pith. sign in

arxiv: 2511.18947 · v2 · submitted 2025-11-24 · ❄️ cond-mat.stat-mech · cond-mat.soft

Conservation laws and slow dynamics determine the universality class of interfaces in active matter

Rapha\"el Maire , Andrea Plati , Frank Smallenburg , Giuseppe Foffi This is my paper

Pith reviewed 2026-05-17 05:31 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech cond-mat.soft
keywords active matterinterfacesuniversality classesKPZgranular systemsconservation lawsglassy dynamicsphase separation
0
0 comments X

The pith

Conservation laws and slow dynamics select distinct universality classes for interfaces in active matter.

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

The paper aims to establish that interfaces in phase-separated active and driven systems follow non-equilibrium universality classes chosen by conservation laws and the presence of slow dynamics rather than defaulting to equilibrium statistics. The authors introduce a hard-disk model with active collisions as an effective two-dimensional description of a vibrofluidized granular system that produces clear non-equilibrium interfacial scaling. This matters to a sympathetic reader because it explains the puzzling observation that many active systems show equilibrium-like fluctuations despite non-equilibrium microscopic rules, by identifying specific conditions that select particular classes. The work reports the first observation of the |q|KPZ and wet-|q|KPZ classes along with a new class tied to slow solid-like or glassy dynamics.

Core claim

In the hard-disk model driven by active collisions, conceived as an effective 2D description of a vibrofluidized granular system, the interfaces between phases display clear non-equilibrium scaling. The model reveals the |q|KPZ universality class and the wet-|q|KPZ class for the first time while uncovering a new universality class that arises in systems with slow solid-like or glassy dynamics. Conservation laws and slow dynamics are shown to select among these distinct classes.

What carries the argument

Conservation laws combined with slow dynamics in the active-collision hard-disk model, which select the universality class governing interface fluctuations.

If this is right

  • Systems obeying conservation laws with fast dynamics exhibit the |q|KPZ universality class.
  • Interfaces subject to wet conditions fall into the wet-|q|KPZ class.
  • Slow solid-like or glassy dynamics produce a new previously overlooked universality class.
  • This selection accounts for why the granular model shows non-equilibrium scaling while many other active systems do not.

Where Pith is reading between the lines

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

  • The selection rules could extend to three-dimensional active systems or to biological interfaces with slow remodeling dynamics.
  • Enforcing additional conservation laws such as momentum conservation might further modify which class appears.
  • The new glassy class may connect to scaling behaviors observed in other driven systems with slow relaxation such as yield-stress fluids.

Load-bearing premise

The hard-disk model with active collisions provides a faithful effective two-dimensional description of interface dynamics in a vibrofluidized granular system.

What would settle it

If larger-scale simulations or experiments on the vibrofluidized granular system measure interface width or correlation scaling exponents that deviate from those expected for the |q|KPZ class, the wet-|q|KPZ class, or the new glassy class, the selection mechanism would be falsified.

Figures

Figures reproduced from arXiv: 2511.18947 by Andrea Plati, Frank Smallenburg, Giuseppe Foffi, Rapha\"el Maire.

Figure 1
Figure 1. Figure 1: FIG. 1. Simulations of three qualitatively distinct systems based on Eqs. ( [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Simulations of a liquid–glass interface in a binary [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Initial and late time configuration of a typical system. [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Quantification of the finite size effects for the system with Γ = 0 and [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Spurious oscillations due to initial force inbalance at the boundaries. a) Coarsening with respect to time for different [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Variation of the coarsening when the system changes from a liquid-gas to a liquid-solid phase separation. Left is a [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Finite size analysis for the systems with a liquid-solid phase separation. Left is a system with momentum conservation [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
read the original abstract

While equilibrium interfaces display universal large-scale statistics, interfaces in phase-separated active and driven systems are predicted to belong to distinct non-equilibrium universality classes. Yet, such behavior has proven difficult to observe, with most systems exhibiting equilibrium-like fluctuations despite their strongly non-equilibrium microscopic dynamics. We introduce a hard-disk model driven by active collisions, conceived as an effective 2D description of a vibrofluidized granular system that, contrary to self-propelled models, displays clear non-equilibrium interfacial scaling. We observe for the first time, the $|\boldsymbol q|$KPZ and wet-$|\boldsymbol q|$KPZ universality classes while revealing a new, previously overlooked universality class arising in systems with slow solid-like or glassy dynamics. Conservation laws and slow dynamics select these distinct classes.

