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Jamming transition in an active exclusion process

T0 review · 3 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Adding run-and-tumble self-propulsion to a one-dimensional hard-core particle gas suppresses the jamming transition and, for slow enough orientation flips, removes the jammed phase entirely.

desk verdict A credible, well-analyzed study showing activity can suppress the jamming transition in a 1D active exclusion process, though the 'eliminate jamming' claim rests on a mobility cutoff and excluded low-density data. read the letter →

arxiv 2608.11041 v1 pith:XUD45QEK submitted 2026-08-11 cond-mat.stat-mech

Kavita Jain , Sakuntala Chatterjee This is my paper · ORCID
classification cond-mat.stat-mech
keywords jammingtransitionactivematterexclusionprocessrun-and-tumbleparticlesmeanfieldtheorymobilityholeclusterszero-range
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper studies a one-dimensional exclusion process whose hard-core particles carry a self-propulsion direction, $\eta=\pm 1$, that flips at rate $\gamma$. With hop rate $u_n = u_\infty(1 + b/n)$ for $b>2$, the passive limit $\gamma\to\infty$ is a known jamming transition between a low-density jammed phase with a macroscopic hole cluster and a high-density fluid phase. The paper's main claim is that finite activity pushes the critical density downward and that for sufficiently small $\gamma$ the jammed phase disappears entirely, leaving only the fluid phase. This matters because it shows activity does not merely shift a nonequilibrium transition; it can destroy it.

What carries the argument

The load-bearing object is the mean mobility $w$, defined as twice the mean hop rate per particle, which takes the value 1 in the jammed phase and values below 1 in the fluid phase; the phase boundary is read off from where $w$ crosses one. The companion objects are the hole-cluster distributions $P^{\alpha\beta}_n$ for boundaries of type $\alpha,\beta=\pm 1$, whose generating functions obey a system of mean-field equations that the paper closes by numerical integration or by perturbation theory. The mechanism the paper identifies is a competition between hopping and orientation switching: at large $\gamma$, particles tumble before they can execute a directed hop, recovering the passive kinetics; at small $\gamma$, a particle at the edge of a hole cluster hops in its own direction before tumbling, and the jam is destabilized.

What would settle it

Simulate rings of length $L=1024$, $2048$, and $4096$ at $b=2.5$, $\gamma=0.5$, and densities $\rho=0.02,\dots,0.30$. If $w(\rho)$ approaches 1 from below as $L$ grows at any density below the reported boundary, or if the hole-cluster distribution develops a macroscopic component, then a jammed phase exists at small $\gamma$ and activity does not eliminate jamming; if $w$ stays strictly below 1 and the distribution stays exponential, the claim survives. An analytic proof that $w\le 1$ in the active jammed phase would replace the numerical thresholds and settle the boundary criterion.

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Extended reading notes

Core claim

Working with Monte Carlo simulations and a mean-field closure, the paper argues that the jamming transition of the passive model survives only above a switching-rate threshold. For $b=2.5$ and $u_\infty=0.1$, the measured phase boundary in the $\gamma$--$\rho$ plane ends near $\gamma\approx 1$: for smaller $\gamma$ the mean mobility $w$ never reaches one, so the system is fluid at all densities, while for larger $\gamma$ the critical density $\rho_c$ lies below the passive value $r_c=(b-2)/(b-1)$ and decreases as $\gamma$ decreases. In the fluid phase the active mobility is smaller than the passive mobility at the same density, with the difference decaying as $\gamma^{-1}$ at large $\gamma$. In the double limit $\rho,\gamma\to 0$ at fixed $s=\rho/\gamma$, the mobility is $w_s\approx 1-B(b)\rho/\gamma$ for $s\ll 1$ and $w_s\approx 4/s$ for $s\gg 1$, independent of $b$; and the hole-cluster size distribution becomes exponential at small $\gamma$, the hallmark of a fluid.

Load-bearing premise

The conclusion that small $\gamma$ removes the jammed phase rests on the assumption that the mean mobility is bounded above by one in any jammed phase, so the numerical thresholds ($w=0.99$ in simulations, $w=1.003$ in mean field) genuinely mark the phase boundary; the paper notes in Sec. VII that $w\le 1$ has not been rigorously proved for the active model, and it discards low-density data near $\gamma\approx 1$ as unreliable due to finite-size effects.

Editorial extensions

If this is right

  • For fixed $b>2$ there is a finite switching threshold below which no jammed phase exists at any density; for $b=2.5$ the data place it near $\gamma\approx 1$.
  • Above that threshold the critical density obeys $\rho_c(\gamma)<r_c=(b-2)/(b-1)$ and decreases with decreasing $\gamma$, so at fixed density the critical $b$ increases with activity.
  • In the fluid phase the active mobility is always below the passive value at the same density, with a leading correction proportional to $\gamma^{-1}$.
  • In the low-density, high-activity scaling regime the mobility crosses over from the passive-fluid form $1-B(b)\rho/\gamma$ to the universal active-fluid form $4\gamma/\rho$ for $s=\rho/\gamma\gg 1$, independent of $b$.
  • At small switching rates the hole-cluster size distribution is exponential, so no macroscopic hole cluster forms; this is the direct signature that the jammed phase is absent.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • An implication the paper leaves implicit is that the same boundary-hopping mechanism should weaken condensation in other zero-range-type models: any directed move that can occur before a flip attacks the jam boundary, so activity may generically suppress rather than merely shift such transitions.
  • The paper uses the line $\rho=\gamma$ to separate passive-fluid from active-fluid behavior; a natural test is whether this is a genuine sharp transition or a smooth crossover as $L$ grows.
  • The universal $4/s$ mobility tail for $s\gg 1$ hints at a scaling law tied to the absorbing $\gamma=0$ state; checking hop-rate families such as $u_n=u_\infty(1+b/n^\nu)$ would show whether the exponent is universal.
  • The mobility overshoot above 1 near the reported threshold is attributed to finite size; if a rigorous upper bound $w\le 1$ in the jammed phase were established, the threshold estimate could be replaced by an exact boundary.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper studies a one-dimensional lattice gas of hard-core particles with an internal ±1 orientation that flips at rate γ; a particle hops into a neighboring hole in its orientation direction with rate u_n = u_∞(1 + b/n), b > 2. In the passive limit γ → ∞ this reduces to a known exclusion process with a jamming transition at density ρ_c = (b−2)/(b−1). Using Monte Carlo simulations, numerical integration of a mean-field closure, and perturbation theory, the authors report that finite switching activity moves the critical density downward, that for sufficiently small γ the mobility never reaches one so the system remains fluid at all densities, and that in the low-density, low-γ scaling limit the mobility has the universal form w ≈ 4γ/ρ for ρ ≫ γ. The paper also presents hole-cluster distributions and largest-cluster statistics supporting a change of cluster structure with γ.

Significance. If the central claim is correct, the paper makes a clean conceptual point: activity does not merely shift the canonical jamming transition but can remove it, with a phase diagram in the (γ, ρ) plane and a nontrivial low-density scaling regime. The manuscript is careful in several respects: the passive limit is reviewed in Appendix A, the large-γ perturbation is solved against boundary conditions in Appendix E, the small-γ scaling is derived from mean-field generating functions in Appendix F, and the universal 4/s mobility is checked against the exact b=0 solution and against simulations and mean-field numerics in Fig. 3. These internal consistencies make the analytical framework credible. The main reservation is that the headline phase boundary for γ < 1 rests on arbitrary mobility thresholds and on a region of the phase diagram from which the most relevant data are excluded, so the claim that activity can eliminate jamming is not yet demonstrated at the same level as the scaling results.

