pith. machine review for the scientific record. sign in

arxiv: 2603.22424 · v2 · submitted 2026-03-23 · ❄️ cond-mat.stat-mech

Recognition: no theorem link

How active field theories couple to external potentials

Yariv Kafri , Julien Tailleur
Authors on Pith no claims yet

Pith reviewed 2026-05-15 00:30 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech
keywords active field theoriesexternal potentialsactive Brownian particlesperturbative expansiondensity gradientsboundary accumulationnonequilibrium dynamics
0
0 comments X

The pith

Active field theories require a non-trivial coupling between density gradients and external potential gradients.

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

The paper derives the minimal additional terms needed to couple active field theories to external potentials through a systematic expansion in particle persistence time. This expansion applied to active Brownian particles produces a coupling that links density gradients directly to potential gradients. The resulting terms reproduce key nonequilibrium signatures such as particle accumulation at boundaries and density variations far from the potential. The same procedure extends to interacting particles and to spatial variations in propulsion speed.

Core claim

Performing a perturbative expansion in the persistence time for active Brownian particles yields extra terms in the continuity equation that couple the density field to the gradient of the external potential. These terms are the simplest additions required to recover nonequilibrium features including boundary accumulation and far-field density modulation. The derivation carries over directly to pairwise-interacting particles and to systems with spatially modulated propulsion speeds.

What carries the argument

The systematic perturbative expansion in the particle persistence time, which generates the minimal coupling between density and potential gradients.

If this is right

  • The coupling term produces accumulation of active particles at potential boundaries.
  • It generates far-field density modulations away from the potential.
  • The same expansion applies without change to particles that interact through pairwise forces.
  • It also handles cases in which the propulsion speed varies spatially.

Where Pith is reading between the lines

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

  • The same expansion technique could be applied to derive couplings in other nonequilibrium field theories.
  • Numerical checks of the predicted density profiles in confined geometries would provide direct tests.
  • The derived terms may alter collective dynamics when active particles are placed in complex or time-varying potentials.

Load-bearing premise

The lowest-order terms generated by the expansion in persistence time are sufficient to capture the essential coupling without requiring higher-order corrections.

What would settle it

Compare the steady-state density profile predicted by the augmented field theory against direct simulations of active Brownian particles in a simple external potential such as a harmonic trap or a linear ramp.

read the original abstract

We study the simplest terms that need to be included in active field theories to couple them to external potentials. To do so, we consider active Brownian particles and implement a systematic perturbative expansion in the particle persistence time. The result is a non-trivial coupling between density and potential gradients, which accounts for the nonequilibrium features of active particles in the presence of an external potential, from boundary accumulation to far-field density modulation. We show how the method can be applied to particles interacting via pairwise forces and to spatial modulations of the propulsion speed.

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 / 0 minor

Summary. The paper derives the minimal coupling terms needed in active field theories for external potentials by performing a systematic perturbative expansion in the persistence time τ of active Brownian particles. The resulting non-trivial coupling between density and potential gradients is claimed to capture nonequilibrium features such as boundary accumulation and far-field density modulation; the method is extended to pairwise-interacting particles and to spatially varying propulsion speeds.

Significance. If the expansion is valid in the relevant regime, the work supplies a controlled route to include leading nonequilibrium corrections in continuum active-matter models, which would be useful for describing confined active particles and motility-induced phenomena under external fields.

major comments (1)
  1. [central derivation (abstract and main expansion)] The perturbative expansion in persistence time τ retains only the lowest-order gradient coupling, yet the nonequilibrium signatures (boundary accumulation, far-field modulation) are typically strongest when the persistence length vτ is comparable to the potential variation scale; the manuscript provides no explicit error bound, comparison to exact solutions, or resummation argument to justify that the truncation remains accurate in this regime.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback on our manuscript. We address the single major comment below.

read point-by-point responses

  1. Referee: The perturbative expansion in persistence time τ retains only the lowest-order gradient coupling, yet the nonequilibrium signatures (boundary accumulation, far-field modulation) are typically strongest when the persistence length vτ is comparable to the potential variation scale; the manuscript provides no explicit error bound, comparison to exact solutions, or resummation argument to justify that the truncation remains accurate in this regime.

