanglement asymmetry and provides a simple microscopic mechanism for the quantum Mpemba effect: stronger initial symmetry breaking corresponds to a denser particle configuration, which enhances the frequency of particle encounters and thereby accelerates symmetry restoration.
The quantum Mpemba effect, an anomalous relaxation phenomenon, has recently attracted much attention. However, how various types of noise, which are ubiquitous in real systems, may affect the quantum Mpemba effect remains unknown. Here, we address this gap by constructing a general dynamical framework for finite-dimensional open quantum systems under random telegraph noise. We identify a mechanism for the quantum Mpemba effect whereby noise-induced deceleration of the relaxation process in typical initial states can either induce or suppress the effect. This result underscores the potential of noise-traditionally viewed as disruptive-as a tool for manipulating relaxation pathways in quantum systems. Moreover, this mechanism leads to a counterintuitive effect—the decoherence rate may be slowed down by noise. How external noise changes the quantum Mpemba effect, where a state farther from equilibrium can relax faster, remains poorly understood. We show that random telegraph noise introduces extra dynamical modes in an enlarged description, slowing selected states and thereby inducing or suppressing this effect.
We investigate the quantum Mpemba effect in the relaxation of open quantum systems whose effective dynamics is described by Davies maps. We introduce a class of unitary transformations constructed from permutation matrices that, when applied to an initial state, (i) suppress the slowest decaying modes of the nonunitary dynamics and (ii) maximize the state's distinguishability from the steady state. The first condition ensures exponentially faster convergence to equilibrium, while the second implies that a quantum system initially further from equilibrium can approach it more rapidly than one that starts closer. This protocol thus realizes a genuine Mpemba effect, and its simulation requires low computational effort. We prove that, for any initial state, there exists a permutation matrix that maximizes its distance from equilibrium with respect to a chosen information-theoretic distinguishability measure. We illustrate our findings for a two-level system, as well as for the nonunitary dynamics of the transverse-field Ising chain and the XXZ chain, each weakly coupled to a bosonic thermal bath. In these cases, the quantum Mpemba effect is demonstrated using the Hilbert-Schmidt distance, quantum relative entropy, and trace distance. Overall, our results provide a versatile framework for engineering a genuine quantum Mpemba effect in Markovian open quantum systems.