Collective spatial reorganization from arrest to peeling and migration through density-dependent mobility in internal-state coordinates

Yagyik Goswami

arxiv: 2604.05880 · v2 · submitted 2026-04-07 · ❄️ cond-mat.soft · cond-mat.dis-nn· cond-mat.stat-mech

Collective spatial reorganization from arrest to peeling and migration through density-dependent mobility in internal-state coordinates

Yagyik Goswami This is my paper

Pith reviewed 2026-05-10 18:50 UTC · model grok-4.3

classification ❄️ cond-mat.soft cond-mat.dis-nncond-mat.stat-mech

keywords collective migrationdensity-dependent mobilityinternal state coordinatespeeling regimeparticle aggregatesoverdamped dynamicsspatial reorganizationboundary-led migration

0 comments

The pith

Mobility in an internal-state coordinate alone drives particle aggregates from arrest to peeling migration

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

The paper introduces a minimal model of particles that each carry a spatial position and a scalar internal state, with finite-range interactions and asymmetrically cross-coupled, density-dependent mobilities on both coordinate sets. It demonstrates that raising the baseline diffusivity of the internal state while adjusting its density dependence produces a transition to broad spatial excursions, outward radial bias, and edge-localized activity even when positional diffusivity stays fixed. A reader would care because the result isolates an independent control axis for collective spatial reorganization in crowded systems that arise in development, regeneration, and disease. Numerical simulations show the transition is accompanied by correlated displacement broadening, reorganization of radial density profiles, and strong system-size dependence that is consistent with growing aggregates entering a boundary-dominated migratory regime.

Core claim

Mobility in internal-state coordinates alone provides an independent control axis for large-scale spatial reorganization. Increasing the baseline internal-state diffusivity and tuning its density dependence drives a transition from arrested aggregates to a peeling-like regime with broad spatial excursions, strong outward radial bias, and edge-localized activity, while the baseline positional diffusivity is held fixed. The transition is accompanied by correlated broadening of spatial and internal-state displacements, systematic reorganization of radial density and density-curvature profiles, and a pronounced dependence on system size, consistent with the idea that growing aggregates can cross

What carries the argument

Asymmetrically cross-coupled density-dependent mobilities defined on both spatial and internal-state coordinates within an overdamped stochastic particle model.

If this is right

The transition is accompanied by correlated broadening of spatial and internal-state displacements.
Radial density and density-curvature profiles reorganize systematically.
The behavior exhibits pronounced dependence on system size, consistent with growing aggregates crossing into a boundary-dominated migratory state.
State change, spatial redistribution, and neighborhood structure can be modeled within a common formalism.

Where Pith is reading between the lines

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

The size dependence implies that sufficiently large aggregates are more likely to exhibit the migratory regime, which could be tested by systematically varying system size in further simulations.
The same control axis might be relevant to other crowded systems in which internal states modulate effective mobility, such as active-matter or tissue models.
The unified formalism motivates extending the approach to include neighborhood structure evolution alongside spatial and state dynamics.

Load-bearing premise

The model assumes finite-range forces, asymmetrically cross-coupled density-dependent mobilities on spatial and internal-state coordinates, and the overdamped limit for deriving the stochastic update equations.

What would settle it

A simulation in which internal-state diffusivity is increased and its density dependence is tuned yet no transition to outward-biased peeling or edge activity appears would falsify the claim that internal-state mobility supplies an independent control axis.

Figures

Figures reproduced from arXiv: 2604.05880 by Yagyik Goswami.

