Understanding relaxation dynamics in open quantum systems is a central problem in nonequilibrium quantum physics. Here we investigate the quantum Mpemba effect in the spin-boson model. In the weak-coupling Markovian regime we show that the occurrence of the effect strongly depends on the choice of distance measure at low temperature: while it appears in the trace distance, it can disappear in the quantum relative entropy. Going beyond the weak-coupling approximation, numerically exact simulations of the full system-bath dynamics reveal that increasing coupling enhances the effect in the trace distance and restores it in the quantum relative entropy. For all spin-bath couplings prior to delocalized-localized quantum phase transition, we uncover a simple geometric structure of the effect on the Bloch sphere: within the excited-state hemisphere, pairs of states related by rotations generically exhibit relaxation-order inversion. These results highlight the role of geometry and system-environment correlations in anomalous quantum relaxation.
Understanding relaxation dynamics in open quantum systems is a central problem in nonequilibrium quantum physics. Here we investigate the quantum Mpemba effect in the spin-boson model. In the weak-coupling Markovian regime we show that the occurrence of the effect strongly depends on the choice of distance measure at low temperature: while it appears in the trace distance, it can disappear in the quantum relative entropy. Going beyond the weak-coupling approximation, numerically exact simulations of the full system-bath dynamics reveal that increasing coupling enhances the effect in the trace distance and restores it in the quantum relative entropy. For all spin-bath couplings prior to delocalized-localized quantum phase transition, we uncover a simple geometric structure of the effect on the Bloch sphere: within the excited-state hemisphere, pairs of states related by rotations generically exhibit relaxation-order inversion. These results highlight the role of geometry and system-environment correlations in anomalous quantum relaxation.
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.
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.
We investigate the quantum Mpemba effect in a dissipative Dicke model, which consists of a spin-1/2 ensemble coupled to a bosonic mode, which in turn is coupled to a bosonic bath. We derive a sufficient criterion for occurrence of the quantum Mpemba effect, characterized by quantum coherence, in this model. We introduce the phenomenon of role reversal in the Mpemba effect, wherein changes in the system parameters invert the relaxation ordering of a given pair of initial states that exhibit the Mpemba effect, causing the faster-relaxing state to become slower and vice versa. We find the existence of role reversal in Mpemba effect for this Dicke model using different relaxation measures, including differential quantum coherence and entanglement, and trace distance, between the time-evolved and steady states.
Abstract We study the local relaxation of closed quantum systems through the relative entropy between the reduced density matrix and its long time limit. We show, using analytic arguments combined with numerical checks, that this relative entropy can be very well approximated by an entropy difference, affording a significant computational advantage. We go on to relate this to the entanglement asymmetry of the subsystem with respect to time translation invariance. In doing this, we obtain a simple probe of the relaxation dynamics of closed many-body systems and use it to re-examine the quantum Mpemba effect, wherein states can relax faster if they are initially further from equilibrium. We reproduce earlier instances of the effect related to symmetry restoration as well as uncover new cases in the absence of such symmetries. For integrable models, we obtain the criteria for this to occur using the quasiparticle picture. Lastly, we show that, in models obeying the entanglement membrane picture, the quantum Mpemba effect cannot occur for a large class of initial states.
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.
The transition from weakly damped coherent motion to localization in the context of the spin-boson model has been the subject of numerous studies with distinct behavior depending on the form of the phonon-bath spectral density $J\left(\ensuremath{\omega}\right)\ensuremath{\propto}{\ensuremath{\omega}}^{s}$. Sub-Ohmic (s<1) and Ohmic (s=1) spectral densities show a clear localization transition at zero temperature and zero bias, while for super-Ohmic (s>1) spectral densities this transition disappears. In this paper, we consider the influence of the phonon-bath spectral density on the nonequilibrium dynamics of a quantum dot with electron-phonon interactions described by the extended Holstein model. Using the reduced density matrix formalism combined with the multilayer multiconfiguration time-dependent Hartree approach, we investigate the dynamic response, the time scales for relaxation, as well as the existence of multiple long-lived solutions as the system-bath coupling changes from the sub- to the super-Ohmic cases. Bistability is shown to diminish for increasing powers of s similar to the spin-boson case. However, the physical mechanism and the dependence on the model parameters such as the typical bath frequency ${\ensuremath{\omega}}_{c}$ and the polaron shift $\ensuremath{\lambda}$ are rather distinct.