Relaxation in open quantum systems is fundamental to quantum science and technologies. Yet, the influence of the initial state on relaxation remains a central, largely unanswered question. Here, by systematically characterizing the relaxation behavior of generic initial states, we uncover a typicality phenomenon in high-dimensional open quantum systems: relaxation becomes nearly initial-state-independent as system size increases under verifiable conditions. Crucially, we prove this typicality for thermalization processes above a size-independent temperature. Our findings extend the typicality to open quantum dynamics, in turn identifying a class of systems where two widely used quantities -- the Liouvillian gap and the maximal relaxation time -- merit re-examination. We formalize this with two new concepts: the 'typical strong Mpemba effect' and the 'typical relaxation time'. Beyond these conceptual advances, our results provide practical implications: a scalable route to accelerating relaxation and a typical mixing-time benchmark that complements conventional worst-case metrics for quantum simulations and state preparation.
Relaxation in open quantum systems is fundamental to quantum science and technologies. Yet, the influence of the initial state on relaxation remains a central, largely unanswered question. Here, by systematically characterizing the relaxation behavior of generic initial states, we uncover a typicality phenomenon in high-dimensional open quantum systems: relaxation becomes nearly initial-state-independent as system size increases under verifiable conditions. Crucially, we prove this typicality for thermalization processes above a size-independent temperature. Our findings extend the typicality to open quantum dynamics, in turn identifying a class of systems where two widely used quantities -- the Liouvillian gap and the maximal relaxation time -- merit re-examination. We formalize this with two new concepts: the 'typical strong Mpemba effect' and the 'typical relaxation time'. Beyond these conceptual advances, our results provide practical implications: a scalable route to accelerating relaxation and a typical mixing-time benchmark that complements conventional worst-case metrics for quantum simulations and state preparation.
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.
An ancient and counterintuitive phenomenon known as the Mpemba effect (water can cool faster when initially heated up) showcases the critical role of initial conditions in relaxation processes. How to realize and utilize this effect for speeding up relaxation is an important but challenging task in purely quantum system till now. Here, we experimentally study the strong Mpemba effect in a single trapped ion system in which an exponentially accelerated relaxation in time is observed by preparing an optimal quantum initial state with no excitation of the slowest decaying mode. Also, we demonstrate that the condition of realizing such effect coincides with the Liouvillian exceptional point, featuring the coalescence of both the eigenvalues and the eigenmodes of the systems. Our work provides an efficient strategy to engineer the dynamics of open quantum system, and suggests a link unexplored yet between the Mpemba effect and the non-Hermitian physics. The Mpemba effect is an archetype for various anomalous relaxation phenomena. Here, the authors experimentally study a quantum version of the Mpemba effect in a single trapped ion system, where relaxation is exponentially accelerated by removing the excitation of the slowest decaying mode. This phenomenon, seen in Markovian open quantum systems containing Liouvillian exceptional points, indicates a link between the Mpemba effect and non-Hermitian physics.
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 Mpemba effect refers to the anomalous relaxation of a quantum state that, despite being initially farther from equilibrium, relaxes faster than a closer counterpart. Detecting such a quantum Mpemba effect typically requires full knowledge of the quantum state during its time evolution, which is an experimentally challenging task since state tomography becomes exponentially difficult as system size increases. This poses a significant obstacle in studying Mpemba effect in complex many-body systems. In this work, we demonstrate that this limitation can be overcome by identifying suitable observables that signal rapid relaxation. Moreover, as long as the system equilibrates to a known unique steady-state, it is possible to fully detect the occurrence of quantum Mpemba effect just by measuring the observable for known state preparations. Our approach thus significantly reduces experimental complexity and offers a practical route for observing the quantum Mpemba effect in complex and extended multi-qubit setups.
The behavior of systems far from equilibrium is often complex and unpredictable, challenging and sometimes overturning the physical intuition derived from equilibrium scenarios. One striking example of this is the Mpemba effect, which implies that non-equilibrium states can sometimes relax more rapidly when they are further from equilibrium. Despite a rich historical background, the precise conditions and mechanisms behind this phenomenon remain unclear. Recently, there has been growing interest in investigating accelerated relaxation and Mpemba-like effects within quantum systems. In this work, we explore a quantum manifestation of the Mpemba effect in a simple and paradigmatic model of open quantum systems: the damped quantum harmonic oscillator, which describes the relaxation of a bosonic mode in contact with a thermal bath at finite temperature T . By means of an exact analytical analysis of the relaxation dynamics based on the method of moments in both population and coherence subspaces, we demonstrate that any initial distribution of populations with the first r moments exactly matching those of the equilibrium distribution shows a super-accelerated relaxation to equilibrium at a rate linearly increasing with r , leading to a pronounced Mpemba effect. In particular, one can find a broad class of far-from-equilibrium distributions that relax to equilibrium faster than any other initial thermal state with a temperature T ′ arbitrarily close to T . The super-accelerated relaxation effect is shown to persist even for a broad class of initial states with non-vanishing coherences, and a general criterion for the observation of super-accelerated thermalization is presented.
Since its rediscovery in the twentieth century, the Mpemba effect, where a far-from-equilibrium state may relax faster than a state closer to equilibrium, has been extensively studied in classical systems and has recently received attention in quantum systems. Many theories explaining this counter-intuitive behavior in classical systems rely on memory effects. However, in quantum systems, the relation between the Mpemba effect and memory has remained unexplored. In this Letter, we consider general non-Markovian open quantum systems and reveal new classes of quantum Mpemba effects, with no analog in Markovian quantum dynamics. Generically, open quantum dynamics possess a finite memory time and a unique steady state. Because of non-Markovian dynamics, even if the system is initialized in the steady state it can take a long time to relax back. We find other initial states that reach the steady state much faster. Most notably, we demonstrate that there can be an initial state in which the system reaches the steady state within the finite memory time itself, giving the fastest possible relaxation to stationarity. We verify the effect for quantum dot systems coupled to electronic reservoirs in equilibrium and nonequilibrium setups at weak, intermediate and strong coupling. Our Letter provides new insights into the rich physics underlying accelerated relaxation in quantum systems.