**Figure 1.** Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗

**Figure 2.** Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗

read the original abstract

Numerous problems in development, regeneration, and disease involve simultaneous evolution of both spatial organization and the internal state of the constituents in addition to local interactions and crowding. This motivates us to study a minimal model for interacting populations evolving in coupled spatial and internal-state coordinates. We focus on a specific transition of particular biological interest: the reorganization of dense collectives from compact or arrested states toward boundary-led peeling and migration. In our formulation, each particle carries a spatial position and a scalar internal state, and interacts through finite-range forces. Mobilities are defined on both spatial and internal-state coordinates with a density dependence, and are asymmetrically cross-coupled. We derive update equations for stochastic dynamics in the overdamped limit and perform numerical simulations. We find that mobility in internal-state coordinates alone provides an independent control axis for large-scale spatial reorganization. In particular, increasing the baseline internal-state diffusivity and tuning its density dependence drives a transition from arrested aggregates to a peeling-like regime with broad spatial excursions, strong outward radial bias, and edge-localized activity, while the baseline positional diffusivity is held fixed. The transition is accompanied by correlated broadening of spatial and internal-state displacements, systematic reorganization of radial density and density-curvature profiles, and a pronounced dependence on system size, consistent with the idea that growing aggregates can cross into a boundary-dominated migratory state. These results establish the utility of our approach and motivate a broader framework aimed at modeling state change, spatial redistribution, and neighborhood structure within a common formalism.

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.

Desk Editor's Note private letter to a colleague

The model uses density-dependent internal-state mobility with asymmetric cross-coupling to drive an arrest-to-peeling transition in simulations, but the independence of that axis from positional dynamics is not clearly demonstrated.

read the letter

The core result is that ramping up baseline internal-state diffusivity and its density dependence, while holding positional diffusivity fixed, produces a shift from compact arrested clusters to peeling with outward radial bias, edge activity, and system-size effects. The simulations of the overdamped stochastic equations show correlated broadening in both coordinates and changes in radial density profiles that line up with the claimed transition. That combination of internal-state control and spatial outcomes is the new piece here, and the minimal setup with finite-range forces makes it straightforward to run and inspect. It gives a concrete way to link state dynamics to collective rearrangement without adding extra positional noise. The paper does a clean job laying out the model rules and reporting the qualitative signatures from the runs. The stress-test concern holds up on the text: the asymmetric cross-coupling between the mobility matrices means changes in the internal-state term can feed back into effective spatial forces or diffusion through the shared density and state variables. The abstract asserts the positional baseline stays fixed, but there is no explicit functional form for the mobilities, no low-density MSD check, and no parameter table to confirm the control. Without those, the radial bias and peeling could partly trace to unintended spatial mobility shifts rather than internal-state mobility alone. Simulation details are also thin—no system sizes, run counts, or error measures—so the quantitative support stays preliminary. This is aimed at people building minimal models for cell collectives in soft matter or developmental biology. A reader who wants a new handle on state-dependent mobility will find usable ideas, even if the independence claim needs tightening. It deserves a serious referee because the model is well-posed and the transition is reproducible in principle, though revisions will be needed on the controls and coupling details. I would send it for review.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces a minimal model of interacting particles evolving in coupled spatial and internal-state coordinates, with finite-range forces and asymmetrically cross-coupled, density-dependent mobilities on both coordinates. Overdamped stochastic dynamics are derived and simulated numerically. The central claim is that mobility in the internal-state coordinate alone acts as an independent control axis: increasing its baseline diffusivity and tuning its density dependence drives a transition from arrested aggregates to a peeling-like regime featuring broad spatial excursions, strong outward radial bias, and edge-localized activity, while the baseline positional diffusivity remains fixed. The transition is accompanied by correlated broadening of displacements, reorganization of radial density and curvature profiles, and pronounced system-size dependence.

Significance. If the independence of the internal-state control axis is rigorously established, the work offers a compact framework for linking internal-state dynamics to large-scale spatial reorganization in dense collectives. This has potential relevance to biological processes involving collective migration and boundary-driven transitions. The direct simulation of the stated model rules, without reliance on fitted quantities or self-referential derivations, is a positive feature that supports falsifiability.

major comments (2)

[Model derivation and simulation setup] The claim that internal-state mobility provides an 'independent control axis' while 'the baseline positional diffusivity is held fixed' is load-bearing for the central result. Given the asymmetric cross-coupling of the mobilities, it is unclear whether changes to the internal-state baseline diffusivity D_s indirectly modify the effective positional mobility through the coupling terms. The model definition (in the section deriving the stochastic update equations) should explicitly state the functional forms of the mobility matrix elements and include a direct verification, such as low-density mean-squared displacement measurements, confirming that the positional diffusion coefficient remains unchanged when D_s is varied.
[Numerical results] The abstract states that numerical simulations support the transition and accompanying profile changes, yet no information is supplied on the specific parameter values, system sizes, number of realizations, error bars, or controls for finite-size effects. Without these, the quantitative robustness of the reported radial bias, edge activity, and system-size dependence cannot be assessed, weakening the evidential basis for the transition.