major comments (3)
  1. [Sec. III, Fig. 1d] The central claim that the system remains fluid for all densities when γ < 1 is based on the criterion that the phase boundary is the maximum density at which the mobility equals 0.99 (Monte Carlo) or 1.003 (mean field), and the text states that low-density data near γ ≈ 1 are excluded as unreliable. This is exactly the region that matters, because Eq. (19a) predicts w ≈ 1 − B(b)ρ/γ for ρ ≪ γ; for any γ < 1 the mobility will approach 1 as ρ decreases, and finite-size effects can prevent the threshold from being crossed even if a jammed state exists. The authors should either present a system-size-scaling analysis of the hole-cluster distribution or of ⟨h_max⟩ in the low-density region, or otherwise prove that no extensive hole cluster appears for γ < 1, before the activity-inhibits-jamming conclusion can be regarded as established.
  2. [Sec. VII] The paper explicitly states that it has not rigorously shown that the mobility is bounded above by one in the jammed phase. This is load-bearing because the passive jammed phase is identified precisely by w = 1, and the argument that γ < 1 has no jammed phase assumes that a jammed phase would make the mobility reach the threshold. If a jammed phase with w < 1 existed, Figs. 1a and 1d would not distinguish it from the fluid phase. The exponential hole-cluster distributions in Fig. 4 are more direct evidence, but they are shown for one density (ρ = 0.125) and one b (2.5); a quantitative test of extensivity of the largest hole cluster as a function of L, at several densities below ρ = γ, is needed to close this gap.
  3. [Sec. III, Figs. 1a-1d] The Monte Carlo data are presented without error bars or numbers of independent runs, and the mean-field curves are obtained from a single truncation n_max = 1024. Since the phase boundary is read off a mobility threshold at the 1% level, the statistical and truncation uncertainties are of the same order as the effect used to define ρ_c; in fact, the overshoot of the mobility above 1 noted in Sec. III shows that O(1%) finite-size deviations are present. The authors should provide error bars, a system-size dependence for the threshold density, and a check that the mean-field boundary is stable with respect to n_max.
minor comments (4)
  1. [Abstract] There are several typographical and ligature artifacts (e.g., 'sufficiently' in the Abstract) that should be cleaned before publication.
  2. [Appendix E, Eq. (E.9)] The Euler constant is denoted γ_e, which is easily confused with the switching rate γ; a different symbol such as γ_E would avoid ambiguity.
  3. [Eq. (19) and Fig. 1d] The crossover line ρ = γ is drawn in the same panel as the jammed/fluid boundary; since the paper itself describes ρ = γ as a demarcation of passive-fluid and active-fluid behavior rather than a phase transition, using a dashed or shaded line with an explicit 'crossover' label would prevent misinterpretation.
  4. [Fig. 4(a)] The definition P(n) = Σ_{α,β} P^{αβ}_n appears only in the caption; the panel legend 'size distribution of clusters' could be made more explicit by stating the summation directly in the panel.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the derivation chain is self-contained; the threshold-based phase diagram and the admitted unproven bound are correctness caveats, not circular reductions.

full rationale

The paper's central derivations are self-contained. The passive critical density is reviewed via the exact ZRP mapping in Appendix A (Eq. A.6) rather than imported from the present authors' prior work. The large-gamma correction solves the inhomogeneous mean-field equation (E.1)-(E.9) with boundary/normalization conditions, giving an explicit w1. The small-gamma mobility follows from the generating-function equation (F.5), which for b>0 reduces to w about 4/s without fitting any parameter to data and then renaming it a prediction. The mobility thresholds 0.99 and 1.003 used to draw Fig. 1d are numerical conventions for locating the phase boundary, not inputs whose identity generates the claimed rho_c(gamma) trend. Section VII explicitly concedes that w <= 1 in the jammed phase has not been shown rigorously, and Section III labels very low-density data near gamma about 1 as unreliable; these are limitations of evidence for the claim that activity can inhibit jamming, but they are not circularity. Self-citations ([37], [38], [49], [53]) appear only in contextual background or related-model discussions and are not load-bearing for the phase-transition mechanism. No step reduces, by construction or by self-citation, to its own input.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The model introduces no new physical entities. The free parameters are the model-defining hop-rate parameter b, the hop-rate scale u_infinity, and the hand-chosen mobility thresholds used to define the phase boundary. The main axioms are the mean-field factorization and the unproved w <= 1 bound in the jammed phase, the latter explicitly acknowledged by the authors. The perturbation theories rely on these assumptions.

