- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

General theory for group resetting with application to avoidance

Juhee Lee1,*, Seong-Gyu Yang1,2,*, Hye Jin Park3,4,†, and Ludvig Lizana1,‡

  • 1Integrated Science Lab, Department of Physics, Umeå University, SE-90187 Umeå, Sweden
  • 2Department of Physics and Institute of Basic Science, Sungkyunkwan University, Suwon 16419, Republic of Korea
  • 3Department of Physics, Inha University, Incheon 22212, Republic of Korea
  • 4Institute of Quantum Science, Inha University, Incheon 22212, Republic of Korea

  • *These authors contributed equally to this work.
  • †Contact author: hyejin.park@inha.ac.kr
  • ‡Contact author: ludvig.lizana@umu.se
PDF

Phys. Rev. Research 8, 013227 – Published 2 March, 2026

DOI: https://doi.org/10.1103/zxff-tkq5

Abstract

We present a general theoretical framework for group-resetting dynamics in a potential landscape. While traditional resetting models typically focus on a single particle, we consider a group of particles whose collective dynamics govern the resetting. We extend existing resetting theories to cover extreme-value group resetting. This has applications from bacterial evolution under antibiotic pressure to swarm-search optimization. Using renewal theory, we derive a Fokker-Planck equation for the spatial distribution of the group's center of mass, treated as an effective particle. This formalism yields analytical expressions for key observables such as the stationary mean position and variance. We also study a group avoidance problem, where the particles must avoid an undesirable region. Such problems have recently been studied in contexts such as preventing critically high water levels in dams and controlling excessive financial leverage. Our framework offers insights into how resetting can optimize group-level search and avoidance strategies.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (61)

  1. M. R. Evans and S. N. Majumdar, Diffusion with optimal resetting, J. Phys. A: Math. Theor. 44, 435001 (2011).
  2. A. Pal and S. Reuveni, First passage under restart, Phys. Rev. Lett. 118, 030603 (2017).
  3. A. Chechkin and I. M. Sokolov, Random search with resetting: A unified renewal approach, Phys. Rev. Lett. 121, 050601 (2018).
  4. X. Durang, S. Lee, L. Lizana, and J.-H. Jeon, First-passage statistics under stochastic resetting in bounded domains, J. Phys. A: Math. Theor. 52, 224001 (2019).
  5. U. Harbola, Stochastic dynamics of a non-Markovian random walk in the presence of resetting, Phys. Rev. E 109, 064148 (2024).
  6. V. Shkilev, Continuous-time random walk under time-dependent resetting, Phys. Rev. E 96, 012126 (2017).
  7. V. Shkilev and I. Sokolov, Subdiffusive continuous time random walks with power-law resetting, J. Phys. A: Math. Theor. 55, 484003 (2022).
  8. A. Masó-Puigdellosas, D. Campos, and V. Méndez, Stochastic movement subject to a reset-and-residence mechanism: Transport properties and first arrival statistics, J. Stat. Mech. (2019) 033201.
  9. K. Goswami, Stochastic resetting in a nonequilibrium environment, Phys. Rev. E 111, 014150 (2025).
  10. A. S. Bodrova, A. V. Chechkin, and I. M. Sokolov, Nonrenewal resetting of scaled Brownian motion, Phys. Rev. E 100, 012119 (2019).
  11. V. Méndez, A. Masó-Puigdellosas, and D. Campos, Nonstandard diffusion under Markovian resetting in bounded domains, Phys. Rev. E 105, 054118 (2022).
  12. A. R. Mesquita, J. P. Hespanha, and K. Åström, Optimotaxis: A stochastic multi-agent optimization procedure with point measurements, in International Workshop on Hybrid Systems: Computation and Control (Springer Berlin, Heidelberg, 2008), pp. 358–371.
  13. J. Kennedy and R. Eberhart, Particle swarm optimization, in Proceedings of the ICNN’95-International Conference on Neural Networks (IEEE, Perth, WA, Australia, 1995), Vol. 4, pp. 1942–1948.
  14. D. Wang, D. Tan, and L. Liu, Particle swarm optimization algorithm: An overview, Soft Comput. 22, 387 (2018).
  15. J. Davies and D. Davies, Origins and evolution of antibiotic resistance, Microbiol. Mol. Biol. Rev. 74, 417 (2010).
  16. H. C. Neu, The crisis in antibiotic resistance, Science 257, 1064 (1992).
  17. J. M. Munita and C. A. Arias, Mechanisms of antibiotic resistance, Microbio. Spectr. 4, 10.1128/microbiolspec.vmbf-0016-2015 (2016).
  18. J. M. Blair, M. A. Webber, A. J. Baylay, D. O. Ogbolu, and L. J. Piddock, Molecular mechanisms of antibiotic resistance, Nat. Rev. Microbiol. 13, 42 (2015).
  19. F. I. Arias-Sánchez, B. Vessman, and S. Mitri, Artificially selecting microbial communities: If we can breed dogs, why not microbiomes? PLoS Biol. 17, e3000356 (2019).
  20. Á. Sánchez et al., Directed evolution of microbial communities, Annu. Rev. Biophys. 50, 323 (2021).
  21. J. L. Thomas, J. Rowland-Chandler, and W. Shou, Artificial selection of microbial communities: What have we learnt and how can we improve? Curr. Opin. Microbiol. 77, 102400 (2024).
  22. A. Nagar and S. Gupta, Stochastic resetting in interacting particle systems: A review, J. Phys. A: Math. Theor. 56, 283001 (2023).
  23. U. Basu, A. Kundu, and A. Pal, Symmetric exclusion process under stochastic resetting, Phys. Rev. E 100, 032136 (2019).
  24. O. Sadekar and U. Basu, Zero-current nonequilibrium state in symmetric exclusion process with dichotomous stochastic resetting, J. Stat. Mech. (2020) 073209.
  25. S. Karthika and A. Nagar, Totally asymmetric simple exclusion process with resetting, J. Phys. A: Math. Theor. 53, 115003 (2020).
  26. S. Gupta, S. N. Majumdar, and G. Schehr, Fluctuating interfaces subject to stochastic resetting, Phys. Rev. Lett. 112, 220601 (2014).
  27. S. Gupta and A. Nagar, Resetting of fluctuating interfaces at power-law times, J. Phys. A: Math. Theor. 49, 445001 (2016).
  28. M. Magoni, S. N. Majumdar, and G. Schehr, Ising model with stochastic resetting, Phys. Rev. Res. 2, 033182 (2020).
  29. X. Durang, M. Henkel, and H. Park, The statistical mechanics of the coagulation–diffusion process with a stochastic reset, J. Phys. A: Math. Theor. 47, 045002 (2014).
  30. P. Grange, Non-conserving zero-range processes with extensive rates under resetting, J. Phys. Commun. 4, 045006 (2020).
  31. M. Biroli, H. Larralde, S. N. Majumdar, and G. Schehr, Extreme statistics and spacing distribution in a Brownian gas correlated by resetting, Phys. Rev. Lett. 130, 207101 (2023).
  32. O. Tal-Friedman, Y. Roichman, and S. Reuveni, Diffusion with partial resetting, Phys. Rev. E 106, 054116 (2022).
  33. C. Di Bello, A. V. Chechkin, A. K. Hartmann, Z. Palmowski, and R. Metzler, Time-dependent probability density function for partial resetting dynamics, New J. Phys. 25, 082002 (2023).
  34. S. N. Majumdar, S. Sabhapandit, and G. Schehr, Random walk with random resetting to the maximum position, Phys. Rev. E 92, 052126 (2015).
  35. B. De Bruyne, J. Randon-Furling, and S. Redner, Optimization in first-passage resetting, Phys. Rev. Lett. 125, 050602 (2020).
  36. B. De Bruyne, J. Randon-Furling, and S. Redner, Optimization and growth in first-passage resetting, J. Stat. Mech. (2021) 013203.
  37. M. R. Evans, S. N. Majumdar, and G. Schehr, Stochastic resetting and applications, J. Phys. A: Math. Theor. 53, 193001 (2020).
  38. M. Biroli, S. N. Majumdar, and G. Schehr, Critical number of walkers for diffusive search processes with resetting, Phys. Rev. E 107, 064141 (2023).
  39. M. Siboni, P. Sasorov, and B. Meerson, Fluctuations of a swarm of Brownian bees, Phys. Rev. E 104, 054131 (2021).
  40. R. Singh and S. Singh, Capture of a diffusing lamb by a diffusing lion when both return home, Phys. Rev. E 106, 064118 (2022).
  41. R. A. Fisher and L. H. C. Tippett, Limiting forms of the frequency distribution of the largest or smallest member of a sample, Math. Proc. Camb. Phil. Soc. 24, 180 (1928).
  42. A. Hansen, The three extreme value distributions: An introductory review, Front. Phys. 8, 604053 (2020).
  43. D. E. Cartwright and M. S. Longuet-Higgins, The statistical distribution of the maxima of a random function, Proc. R. Soc. A 237, 212 (1956).
  44. G. E. Uhlenbeck and L. S. Ornstein, On the theory of the Brownian motion, Phys. Rev. 36, 823 (1930).
  45. C. Gardiner, Stochastic Methods, 4th ed. (Springer Berlin, Heidelberg, 2009).
  46. P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations (Springer Berlin, Heidelberg, 1992).
  47. M. R. Evans, S. N. Majumdar, and G. Schehr, An exactly solvable predator prey model with resetting, J. Phys. A: Math. Theor. 55, 274005 (2022).
  48. G. Mercado-Vásquez and D. Boyer, Lotka–Volterra systems with stochastic resetting, J. Phys. A: Math. Theor. 51, 405601 (2018).
  49. A. Miron and S. Reuveni, Diffusion with local resetting and exclusion, Phys. Rev. Res. 3, L012023 (2021).
  50. R. Singh, T. Sandev, and S. Singh, Bernoulli trial under restarts: A comparative study of resetting transitions, Phys. Rev. E 108, L052106 (2023).
  51. T. T. Da Silva and M. D. Fragoso, The interplay between population genetics and diffusion with stochastic resetting, J. Phys. A: Math. Theor. 51, 505002 (2018).
  52. O. Vilk, M. Assaf, and B. Meerson, Fluctuations and first-passage properties of systems of Brownian particles with reset, Phys. Rev. E 106, 024117 (2022).
  53. P. Krapivsky, O. Vilk, and B. Meerson, Competition in a system of Brownian particles: Encouraging achievers, Phys. Rev. E 106, 034125 (2022).
  54. P. Sasorov, A. Vilenkin, and N. R. Smith, Probabilities of moderately atypical fluctuations of the size of a swarm of Brownian bees, Phys. Rev. E 107, 014140 (2023).
  55. K. S. Olsen, Steady-state moments under resetting to a distribution, Phys. Rev. E 108, 044120 (2023).
  56. F. Mori, K. S. Olsen, and S. Krishnamurthy, Entropy production of resetting processes, Phys. Rev. Res. 5, 023103 (2023).
  57. V. Mendez, R. Flaquer-Galmés, and D. Campos, First-passage time of a Brownian searcher with stochastic resetting to random positions, Phys. Rev. E 109, 044134 (2024).
  58. M. Dahlenburg, A. V. Chechkin, R. Schumer, and R. Metzler, Stochastic resetting by a random amplitude, Phys. Rev. E 103, 052123 (2021).
  59. D. Boyer, M. R. Evans, and S. N. Majumdar, Long time scaling behaviour for diffusion with resetting and memory, J. Stat. Mech. (2017) 023208.
  60. J. Lee, W. Shou, and H. J. Park, The success of artificial selection for collective composition hinges on initial and target values, eLife 13, RP97461 (2025).
  61. All code for numerical calculations is provided in the Git repository, https://github.com/lizanalab/lee2026general.

Outline

Information

Phys. Rev. Research 8, 013227– Published 2 March, 2026
  • Received 13 May 2025
  • Revised 15 October 2025
  • Accepted 6 February 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation