- 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
  • Letter
  • Open Access

Enhanced particle diffusion in fluctuating binary environments

Fivos Perakis1,2,*, Takeshi Kawasaki3,4, and Shinji Saito2,5,†

  • *Contact author: f.perakis@fysik.su.se
  • †Contact author: shinji@ims.ac.jp
PDF

Phys. Rev. Research 8, L012015 – Published 15 January, 2026

DOI: https://doi.org/10.1103/1rnr-11yb

Abstract

We investigate single-particle diffusion in a two-state Langevin model where the friction coefficient randomly switches between low-friction (liquidlike) and high-friction (glassylike) states. The dynamics are governed by the ratio between the friction switching time τ and the intrinsic velocity relaxation time τ0. For fast switching (τ/τ0≲1), the motion is homogeneous and Brownian, whereas for slow switching (τ/τ0≫1) the particle exhibits intermittent dynamics and an enhanced diffusion coefficient. Analysis of the single-particle overlap function Q(t) and the dynamic susceptibility χ4(t) reveals decoupling of the diffusion coefficient from the average friction upon cooling, which coincides with increasing temporal dynamic heterogeneity. This minimal model provides a transparent framework for understanding single-particle transport in media with temporally fluctuating local mobility and intermittent fast/slow dynamical regimes.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (45)

