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A state prepared farther from equilibrium relaxes faster than a closer one in a disordered diamond spin network, with the crossing time tunable over orders of magnitude.

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2026-08-01 08:53 UTC pith:GYOCLFAI

load-bearing objection Strong experimental claim of a tunable Mpemba effect in a disordered spin network, but the readout-filtered polarization metric needs validation before the crossing is taken as a genuine distance-to-equilibrium effect. the 3 major comments →

arxiv 2607.21669 v1 pith:GYOCLFAI submitted 2026-07-23 quant-ph cond-mat.stat-mech

Tunable Mpemba Effect in a Prethermal Many-Body Spin Network

Chaitali Shah , Cooper M. Selco , Leo Joon Il Moon , Ashok Ajoy This is my paper
classification quant-ph cond-mat.stat-mech
keywords Mpemba effectprethermalizationFloquet drivingnuclear spin relaxationdisordered spin networksdiamond NV centerspolarization transportmany-body relaxation
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Using a field-cycling protocol to prepare distinct spatial polarization profiles in a 13C nuclear-spin network in diamond, and Floquet driving to stabilize a long-lived prethermal regime, the paper reports reproducible Mpemba crossings: a state prepared initially farther from equilibrium relaxes faster than one initially closer, with the curves crossing at t_x ≈ 8 s. By varying the hyperpolarization duration t_h and the wait duration t_w, the crossing time is tuned over several orders of magnitude, from late-time thermalization into the prethermal plateau. Semiclassical simulations trace the origin to the mode structure of the disordered network: randomly placed paramagnetic defects create fast-relaxing zones, while defect-poor regions support the slowest collective relaxation mode, and the crossing is set by the initial state's overlap with that mode. If the claims hold, this is the first Mpemba effect in an extended many-body spin network and the first experimental demonstration of Mpemba dynamics in a prethermal state.

Core claim

The authors claim that native spatial disorder reorders relaxation trajectories in an extended many-body system. Concretely, a 13C nuclear-spin ensemble in a nitrogen-doped diamond, prepared with (t_h, t_w) = (60,0) s, starts with higher total polarization yet relaxes more quickly than a state prepared with (150,150) s; the two curves cross at t_x ≈ 8 s while both relax toward the same unpolarized equilibrium under identical Floquet driving. The crossing time is tunable over orders of magnitude by varying the two preparation durations, and the crossings persist when the distance to equilibrium is quantified by KL divergence within the model. The underlying mechanism is the overlap of the ini

What carries the argument

The central object is the eigenmode decomposition p(t) = Σ_j a_j v_j e^(-λ_j t) of the nuclear polarization vector under the generator M(t), which combines dipolar spin transport, defect-mediated r^(-6) relaxation, and (during preparation) NV injection. The slowest-decaying mode v_0, localized in regions far from paramagnetic defects, acts as the bottleneck for relaxation; the Mpemba crossing occurs when the initially farther-from-equilibrium state has smaller overlap a_0 with v_0 than the initially closer state. Two preparation knobs—hyperpolarization duration t_h and low-field wait t_w—control the spatial distribution of polarization and hence a_0, while Floquet driving (a periodic pulse s

Load-bearing premise

The experiment assumes that the total nuclear polarization is a trustworthy yardstick for how far a state is from equilibrium; if another, correlation-sensitive measure disagrees, the reported crossing could be an artifact of that yardstick.

What would settle it

Compute the many-body KL divergence or another correlation-sensitive distance to equilibrium directly from the measured spin states and re-examine the two relaxation trajectories; if the curves no longer cross, the Mpemba claim rests on the choice of the polarization metric rather than on the dynamics.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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If this is right