    Authors: We agree that the expansion is formally controlled only for small τ (with vτ much smaller than the potential scale). The leading-order gradient coupling is nevertheless the minimal term required to recover the correct nonequilibrium phenomenology from the microscopic dynamics; higher orders would only renormalize coefficients without changing the structure. The manuscript does not claim quantitative accuracy outside the small-τ regime. We will revise the text to (i) state the validity regime explicitly, (ii) add a brief discussion of the truncation error scaling, and (iii) include a comparison of the derived density profiles against direct numerical integration of the active Brownian particle equations for moderate τ values. revision: partial

Circularity Check

0 steps flagged

No circularity: derivation proceeds from standard ABP equations via explicit perturbative expansion in persistence time

full rationale

The paper starts from the established equations of motion for active Brownian particles and performs a systematic perturbative expansion in the persistence time τ to obtain the coupling terms between density and potential gradients. This is a forward derivation rather than a self-referential definition or a fit renamed as a prediction. No load-bearing step reduces to a self-citation chain, an ansatz smuggled via prior work, or a uniqueness theorem imported from the authors themselves. The resulting non-trivial coupling is an output of the expansion, not an input. The skeptic concern about truncation validity in the vτ ~ potential-length regime is a question of approximation accuracy, not circularity in the derivation itself.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on the validity of the perturbative expansion in persistence time for active Brownian particles and the assumption that this captures the essential nonequilibrium coupling.

axioms (1)
  • domain assumption Active Brownian particle dynamics can be systematically expanded in small persistence time to obtain effective field theory couplings.
    Invoked to justify the derivation of the density-potential coupling term.

pith-pipeline@v0.9.0 · 5373 in / 1043 out tokens · 28510 ms · 2026-05-15T00:30:16.654844+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. Unifying hydrodynamic theory for motility-regulated active matter: from single particles to interacting polymers

    cond-mat.stat-mech 2026-04 unverdicted novelty 6.0

    Derives unifying hydrodynamics for motility-regulated active matter from particles to polymers, captured by orientation autocorrelation tensor, and identifies anti-MIPS in quorum-sensing polymers.

Reference graph

Works this paper leans on

49 extracted references · 49 canonical work pages · cited by 1 Pith paper · 2 internal anchors

  1. [1]

    First-passage time of run-and-tumble particles

    L Angelani, R Di Leonardo, and M Paoluzzi. “First-passage time of run-and-tumble particles”. In:The European Physical Journal E37.7 (2014), p. 59 (cit. on p. 14)

    work page 2014

  2. [2]

    Generic Long-Range Interactions Between Passive Bodies in an Active Fluid

    Yongjoo Baek et al. “Generic Long-Range Interactions Between Passive Bodies in an Active Fluid”. In:Physical Review Letters120.5 (Jan. 2018), p. 058002.issn: 0031-9007, 1079-7114.doi:10 . 1103 / PhysRevLett.120.058002.url:https://link.aps.org/doi/10.1103/PhysRevLett.120.058002 (visited on 04/20/2020) (cit. on pp. 5, 7, 12)

    work page doi:10.1103/physrevlett.120.058002 2018

  3. [3]

    ActiveParticlesinComplexandCrowdedEnvironments

    ClemensBechingeretal.“ActiveParticlesinComplexandCrowdedEnvironments”.In:Reviews of Modern Physics88.4 (Nov. 2016), p. 045006.issn: 0034-6861, 1539-0756.doi:10.1103/RevModPhys.88.045006. url:https://link.aps.org/doi/10.1103/RevModPhys.88.045006(visited on 05/10/2020) (cit. on p. 1)

    work page doi:10.1103/revmodphys.88.045006 2016

  4. [4]

    Disordered boundaries destroy bulk phase separation in scalar active matter

    Ydan Ben Dor et al. “Disordered boundaries destroy bulk phase separation in scalar active matter”. In: Physical Review E105.4 (2022), p. 044603 (cit. on pp. 1, 12)

    work page 2022

  5. [5]

    Microscopic theory for the phase separation of self- propelled repulsive disks

    Julian Bialké, Hartmut Löwen, and Thomas Speck. “Microscopic theory for the phase separation of self- propelled repulsive disks”. In:Europhysics Letters103.3 (2013), p. 30008 (cit. on p. 2)

    work page 2013

  6. [6]

    Burekovi´ c, F

    Sumeja Bureković et al. “Active Cahn–Hilliard theory for non-equilibrium phase separation: quantitative macroscopic predictions and a microscopic derivation”. In:arXiv preprint arXiv:2601.16539(2026) (cit. on p. 12)

    work page arXiv 2026

  7. [7]

    When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation

    M. E. Cates and J. Tailleur. “When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation”. In:EPL (Europhysics Letters)101.2 (Jan. 2013), p. 20010.issn: 0295-5075, 1286-4854.doi:10.1209/0295-5075/101/20010.url:http://stacks.iop. org/0295- 5075/101/i=2/a=20010?key=crossref.fdb86cf361ef9e6a...

    work page doi:10.1209/0295-5075/101/20010.url:http://stacks.iop 2013

  8. [8]

    Active phase separation: new phenomenology from non-equilibrium physics

    Michael E Cates and Cesare Nardini. “Active phase separation: new phenomenology from non-equilibrium physics”. In:Reports on Progress in Physics88.5 (2025), p. 056601 (cit. on pp. 2, 10)

    work page 2025

  9. [9]

    Exotic Hadrons at LHCb

    Michael E. Cates and Julien Tailleur. “Motility-Induced Phase Separation”. In:Annual Review of Con- densed Matter Physics6.1 (Mar. 2015), pp. 219–244.issn: 1947-5454, 1947-5462.doi:10.1146/annurev- conmatphys - 031214 - 014710.url:http : / / www . annualreviews . org / doi / 10 . 1146 / annurev - conmatphys-031214-014710(visited on 01/21/2020) (cit. on p. 7)

    work page doi:10.1146/annurev- 2015

  10. [10]

    Run-and-tumble particle in one-dimensional confining potentials: Steady-state, relaxation, and first-passage properties

    Abhishek Dhar et al. “Run-and-tumble particle in one-dimensional confining potentials: Steady-state, relaxation, and first-passage properties”. In:Physical Review E99.3 (2019), p. 032132 (cit. on p. 14). 15

    work page 2019

  11. [11]

    Bacterialratchetmotors

    RobertoDiLeonardoetal.“Bacterialratchetmotors”.In:Proceedings of the National Academy of Sciences 107.21 (2010), pp. 9541–9545 (cit. on p. 1)

    work page 2010

  12. [12]

    Run-and-tumble dynamics of self-propelled particles in confinement

    Jens Elgeti and Gerhard Gompper. “Run-and-tumble dynamics of self-propelled particles in confinement”. In:Europhysics Letters109.5 (2015), p. 58003 (cit. on p. 14)

    work page 2015

  13. [13]

    Self-propelled rods near surfaces

    Jens Elgeti and Gerhard Gompper. “Self-propelled rods near surfaces”. In:EPL (Europhysics Letters) 85.3 (2009), p. 38002 (cit. on p. 1)

    work page 2009

  14. [14]

    Wall accumulation of self-propelled spheres

    Jens Elgeti and Gerhard Gompper. “Wall accumulation of self-propelled spheres”. In:Europhysics Letters 101.4 (2013), p. 48003 (cit. on p. 1)

    work page 2013

  15. [15]

    Dynamics of self-propelled particles under strong confinement

    Yaouen Fily, Aparna Baskaran, and Michael F Hagan. “Dynamics of self-propelled particles under strong confinement”. In:Soft matter10.30 (2014), pp. 5609–5617 (cit. on p. 2)

    work page 2014

  16. [16]

    Athermal Phase Separation of Self-Propelled Particles with No Alignment

    Yaouen Fily and M. Cristina Marchetti. “Athermal Phase Separation of Self-Propelled Particles with No Alignment”. In:Physical Review Letters108.23 (June 2012), p. 235702.issn: 0031-9007, 1079-7114.doi: 10.1103/PhysRevLett.108.235702.url:https://link.aps.org/doi/10.1103/PhysRevLett.108. 235702(visited on 04/22/2020) (cit. on p. 9)

    work page doi:10.1103/physrevlett.108.235702.url:https://link.aps.org/doi/10.1103/physrevlett.108 2012

  17. [17]

    How Far from Equilibrium Is Active Matter?