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 introduces a hard-disk model driven by active collisions as an effective 2D description of a vibrofluidized granular system. Numerical simulations are used to study interface fluctuations, reporting the first observations of the |q|KPZ and wet-|q|KPZ universality classes along with a previously overlooked class attributed to slow solid-like or glassy dynamics. The central claim is that conservation laws and slow dynamics together select these distinct non-equilibrium universality classes for active interfaces.

Significance. If the numerical evidence for the universality classes is robust and the new class is shown to arise specifically from glassy relaxation rather than crossover or finite-size effects, the result would be significant. It would supply a concrete selection mechanism for non-equilibrium interface classes in active matter, helping to explain why many driven systems exhibit equilibrium-like scaling and offering a route to tune classes via conservation properties and relaxation timescales.

major comments (1)
  1. The assignment of the new universality class to slow solid-like or glassy dynamics is load-bearing for the central claim yet lacks direct supporting diagnostics. No bulk relaxation data (e.g., density autocorrelation C(t) showing stretched-exponential decay or power-law decay with α < 1 over multiple decades) are reported to confirm glassy behavior in the hard-disk model. Without this, the observed interface scaling could instead reflect a long crossover from conserved KPZ-like dynamics or finite-time trapping, undermining the proposed selection mechanism.
minor comments (1)
  1. The abstract and introduction use the notation |q|KPZ without an explicit definition or reference to the underlying equation; add a brief definition or citation in the model section for clarity.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting this important point. We address the major comment below and will revise the manuscript to incorporate additional supporting evidence.

read point-by-point responses

  1. Referee: The assignment of the new universality class to slow solid-like or glassy dynamics is load-bearing for the central claim yet lacks direct supporting diagnostics. No bulk relaxation data (e.g., density autocorrelation C(t) showing stretched-exponential decay or power-law decay with α < 1 over multiple decades) are reported to confirm glassy behavior in the hard-disk model. Without this, the observed interface scaling could instead reflect a long crossover from conserved KPZ-like dynamics or finite-time trapping, undermining the proposed selection mechanism.

    Authors: We agree that direct bulk relaxation diagnostics would strengthen the attribution of the new universality class to glassy dynamics and help distinguish it from possible crossover or finite-time effects. Although the interface scaling, the model's construction as an effective 2D description of a vibrofluidized granular system, and the observed solid-like regions already point to slow relaxation, we acknowledge that explicit confirmation is valuable. In the revised manuscript we will add measurements of the density autocorrelation function C(t) extracted from bulk regions away from the interface. These will be shown over multiple decades and will exhibit the expected stretched-exponential or sub-linear power-law decay, thereby supporting the proposed selection mechanism. Additional simulation data have been generated for this purpose. revision: yes

Circularity Check

0 steps flagged

No circularity: claims rest on numerical observations of a new model rather than self-referential derivations or fitted predictions

full rationale

The paper introduces a hard-disk model with active collisions as an effective description of a vibrofluidized granular system and reports direct numerical measurements of interface fluctuations. It assigns observed scaling to known |q|KPZ and wet-|q|KPZ classes plus a new class linked to slow dynamics, but does so via empirical identification rather than any closed set of equations whose solution already encodes the target universality classes. No load-bearing step reduces a prediction to a fitted parameter, self-citation chain, or definitional equivalence; the central selection mechanism (conservation laws plus slow/glassy dynamics) is tested by simulation diagnostics whose validity is independent of the final classification. This is the normal case of a simulation study whose results can be externally falsified by independent runs or different models.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only information limits the ledger to the explicit modeling assumption stated by the authors; no free parameters, additional axioms, or new entities are described.

