Whether a quantum Mpemba effect occurs can depend on how distance from stationarity is measured. We show that agreement across normalized operator-convex Petz divergences is decided by a one-parameter $χ^2$ profile. Its sign fixes the common order, alternating sign margins guarantee repeated crossings, and finite dimension yields a polynomial positivity test. The same profile explains diagnostic-independent late-time order for a simple real slow mode and isolates coherence as the local source of diagnostic dependence. In a trapped-ion qutrit ideal model, the reported preparation gives diagnostic-selective crossings, while a nearby preparation is a floating-point candidate for two family-wide reversals. The framework turns diagnostic robustness into a tractable control problem.
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12 pages, 3 figures. Includes Supplemental Material
Whether a quantum Mpemba effect occurs can depend on how distance from stationarity is measured. We show that agreement across normalized operator-convex Petz divergences is decided by a one-parameter χ2 profile. Its sign fixes the common order, alternating sign margins guarantee repeated crossings, and finite dimension yields a polynomial positivity test. The same profile explains diagnostic-independent late-time order for a simple real slow mode and isolates coherence as the local source of diagnostic dependence. In a trapped-ion qutrit ideal model, the reported preparation gives diagnostic-selective crossings, while a nearby preparation is a floating-point candidate for two family-wide reversals. The framework turns diagnostic robustness into a tractable control problem.
Unrefereed research candidate. When two copies of a system, one hotter and one cooler, relax in the same bath, the Markovian Mpemba effect is a crossing of their distances from equilibrium. This package gives a sufficient test that rules out such crossings at every time: if the dynamics and its time reverse preserve the cone of observables with nondecreasing arithmetic prefix means, cooling Gibbs preparations stay ordered for relative entropy (both orientations), squared Hellinger and Rényi divergences of order 0<α≤2, including for common schedules of noncommuting stages. For complete-graph bosonic population rates with common coupling, the test holds for every spectrum and bath temperature exactly when the spontaneous jump weight is concave; Ohmic baths with large enough cutoff, Drude–Lorentz and sub-Ohmic weights qualify on explicit ranges, super-Ohmic weights do not. A certified super-Ohmic example (J=d3) shows an actual relative-entropy crossing. Limits: an exact five-state cone-preserving example has a brief total-variation reversal, and for every N≥4 there are N-level systems with a slow-mode inversion although no proper induced subsystem shows one. The archive contains the 27-page manuscript (PDF and LaTeX), exact rational and interval certificates, a reproduction runner, semantic negative controls, CI and SHA-256 sums. Assurance: written proofs, exact certificates, internal AI-assisted review only (not peer review, independent reproduction or formal verification); the closest antecedent (Avitan et al. 2026) already excludes the slow-mode effect for Ohmic and sub-Ohmic spectra. Creator: Anonymous. Text and data CC0-1.0; code MIT.
Closed chaotic quantum systems relax after a quench into a Gibbs ensemble. At late times, the relaxation speed is determined by their conservation laws and hydrodynamics. As a result, there exist pairs of initial states which thermalize to the same ensemble, yet exhibit drastically different hydrodynamic relaxation. We show in two chaotic spin chains how this enables a simple and robust realization of the quantum Mpemba effect: a system initially closer to equilibrium relaxes slower than one that starts farther away, despite both approaching the same final state.
We explore the role of exceptional points and complex eigenvalues on the occurrence of the quantum Mpemba effect. To this end, we study a two-level driven dissipative system subjected to an oscillatory electric field and dissipative coupling with the environment. We find that both exceptional points and complex eigenvalues can lead to multiple quantum Mpemba effect. It occurs in an observable when time-evolved copies corresponding to two different initial conditions, one initially having higher observable value compared to the other and both relaxing towards the same steady state, intersect each other more than once during their relaxation process. Each of the intersections denotes a quantum Mpemba effect and marks the reversal of identities between the two copies, i.e., the copy with higher observable value before the intersection becomes the lower-valued copy (and vice versa) after the intersection. Such multiple intersections originate from additional algebraic time dependence at the exceptional points and due to oscillatory relaxation in the case of complex eigenvalues. We provide analytical results for quantum Mpemba effect in the density matrix in presence of coherence. Depending on the control parameters (drive and dissipation), observables such as energy, von Neumann entropy, temperature, etc., exhibit either single or multiple quantum Mpemba effect. However, the distance from steady state measured in terms of the Kullback-Leibler divergence shows only single quantum Mpemba effect although the corresponding speed gives rise to either single or multiple quantum Mpemba effect.
The quantum Mpemba effect (ME) in Markovian systems is conventionally explained by a smaller overlap between the initial state and the slowest decay mode (SDM). Such state, initially farther away from equilibrium or steady state, relaxes faster than closer ones, resulting to a crossing of their trajectories. This picture, by neglecting the transient dynamics, holds in the long-time limit. Here we experimentally observe multiple trajectory crossings (multi-ME) in the relaxation dynamics of a trapped ion. Such novel dynamics takes place in a unusual scenario where the initial state instead has a larger overlap with the SDM. We develop a theoretical framework based on relaxation speed to understand the multi-ME. We show that the initial relaxation speed is governed by the fastest decay mode, which together with the SDM overlap gives a phase diagram that reveals both the occurrence and the types of quantum ME observed in our experiment. Our study goes beyond the simple picture based on the long-time limit, tracks continuously the quantum ME dynamics, and establishes a comprehensive framework to describe the transient quantum relaxation.
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.
Abstract The quantum Mpemba effect (QMPE) is characterized by a state initially farther from equilibrium relaxing faster than one closer to it. In this work, we investigate the QMPE in an open central-spin model, and examine whether the QMPE emerges when the spins’ system is subjected to their independent noisy environment for different initial states. Simultaneously, we analyze the influence of the noisy environment on the dynamics and demonstrate that tuning local noise strengths can induce the QMPE. Furthermore, we systematically explore finite-size effects by varying the number of peripheral spins. In addition, we investigate the Pontus Mpemba effect within the same framework, demonstrating that an auxiliary decohering environment can accelerate the approach to stationarity. To observe the effect, we select the trace distance, energy, and l 1 -norm coherence as observables. By combining initial-state engineering (global rotation operations) with the modulation of the noisy environment, we clearly reveal the physical mechanisms for inducing and controlling the QMPE in this model. Our results show that both rotating the initial states and applying non-uniform local noises can alter the relaxation rate ordering among different states, leading to crossings in the evolution curves of various physical quantities, that is, the realization of the QMPE. This finding provides a new perspective for manipulating anomalous relaxation behavior in the quantum many-body system and open quantum system.