free parameters (3)
  • b (hop-rate enhancement parameter) = 2.5, 3.5, 4.75 (varied)
    Model parameter in u_n = u_infinity(1 + b/n). It is chosen by hand, not fitted. The central claim (activity suppresses jamming) is expected to hold for any b > 2, but the critical density and the threshold gamma depend on b.
  • u_infinity (hop-rate scale) = 1 (theory), 0.1 (simulations)
    Time is measured in units of 1/u_infinity in the theory. In simulations u_infinity = 0.1 is chosen to keep u_n < 1 for all n. It is a scale, not fitted.
  • mobility thresholds for phase boundary = 0.99 (MC), 1.003 (MFT)
    The critical density rho_c is defined as the maximum density where the mean mobility is 0.99 (simulations) or 1.003 (mean field). These thresholds are chosen by hand and affect the reported phase diagram, especially the claim that the jammed phase disappears for gamma < 1.
assumptions (4)
  • domain assumption The mean-field approximation ignores spatial correlations and factorizes joint distributions.
    Used to derive the dynamical equations (B.1)-(B.4) in Appendix B; the resulting phase diagram is compared with 1D simulations and is not exact.
  • domain assumption For gamma > 0 the process has a unique stationary state reached from arbitrary initial conditions.
    Assumed implicitly in the mean-field integration and in the interpretation of Monte Carlo data (Sec. II C, III); for gamma = 0 the absorbing states are initial-condition dependent, as the paper notes.
  • ad hoc to paper The mobility is bounded above by one in the jammed phase (w <= 1).
    This bound is used to locate the jammed-fluid boundary via w = 1. Sec. VII states the bound has not been proved rigorously for the active model.
  • domain assumption The ZRP-to-EP mapping of Evans and Hanney is valid for the passive limit and guides the mean-field equations for the active model.
    Invoked in Sec. II A and Appendix A to connect to the known jamming transition and to justify the product-measure-like stationary structure in the passive limit.

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Cite this review

Pith. "Pith review of Jamming transition in an active exclusion process." pith.science (2026). https://pith.science/paper/XUD45QEK

@misc{pith2026260811041,
  author       = {Pith},
  title        = {Pith review of: Jamming transition in an active exclusion process},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XUD45QEK}},
  note         = {Machine review of arXiv:2608.11041}
}
read the original abstract

Multiple studies on active matter have shown that activity can induce or suppress a phase transition, or modify the critical behavior of a passive system. Here we investigate how activity affects the jamming transition which is a paradigmatic example of nonequilibrium phase transitions in passive systems. We consider a one-dimensional system of active particles with hardcore interactions and a direction of self-propulsion which can be reversed at a given switching rate. For a class of particle hop rates and infinite switching rate, our model reduces to a passive system which is known to exhibit a transition between a high-density fluid phase and a low-density jammed phase in the stationary state. Using Monte Carlo simulations and a mean field theory, we study how the mean mobility of the particle and the hole cluster distribution vary with density and finite switching rate. Our main result is that activity hinders the formation of jam and can even inhibit it; more precisely, we find that the jamming transition occurs at a critical density that decreases with decreasing switching rate, and at sufficiently small switching rate, the system exists only in the fluid phase.

Figures

Figures reproduced from arXiv: 2608.11041 by the authors.

Figure 1
Figure 1. FIG. 1. Mean particle mobility defined in ( [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Deviation, [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Mean mobility [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Probability distribution of the largest hole cluster size for various values of [PITH_FULL_IMAGE:figures/full_fig_p015_5.png]

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