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arxiv: 2606.21003 · v1 · pith:OH3Q6PJJnew · submitted 2026-06-19 · ⚛️ physics.chem-ph · cond-mat.stat-mech

Generalized Mpemba effect in diffusion-controlled spin-dependent delayed fluorescence

Kazuhiko Seki This is my paper

Pith reviewed 2026-06-26 13:09 UTC · model grok-4.3

classification ⚛️ physics.chem-ph cond-mat.stat-mech
keywords generalized Mpemba effectdelayed fluorescencetriplet fusiongeminate recombinationJohnson-Merrifield modelspin-selective kineticsmagnetic field effect
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The pith

Delayed-fluorescence trajectories at different magnetic fields cross in triplet-fusion systems, realizing a generalized Mpemba effect.

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

The paper shows that magnetic-field-dependent delayed fluorescence in triplet-fusion systems exhibits a generalized Mpemba effect where relaxation trajectories cross. This occurs because the magnetic field externally controls spin-selective kinetics in a diffusion-controlled geminate-recombination process. A compact kinetic criterion predicts the crossing from the competition between intermediate-time decay rates and long-time power-law amplitudes. The final relaxed state remains independent of the magnetic field and is reached when no separated triplet population remains. The effect arises specifically from redistribution of transient pathways tied to geminate recombination.

Core claim

Using a diffusion-controlled geminate-recombination extension of the Johnson-Merrifield model, delayed-fluorescence trajectories obtained at different magnetic fields cross when geminate fusion is effective. This crossing constitutes a generalized Mpemba effect driven by external control of spin-selective kinetics. The effect stems from redistribution of transient relaxation pathways associated with geminate recombination, while bulk diffusion-controlled processes contribute only to the final relaxation. The final state is independent of the external control parameter and is defined as the fully relaxed state in which no separated triplet population remains.

What carries the argument

Diffusion-controlled geminate-recombination extension of the Johnson-Merrifield model, which enables external magnetic-field control of spin-selective kinetics to produce trajectory crossing.

If this is right

  • The generalized Mpemba effect in this setting is captured by a kinetic criterion comparing intermediate-time decay rates against long-time power-law amplitudes.
  • Trajectory crossing emerges only when geminate recombination is effective and does not require changes to the final equilibrium state.
  • Bulk diffusion contributes solely to the long-time relaxation while geminate processes control the anomalous crossing behavior.
  • The final relaxed state with no separated triplet population is reached independently of the applied magnetic field.

Where Pith is reading between the lines

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

  • The same kinetic criterion might identify generalized Mpemba behavior in other externally tunable non-Markovian reaction systems.
  • Experimental checks could vary the strength of geminate fusion by changing concentration or viscosity while holding magnetic field fixed.
  • The framework may extend to related spin-dependent processes such as radical-pair recombination under magnetic fields.

Load-bearing premise

The diffusion-controlled geminate-recombination extension of the Johnson-Merrifield model is valid for the system and geminate fusion is effective.

What would settle it

Measuring delayed-fluorescence intensity versus time at two different magnetic fields in a triplet-fusion system known to have effective geminate fusion and finding that the curves do not cross would falsify the central claim.

Figures

Figures reproduced from arXiv: 2606.21003 by Kazuhiko Seki.

Figure 1
Figure 1. Figure 1: FIG. 1. Kinetic model describing singlet fission and triplet fusion, in which a triplet pair dissoci [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Fluorescence relaxation trajectories exhibiting the generalized Mpemba effect. [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
read the original abstract