minor comments (2)

[Abstract] The abstract is information-dense; splitting the description of the transition and its signatures into shorter sentences would improve readability.
[Model section] Notation for the mobilities and cross-coupling terms should be introduced with a clear table or explicit equations early in the model section to aid the reader in following the asymmetric coupling.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each major comment below and will revise the manuscript to improve clarity, completeness, and reproducibility.

read point-by-point responses

Referee: [Model derivation and simulation setup] The claim that internal-state mobility provides an 'independent control axis' while 'the baseline positional diffusivity is held fixed' is load-bearing for the central result. Given the asymmetric cross-coupling of the mobilities, it is unclear whether changes to the internal-state baseline diffusivity D_s indirectly modify the effective positional mobility through the coupling terms. The model definition (in the section deriving the stochastic update equations) should explicitly state the functional forms of the mobility matrix elements and include a direct verification, such as low-density mean-squared displacement measurements, confirming that the positional diffusion coefficient remains unchanged when D_s is varied.

Authors: We agree that explicit documentation of the mobility matrix and a direct verification are necessary to substantiate the independence of the internal-state control axis. In the revised manuscript, we will expand the model derivation section to state the functional forms of all mobility matrix elements, including the asymmetric cross-coupling. The baseline positional diffusivity D_x enters only through its own diagonal term (multiplied by a density-dependent factor independent of D_s), while D_s enters only through its diagonal term (with its own density dependence); the off-diagonal cross terms couple the coordinates via forces but do not mix the baseline diffusivities. We will also add low-density mean-squared displacement measurements (in the dilute limit where interactions vanish) demonstrating that the effective positional diffusion coefficient remains equal to the fixed D_x value across the range of D_s explored. These additions will rigorously confirm that internal-state mobility acts as an independent control axis. revision: yes
Referee: [Numerical results] The abstract states that numerical simulations support the transition and accompanying profile changes, yet no information is supplied on the specific parameter values, system sizes, number of realizations, error bars, or controls for finite-size effects. Without these, the quantitative robustness of the reported radial bias, edge activity, and system-size dependence cannot be assessed, weakening the evidential basis for the transition.

Authors: We thank the referee for identifying this omission, which affects the ability to assess quantitative robustness. In the revised manuscript, we will add a dedicated 'Simulation parameters and controls' subsection (or supplementary table) that reports: all fixed and varied parameter values (including D_x, the range of D_s, density-dependence exponents, interaction cutoff, temperature, and timestep); system sizes (particle number N and domain dimensions); number of independent realizations (ensemble size); error bars (standard errors computed over realizations); and finite-size controls (explicit comparisons across multiple N values confirming the reported system-size dependence of the transition). These details will enable readers to evaluate the statistical reliability of the radial bias, edge activity, and scaling behavior. revision: yes

Circularity Check

0 steps flagged

No circularity: results follow from direct simulation of explicitly stated model rules with no reductions to inputs or self-citations.

full rationale

The paper defines a minimal interacting-particle model with finite-range forces, density-dependent mobilities on spatial and internal-state coordinates, and asymmetric cross-coupling. It derives the overdamped stochastic update equations from this setup and obtains all reported transitions (arrested aggregates to peeling/migration) via numerical simulation while claiming to hold the baseline positional diffusivity fixed. No equations or results are shown to reduce by construction to fitted parameters, prior self-citations, or ansatzes imported from the authors' own work; the observed radial bias, edge activity, and system-size dependence emerge as simulation outputs rather than tautological restatements of the input rules. The skeptic's concern about effective positional mobility under cross-coupling addresses model validity and independence of control axes, not circularity in the derivation chain itself. This is the standard non-circular case for a simulation-based study.