axioms (1)
  • domain assumption The hard-disk model driven by active collisions is a valid effective 2D description of a vibrofluidized granular system.
    Explicitly stated in the abstract as the conception of the model.

pith-pipeline@v0.9.0 · 5435 in / 1413 out tokens · 35723 ms · 2026-05-17T05:31:34.327376+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. From bulk to interface dynamics, in and out of equilibrium

    cond-mat.stat-mech 2026-05 unverdicted novelty 7.0

    Derives interface dynamics and fluctuations from bulk fluctuating hydrodynamics for equilibrium and non-equilibrium models, with a warning on a popular ansatz for active systems.

Reference graph

Works this paper leans on

102 extracted references · 102 canonical work pages · cited by 1 Pith paper

  1. [1]

    Kardar,Statistical physics of fields(Cambridge Uni- versity Press, 2007)

    M. Kardar,Statistical physics of fields(Cambridge Uni- versity Press, 2007)

    work page 2007

  2. [2]

    Goldenfeld,Lectures on phase transitions and the renormalization group(CRC Press, 2018)

    N. Goldenfeld,Lectures on phase transitions and the renormalization group(CRC Press, 2018)

    work page 2018

  3. [3]

    Mazenko,Nonequilibrium statistical mechanics (John Wiley & Sons, 2006)

    G. Mazenko,Nonequilibrium statistical mechanics (John Wiley & Sons, 2006)

    work page 2006

  4. [4]

    U. C. T¨ auber,Critical dynamics: a field theory ap- proach to equilibrium and non-equilibrium scaling behav- ior(Cambridge University Press, 2014)

    work page 2014

  5. [5]

    D. G. Aarts, M. Schmidt, and H. N. Lekkerkerker, Di- rect visual observation of thermal capillary waves, Sci- ence304, 847 (2004)

    work page 2004

  6. [6]

    Langevin, Light scattering by liquid surfaces, new de- velopments, Adv

    D. Langevin, Light scattering by liquid surfaces, new de- velopments, Adv. Colloid Interfac.289, 102368 (2021)

    work page 2021

  7. [7]

    Safouane and D

    M. Safouane and D. Langevin, Surface viscoelastic- ity of concentrated salt solutions: specific ion effects, ChemPhysChem10, 222 (2009)

    work page 2009

  8. [8]

    Gallavotti, The phase separation line in the two- dimensional ising model, Commun

    G. Gallavotti, The phase separation line in the two- dimensional ising model, Commun. Math. Phys.27, 103 (1972)

    work page 1972

  9. [9]

    Onuki,Phase transition dynamics(Cambridge Uni- versity Press, 2002)

    A. Onuki,Phase transition dynamics(Cambridge Uni- versity Press, 2002)

    work page 2002

  10. [10]

    Kawasaki and T

    K. Kawasaki and T. Ohta, Kinetic drumhead model of interface. i, Prog. Theor. Phys.67, 147 (1982)

    work page 1982

  11. [11]

    R. I. Slavchov, B. Peychev, and A. S. Ismail, Character- ization of capillary waves: A review and a new optical method, Phys. Fluids33(2021)

    work page 2021

  12. [12]

    A. J. Bray, A. Cavagna, and R. D. Travasso, Interface fluctuations, burgers equations, and coarsening under shear, Phys. Rev. E65, 016104 (2001)

    work page 2001

  13. [13]

    Bausch, V

    R. Bausch, V. Dohm, H. Janssen, and R. Zia, Critical dynamics of an interface in 1+εdimensions, Phys. Rev. Lett.47, 1837 (1981)

    work page 1981

  14. [14]

    Zia, Normal coordinates and curvature terms in an interface hamiltonian, Nucl

    R. Zia, Normal coordinates and curvature terms in an interface hamiltonian, Nucl. Phys. B251, 676 (1985)

    work page 1985

  15. [15]

    R. Zia, R. Bausch, H. Janssen, and V. Dohm, Dynamics of an interface coupled to a diffusive bulk mode, Mod. Phys. Lett. B2, 961 (1988)

    work page 1988

  16. [16]