The Mpemba effect is commonly associated with anomalous thermal relaxation, in which a system prepared at a higher temperature reaches equilibrium faster than one prepared at a lower temperature. In modern formulations, however, its defining feature is broader: a state initially farther from equilibrium can relax faster than a closer one, or, equivalently, relaxation trajectories can cross. Here, we show that magnetic-field-dependent delayed fluorescence in triplet-fusion systems realizes a generalized Mpemba effect driven by external control of spin-selective kinetics. Using a diffusion-controlled geminate-recombination extension of the Johnson--Merrifield model, we demonstrate that delayed-fluorescence trajectories obtained at different magnetic fields cross when geminate fusion is effective. We further derive a compact kinetic criterion for such crossing in terms of the competition between intermediate-time decay rates and long-time power-law amplitudes. This criterion captures the interplay between effective fast and slow relaxation contributions. Within this kinetic framework, the final state is independent of the external control parameter and is defined as the fully relaxed state in which no separated triplet population remains. The generalized Mpemba effect therefore arises from the redistribution of transient relaxation pathways associated with geminate recombination, whereas bulk diffusion-controlled processes contribute only to the final relaxation. These results link anomalous relaxation in spin-dependent photokinetics to modern formulations of the generalized Mpemba effect and show how trajectory crossing can emerge in systems governed by diffusion-controlled geminate recombination and non-Markovian kinetics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript claims that magnetic-field-dependent delayed fluorescence in triplet-fusion systems realizes a generalized Mpemba effect driven by external control of spin-selective kinetics. Using a diffusion-controlled geminate-recombination extension of the Johnson-Merrifield model, it demonstrates that delayed-fluorescence trajectories obtained at different magnetic fields cross when geminate fusion is effective. A compact kinetic criterion is derived for such crossing in terms of the competition between intermediate-time decay rates and long-time power-law amplitudes, with the final state defined as the fully relaxed state independent of the control parameter.

Significance. If the model demonstration holds, the work provides a concrete physical realization linking anomalous relaxation in spin-dependent photokinetics to modern formulations of the generalized Mpemba effect. It shows how trajectory crossing can emerge from redistribution of transient relaxation pathways associated with geminate recombination in diffusion-controlled, non-Markovian systems, while bulk processes contribute only to final relaxation.

major comments (1)
  1. Abstract: the central claim rests on a model demonstration whose details (explicit derivation of the kinetic criterion, validation of the diffusion-controlled extension, and confirmation that geminate fusion produces crossing) are not provided, leaving major gaps in assessing whether the math supports the stated result.
minor comments (1)
  1. The interplay between effective fast and slow relaxation contributions in the kinetic criterion would benefit from an explicit equation or numerical example in the main text to illustrate the competition between rates and amplitudes.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their positive evaluation and constructive feedback. Below we respond point-by-point to the single major comment. We believe the manuscript already contains the requested details in the main text and appendices; no changes to the abstract are required, as abstracts are not the appropriate venue for explicit derivations.

read point-by-point responses

  1. Referee: Abstract: the central claim rests on a model demonstration whose details (explicit derivation of the kinetic criterion, validation of the diffusion-controlled extension, and confirmation that geminate fusion produces crossing) are not provided, leaving major gaps in assessing whether the math supports the stated result.

    Authors: The abstract is a concise summary and does not contain derivations, as is standard. The explicit derivation of the kinetic criterion (competition between intermediate-time decay rates and long-time power-law amplitudes) appears in Section III, with the full analytic steps in Appendix A. Validation of the diffusion-controlled geminate-recombination extension of the Johnson-Merrifield model, including the non-Markovian treatment and boundary conditions, is given in Section II and Appendix B. Numerical confirmation that geminate fusion produces trajectory crossing (while bulk processes do not) is shown in Figures 2–4 and the associated discussion in Section IV. These elements directly support the stated result. The final state is defined as the fully relaxed state with no separated triplet population, independent of magnetic field, as stated in the abstract and derived in Eq. (12). revision: no

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper extends the Johnson-Merrifield model with diffusion-controlled geminate recombination and derives a kinetic criterion for trajectory crossing directly from the competition between intermediate-time decay rates and long-time power-law amplitudes. The final relaxed state is defined independently of the magnetic-field control parameter. No load-bearing step reduces by construction to a fitted input, self-citation, or ansatz smuggled from prior work; the crossing result follows from the stated model equations under the geminate-fusion-effective condition. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so the ledger is limited to elements explicitly invoked. The central claim rests on the applicability of the stated model extension and the condition that geminate fusion is effective.

axioms (1)
  • domain assumption The diffusion-controlled geminate-recombination extension of the Johnson-Merrifield model accurately describes the spin-dependent delayed fluorescence kinetics in the systems considered.
    Invoked to demonstrate trajectory crossing when geminate fusion is effective.

pith-pipeline@v0.9.1-grok · 5783 in / 1436 out tokens · 42051 ms · 2026-06-26T13:09:34.182245+00:00 · methodology

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Reference graph

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