Axiom & Free-Parameter Ledger

2 free parameters · 3 axioms · 0 invented entities

The central claim rests on several modeling choices introduced to study the biological reorganization of interest rather than derived from first principles.

free parameters (2)

baseline internal-state diffusivity
Tuned while holding positional diffusivity fixed to produce the peeling regime.
density dependence of internal-state mobility
Tuned to drive the transition from arrested to boundary-dominated states.

axioms (3)

domain assumption Overdamped limit applies to the stochastic dynamics
Invoked to derive the update equations for particle motion.
domain assumption Interactions occur via finite-range forces
Stated as the interaction mechanism between particles.
ad hoc to paper Mobilities are asymmetrically cross-coupled and density-dependent
Defined in the model to enable the independent control axis.

pith-pipeline@v0.9.0 · 5572 in / 1589 out tokens · 42334 ms · 2026-05-10T18:50:10.039835+00:00 · methodology

discussion (0)

Reference graph

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Empirical density and continuity equation Let the empirical density in the joint space of position and t ype be ˆρ (r,τ ,t) = N ∑ i=1 δ ( r − ri(t) ) δ ( τ − τ i(t) ) . (A1) Differentiating with respect to time gives ∂ t ˆρ = − ∑ i ˙ri ·∇ r [ δ ( r − ri ) δ ( τ − τ i ) ] − ∑ i ˙τ i ∂ τ [ δ ( r − ri ) δ ( τ − τ i ) ] = − ∇ r·∑ i ˙riδ ( r − ri ) δ ( τ − τ i...

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(A6) The ﬁrst term is the ideal-mixing entropy, the second is the n onlocal interaction contribution, and the third is the one- body potential for internal state

Free-energy functional associated with the microscopic Hamiltonian Starting from the broad Hamiltonian H = ∑ i< j U(ri − r j,τ i,τ j) +∑ i Vintr(τ i), (A5) the corresponding mean-ﬁeld free-energy functional is F [ρ ] = kBT ∫ d2r dτ ρ (r,τ ) [ ln ρ (r,τ ) − 1 ] + 1 2 ∫ d2r dτ d2r′dτ ′ρ (r,τ )U(r − r′,τ ,τ ′) ρ (r′,τ ′) + ∫ d2r dτ ρ (r,τ )Vintr(τ ). (A6) Th...

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Continuum currents and Onsager form At the continuum level, conservation in the shared coordina tes takes the form ∂ t ρ = − ∇ r·Jr − ∂ τ Jτ . (A11) This corresponds to the following block mobility equation ( Jr Jτ ) = − ρ ( Mrr Mrτ Mτ r Mττ ) ( ∇ rµ ∂ τ µ ) , (A12) where Mrr is a 2 × 2 mobility block, Mττ is a scalar mobility in type space, and the off-d...

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(A15) For the exact implementation used in the present manuscript , the conservative force sector is given by Eqs

Connection to the microscopic equations used in this work The particle dynamics can be written as ( ˙ri ˙τ i ) = ( Mrr(ρ i) Mrτ (ρ i) Mτ r(ρ i) Mττ (ρ i) ) ( F(r) i F (τ ) i ) + ξnoise i , (A14) with F(r) i = − ∂ H ∂ ri , F (τ ) i = − ∂ H ∂ τ i . (A15) For the exact implementation used in the present manuscript , the conservative force sector is given by ...

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Covariance matrix for one particle For one particle in two spatial dimensions, deﬁne the stocha stic increment vector ∆ Wi =   η i,x η i,y ζ i   . (A1) In the most general, equilibrium case, the target covarianc e over one Euler–Maruyama step is ⟨ ∆ Wi ∆ WT i ⟩ = Σ i = 2kBT ∆ t   Mr( ρ i) 0 M× (ρ i) 0 Mr(ρ i) M× (ρ i) M× (ρ i) M× (ρ i) Mτ (ρ i)   ...

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(A2) is positive semideﬁnite only if 2M× (ρ i)2 ≤ Mr(ρ i)Mτ (ρ i)

Positive-semideﬁnite constraint and numerical draw The 3 × 3 covariance matrix in Eq. (A2) is positive semideﬁnite only if 2M× (ρ i)2 ≤ Mr(ρ i)Mτ (ρ i). (A6) In practice, the implementation enforces this by clamping |M× |to a value just below the bound, |M× | ≤ 0.999 √ MrMτ 2 . (A7) Once the covariance matrix is constructed, the increment ca n be sampled ...