  • An extended, disordered many-body spin network can exhibit the Mpemba effect without engineered potentials or tailored dissipation; native disorder is sufficient.
  • State preparation alone, not the drive or the equilibrium state, can shift a Mpemba crossing from late-time thermalization into the prethermal plateau, implying Mpemba physics is controllable within long-lived driven states.
  • The relaxation-mode picture gives design rules: defect density and geometry shape the slow modes, transport sets their spatial extent, and initial-state preparation sets their weight, so disorder can be used as a resource.
  • A semiclassical polarization-transport model with fixed parameters reproduces the observed polarization buildup, wait-time depletion, and crossings, supporting the claim that the effect is robust to the microscopic details.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Inference: the same overlap logic implies an inverse design recipe: to deliberately slow relaxation of a hyperpolarized ensemble, prepare a state whose spatial profile resembles the slowest mode; to accelerate thermalization, avoid that mode. This could be tested by shaping the initial profile with gradients or targeted RF.
  • Inference: because the KL-divergence check is done only in the semiclassical product-state model, a full many-body metric including correlations on the experimental data could either confirm or overturn the polarization-based crossing; that measurement would cleanly separate the metric question from the physics.
  • Inference: the tunability over orders of magnitude suggests practical uses in quantum sensing and qubit reset, where one may want either to preserve nuclear polarization or to erase it quickly, by choosing t_h and t_w accordingly.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper reports an experimental observation of a tunable Mpemba effect in a disordered 13C nuclear-spin network in diamond under Floquet driving. Field cycling at 36 mT is used to prepare two classes of initial polarization states, distinguished by hyperpolarization duration t_h and wait duration t_w; after shuttling to 7.3 T, relaxation is tracked quasi-continuously with a Floquet NMR readout. The central observation is a reproducible crossing, at t× ≈ 8 s, between a state prepared with (t_h,t_w) = (60,0) s, which starts farther from equilibrium, and one prepared with (150,150) s, which starts closer. The crossing time is reported to be tunable over several orders of magnitude. A semiclassical hopping model with four fitted parameters is used to argue that the effect arises from the overlap of the initial spatial polarization profile with the slowest collective relaxation mode, which is localized in defect-poor regions; a KL-divergence check within the same model is presented as evidence that the crossing is not an artifact of using total polarization as the distance measure.

Significance. If the central claim holds, this would be the first observation of the Mpemba effect in an extended, interacting many-body spin network and the first experimental demonstration of Mpemba dynamics in a prethermal regime. The experiment is substantial: it combines a purpose-built field-cycling hyperpolarization platform, a high-speed NMR spectrometer, and a Floquet readout capable of tracking relaxation over minutes. The proposed mechanism—disorder-generated heterogeneous relaxation with a slow mode localized away from paramagnetic defects—is physically appealing and connects the Mpemba effect to mode-selective state preparation in a way that could inform hyperpolarization and quantum-sensing applications. The paper also provides a phase diagram and a model-based KL check, which are useful even if not fully independent of the fitted model.

major comments (3)
  1. [Main text, Fig. 1C; SM S3; SM S4] The distance-to-equilibrium metric is load-bearing and is not adequately justified. The main text states that 'total nuclear polarization provides a valid measure of distance from equilibrium, satisfying the monotonicity, temperature-ordering, and convexity criteria [17],' but no proof or argument is supplied. More importantly, SM S3 states that the reported polarization is not the full nuclear polarization: it is summed only over spins whose hyperfine coupling to every electron lies below the readout excitation bandwidth, while strongly coupled spins are retained in the dynamics but are invisible to the measurement. No argument is given that this hyperfine-filtered partial sum satisfies the Lu–Raz criteria. Transport between the visible and invisible populations can change the filtered signal without changing the true distance to equilibrium, so the observed crossing at t× ≈ 8 s could b
  2. [Fig. 1C and Fig. 2A–C; SM S1] The central experimental observation lacks statistical support. The relaxation trajectories in Fig. 1C and Fig. 2 are presented without error bars, confidence bands, or the number of repeated runs, despite the claim of reproducibility and the statement that parameter values were randomized between runs to minimize systematic errors. A crossing time of t× ≈ 8 s is meaningless without a measure of run-to-run scatter, especially because the two trajectories in Fig. 1C are close in polarization near the crossing. The authors should report repeat measurements, standard errors or confidence intervals, and, where relevant, the propagation of calibration uncertainty from the polarization enhancement factor used to convert signal to absolute polarization.
  3. [SM S3 A–B; Eq. (1)–(2); Fig. 3C–E] The mechanistic explanation is derived from a semiclassical model with four adjustable parameters (κ = 0.13, η_LF = 0.0022, ξ = 10^-5, η_HF = 0.005) that are fitted to the same experimental polarization buildup, wait-time depletion, and relaxation data. The eigenmode decomposition and the overlap coefficients a0 in Fig. 3B are outputs of this fitted model, so the claim that the Mpemba crossing is 'set by the initial state overlap with the slowest mode' is not independently established by the data. This is not circular in a strict logical sense, because the fitted model could still make falsifiable predictions, but the paper does not identify which predictions are made without refitting. The authors should state clearly which model outputs are robust to parameter variation, and ideally test the phase diagram in Fig. 3D against new (t_h,t_w) combinations that were not used in the fitting.
minor comments (4)
  1. [SM S3 A] Typo: 'paramegntic impurity' should be 'paramagnetic impurity' in the sentence defining d_iµ.
  2. [Fig. 2A/B] The 'normalized polarization' curves are normalized to their initial values, but this is not stated in the figure caption. Please state this explicitly, and indicate whether the crossing times in Fig. 2C are extracted from absolute or normalized curves.
  3. [Main text, Fig. 1C] The two states in Fig. 1C appear to have very similar initial polarization values (approximately 0.2% versus 0.21%). Please clarify how 'initially farther from equilibrium' is established given the calibration uncertainty and the closeness of the two values.
  4. [SM S4] The KL-divergence expression contains log2(1 ± p_i(t)), which is singular for fully polarized spins; a sentence on how such edge cases are handled (or why they do not occur for these initial states with |p_i| well below 1) would be helpful.

Circularity Check

1 steps flagged

Experimental Mpemba crossing is measured directly and is not circular; the model-based KL validation and mode-overlap explanation inherit parameters fitted to the same polarization data, so they do not independently confirm the metric.

specific steps
  1. fitted input called prediction [Main text, 'Relaxation-mode origin' (final paragraph); Supplemental Material S4]
    "Because the model neglects interspin correlations, the KL divergence is evaluated under a product-state approximation (see Supplemental Material Sec. S4). Fig. 3E shows the KL divergence for the same pair of states considered in Fig. 3C. The KL-divergence curves cross at approximately the same time as the polarization curves, confirming that the observed Mpemba effect is not an artifact of using total polarization as a measure of proximity to equilibrium."

    The KL check is not an independent experimental validation: it is evaluated within the same semiclassical model whose prefactors κ, η_LF, η_HF, and ξ were fitted to the experimental polarization buildup and low-field relaxation data (SM S3A/B). The KL curves therefore inherit the fitted dynamics and the same filtered readout definition of polarization, so their crossing is a consequence of the fitted model rather than independent evidence that the total-polarization metric is not producing an artifact.

full rationale

The central observation—a reproducible Mpemba crossing in the measured polarization trajectories with a crossing time tunable over orders of magnitude—is an experimental measurement that does not reduce to the semiclassical model or to any fitted parameter. The crossing is defined with respect to the total (readout-filtered) polarization signal, and while the validity of that metric as a Lu–Raz distance is asserted rather than proven, that is a correctness/validity concern, not a circularity by construction. The model-based elements (mode-overlap interpretation, Fig. 3A–C, phase diagram Fig. 3D, and KL check Fig. 3E) are transparently simulations using parameters fixed to experimental buildup/relaxation data; they are not used to manufacture the raw experimental crossing. However, the KL check is presented as confirming that the effect is not an artifact of the polarization metric, even though it is computed from the same fitted model and therefore cannot independently validate that metric. This is a partial circular-validation step, but it does not undermine the independent experimental crossing itself.