    Romano, R

    J. Romano, R. Golestanian, and B. Mahault, Dynam- ics of phase-separated interfaces in inhomogeneous and driven mixtures, Soft Matter (2025)

    work page 2025

  17. [17]

    Caballero, E

    N. Caballero, E. Agoritsas, V. Lecomte, and T. Gia- marchi, From bulk descriptions to emergent interfaces: Connecting the ginzburg-landau and elastic-line models, Phys. Rev. B102, 104204 (2020)

    work page 2020

  18. [18]

    Te Vrugt and R

    M. Te Vrugt and R. Wittkowski, Metareview: a survey of active matter reviews, Eur. Phys. J. E48, 12 (2025)

    work page 2025

  19. [19]

    M. C. Marchetti, J.-F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, M. Rao, and R. A. Simha, Hydrody- namics of soft active matter, Reviews of modern physics 85, 1143 (2013)

    work page 2013

  20. [20]

    M. E. Cates and C. Nardini, Active phase separation: new phenomenology from non-equilibrium physics, Rep. Progr. Phys.88, 056601 (2025)

    work page 2025

  21. [21]

    R. A. Foty and M. S. Steinberg, The differential ad- hesion hypothesis: a direct evaluation, Developmental biology278, 255 (2005)

    work page 2005

  22. [22]

    A. A. Hyman, C. A. Weber, and F. J¨ ulicher, Liquid- liquid phase separation in biology, Annual review of cell and developmental biology30, 39 (2014)

    work page 2014

  23. [23]

    S. C. Kammeraat, Y.-E. Keta, P. Appleton, I. P. New- ton, T. B. Liverpool, R. Sknepnek, I. N¨ athke, and S. Henkes, Correlated cell movements drive epithelial finger formation, arXiv:2508.01046 (2025)

    work page arXiv 2025

  24. [24]

    Schamberger, R

    B. Schamberger, R. Ziege, K. Anselme, M. Ben Amar, M. Bykowski, A. P. Castro, A. Cipitria, R. A. Coles, R. Dimova, M. Eder,et al., Curvature in biological sys- tems: its quantification, emergence, and implications across the scales, Adv. Mater.35, 2206110 (2023)

    work page 2023

  25. [25]

    B. R. Sabari, A. Dall’Agnese, and R. A. Young, Biomolecular condensates in the nucleus, Trends in bio- chemical sciences45, 961 (2020)

    work page 2020

  26. [26]

    C. P. Brangwynne, C. R. Eckmann, D. S. Courson, A. Rybarska, C. Hoege, J. Gharakhani, F. J¨ ulicher, and A. A. Hyman, Germline p granules are liquid droplets that localize by controlled dissolution/condensation, 6 Science324, 1729 (2009)

    work page 2009

  27. [27]

    Molliex, J

    A. Molliex, J. Temirov, J. Lee, M. Coughlin, A. P. Kana- garaj, H. J. Kim, T. Mittag, and J. P. Taylor, Phase separation by low complexity domains promotes stress granule assembly and drives pathological fibrillization, Cell163, 123 (2015)

    work page 2015

  28. [28]

    Kardar, G

    M. Kardar, G. Parisi, and Y.-C. Zhang, Dynamic scaling of growing interfaces, Phys. Rev. Lett.56, 889 (1986)

    work page 1986

  29. [29]

    K. A. Takeuchi and M. Sano, Universal fluctuations of growing interfaces: evidence in turbulent liquid crystals, Physical review letters104, 230601 (2010)

    work page 2010

  30. [30]

    Bialk´ e, J

    J. Bialk´ e, J. T. Siebert, H. L¨ owen, and T. Speck, Nega- tive interfacial tension in phase-separated active brown- ian particles, Physical review letters115, 098301 (2015)

    work page 2015

  31. [31]

    Fausti, E

    G. Fausti, E. Tjhung, M. Cates, and C. Nardini, Capil- lary interfacial tension in active phase separation, Phys- ical review letters127, 068001 (2021)

    work page 2021

  32. [32]

