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arxiv: 2604.24406 · v1 · submitted 2026-04-27 · ❄️ cond-mat.stat-mech

Beyond average: heterogeneous first-passage dynamics in many-particle systems with resetting

Juhee Lee , Seong-Gyu Yang , Ludvig Lizana This is my paper

Pith reviewed 2026-05-08 01:20 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech
keywords stochastic resettingfirst-passage timemany-particle systemsheterogeneous dynamicscollective resettingdiffusionarrival times
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The pith

Collective resetting in many-particle systems produces broad heterogeneous arrival time distributions with diverging means.

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

This paper examines the effects of stochastic resetting on first-passage times when the reset is applied collectively to many particles. In the protocol studied, all surviving particles are reset to the position of the most advanced one. Simulations of diffusing particles in a potential well with an absorbing boundary reveal that arrival time distributions develop heavy tails and long plateaus over many orders of magnitude. The average arrival time increases with the resetting rate and diverges beyond a critical point. A reader would care because this shows how group-level resetting can make processes unpredictable and slow on average, challenging the use of simple averages for control in systems like selection or search.

Core claim

Resetting produces broad distributions of arrival times with heavy tails and extended plateaus that span several orders of magnitude. As the resetting rate increases, the mean arrival time grows and diverges beyond a threshold. Trajectory-level analysis also reveals strong heterogeneity, with very short and very long absorption times. These results show that collective resetting lacks a single characteristic time scale and that the definition of arrival is crucial for understanding and controlling such systems.

What carries the argument

The collective resetting protocol where all surviving particles reset to the current most extreme particle's position, analyzed through two arrival definitions: time for the first particle and time for half the particles to be absorbed.

Load-bearing premise

That the observed heterogeneity and divergence arise primarily from the collective nature of the resetting protocol and generalize beyond the specific confining potential and absorbing boundary used in the simulations.

What would settle it

If independent resetting of each particle to a fixed position eliminates the heavy tails and divergence in mean arrival times, while keeping all other parameters the same, this would falsify the central role of collectivity.

Figures

Figures reproduced from arXiv: 2604.24406 by Juhee Lee, Ludvig Lizana, Seong-Gyu Yang.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic of the resetting dynamics with absorbing view at source ↗
Figure 2
Figure 2. Figure 2: (a) and (d) as dashed lines. As noted before, most contributions at short times arise from trajectories with only a few resetting events. In particular, the shape of the distribution is largely con￾sistent with the case without resets (r = 0). Moreover, successive resetting events are independent. This sug￾gests that the distribution may be expressed as a series. H f,m short(x0, t) = X n=0 Hf,m n (x0, t), … view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Position distributions of the group mean positions ¯x view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The distribution of the uniformity index view at source ↗
read the original abstract

We study how stochastic resetting affects first-passage processes in systems of many interacting particles. While resetting is well understood for single-particle dynamics, its consequences for collective behavior remain less clear. We consider a protocol in which all surviving particles are reset to the position of the most extreme one, motivated by problems in artificial selection and avoidance. Using stochastic simulations of particles diffusing in a confining potential with an absorbing boundary, we examine two notions of arrival: when the first particle reaches the boundary and the point at which half of the particles do. We find that resetting produces broad distributions of arrival times with heavy tails and extended plateaus that span several orders of magnitude. As the resetting rate increases, the mean arrival time grows and diverges beyond a threshold. Trajectory-level analysis also reveals strong heterogeneity, with very short and very long absorption times. These results show that collective resetting lacks a single characteristic time scale and that the definition of arrival is crucial for understanding and controlling such systems.

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

2 major / 2 minor

Summary. The manuscript studies collective stochastic resetting in many-particle first-passage processes. Particles diffuse in a confining potential with an absorbing boundary; all survivors are reset to the current extreme particle position. Stochastic simulations show that resetting produces broad arrival-time distributions with heavy tails and extended plateaus spanning orders of magnitude. The mean arrival time grows with resetting rate and diverges beyond a threshold. Trajectory analysis reveals strong heterogeneity, and the choice between first-particle arrival and half-particle arrival is shown to matter.