Axiom & Free-Parameter Ledger

4 free parameters · 7 axioms · 0 invented entities

The central claim rests on a semiclassical model with four fitted parameters and several physical approximations. The model is used both to reproduce the experimental data and to compute the slow-mode overlap that constitutes the explanatory mechanism. The experimental observation itself does not depend on the fitted parameters, but the interpretation does.

free parameters (4)
  • κ = 0.13
    Dimensionless prefactor treated as an adjustable parameter accounting for approximations in the semi-classical hopping model (S3 A). Fixed to 0.13 for all simulations.
  • η_LF = 0.0022
    Effective model parameter for low-field relaxation, chosen to achieve quantitative agreement with experimentally observed low-field relaxation dynamics (S3 A).
  • ξ = 10^-5
    Phenomenological parameter for polarization injection rate, chosen so that the simulated polarization buildup matches the experimentally inferred value (S3 A). Single value used for all simulations.
  • η_HF = 0.005
    Effective model parameter for high-field Floquet-regime relaxation, 'taken to be a fixed value' without independent derivation (S3 B).
axioms (7)
  • domain assumption Secular approximation for nuclear dipolar Hamiltonian: the 13C Larmor frequency is much larger than the average nearest-neighbor coupling (~60 Hz) across all relevant fields.
    Invoked in main text after Eq. 1 for nuclear-nuclear interaction; validates truncation of dipolar terms.
  • domain assumption Markovian hopping model with Gaussian zero-mean noise and exponential correlation functions for the nuclear and electron baths.
    Used throughout S3 C to derive hopping rates W_LF and the form of relaxation R_LF/R_HF.
  • domain assumption Bath spins are uncorrelated with each other; cross-correlation terms are neglected in the derivation of Γ_ij.
    Explicitly stated in S3 C: 'Ignoring cross terms (i.e., assuming the bath spins are uncorrelated with each other)' leads to the simplified hopping rate.
  • domain assumption Electron-induced relaxation is spatially local and scales as r^-6.
    Classic result from paramagnetic relaxation theory (Lowe-Tse, Ref. [35]) used in S3 A/B for R_LF and R_HF.
  • domain assumption Floquet driving is adequately described by the first-order average Hamiltonian, scaling dipolar couplings by 1/2.
    Used in S3 B to relate W_HF = (1/4) W_LF; relies on high-frequency expansion [40,41,54].
  • domain assumption Product-state approximation for the KL divergence, neglecting interspin correlations.
    Explicitly stated in S4; needed to make KL divergence tractable, and acknowledged to be an approximation.
  • domain assumption Each disorder realization contains only one NV center (forced) plus ~5 P1 centers, with periodic boundaries; this represents the experimental sample.
    S3 A describes the lattice realization; the sparse defect density is meant to match the natural-abundance diamond, but the finite size and single NV per realization are approximations.

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Cite this review

Pith. "Pith review of Tunable Mpemba Effect in a Prethermal Many-Body Spin Network." pith.science (2026). https://pith.science/paper/GYOCLFAI

@misc{pith2026260721669,
  author       = {Pith},
  title        = {Pith review of: Tunable Mpemba Effect in a Prethermal Many-Body Spin Network},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GYOCLFAI}},
  note         = {Machine review of arXiv:2607.21669}
}
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read the original abstract

Relaxation in an interacting system is determined not only by its initial distance from equilibrium, but also by the relaxation modes populated by the initial state. Here we experimentally observe and control the Mpemba effect, in which a state farther from equilibrium overtakes one initially closer, in an extended, disordered $^{13}$C nuclear-spin network in diamond. Field cycling allows us to prepare distinct spatial polarization profiles by independently controlling hyperpolarization and defect-mediated relaxation. We then track their evolution under Floquet driving, which stabilizes a long-lived prethermal regime. We observe reproducible Mpemba crossings and tune the crossing time over several orders of magnitude, from late-time thermalization into the prethermal plateau. Semiclassical simulations show that randomly positioned paramagnetic defects create fast-relaxing regions and defect-poor regions that support the slowest collective relaxation mode. The Mpemba crossings are set by the initial state overlap with this mode. Our results demonstrate anomalous relaxation within a prethermal many-body regime and identify disorder, transport, and mode-selective state preparation as resources for controlling relaxation in extended spin networks.

Figures

Figures reproduced from arXiv: 2607.21669 by Ashok Ajoy, Chaitali Shah, Cooper M. Selco, Leo Joon Il Moon.

Figure 1
Figure 1. Figure 1: (A) State preparation at 36 mT consists of hyperpolarization for duration [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (A) Normalized relaxation curves for increasing [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (A) 2D projection of spatial profile of slowest eigenmode [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

discussion (0)

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