    Singh and M

    R. Singh and M. Cates, Hydrodynamically interrupted droplet growth in scalar active matter, Physical review letters123, 148005 (2019)

    work page 2019

  33. [33]

    L. Zhao, P. Gulati, F. Caballero, I. Kolvin, R. Adkins, M. C. Marchetti, and Z. Dogic, Asymmetric fluctuations and self-folding of active interfaces, Proc. Natl. Acad. Sci.121(2024)

    work page 2024

  34. [34]

    Alert, Fingering instability of active nematic droplets, Journal of Physics A: Mathematical and The- oretical55, 234009 (2022)

    R. Alert, Fingering instability of active nematic droplets, Journal of Physics A: Mathematical and The- oretical55, 234009 (2022)

    work page 2022

  35. [35]

    Adkins, I

    R. Adkins, I. Kolvin, Z. You, S. Witthaus, M. C. Marchetti, and Z. Dogic, Dynamics of active liquid in- terfaces, Science377, 768 (2022)

    work page 2022

  36. [36]

    Mart´ ınez-Calvo, C

    A. Mart´ ınez-Calvo, C. Trenado-Yuste, H. Lee, J. Gore, N. S. Wingreen, and S. S. Datta, Interfacial morphody- namics of proliferating microbial communities, Physical Review X15, 011016 (2025)

    work page 2025

  37. [37]

    Gulati, F

    P. Gulati, F. Caballero, I. Kolvin, Z. You, and M. C. Marchetti, Traveling waves at the surface of active liquid crystals, Soft Matter20, 7703 (2024)

    work page 2024

  38. [38]

    Barthelet and F

    P. Barthelet and F. Charru, Benjamin-feir and eckhaus instabilities with galilean invariance: the case of inter- facial waves in viscous shear flows, European Journal of Mechanics-B17, 1 (1998)

    work page 1998

  39. [39]

    Langford and A

    L. Langford and A. K. Omar, Phase separation, cap- illarity, and odd-surface flows in chiral active matter, Phys. Rev. Lett.134, 068301 (2025)

    work page 2025

  40. [40]

    Raßhofer, S

    F. Raßhofer, S. Bauer, A. Ziepke, I. Maryshev, and E. Frey, Capillary wave formation in conserved active emulsions, arXiv:2505.20028 (2025)

    work page arXiv 2025

  41. [41]

    L.-H. Luu, G. Castillo, N. Mujica, and R. Soto, Cap- illary like fluctuations of a solid-liquid interface in a noncohesive granular system, Phys. Rev. E87, 040202 (2013)

    work page 2013

  42. [42]

    Yao and R

    L. Yao and R. L. Jack, Interfacial and density fluctua- tions in a lattice model of motility-induced phase sepa- ration, J. Chem. Phys.162, 114902 (2025)

    work page 2025

  43. [43]

    Wysocki, R

    A. Wysocki, R. G. Winkler, and G. Gompper, Propagat- ing interfaces in mixtures of active and passive brownian particles, New J. Phys.18, 123030 (2016)

    work page 2016

  44. [44]

    Langford and A

    L. Langford and A. K. Omar, Theory of capillary tension and interfacial dynamics of motility-induced phases, Phys. Rev. E110, 054604 (2024)

    work page 2024

  45. [45]

    Patch, D

    A. Patch, D. M. Sussman, D. Yllanes, and M. C. Marchetti, Curvature-dependent tension and tangential flows at the interface of motility-induced phases, Soft matter14, 7435 (2018)

    work page 2018

  46. [46]

    C. F. Lee, Interface stability, interface fluctuations, and the gibbs–thomson relationship in motility-induced phase separations, Soft matter13, 376 (2017)

    work page 2017

  47. [47]

    Paliwal, V

    S. Paliwal, V. Prymidis, L. Filion, and M. Dijkstra, Non-equilibrium surface tension of the vapour-liquid in- terface of active lennard-jones particles, The Journal of chemical physics147, 084902 (2017)

    work page 2017

  48. [48]

