We investigate the quantum Mpemba effect from the perspective of nonequilibrium quantum thermodynamics by studying relaxation dynamics of quantum systems coupled to a Markovian heat bath, which are described by Davies maps. Starting from a state with coherences in the energy eigenbasis, we demonstrate that an exponential speedup to equilibrium will always occur if the state is transformed to a diagonal state in the energy eigenbasis, provided that the spectral gap of the generator is defined by a complex eigenvalue. When the transformed state has a higher nonequilibrium free energy, we argue using thermodynamic reasoning that this is a genuine quantum Mpemba effect. Furthermore, we show how a unitary transformation on an initial state can always be constructed to yield the effect and demonstrate our findings by studying the dynamics of both the nonequilibrium free energy and the irreversible entropy production in single and multiqubit examples.
We investigate the quantum Mpemba effect from the perspective of nonequilibrium quantum thermodynamics by studying relaxation dynamics of quantum systems coupled to a Markovian heat bath, which are described by Davies maps. Starting from a state with coherences in the energy eigenbasis, we demonstrate that an exponential speedup to equilibrium will always occur if the state is transformed to a diagonal state in the energy eigenbasis, provided that the spectral gap of the generator is defined by a complex eigenvalue. When the transformed state has a higher nonequilibrium free energy, we argue using thermodynamic reasoning that this is a genuine quantum Mpemba effect. Furthermore, we show how a unitary transformation on an initial state can always be constructed to yield the effect and demonstrate our findings by studying the dynamics of both the nonequilibrium free energy and the irreversible entropy production in single and multiqubit examples.
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.
In recent years, the quantum Mpemba effect (QME) which occurs when an out-of-equilibrium system reaches equilibrium faster than another that is closer to equilibrium has attracted significant attention from the scientific community as an intriguing and counterintuitive phenomenon. It generalizes its classical counterpart, extending the concept beyond thermal equilibration. This paper approaches the QME for Markovian open quantum systems from different perspectives. Firstly, we propose a physical mechanism based on decoherence-free subspaces. Secondly, we show that a macroscopic enhancement of the decay rate that scales linearly with system size can be obtained, leading to an extreme version of the phenomenon on Markovian open quantum systems. Thirdly, we study the Mpemba effect through the unravelings of Davies maps, revealing subtleties in the figures of merit which are chosen for obtaining the QME. Lastly, we propose a microscopic model for a better understanding of thermal bath dynamics in this context.
The Mpemba effect has initially been noticed in macroscopic systems-namely that hot water can freeze faster than cold water-but recently its extension to open quantum systems has attracted significant attention. This phenomenon can be explained in the context of nonequilibrium thermodynamics of Markovian systems, relying on the amplitudes of different decay modes of the system dynamics. Here, we study the Mpemba effect in a single-level quantum dot coupled to a thermal bath, highlighting the role of the sign and magnitude of the electron-electron interaction in the occurrence of the Mpemba effect. We gain physical insights into the decay modes from a dissipative symmetry of this system called fermionic duality. Based on this analysis of the relaxation to equilibrium of the dot, we derive criteria for the occurrence of the Mpemba effect using two thermodynamically relevant measures of the distance to equilibrium, the nonequilibrium free energy and the dot energy. We furthermore compare this effect to a possible exponential speedup of the relaxation. Finally, we propose experimentally relevant schemes for the state preparation and explore different ways of observing the Mpemba effect in quantum dots in experiments.
The Mpemba effect, where a system initially farther from equilibrium relaxes faster than one closer to equilibrium, has been extensively studied in classical systems and recently explored in quantum settings. While previous studies of the quantum Mpemba effect (QME) have largely focused on isolated systems with global symmetries, we argue that the QME is ubiquitous in generic, nonintegrable many-body systems lacking such symmetries, including U(1) charge conservation, spatial symmetries, and even energy conservation. Using paradigmatic models such as the quantum Ising model with transverse and longitudinal fields, we show that the QME can be understood through the energy density of initial states and their inverse participation ratio in the energy eigenbasis. Our findings provide a unified framework for the QME, linking it with classical thermal relaxation.
Coherence is an inherently quantum property that deeply affects microscopic processes, including thermalization phenomena. A striking example is the quantum Mpemba effect (QME), in which a system can exhibit anomalous relaxation, thermalizing faster from a state initially farther from equilibrium than from one closer. Here, we experimentally investigate the genuine QME and observe how the dynamics of a spin-1/2 system interacting with a heat sink can be sped-up to equilibrium. The mechanism underlying this speed-up is uncovered through detailed analysis of the heat exchange process. Furthermore, we apply the QME in a quantum Otto refrigerator, thereby increasing its cooling power. This proof-of-concept experiment unveils new practical paths for improving quantum thermal tasks.
The quantum Mpemba effect describes the unusual relaxation of a quantum system where if starting from a state far from equilibrium reaches equilibrium faster than starting from a closer state. In this work, the steepest-entropy ascent quantum thermodynamics framework is used to model this effect in a three-level ion system coupled to a short-life level which acts as an environment. The four-level Hilbert space is reduced to an effective three-dimensional description via the Feshbach projection, where the resulting model parameters are determined by a differential evolution algorithm. Predictions of both the steepest-entropy-ascent and Lindblad frameworks agree well with experimental data for all three initial conditions considered. In addition it is shown that, independently of the Mpemba condition, the relaxation parameter τD is an emergent thermodynamic quantity whose step-function time dependence arises from a near-indetermination at the metastable state, resolved by the two-timescale structure of the dissipative dynamics, with a step height τD+/τD−(∣λf∣/∣λs∣)r set by the ratio of the linearised relaxation rates at the metastable state times a geometric factor r fixed by the curvature of the entropy and free-energy-variance surfaces there. Furthermore, it is also established the correspondence between the Lindblad and steepest-entropy-ascent order parameters as spectral and geometric suppression of the same slow dissipative mode, and it is shown that for isolated systems with a negative nonequilibrium inverse temperature, as realized in the case studied here, the genuine Mpemba free-energy ordering is equivalent to an entropy ordering.