    Étienne Fodor et al. “How Far from Equilibrium Is Active Matter?” In:Phys. Rev. Lett.117.3 (July 2016), p. 038103.doi:10.1103/PhysRevLett.117.038103.url:http://link.aps.org/doi/10.1103/ PhysRevLett.117.038103(cit. on pp. 2, 12)

    work page doi:10.1103/physrevlett.117.038103.url:http://link.aps.org/doi/10.1103/ 2016

  18. [18]

    A wall of funnels concentrates swimming bacteria

    Peter Galajda et al. “A wall of funnels concentrates swimming bacteria”. In:Journal of bacteriology189.23 (2007), pp. 8704–8707 (cit. on p. 1)

    work page 2007

  19. [19]

    Dubkov, and Davide Valenti

    Omer Granek et al. “Bodies in an interacting active fluid: far-field influence of a single body and interaction between two bodies”. In:Journal of Statistical Mechanics: Theory and Experiment2020.6 (June 2020), p. 063211.issn: 1742-5468.doi:10.1088/1742- 5468/ab7f34.url:https://iopscience.iop.org/ article/10.1088/1742-5468/ab7f34(visited on 07/06/2020) (c...

    work page doi:10.1088/1742- 2020

  20. [20]

    Colloquium: Inclusions, boundaries, and disorder in scalar active matter

    Omer Granek et al. “Colloquium: Inclusions, boundaries, and disorder in scalar active matter”. In:Reviews of Modern Physics96.3 (2024), p. 031003 (cit. on pp. 1, 5, 7)

    work page 2024

  21. [21]

    Self-induced polar order of active Brownian particles in a harmonic trap

    Marc Hennes, Katrin Wolff, and Holger Stark. “Self-induced polar order of active Brownian particles in a harmonic trap”. In:Physical review letters112.23 (2014), p. 238104 (cit. on p. 2)

    work page 2014

  22. [22]

    Acoldtracerinahotbath:Inandoutofequilibrium

    AmerAl-Hiyasat,SunghanRo,andJulienTailleur.“Acoldtracerinahotbath:Inandoutofequilibrium”. In:arXiv preprint arXiv:2501.04930(2025) (cit. on p. 12)

    work page arXiv 2025

  23. [23]

    Statistical mechanics of a cold tracer in a hot bath

    Amer Al-Hiyasat, Sunghan Ro, and Julien Tailleur. “Statistical mechanics of a cold tracer in a hot bath”. In:arXiv preprint arXiv:2503.01998(2025) (cit. on p. 12)

    work page arXiv 2025

  24. [24]

    A "missing" family of classical orthogonal polynomials

    J. H. Irving and John G. Kirkwood. “The Statistical Mechanical Theory of Transport Processes. IV. The Equations of Hydrodynamics”. In:The Journal of Chemical Physics18.6 (1950), pp. 817–829.issn: 00219606.doi:10.1063/1.1747782. arXiv:1011.1669v3(cit. on p. 9)

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1063/1.1747782 1950

  25. [25]

    Field theory of active chiral hard disks: a first-principles approach to steric interactions

    Erik Kalz, Abhinav Sharma, and Ralf Metzler. “Field theory of active chiral hard disks: a first-principles approach to steric interactions”. In:Journal of Physics A: Mathematical and Theoretical57.26 (2024), p. 265002 (cit. on p. 2)

    work page 2024

  26. [26]

    Towards a liquid-state theory for active matter

    Yuting Irene Li et al. “Towards a liquid-state theory for active matter”. In:Europhysics Letters142.5 (2023), p. 57004 (cit. on p. 2)

    work page 2023

  27. [27]

    Hydrodynamics of soft active matter

    M Cristina Marchetti et al. “Hydrodynamics of soft active matter”. In:Reviews of Modern Physics85.3 (2013), p. 1143 (cit. on p. 2)

    work page 2013

  28. [28]

    Statistical mechanics of active Ornstein-Uhlenbeck particles

    David Martin et al. “Statistical mechanics of active Ornstein-Uhlenbeck particles”. In:Physical Review E 103.3 (2021). Publisher: APS, p. 032607 (cit. on p. 12)

    work page 2021

  29. [29]

    Entropy Production in Field Theories without Time-Reversal Symmetry: Quan- tifying the Non-Equilibrium Character of Active Matter

    Cesare Nardini et al. “Entropy Production in Field Theories without Time-Reversal Symmetry: Quan- tifying the Non-Equilibrium Character of Active Matter”. In:Phys. Rev. X7.2 (Apr. 2017). Publisher: American Physical Society, p. 021007.doi:10.1103/PhysRevX.7.021007.url:https://link.aps.org/ doi/10.1103/PhysRevX.7.021007(cit. on p. 2)

    work page doi:10.1103/physrevx.7.021007.url:https://link.aps.org/ 2017

  30. [30]

    Hydrodynamic equations and near critical large deviations of active lattice gases

    Luke Neville. “Hydrodynamic equations and near critical large deviations of active lattice gases”. In: Journal of Statistical Mechanics: Theory and Experiment2025.3 (2025), p. 033204 (cit. on p. 2). 16

    work page 2025

  31. [31]

    Mechanical theory of nonequilibrium coexistence and motility-induced phase separation

    Ahmad K Omar et al. “Mechanical theory of nonequilibrium coexistence and motility-induced phase separation”. In:Proceedings of the National Academy of Sciences120.18 (2023), e2219900120 (cit. on pp. 2, 7, 9)

    work page 2023

  32. [32]

    A run-and-tumble particle around a spherical obstacle: the steady-state distribution far-from-equilibrium

    Thibaut Arnoulx de Pirey and Frédéric van Wijland. “A run-and-tumble particle around a spherical obstacle: the steady-state distribution far-from-equilibrium”. In:Journal of Statistical Mechanics: Theory and Experiment2023.9 (2023), p. 093202 (cit. on p. 14)

    work page 2023

  33. [33]

    Run-and-tumble particles in two dimensions: Marginal position distributions

    Ion Santra, Urna Basu, and Sanjib Sabhapandit. “Run-and-tumble particles in two dimensions: Marginal position distributions”. In:Physical Review E101.6 (2020), p. 062120 (cit. on p. 14)

    work page 2020

  34. [34]

    Swimming bacteria power microscopic gears

    Andrey Sokolov et al. “Swimming bacteria power microscopic gears”. In:Proceedings of the National Academy of Sciences107.3 (2010), pp. 969–974 (cit. on p. 1)

    work page 2010

  35. [35]

    Active brownian particles and run-and-tumble particles: A comparative study

    A. P. Solon, M. E. Cates, and J. Tailleur. “Active brownian particles and run-and-tumble particles: A comparative study”. In:The European Physical Journal Special Topics224.7 (July 2015), pp. 1231–1262. issn: 1951-6355, 1951-6401.doi:10.1140/epjst/e2015-02457-0.url:http://link.springer.com/ 10.1140/epjst/e2015-02457-0(visited on 09/23/2019) (cit. on p. 2)

    work page doi:10.1140/epjst/e2015-02457-0.url:http://link.springer.com/ 2015

  36. [36]

    Generalized thermodynamics of motility-induced phase separation: phase equi- libria, Laplace pressure, and change of ensembles

    Alexandre P Solon et al. “Generalized thermodynamics of motility-induced phase separation: phase equi- libria, Laplace pressure, and change of ensembles”. In:New Journal of Physics20.7 (July 2018), p. 075001. issn: 1367-2630.doi:10.1088/1367-2630/aaccdd.url:http://stacks.iop.org/1367-2630/20/i=7/ a=075001?key=crossref.df8f6df5bbc5cd65974dbf3bfac256f6(visi...

    work page doi:10.1088/1367-2630/aaccdd.url:http://stacks.iop.org/1367-2630/20/i 2018

  37. [37]

    du Buisson and H

    Alexandre P. Solon et al. “Generalized thermodynamics of phase equilibria in scalar active matter”. In: Physical Review E97.2 (Feb. 2018), p. 020602.issn: 2470-0045, 2470-0053.doi:10.1103/PhysRevE. 97.020602.url:https://link.aps.org/doi/10.1103/PhysRevE.97.020602(visited on 09/22/2019) (cit. on pp. 2, 7–9)

    work page doi:10.1103/physreve 2018

  38. [38]

    Pressure and Phase Equilibria in Interacting Active Brownian Spheres

    Alexandre P. Solon et al. “Pressure and Phase Equilibria in Interacting Active Brownian Spheres”. In:Physical Review Letters114.19 (May 2015), p. 198301.issn: 0031-9007, 1079-7114.doi:10.1103/ PhysRevLett.114.198301.url:https://link.aps.org/doi/10.1103/PhysRevLett.114.198301 (visited on 09/04/2019) (cit. on p. 9)

    work page doi:10.1103/physrevlett.114.198301 2015

  39. [39]

    Kinetic theory of motility induced phase separation for active Brownian particles

    Rodrigo Soto, Martín Pinto, and Ricardo Brito. “Kinetic theory of motility induced phase separation for active Brownian particles”. In:Physical Review Letters132.20 (2024), p. 208301 (cit. on p. 2)

    work page 2024

  40. [40]

    Coexistence of active Brownian disks: Van der Waals theory and analytical results

    Thomas Speck. “Coexistence of active Brownian disks: Van der Waals theory and analytical results”. In: Physical Review E103.1 (2021), p. 012607 (cit. on pp. 2, 7, 9)

    work page 2021

  41. [41]

    131.100803

    J. Tailleur and M. E. Cates. “Statistical Mechanics of Interacting Run-and-Tumble Bacteria”. In:Physical Review Letters100.21 (May 2008), p. 218103.issn: 0031-9007, 1079-7114.doi:10.1103/PhysRevLett. 100 . 218103.url:https : / / link . aps . org / doi / 10 . 1103 / PhysRevLett . 100 . 218103(visited on 09/22/2019) (cit. on pp. 1, 2, 14)

    work page doi:10.1103/physrevlett 2008

  42. [42]

    Sedimentation, trapping, and rectification of dilute bacteria

    Julien Tailleur and ME Cates. “Sedimentation, trapping, and rectification of dilute bacteria”. In:EPL (Europhysics Letters)86.6 (2009), p. 60002 (cit. on p. 14)

    work page 2009

  43. [43]

    Microscopic field theory for active Brownian particles with translational and rotational inertia

    Michael te Vrugt. “Microscopic field theory for active Brownian particles with translational and rotational inertia”. In:arXiv preprint arXiv:2602.11916(2026) (cit. on p. 2)

    work page arXiv 2026

  44. [44]

    How to derive a predictive field theory for active Brownian particles: a step-by-step tutorial

    Michael te Vrugt, Jens Bickmann, and Raphael Wittkowski. “How to derive a predictive field theory for active Brownian particles: a step-by-step tutorial”. In:Journal of Physics: Condensed Matter35.31 (2023), p. 313001 (cit. on p. 2)

    work page 2023

  45. [45]

    Steady-state distributions of ideal active Brownian particles under confinement and forcing

    Caleb G Wagner, Michael F Hagan, and Aparna Baskaran. “Steady-state distributions of ideal active Brownian particles under confinement and forcing”. In:Journal of Statistical Mechanics: Theory and Experiment2017.4 (2017), p. 043203 (cit. on p. 2)

    work page 2017

  46. [46]

    Scalar phi4 field theory for active-particle phase separation

    Raphael Wittkowski et al. “Scalar phi4 field theory for active-particle phase separation”. In:Nature communications5 (2014) (cit. on p. 2)

    work page 2014

  47. [47]

    Nonlocal stationary probability distributions and es- cape rates for an active Ornstein–Uhlenbeck particle

    Eric Woillez, Yariv Kafri, and Vivien Lecomte. “Nonlocal stationary probability distributions and es- cape rates for an active Ornstein–Uhlenbeck particle”. In:Journal of Statistical Mechanics: Theory and Experiment2020.6 (2020), p. 063204 (cit. on p. 12)

    work page 2020

  48. [48]

    Active particles in a tube: A generalized entropy potential approach

    Yongfeng Zhao. “Active particles in a tube: A generalized entropy potential approach”. In:Physical Review Research7.1 (2025), p. 013015 (cit. on p. 2). 17

    work page 2025

  49. [49]

    Active Young-Dupr\'e Equation: How Self-organized Currents Stabilize Partial Wetting

    Yongfeng Zhao et al. “Active Young-Dupr\’e Equation: How Self-organized Currents Stabilize Partial Wetting”. In:arXiv preprint arXiv:2405.20651(2024) (cit. on p. 2). 18

    work page internal anchor Pith review Pith/arXiv arXiv 2024