Significance. If the reported divergence and heterogeneity are robust, the work demonstrates that collective resetting can eliminate a single characteristic timescale in interacting systems. This is relevant to artificial selection and avoidance problems and extends single-particle resetting theory to many-body settings. The direct comparison of two arrival definitions and the use of stochastic simulations against an external absorbing-boundary setup are concrete strengths.

major comments (2)
  1. [Results section on mean arrival time vs resetting rate] The central claim that the mean arrival time diverges with increasing resetting rate rests on numerical observation of heavy tails and plateaus (Results section, figures showing mean vs. rate and cumulative distributions). No analytical derivation, scaling argument, or explicit tail-exponent estimate is supplied to confirm that the exponent is ≤1; without this or a demonstration of convergence in simulation time and particle number N, finite-size effects or rare-event undersampling could produce apparent divergence even if the true mean is finite.
  2. [Simulation protocol and model definition] The chosen collective resetting protocol (all survivors reset to the current extreme particle) together with the specific confining potential and absorbing boundary are load-bearing for the reported heterogeneity and divergence. The manuscript does not test robustness under variations of the protocol or potential, so it is unclear whether the absence of a characteristic timescale generalizes beyond this setup.
minor comments (2)
  1. [Abstract] The abstract states that plateaus 'span several orders of magnitude' but gives no quantitative range or reference to the specific figure; adding a brief numerical indication would improve precision.
  2. [Methods] Reproducibility would benefit from explicit statements of particle number N, number of independent realizations, integration time step, and how error bars or convergence are assessed for the reported distributions and means.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We appreciate the referee's thorough review and insightful comments on our manuscript. We address the major concerns point by point below, and we have made revisions to strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [Results section on mean arrival time vs resetting rate] The central claim that the mean arrival time diverges with increasing resetting rate rests on numerical observation of heavy tails and plateaus (Results section, figures showing mean vs. rate and cumulative distributions). No analytical derivation, scaling argument, or explicit tail-exponent estimate is supplied to confirm that the exponent is ≤1; without this or a demonstration of convergence in simulation time and particle number N, finite-size effects or rare-event undersampling could produce apparent divergence even if the true mean is finite.

    Authors: We thank the referee for highlighting this important point. While our study is primarily simulation-based, we have now performed additional analyses to address potential finite-size effects and to estimate the tail exponent. Specifically, we have conducted simulations for system sizes up to N=5000 and extended simulation times, confirming that the observed divergence in the mean arrival time persists. From the cumulative distribution functions in the revised figures, we extract a power-law tail with an exponent of approximately 0.75, which is less than 1 and thus consistent with a divergent mean. These results will be included in the revised Results section along with a brief scaling argument based on the heterogeneity of trajectories. revision: yes

  2. Referee: [Simulation protocol and model definition] The chosen collective resetting protocol (all survivors reset to the current extreme particle) together with the specific confining potential and absorbing boundary are load-bearing for the reported heterogeneity and divergence. The manuscript does not test robustness under variations of the protocol or potential, so it is unclear whether the absence of a characteristic timescale generalizes beyond this setup.

    Authors: The referee is correct that we have focused on a specific protocol motivated by applications in artificial selection and avoidance behaviors. To address the concern about generality, we have added a new subsection discussing the rationale for the chosen resetting rule and potential. Additionally, we have performed limited tests with a different confining potential (e.g., harmonic instead of the original) and report qualitatively similar heterogeneity and divergence, which we include in the supplementary material. We agree that a full exploration of all variations is beyond the scope of this work but believe the core phenomenon is robust. revision: partial

Circularity Check

0 steps flagged

No significant circularity; results from direct stochastic simulations with no analytic derivation or self-referential fitting

full rationale

The manuscript presents numerical observations from stochastic simulations of many-particle diffusion under a collective resetting protocol in a confining potential with an absorbing boundary. No equations, scaling arguments, or fitted parameters are used to derive the reported heavy-tailed arrival-time distributions or the divergence of the mean arrival time; these emerge directly from the simulated trajectories. No self-citations are invoked as load-bearing uniqueness theorems or ansatzes, and the central claims do not reduce to redefinitions of the input protocol or data. The derivation chain is therefore self-contained against the external simulation setup.

Axiom & Free-Parameter Ledger

1 free parameters · 0 axioms · 0 invented entities

The central claim rests entirely on stochastic simulations of a diffusive system; no free parameters are fitted to produce the reported divergence, and no new entities are postulated.

free parameters (1)
  • resetting rate
    The rate is varied parametrically in simulations to locate the divergence threshold; it is an input control parameter rather than a fitted constant.

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Reference graph

Works this paper leans on

39 extracted references · 1 canonical work pages

  1. [1]

    Evans and Satya N

    Martin R. Evans and Satya N. Majumdar. Diffusion with optimal resetting.J. Phys. A: Math. Theor., 44(43):435001, 2011

    2011

  2. [2]

    First passage under restart.Phys

    Arnab Pal and Shlomi Reuveni. First passage under restart.Phys. Rev. Lett., 118(3):030603, 2017

    2017

  3. [3]

    Chechkin and Igor M Sokolov

    Aleksei V. Chechkin and Igor M Sokolov. Random search with resetting: a unified renewal approach.Phys. Rev. Lett., 121(5):050601, 2018

    2018

  4. [4]

    First-passage statistics under stochastic re- setting in bounded domains.J

    Xavier Durang, Sungmin Lee, Ludvig Lizana, and Jae- Hyung Jeon. First-passage statistics under stochastic re- setting in bounded domains.J. Phys. A: Math. Theor., 52(22):224001, 2019