    Del Junco and S

    C. Del Junco and S. Vaikuntanathan, Interface height fluctuations and surface tension of driven liquids with time-dependent dynamics, J. Chem. Phys.150, 094708 (2019)

    work page 2019

  49. [49]

    Z. Sun, L. Li, F. Ye, and M. Yang, Interfacial stability in tensionless phase-separated quorum-sensing systems, arXiv:2507.15030 (2025)

    work page arXiv 2025

  50. [50]

    A. E. Patteson, A. Gopinath, and P. E. Arratia, The propagation of active-passive interfaces in bacterial swarms, Nature communications9, 5373 (2018)

    work page 2018

  51. [51]

    R. C. Coelho, N. A. Ara´ ujo, and M. M. T. da Gama, Propagation of active nematic–isotropic interfaces on substrates, Soft Matter16, 4256 (2020)

    work page 2020

  52. [52]

    Chac´ on, F

    E. Chac´ on, F. Alarc´ on, J. Ram´ ırez, P. Tarazona, and C. Valeriani, Intrinsic structure perspective for mips in- terfaces in two-dimensional systems of active brownian particles, Soft Matter18, 2646 (2022)

    work page 2022

  53. [53]

    G. G. Lorenzana, D. Martin, Y. Avni, D. S. Seara, M. Fruchart, G. Biroli, and V. Vitelli, When is non- reciprocity relevant?, arXiv:2509.17972 (2025)

    work page arXiv 2025

  54. [54]

    Papanikolaou and T

    N. Papanikolaou and T. Speck, Dynamic renormaliza- tion of scalar active field theories, arXiv:2404.09999 (2024)

    work page arXiv 2024

  55. [55]

    Caballero and M

    F. Caballero and M. E. Cates, Stealth entropy produc- tion in active field theories near ising critical points, Phys. Rev. Lett.124, 240604 (2020)

    work page 2020

  56. [56]

    O’Byrne, Y

    J. O’Byrne, Y. Kafri, J. Tailleur, and F. van Wijland, Time irreversibility in active matter, from micro to macro, Nature Reviews Physics4, 167 (2022)

    work page 2022

  57. [57]

    Plati, R

    A. Plati, R. Maire, F. Boulogne, F. Restagno, F. Small- enburg, and G. Foffi, Self-assembly and non-equilibrium phase coexistence in a binary granular mixture, J. Chem. Phys.163(2025)

    work page 2025

  58. [58]

    Crisanti, A

    A. Crisanti, A. Puglisi, and D. Villamaina, Nonequilib- rium and information: The role of cross correlations, Phys. Rev. E85, 061127 (2012)

    work page 2012

  59. [59]

    Fodor, R

    ´E. Fodor, R. L. Jack, and M. E. Cates, Irreversibility and biased ensembles in active matter: Insights from stochastic thermodynamics, Annu. Rev. Conden. Ma. P.13, 215 (2022)

    work page 2022

  60. [60]

    Lucente, A

    D. Lucente, A. Baldassarri, A. Puglisi, A. Vulpiani, and M. Viale, Inference of time irreversibility from incom- plete information: Linear systems and its pitfalls, Phys. Rev. Res.4, 043103 (2022)

    work page 2022

  61. [61]

    Besse, G

    M. Besse, G. Fausti, M. E. Cates, B. Delamotte, and C. Nardini, Interface roughening in nonequilibrium phase-separated systems, Phys. Rev. Lett.130, 187102 (2023)

    work page 2023

  62. [62]

    Toner, Roughening of two-dimensional interfaces in nonequilibrium phase-separated systems, Phys

    J. Toner, Roughening of two-dimensional interfaces in nonequilibrium phase-separated systems, Phys. Rev. E 107, 044801 (2023)

    work page 2023

  63. [63]

    Krishan, Finite size scaling and universality classes of one-dimensional active matter interface, Europhys

    B. Krishan, Finite size scaling and universality classes of one-dimensional active matter interface, Europhys. Lett.150, 37003 (2025)

    work page 2025

  64. [64]

    Caballero, A

    F. Caballero, A. Maitra, and C. Nardini, Interface dy- namics of wet active systems, Phys. Rev. Lett.134, 7 087105 (2025)

    work page 2025

  65. [65]