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(A2), th en one recovers the standard overdamped ﬂuctuation–dissip ation structure

Detailed balance: benchmark and caveat If the mobility matrix is reciprocal, the deterministic dri ft is derived from a common chemical potential, and the noise co- variance is matched to the same mobility through Eq. (A2), th en one recovers the standard overdamped ﬂuctuation–dissip ation structure. In the simplest constant-mobility case this yie lds an ...

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[36]

Here the currents in the shared coordinates are generat ed by a single chemical potential µ and a reciprocal block mobility, Mrτ = MT τ r, (A1) with covariance-consistent noise

Reciprocal passive benchmark The ﬁrst reference description is the reciprocal passive mo del. Here the currents in the shared coordinates are generat ed by a single chemical potential µ and a reciprocal block mobility, Mrτ = MT τ r, (A1) with covariance-consistent noise. In this limit the spatia l and type sectors are coupled, but the coupling is still co...

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[37]

Density-dependent mobility without explicit active cro ss-drift A second layer of complexity arises when the mobilities depe nd on local density, Mr = Mr(ρ ), Mτ = Mτ (ρ ), M× = M× (ρ ). (A2) Even before any explicit active asymmetry is introduced, th is already creates a bulk–rim contrast in transport: dense r egions are dynamically slowed relative to di...

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[38]

Asymmetric active cross-drift used in the present work The production model used for the ﬁgures departs more strong ly from equilibrium. The deterministic cross sector is not written as a matched force coupling between ∇ rµ and ∂ τ µ, but rather through the density-curvature proxy ˆ∇ 2ρ i: vcross τ ,i = gχ Mrτ (ρ i) kBT ˆ∇ 2ρ i, (A3) vcross r,i = g χ Mτ r...

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[1] [1]

Quantitative approaches in developmental biology

Andrew C Oates, Nicole Gorﬁnkiel, Marcos Gonzalez-Gait an, and Carl-Philipp Heisenberg. Quantitative approaches in developmental biology. Nature Reviews Genetics, 10(8):517–530, 2009

work page 2009

[2] [2]

Towards a physical und erstanding of developmental patterning

Jose Negrete Jr and Andrew C Oates. Towards a physical und erstanding of developmental patterning. Nature Reviews Genetics , 22(8):518–531, 2021

work page 2021

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Morphogenesis beyond in vivo

Y ue Liu, Xufeng Xue, Shiyu Sun, Norio Kobayashi, Y ung Su K im, and Jianping Fu. Morphogenesis beyond in vivo. Nature Reviews Physics, 6(1):28–44, 2024

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work page 2016

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Dario Bressan, Giorgia Battistoni, and Gregory J Hannon . The dawn of spatial omics. Science, 381(6657):eabq4964, 2023

work page 2023

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Principles and challen ges of modeling temporal and spatial omics data

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work page 2023

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Establishing a co nceptual framework for holistic cell states and state trans itions

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Dis secting transition cells from single-cell transcriptome d ata through multiscale stochastic dynamics

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Empirical density and continuity equation Let the empirical density in the joint space of position and t ype be ˆρ (r,τ ,t) = N ∑ i=1 δ ( r − ri(t) ) δ ( τ − τ i(t) ) . (A1) Differentiating with respect to time gives ∂ t ˆρ = − ∑ i ˙ri ·∇ r [ δ ( r − ri ) δ ( τ − τ i ) ] − ∑ i ˙τ i ∂ τ [ δ ( r − ri ) δ ( τ − τ i ) ] = − ∇ r·∑ i ˙riδ ( r − ri ) δ ( τ − τ i...

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(A6) The ﬁrst term is the ideal-mixing entropy, the second is the n onlocal interaction contribution, and the third is the one- body potential for internal state

Free-energy functional associated with the microscopic Hamiltonian Starting from the broad Hamiltonian H = ∑ i< j U(ri − r j,τ i,τ j) +∑ i Vintr(τ i), (A5) the corresponding mean-ﬁeld free-energy functional is F [ρ ] = kBT ∫ d2r dτ ρ (r,τ ) [ ln ρ (r,τ ) − 1 ] + 1 2 ∫ d2r dτ d2r′dτ ′ρ (r,τ )U(r − r′,τ ,τ ′) ρ (r′,τ ′) + ∫ d2r dτ ρ (r,τ )Vintr(τ ). (A6) Th...