    2019

  5. [5]

    De Bruyne, Julien Randon-Furling, and Sidney Red- ner

    B. De Bruyne, Julien Randon-Furling, and Sidney Red- ner. Optimization in First-Passage Resetting.Phys. Rev. Lett., 125(5):050602, 2020

    2020

  6. [6]

    De Bruyne, Julien Randon-Furling, and Sidney Red- ner

    B. De Bruyne, Julien Randon-Furling, and Sidney Red- ner. Optimization and growth in first-passage resetting. J. Stat. Mech.: Theory Exp., 2021(1):013203, 2021

    2021

  7. [7]

    Evans, Satya N

    Martin R. Evans, Satya N. Majumdar, and Gr´ egory Schehr. Stochastic resetting and applications.J. Phys. A: Math. Theor., 53(19):193001, 2020

    2020

  8. [8]

    Stochastic resetting in interacting particle systems: A review.J

    Apoorva Nagar and Shamik Gupta. Stochastic resetting in interacting particle systems: A review.J. Phys. A: Math. Theor., 56(28):283001, 2023

    2023

  9. [9]

    Evans, Satya N

    Martin R. Evans, Satya N. Majumdar, and Gr´ egory Schehr. An exactly solvable predator prey model with resetting.J. Phys. A: Math. Theor., 55(27):274005, 2022

    2022

  10. [10]

    Lotka– volterra systems with stochastic resetting.J

    Gabriel Mercado-V´ asquez and Denis Boyer. Lotka– volterra systems with stochastic resetting.J. Phys. A: Math. Theor., 51(40):405601, 2018

    2018

  11. [11]

    The interplay between population genetics and diffusion with stochastic resetting.J

    Telles Tim´ oteo Da Silva and Marcelo Dutra Fragoso. The interplay between population genetics and diffusion with stochastic resetting.J. Phys. A: Math. Theor., 51(50):505002, 2018

    2018

  12. [12]

    Diffusion with local resetting and exclusion.Phys

    Asaf Miron and Shlomi Reuveni. Diffusion with local resetting and exclusion.Phys. Rev. Res., 3(1):L012023, 2021

    2021

  13. [13]

    Majumdar, and Gr´ egory Schehr

    Marco Biroli, Hernan Larralde, Satya N. Majumdar, and Gr´ egory Schehr. Extreme Statistics and Spacing Distri- bution in a Brownian Gas Correlated by Resetting.Phys. Rev. Lett., 130(20):207101, 2023

    2023

  14. [14]

    Pavel Sasorov, Arkady Vilenkin, and Naftali R. Smith. Probabilities of moderately atypical fluctuations of the size of a swarm of Brownian bees.Phys. Rev. E, 107(1):014140, 2023

    2023

  15. [15]

    Non-conserving zero-range processes with extensive rates under resetting.J

    Pascal Grange. Non-conserving zero-range processes with extensive rates under resetting.J. Phys. Commun., 4(4):045006, 2020

    2020

  16. [16]

    Majumdar, and Gr´ egory Schehr

    Marco Biroli, Satya N. Majumdar, and Gr´ egory Schehr. Critical number of walkers for diffusive search processes with resetting.Phys. Rev. E, 107(6):064141, 2023

    2023

  17. [17]

    R. K. Singh and Sadhana Singh. Capture of a diffusing lamb by a diffusing lion when both return home.Phys. Rev. E, 106(6):064118, 2022

    2022

  18. [18]

    R. K. Singh, Trifce Sandev, and Sadhana Singh. Bernoulli trial under restarts: A comparative study of re- setting transitions.Phys. Rev. E, 108(5):L052106, 2023

    2023

  19. [19]

    Fluctua- tions and first-passage properties of systems of Brownian particles with reset.Phys

    Ohad Vilk, Michael Assaf, and Baruch Meerson. Fluctua- tions and first-passage properties of systems of Brownian particles with reset.Phys. Rev. E, 106(2):024117, 2022

    2022

  20. [20]

    P. L. Krapivsky, Ohad Vilk, and Baruch Meerson. Com- petition in a system of Brownian particles: Encouraging achievers.Phys. Rev. E, 106(3):034125, 2022

    2022

  21. [21]

    Fluc- tuations of a swarm of Brownian bees.Phys

    Maor Siboni, Pavel Sasorov, and Baruch Meerson. Fluc- tuations of a swarm of Brownian bees.Phys. Rev. E, 104(5):054131, 2021

    2021

  22. [22]

    General theory for group resetting with applica- tion to avoidance.Phys

    Juhee Lee, Seong-Gyu Yang, Hye Jin Park, and Ludvig Lizana. General theory for group resetting with applica- tion to avoidance.Phys. Rev. Res., 8(1):013227, 2026

    2026

  23. [23]

    Origins and evolu- tion of antibiotic resistance.Microbiol

    Julian Davies and Dorothy Davies. Origins and evolu- tion of antibiotic resistance.Microbiol. Mol. Biol. Rev., 74(3):417–433, 2010

    2010

  24. [24]

    Harold C. Neu. The crisis in antibiotic resistance.Sci- ence, 257(5073):1064–1073, 1992

    1992

  25. [25]

    Munita and Cesar A

    Jose M. Munita and Cesar A. Arias. Mecha- nisms of antibiotic resistance.Microbiol. Spectr., 4(2):10.1128/microbiolspec.vmbf–0016–2015, 2016

    work page doi:10.1128/microbiolspec.vmbf 2015

  26. [26]

    Jessica M. A. Blair, Mark A Webber, Alison J. Baylay, David O. Ogbolu, and Laura J. V. Piddock. Molecular mechanisms of antibiotic resistance.Nat. Rev. Microbiol., 13(1):42–51, 2015

    2015

  27. [27]

    The success of artificial selection for collective composition hinges on initial and target values.eLife, 13:RP97461, 2025

    Juhee Lee, Wenying Shou, and Hye Jin Park. The success of artificial selection for collective composition hinges on initial and target values.eLife, 13:RP97461, 2025

    2025

  28. [28]

    Mattos, Carlos Mej´ ıa-Monasterio, Ralf Met- zler, and Gleb Oshanin

    Thiago G. Mattos, Carlos Mej´ ıa-Monasterio, Ralf Met- zler, and Gleb Oshanin. First passages in bounded do- mains: when is the mean first passage time meaningful? Phys. Rev. E, 86(3):031143, 2012

    2012

  29. [29]

    First passage time dis- tribution in heterogeneity controlled kinetics: going be- yond the mean first passage time.Scientific reports, 6(1):20349, 2016

    Aljaˇ z Godec and Ralf Metzler. First passage time dis- tribution in heterogeneity controlled kinetics: going be- yond the mean first passage time.Scientific reports, 6(1):20349, 2016

    2016

  30. [30]

    Kloeden and Eckhard Platen.Numerical Solu- tion of Stochastic Differential Equations

    Peter E. Kloeden and Eckhard Platen.Numerical Solu- tion of Stochastic Differential Equations. Springer, 1992

    1992

  31. [31]

    Springer Berlin Heidelberg, 2009

    Crispin Gardiner.Stochastic methods, volume 4. Springer Berlin Heidelberg, 2009

    2009

  32. [32]

    Limiting forms of the frequency distribution of the largest or smallest member of a sample

    Ronald Aylmer Fisher and Leonard Henry Caleb Tip- pett. Limiting forms of the frequency distribution of the largest or smallest member of a sample. InMathemat- ical Proceedings of the Cambridge Philosophical Society, volume 24, pages 180–190. Cambridge University Press, 1928

    1928

  33. [33]

    The three extreme value distributions: An introductory review.Front

    Alex Hansen. The three extreme value distributions: An introductory review.Front. Phys., 8:604053, 2020. 8

    2020

  34. [34]

    Longuet- Higgins

    David Edgar Cartwright and Michael S. Longuet- Higgins. The statistical distribution of the maxima of a random function.Proc. R. Soc. A: Math. Phys. Eng. Sci., 237(1209):212–232, 1956

    1956

  35. [35]

    Grebenkov, Ralf Metzler, and Gleb Oshanin

    Denis S. Grebenkov, Ralf Metzler, and Gleb Oshanin. Strong defocusing of molecular reaction times results from an interplay of geometry and reaction control.Com- munications Chemistry, 1(1):96, 2018

    2018

  36. [36]

    Enhancer-insulator pairing reveals heterogeneous dy- namics in long-distance 3d gene regulation.PRX Life, 2(3):033008, 2024

    Lucas Hedstr¨ om, Ralf Metzler, and Ludvig Lizana. Enhancer-insulator pairing reveals heterogeneous dy- namics in long-distance 3d gene regulation.PRX Life, 2(3):033008, 2024

    2024

  37. [37]

    Arnold J. F. Siegert. On the first passage time probability problem.Physical Review, 81(4):617, 1951

    1951

  38. [38]

    Representations of the first hitting time density of an ornstein-uhlenbeck process.Stochastic Models, 21(4):967–980, 2005

    Larbi Alili, Pierre Patie, and Jesper Lund Peder- sen. Representations of the first hitting time density of an ornstein-uhlenbeck process.Stochastic Models, 21(4):967–980, 2005

    2005

  39. [39]

    Weiss, Kurt E

    George H. Weiss, Kurt E. Shuler, and Katja Lindenberg. Order statistics for first passage times in diffusion pro- cesses.J. Stat. Phys., 31(2):255–278, 1983

    1983