Mpemba Effect in Nonequilibrium Quantum Systems

The Mpemba effect in nonequilibrium quantum systems refers to the counterintuitive phenomenon whereby certain quantum states prepared further from a target steady state can approach that state more rapidly than those initially closer to it. This accelerated relaxation emerges in open quantum systems subject to one or more thermal reservoirs or external drivings that sustain nonequilibrium conditions. Under such circumstances, both classical and quantum observables may exhibit Mpemba and inverse Mpemba effects, with relaxation times determined by the interplay of spectral properties of the governing dynamical generator, initial coherence, and higher‐order statistical moments. In simple bosonic or fermionic models, matching a set of moments to equilibrium can induce “super‐accelerated” thermalisation, while nonequilibrium coherence can either expedite or delay the effect. Beyond its foundational interest, this phenomenon offers new avenues for optimising cooling and state‐preparation protocols in quantum technologies and for probing far‐from‐equilibrium dynamics in engineered quantum platforms.

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Recent studies have extended the Mpemba effect to open quantum setups with persistent nonequilibrium driving. In a two‐site fermionic system coupled to distinct thermal baths, researchers have shown that nonequilibrium conditions greatly expand the regime where both Mpemba and inverse Mpemba effects manifest in quantum correlations. Crucially, they demonstrated that quantum coherence induced by steady energy fluxes makes a significant contribution to these anomalous relaxations—an aspect often missed by conventional Lindbladian descriptions. In a complementary investigation of a damped quantum harmonic oscillator, analytical treatment of the relaxation dynamics revealed that any initial population distribution whose first r moments coincide with those of the steady state decays at a rate proportional to r, leading to super‐accelerated approach to equilibrium. This moment‐matching criterion remains robust in the presence of quantum coherences, offering explicit protocols for rapid thermalisation of bosonic modes.

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Technical terms

Open quantum system: A quantum system interacting with an external environment, resulting in dissipative and decoherent dynamics.

Lindbladian dynamics: A formalism describing the non‐unitary time evolution of a system’s density matrix under Markovian assumptions.

Nonequilibrium steady state: A stable time‐independent state maintained by continuous exchange of energy or particles with external reservoirs.

Quantum coherence: The presence of fixed phase relationships between basis states, which can alter relaxation pathways.

Moment matching: A state‐preparation strategy that aligns certain statistical moments of an initial distribution with those of the target state to induce accelerated relaxation.

References

1. Mpemba effect and super-accelerated thermalization in the damped quantum harmonic oscillator. Quantum (2025).
2. Mpemba effects in nonequilibrium open quantum systems. Physical Review Research (2024).