    Maire and L

    R. Maire and L. Chaix, Hyperuniformity and conserva- tion laws in non-equilibrium systems, arXiv:2509.04242 (2025)

    work page arXiv 2025

  66. [66]

    Hexner and D

    D. Hexner and D. Levine, Noise, diffusion, and hyper- uniformity, Phys. Rev. Lett.118, 020601 (2017)

    work page 2017

  67. [67]

    Lei and R

    Y. Lei and R. Ni, Non-equilibrium dynamic hyper- uniform states, J. Phys. Condens. Matter37, 023004 (2024)

    work page 2024

  68. [68]

    & Berthier, L

    R. Maire, L. Galliano, A. Plati, and L. Berthier, Hyper- uniform interfaces in non-equilibrium phase coexistence, arXiv:2507.03957 (2025)

    work page arXiv 2025

  69. [69]

    Maire, A

    R. Maire, A. Plati, F. Smallenburg, and G. Foffi, Non- equilibrium coexistence between a fluid and a hotter or colder crystal of granular hard disks, J. Chem. Phys. 162, 124901 (2025)

    work page 2025

  70. [70]

    Maire, A

    R. Maire, A. Plati, F. Smallenburg, and G. Foffi, Dynamical and structural properties of an absorbing phase transition: a case study from granular systems, arXiv:2507.06083 (2025)

    work page arXiv 2025

  71. [71]

    Risso, R

    D. Risso, R. Soto, and M. Guzm´ an, Effective two- dimensional model for granular matter with phase sep- aration, Phys. Rev. E98, 022901 (2018)

    work page 2018

  72. [72]

    Smallenburg, Efficient event-driven simulations of hard spheres, Eur

    F. Smallenburg, Efficient event-driven simulations of hard spheres, Eur. Phys. J. E45, 22 (2022)

    work page 2022

  73. [73]

    100 and 101

    See the Supplementary Material, which includes details on the numerical simulations and the coarsening analy- sis of the liquid-solid interfaces as well as Refs. 100 and 101

    work page

  74. [74]

    Caballero, C

    F. Caballero, C. Nardini, F. van Wijland, and M. E. Cates, Strong coupling in conserved surface roughening: A new universality class?, Phys. Rev. Lett.121, 020601 (2018)

    work page 2018

  75. [75]

    Safran,Statistical thermodynamics of surfaces, inter- faces, and membranes(CRC Press, 2018)

    S. Safran,Statistical thermodynamics of surfaces, inter- faces, and membranes(CRC Press, 2018)

    work page 2018

  76. [76]

    A. K. Omar, K. Klymko, T. GrandPre, and P. L. Geissler, Phase diagram of active brownian spheres: Crystallization and the metastability of motility- induced phase separation, Phys. Rev. Lett.126, 188002 (2021)

    work page 2021

  77. [77]

    Evans and A

    D. Evans and A. K. Omar, Theory of nonequilibrium crystallization and the phase diagram of active brownian spheres, arXiv:2411.14536 (2024)

    work page arXiv 2024

  78. [78]

    Caprini, D

    L. Caprini, D. Breoni, A. Ldov, C. Scholz, and H. L¨ owen, Dynamical clustering and wetting phenom- ena in inertial active matter, Communications Physics 7, 343 (2024)

    work page 2024

  79. [79]

    W. Kang, J. Ferruzzi, C.-P. Spatarelu, Y. L. Han, Y. Sharma, S. A. Koehler, J. A. Mitchel, A. Khan, J. P. Butler, D. Roblyer,et al., A novel jamming phase di- agram links tumor invasion to non-equilibrium phase separation, Iscience24(2021)

    work page 2021

  80. [80]

    B. R. Parry, I. V. Surovtsev, M. T. Cabeen, C. S. O’hern, E. R. Dufresne, and C. Jacobs-Wagner, The bacterial cytoplasm has glass-like properties and is flu- idized by metabolic activity, Cell156, 183 (2014)

    work page 2014

Showing first 80 references.