  1. M. D. Ediger, Spatially heterogeneous dynamics in supercooled liquids, Annu. Rev. Phys. Chem. 51, 99 (2000).
  2. P. Schurtenberger, R. A. Chamberlin, G. M. Thurston, J. A. Thomson, and G. B. Benedek, Observation of critical phenomena in a protein-water solution, Phys. Rev. Lett. 63, 2064 (1989).
  3. B. M. Fine, J. Pande, A. Lomakin, O. O. Ogun, and G. B. Benedek, Dynamic critical phenomena in aqueous protein solutions, Phys. Rev. Lett. 74, 198 (1995).
  4. H. Tanaka, Universality of viscoelastic phase separation in dynamically asymmetric fluid mixtures, Phys. Rev. Lett. 76, 787 (1996).
  5. H. Tanaka and Y. Nishikawa, Viscoelastic phase separation of protein solutions, Phys. Rev. Lett. 95, 078103 (2005).
  6. S. R. McGuffee and A. H. Elcock, Diffusion, crowding & protein stability in a dynamic molecular model of the bacterial cytoplasm, PLoS Comput. Biol. 6, e1000694 (2010).
  7. J. L. Watson, E. Seinkmane, C. T. Styles, A. Mihut, L. K. Krüger, K. E. McNally, V. J. Planelles-Herrero, M. Dudek, P. M. McCall, S. Barbiero, et al., Macromolecular condensation buffers intracellular water potential, Nature (London) 623, 842 (2023).
  8. P. Gallo, F. Sciortino, P. Tartaglia, and S.-H. Chen, Slow dynamics of water molecules in supercooled states, Phys. Rev. Lett. 76, 2730 (1996).
  9. L. Xu, P. Kumar, S. V. Buldyrev, S.-H. Chen, P. H. Poole, F. Sciortino, and H. E. Stanley, Relation between the Widom line and the dynamic crossover in systems with a liquid–liquid phase transition, Proc. Natl. Acad. Sci. USA 102, 16558 (2005).
  10. K. H. Kim, A. Späh, H. Pathak, F. Perakis, D. Mariedahl, K. Amann-Winkel, J. A. Sellberg, J. H. Lee, S. Kim, J. Park, K. H. Nam, T. Katayama, and A. Nilsson, Maxima in the thermodynamic response and correlation functions of deeply supercooled water, Science 358, 1589 (2017).
  11. S. Saito, B. Bagchi, and I. Ohmine, Crucial role of fragmented and isolated defects in persistent relaxation of deeply supercooled water, J. Chem. Phys. 149, 124504 (2018).
  12. P. G. Debenedetti, F. Sciortino, and G. H. Zerze, Second critical point in two realistic models of water, Science 369, 289 (2020).
  13. K. H. Kim, A. Späh, H. Pathak, C. Yang, S. Bonetti, K. Amann-Winkel, D. Mariedahl, D. Schlesinger, J. A. Sellberg, D. Mendez, G. van der Schot, H. Y. Hwang, J. Clark, O. Shigeki, T. Tadashi, Y. Harada, H. Ogasawara, T. Katayama, A. Nilsson, and F. Perakis, Anisotropic x-ray scattering of transiently oriented water, Phys. Rev. Lett. 125, 076002 (2020).
  14. K. H. Kim, K. Amann-Winkel, N. Giovambattista, A. Späh, F. Perakis, H. Pathak, M. L. Parada, C. Yang, D. Mariedahl, T. Eklund, et al., Experimental observation of the liquid-liquid transition in bulk supercooled water under pressure, Science 370, 978 (2020).
  15. P. Ballesta, A. Duri, and L. Cipelletti, Unexpected drop of dynamical heterogeneities in colloidal suspensions approaching the jamming transition, Nat. Phys. 4, 550 (2008).
  16. B. Wang, S. M. Anthony, S. C. Bae, and S. Granick, Anomalous yet Brownian, Proc. Natl. Acad. Sci. USA 106, 15160 (2009).
  17. J. Möller and T. Narayanan, Velocity fluctuations in sedimenting Brownian particles, Phys. Rev. Lett. 118, 198001 (2017).
  18. K. Goswami, A. G. Cherstvy, A. Godec, and R. Metzler, Anomalous diffusion of active Brownian particles in responsive elastic gels: Nonergodicity, non-Gaussianity, and distributions of trapping times, Phys. Rev. E 110, 044609 (2024).
  19. M. Seaberg, B. Holladay, J. Lee, M. Sikorski, A. Reid, S. Montoya, G. Dakovski, J. Koralek, G. Coslovich, S. Moeller, W. Schlotter, R. Streubel, S. Kevan, P. Fischer, E. Fullerton, J. Turner, F.-J. Decker, S. Sinha, S. Roy, and J. Turner, Nanosecond x-ray photon correlation spectroscopy on magnetic skyrmions, Phys. Rev. Lett. 119, 067403 (2017).
  20. A. Vailati, H. Bataller, M. M. Bou-Ali, M. Carpineti, R. Cerbino, F. Croccolo, S. U. Egelhaaf, F. Giavazzi, C. Giraudet, G. Guevara-Carrion, D. Horváth, W. Köhler, A. Mialdun, J. Porter, K. Schwarzenberger, V. Shevtsova, and A. De Wit, Diffusion in liquid mixtures, npj Microgravity 9, 1 (2023).
  21. F. H. Stillinger and J. A. Hodgdon, Translation-rotation paradox for diffusion in fragile glass-forming liquids, Phys. Rev. E 50, 2064 (1994).
  22. I. Chang and H. Sillescu, Heterogeneity at the glass transition: Translational and rotational self-diffusion, J. Phys. Chem. B 101, 8794 (1997).
