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.
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.
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. We uncover a simple Bloch sphere picture of the effect: within the excited-state hemisphere, pairs of states related by rotations and having the same Bloch-vector modulus generically exhibit an inversion of their relaxation ordering. This behavior is robust across sub Ohmic, Ohmic, and super Ohmic bath spectra. In the Ohmic and sub Ohmic regimes, the crossing time becomes strongly suppressed upon approaching the critical region, whereas in the super Ohmic regime the effect remains enhanced despite the absence of a finite-coupling localization transition. These results highlight the interplay between geometry, distance measures, system--environment coupling, and bath spectral properties in anomalous quantum relaxation.
Two quantum states may relax toward the same steady state, yet the one that starts farther away can overtake the closer one. This is the quantum Mpemba effect. The same pair can reverse order more than once, but these crossings may depend on the divergence used to compare them. We ask which crossings persist for every normalized operator-convex Petz divergence. Because each such divergence is a positive average of one-parameter χ2 kernels, the problem reduces to the sign of one profile across the full kernel range. Alternating sign margins guarantee repeated family-wide reversals, while finite dimension yields a polynomial positivity test. A simple real slow mode fixes the common late-time order; near stationarity, coherence between unequal-eigenvalue sectors makes the order divergence dependent. In a trapped-ion qutrit ideal model, the reported preparation shows divergence-selective crossings. A nearby preparation is a candidate for at least two family-wide reversals.
The Mpemba effect is a thermodynamic anomaly in which a system farther away in temperature from equilibrium thermalizes before one that is initially closer. The effect has been experimentally observed across a wide range of systems, including water, colloids, and trapped ions. It has recently been the focus of numerous studies aimed at understanding its mechanisms and developing multiple applications. Despite extensive work in the field, clearly determining which types of systems exhibit the Mpemba effect remains an open question. To address this, we derive simple necessary conditions on the transition rates for the Mpemba effect in a Markovian 3-level system and show that they can be applied to study the Mpemba effect in an N-level system. Multiple time scales govern thermalization in these systems. This allows the evolution to occur more quickly across larger temperature differences, explaining the Mpemba effect. We apply our protocol to evaluate which types of systems exhibit the Mpemba effect and, in doing so, explain why the Mpemba effect in Markovian systems remains a thermodynamic anomaly. In particular, due to the maximum entropy principle, our conditions allow us to discard the sub-Ohmic and Ohmic spectra. The latter describes a wide range of physical and chemical phenomena, which will not exhibit the Mpemba effect. Moreover, our results provide a clear path to determine the minimal physical requirements for the Mpemba effect, and we apply them to understand its underlying mechanisms better. Finally, our protocol could help identify relevant parameters for experiments, numerical simulations and diverse applications.
Unrefereed research candidate. When m identical copies of a quantum state of light are measured with Gaussian measurements (linear optics, Gaussian auxiliary modes, homodyne detection), measuring the copies jointly can give more Fisher information than measuring them one by one (Navarro, Morelli, Sanz and Mehboudi, arXiv:2512.20534), who left finite-copy optimality open. For every smooth family of pure single-mode Gaussian states and every m, this package proves the exact maximum of the Fisher information over all fixed (non-adaptive) Gaussian measurements, including ancilla-assisted schemes: a one-angle formula attained by concentrating the mean into one bright output and homodyne detection of every output. It also gives the exact optimum when measurement-seed squeezing is capped (in normalised coordinates), the exact shortfall from the quantum Fisher information (nondecreasing in m, at most one copy's variance information λ2/2, with an explicit limit), and a necessary and sufficient condition for strict collective advantage. The archive contains the 9-page manuscript (PDF and LaTeX), numerical checks with semantic negative controls, CI and SHA-256 sums. Assurance: written proofs; internal AI-assisted review only (not peer review, independent reproduction or formal verification); bounded prior-art search. Mixed states, multimode tangents and adaptive strategies are not covered. Creator: Anonymous. Text CC0-1.0; code MIT.
Unrefereed research candidate. A quantum system evolves under a fixed gate, step by step, and is occasionally reset; the waiting times between resets are independent and may have an infinite mean. Wald, Yao, Platini, Hooley and Carollo (Quantum 9, 1742, 2025, doi:10.22331/q-2025-05-13-1742) inferred from estimates and numerics how the averaged state behaves for the hazard r_n = gamma/(n+1)^alpha. This paper proves it: for alpha < 1 the state converges to a survival-weighted mixture, for alpha = 1 to the dephased state, and for alpha > 1 it approaches a rotating orbit and converges iff the reset state commutes with the gate. For complete resets the behaviour is classified for every renewal clock (finite mean, infinite mean, periodic, defective); a clock makes every finite-dimensional unitary reset system converge iff it is proper and aperiodic. This part is a short consequence of classical renewal theory. The claimed contributions are: the exact infinite-dimensional trace-norm defect 1 - m_pp (continuous spectral mass) for proper infinite-mean clocks, with no trace-norm convergent subsequence unless m_pp = 1; a laboratory-time reduction of imperfect resets (general jump channels, possibly noncommuting) to complete resetting at an effective state under a nonresonance condition (W), which is characterised, decidable for finitely supported clocks and open and dense, but is sufficient, not necessary, and not a classification; and uniform two-term asymptotics, endpoint and near-resonance crossovers for the critical clock gamma/(n+1), with practical time scales (dephasing can need more than 10^9 steps; numerical estimates). The archive contains the manuscript (PDF and LaTeX), a single deterministic verifier with its JSON report, semantic negative controls and SHA-256 sums. Assurance: written proofs; exact finite checks and labelled numerical checks; producer-side clean replay; internal AI-assisted review, AI-assisted adversarial audits before and after revision (OpenAI gpt-6-astra via Codex) and an AI-assisted verification re-review. This is not peer review, independent reproduction or formal verification. Creator: Anonymous. Prose, manuscript and data CC0-1.0; code MIT.
Unrefereed candidate, Anonymous, version 0.2.0-candidate. A finite integer certificate and written analytic argument establish a necessary leakage inequality on the full classical real binary RBM(4,3) visible closure, an eight-point obstruction to universality, a strictly positive excluded law, and non-sharp total-variation lower bounds. A contrasting exact construction represents every distribution on the specified parity-plus-one support. At least four hidden units are necessary; four-hidden sufficiency, smallest excluded support, complete classification, practical training penalties and historical priority are not established. The archive includes solver-free standard-library checkers, exact data, manuscript and PDF, normal/optimized hostile regression controls, source comparison, and one five-role coordinated AI internal editorial round. Producer checks and coordinated reconstruction are not unaffiliated reproduction, human specialist endorsement, journal peer review, or formal verification. The supplied external AI review reports a separate reconstruction but its linked audit ZIP was not retrieved. Original prose and data are CC0; code is MIT; upstream terms are preserved in LICENSES.md. The frozen editorial submission is included separately for audit and is superseded by the final release archive.