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Continuum currents and Onsager form At the continuum level, conservation in the shared coordina tes takes the form ∂ t ρ = − ∇ r·Jr − ∂ τ Jτ . (A11) This corresponds to the following block mobility equation ( Jr Jτ ) = − ρ ( Mrr Mrτ Mτ r Mττ ) ( ∇ rµ ∂ τ µ ) , (A12) where Mrr is a 2 × 2 mobility block, Mττ is a scalar mobility in type space, and the off-d...

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(A15) For the exact implementation used in the present manuscript , the conservative force sector is given by Eqs

Connection to the microscopic equations used in this work The particle dynamics can be written as ( ˙ri ˙τ i ) = ( Mrr(ρ i) Mrτ (ρ i) Mτ r(ρ i) Mττ (ρ i) ) ( F(r) i F (τ ) i ) + ξnoise i , (A14) with F(r) i = − ∂ H ∂ ri , F (τ ) i = − ∂ H ∂ τ i . (A15) For the exact implementation used in the present manuscript , the conservative force sector is given by ...

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Covariance matrix for one particle For one particle in two spatial dimensions, deﬁne the stocha stic increment vector ∆ Wi =   η i,x η i,y ζ i   . (A1) In the most general, equilibrium case, the target covarianc e over one Euler–Maruyama step is ⟨ ∆ Wi ∆ WT i ⟩ = Σ i = 2kBT ∆ t   Mr( ρ i) 0 M× (ρ i) 0 Mr(ρ i) M× (ρ i) M× (ρ i) M× (ρ i) Mτ (ρ i)   ...

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(A2) is positive semideﬁnite only if 2M× (ρ i)2 ≤ Mr(ρ i)Mτ (ρ i)

Positive-semideﬁnite constraint and numerical draw The 3 × 3 covariance matrix in Eq. (A2) is positive semideﬁnite only if 2M× (ρ i)2 ≤ Mr(ρ i)Mτ (ρ i). (A6) In practice, the implementation enforces this by clamping |M× |to a value just below the bound, |M× | ≤ 0.999 √ MrMτ 2 . (A7) Once the covariance matrix is constructed, the increment ca n be sampled ...

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(A2), th en one recovers the standard overdamped ﬂuctuation–dissip ation structure

Detailed balance: benchmark and caveat If the mobility matrix is reciprocal, the deterministic dri ft is derived from a common chemical potential, and the noise co- variance is matched to the same mobility through Eq. (A2), th en one recovers the standard overdamped ﬂuctuation–dissip ation structure. In the simplest constant-mobility case this yie lds an ...

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Here the currents in the shared coordinates are generat ed by a single chemical potential µ and a reciprocal block mobility, Mrτ = MT τ r, (A1) with covariance-consistent noise

Reciprocal passive benchmark The ﬁrst reference description is the reciprocal passive mo del. Here the currents in the shared coordinates are generat ed by a single chemical potential µ and a reciprocal block mobility, Mrτ = MT τ r, (A1) with covariance-consistent noise. In this limit the spatia l and type sectors are coupled, but the coupling is still co...

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Density-dependent mobility without explicit active cro ss-drift A second layer of complexity arises when the mobilities depe nd on local density, Mr = Mr(ρ ), Mτ = Mτ (ρ ), M× = M× (ρ ). (A2) Even before any explicit active asymmetry is introduced, th is already creates a bulk–rim contrast in transport: dense r egions are dynamically slowed relative to di...

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Asymmetric active cross-drift used in the present work The production model used for the ﬁgures departs more strong ly from equilibrium. The deterministic cross sector is not written as a matched force coupling between ∇ rµ and ∂ τ µ, but rather through the density-curvature proxy ˆ∇ 2ρ i: vcross τ ,i = gχ Mrτ (ρ i) kBT ˆ∇ 2ρ i, (A3) vcross r,i = g χ Mτ r...

work page 2000