  23. A. Pacheco-Pozo, M. Balcerek, A. Wyłomanska, K. Burnecki, I. M. Sokolov, and D. Krapf, Langevin equation in heterogeneous landscapes: How to choose the interpretation, Phys. Rev. Lett. 133, 067102 (2024).
  24. P. Massignan, C. Manzo, J. A. Torreno-Pina, M. F. García-Parajo, M. Lewenstein, and G. J. Lapeyre, Nonergodic subdiffusion from Brownian motion in an inhomogeneous medium, Phys. Rev. Lett. 112, 150603 (2014).
  25. C. Van den Broeck, J. M. R. Parrondo, and R. Toral, Noise-induced nonequilibrium phase transition, Phys. Rev. Lett. 73, 3395 (1994).
  26. R. Rozenfeld, J. Łuczka, and P. Talkner, Brownian motion in a fluctuating medium, Phys. Lett. A 249, 409 (1998).
  27. C. R. Doering and J. C. Gadoua, Resonant activation over a fluctuating barrier, Phys. Rev. Lett. 69, 2318 (1992).
  28. N. A. Bustos, C. M. Saad-Roy, A. G. Cherstvy, and C. E. Wagner, Distributed medium viscosity yields quasi-exponential step-size probability distributions in heterogeneous media, Soft Matter 18, 8572 (2022).
  29. F. Nakai, Y. Masubuchi, Y. Doi, T. Ishida, and T. Uneyama, Fluctuating diffusivity emerges even in binary gas mixtures, Phys. Rev. E 107, 014605 (2023).
  30. R. Jain and K. L. Sebastian, Diffusing diffusivity: A new derivation and comparison with simulations, J. Chem. Sci. 129, 929 (2017).
  31. T. Miyaguchi, Generalized Langevin equation with fluctuating diffusivity, Phys. Rev. Res. 4, 043062 (2022).
  32. T. Uneyama, T. Miyaguchi, and T. Akimoto, Relaxation functions of the Ornstein-Uhlenbeck process with fluctuating diffusivity, Phys. Rev. E 99, 032127 (2019).
  33. T. Miyaguchi, T. Uneyama, and T. Akimoto, Brownian motion with alternately fluctuating diffusivity: Stretched-exponential and power-law relaxation, Phys. Rev. E 100, 012116 (2019).
  34. F. Nakai and T. Ishida, Gas diffusion in cement pastes: An analysis using a fluctuating diffusivity model, Constr. Build. Mater. 407, 133411 (2023).
  35. M. V. Chubynsky and G. W. Slater, Diffusing diffusivity: A model for anomalous, yet Brownian, diffusion, Phys. Rev. Lett. 113, 098302 (2014).
  36. T. Uneyama, T. Miyaguchi, and T. Akimoto, Fluctuation analysis of time-averaged mean-square displacement for the Langevin equation with time-dependent and fluctuating diffusivity, Phys. Rev. E 92, 032140 (2015).
  37. A. V. Chechkin, F. Seno, R. Metzler, and I. M. Sokolov, Brownian yet non-Gaussian diffusion: From superstatistics to subordination of diffusing diffusivities, Phys. Rev. X 7, 021002 (2017).
  38. F. Nakai and T. Uneyama, Brownian yet non-Gaussian diffusion of a light particle in heavy gas: Lorentz-gas-based analysis, Phys. Rev. E 108, 044129 (2023).
  39. See Supplemental Material at http://link.aps.org/supplemental/10.1103/1rnr-11yb for details on (1) units and nondimensionalization, (2) mobility from the Green-Kubo relation, (3) intermediate scattering function and relaxation time, and (4) choice of the overlap cutoff parameter.
  40. N. Lačević, F. W. Starr, T. B. Schrøder, and S. C. Glotzer, Spatially heterogeneous dynamics investigated via a time-dependent four-point density correlation function, J. Chem. Phys. 119, 7372 (2003).
  41. T. Kawasaki and K. Kim, Identifying time scales for violation/preservation of Stokes-Einstein relation in supercooled water, Sci. Adv. 3, e1700399 (2017).
  42. H. Pathak, A. Späh, K. Amann-Winkel, F. Perakis, K. K. H. Kim, and A. Nilsson, Temperature dependent anomalous fluctuations in water: Shift of 1 kbar between experiment and classical force field simulations, Mol. Phys. 117, 3232 (2019).
  43. A. Girelli, H. Rahmann, N. Begam, A. Ragulskaya, M. Reiser, S. Chandran, F. Westermeier, M. Sprung, F. Zhang, C. Gutt, and F. Schreiber, Microscopic dynamics of liquid-liquid phase separation and domain coarsening in a protein solution revealed by x-ray photon correlation spectroscopy, Phys. Rev. Lett. 126, 138004 (2021).
  44. K. Hong, D. Song, and Y. Jung, Behavior control of membrane-less protein liquid condensates with metal ion-induced phase separation, Nat. Commun. 11, 5554 (2020).
  45. F. Perakis, T. Kawasaki, and S. Saito, Enhanced particle diffusion in fluctuating binary environments, Data sets, figshare, 10.17045/sthlmuni.30942911.

Outline

Information

Phys. Rev. Research 8, L012015– Published 15 January, 2026
  • Received 26 August 2025
  • Accepted 23 December 2025
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. Funded by Bibsam.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation