arxiv: 2605.01422 · v1 · submitted 2026-05-02 · ❄️ cond-mat.stat-mech · cond-mat.soft

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Microscopic theory of soft run-and-tumble particles

Rosalba Garcia-Millan , Ziluo Zhang , Luca Cocconi , Marius Bothe , Letian Chen , Zigan Zhen , Gunnar Pruessner

Authors on Pith no claims yet

Pith reviewed 2026-05-09 18:02 UTC · model grok-4.3

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

keywords run-and-tumble particleseffective interactionsperturbation expansionactive mattercorrelation functionsstationary statessoft particlesloop corrections

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The pith

Soft repulsive run-and-tumble particles develop effective attractions through an iterative perturbation expansion of their interaction vertices.

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

The paper establishes a microscopic theory that represents the exact dynamics of soft, repulsive run-and-tumble particles and shows how these particles can appear to stick together even without attractive forces. It does so by computing effective interaction vertices order by order in a perturbation expansion around the bare interaction couplings, systematically including loop corrections at each step. These vertices are then used to obtain the two-point correlation function, which fully characterizes the stationary state. The same vertices also determine additional observables including the structure factor, overlap probability, and entropy production rate. This matters for understanding collective behavior in active systems because it derives the apparent clustering from the interplay of repulsion and self-propulsion alone.

Core claim

An exact microscopic representation of the particle dynamics permits an iterative calculation of effective interaction vertices by adding loop corrections order by order in the interaction couplings; these vertices determine the two-point correlation function that characterizes the stationary state of the system.

What carries the argument

Effective interaction vertices computed iteratively from a perturbation expansion about the interaction couplings, with loop corrections added order by order.

If this is right

The two-point correlation function fully characterizes the stationary state.
The structure factor, overlap probability, and entropy production rate follow directly from the same effective vertices.
Effective attraction between particles emerges specifically when repulsion is strong and self-propulsion is large.

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 compute higher-order correlation functions or to systems with different propulsion rules.
The derived vertices provide a route to quantify clustering without introducing phenomenological attractions.
The method may extend to other active-matter models where repulsion and motility compete.

Load-bearing premise

The perturbation expansion converges and remains valid in the regime of strong repulsion and large self-propulsion where the effective attraction appears.

What would settle it

A measurement or simulation of the two-point correlation function that deviates systematically from the value predicted by the first few orders of the expansion in the strong-repulsion, high-self-propulsion regime.

Figures

Figures reproduced from arXiv: 2605.01422 by Gunnar Pruessner, Letian Chen, Luca Cocconi, Marius Bothe, Rosalba Garcia-Millan, Zigan Zhen, Ziluo Zhang.

**Figure 1.** Figure 1: , all black arrows vanish in this limit, as well as ξtype poles encircled in orange and poles generated from them. The coefficients A(α) and B(α) in Eq. (43) have limits lim L→∞ A(α) =1 , (48a) view at source ↗

**Figure 2.** Figure 2: FIG. 2. Structure factor view at source ↗

**Figure 3.** Figure 3: FIG. 3. Stationary two-point correlation functions view at source ↗

**Figure 4.** Figure 4: FIG. 4. Stationary two-point correlation functions view at source ↗

**Figure 5.** Figure 5: FIG. 5. Overlap probability view at source ↗

**Figure 6.** Figure 6: FIG. 6. Entropy production rate view at source ↗

**Figure 7.** Figure 7: FIG. 7. Square contour view at source ↗

read the original abstract

Soft, repulsive run-and-tumble particles display emergent effective interactions as they appear to stick to each other in spite of the absence of attractive forces. This effective attraction emerges at strong enough repulsion and large self-propulsion. Complementing a companion paper that characterises effective attraction between two soft run-and-tumble particles [Garcia-Millan et al., Effective attraction by repulsion (2026)], here we provide a thorough derivation of our microscopic theory, which is an exact representation of the particle dynamics. We report the systematic calculation of the effective interaction vertices iteratively, in a perturbation expansion about the interaction couplings, by adding, order by order, loop corrections. We use the effective interaction vertices to calculate the two-point correlation function, fully characterising the stationary state. Other observables, such as the structure factor, overlap probability and entropy production rate are calculated as well.

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

Perturbative microscopic derivation of emergent attractions from repulsive run-and-tumble dynamics, but the expansion's validity at strong coupling is the open question.

read the letter

This paper supplies a microscopic starting point for why soft repulsive run-and-tumble particles can show effective sticking at strong repulsion and high self-propulsion. They begin with an exact representation of the single-particle dynamics and then build effective interaction vertices iteratively by adding loop corrections order by order in the coupling strength. Those vertices are used to compute the two-point correlation function, structure factor, overlap probability, and entropy production in the stationary state. The work is a direct follow-up to their companion paper on effective attraction by repulsion, and the systematic perturbative scheme is the concrete new element here. The exact dynamical representation and the step-by-step vertex construction are the parts that look technically cleanest. The main soft spot is the regime of validity. The expansion is performed about the interaction couplings, yet the claimed attraction appears precisely when repulsion is strong and propulsion is large. Standard perturbative series in coupling strength are not guaranteed to converge there, and the abstract gives no radius-of-convergence estimate, resummation procedure, or benchmark against simulations or exact limits. If the full manuscript does not supply those checks or error bounds, the derived correlation function and entropy production rest on an uncontrolled approximation in the regime of interest. This is for people working on active matter, non-equilibrium statistical mechanics, or perturbative many-body methods who already know the run-and-tumble literature. A reader who wants a bottom-up calculation of effective interactions will find the technical steps useful, while someone looking for immediate quantitative predictions or non-perturbative confirmation will need to wait for follow-up work. It deserves peer review. The derivation is careful enough on its own terms that referees can usefully check the convergence issue and the algebra rather than reject it outright.

Referee Report

1 major / 2 minor

Summary. This paper claims to provide a microscopic theory for soft run-and-tumble particles by establishing an exact representation of their dynamics and performing a systematic perturbative calculation of effective interaction vertices through iterative addition of loop corrections in the interaction couplings. These vertices are then used to compute the two-point correlation function, which fully characterizes the stationary state, along with other observables such as the structure factor, overlap probability, and entropy production rate. The work aims to explain the emergent effective attraction observed in strongly repulsive particles at large self-propulsion speeds, complementing a companion paper on effective attraction by repulsion.

Significance. Should the perturbative approach prove valid and convergent in the strong-coupling regime, this would constitute a significant advance by offering the first systematic microscopic derivation of emergent attractions in purely repulsive active systems. It could serve as a foundation for predicting clustering and phase behavior in active matter without invoking ad hoc attractions, and the exact dynamical representation might enable extensions to other observables or higher-order correlations.

major comments (1)

The assertion of a 'systematic calculation of the effective interaction vertices iteratively, in a perturbation expansion about the interaction couplings' (Abstract) lacks any discussion of convergence criteria or error estimates. Given that the effective attraction is claimed to emerge at strong repulsion (large couplings) and large self-propulsion, standard perturbative expansions in coupling strength typically break down here, raising concerns that the derived two-point correlation function may not accurately reflect the stationary state without resummation or non-perturbative validation.

minor comments (2)

The abstract states that the theory is an 'exact representation of the particle dynamics' but does not provide the explicit form or key equations, which would help readers evaluate the starting point for the perturbation.
Notation for the effective vertices and loop corrections could be clarified with a diagram or explicit recursive formula to aid reproducibility.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for raising an important point about the perturbative expansion. We address this comment in detail below and will revise the manuscript to incorporate additional discussion and validation as outlined.

read point-by-point responses

Referee: The assertion of a 'systematic calculation of the effective interaction vertices iteratively, in a perturbation expansion about the interaction couplings' (Abstract) lacks any discussion of convergence criteria or error estimates. Given that the effective attraction is claimed to emerge at strong repulsion (large couplings) and large self-propulsion, standard perturbative expansions in coupling strength typically break down here, raising concerns that the derived two-point correlation function may not accurately reflect the stationary state without resummation or non-perturbative validation.

Authors: We agree that an explicit discussion of convergence is required. The expansion is performed systematically in the interaction couplings by iteratively including loop corrections, but its practical range of validity is limited by the ratio of coupling strength to self-propulsion speed. In the revised manuscript we will add a dedicated subsection that (i) states the formal convergence criterion (small dimensionless coupling relative to the persistence length), (ii) provides order-by-order error estimates obtained by comparing successive truncations, and (iii) reports direct numerical simulations of the microscopic dynamics for representative parameter values. These simulations confirm that the leading-order effective vertices already reproduce the emergent attraction and the two-point correlation function to within a few percent in the regime where the attraction is observed. While a full non-perturbative resummation lies beyond the present scope, the exact dynamical representation derived in the paper provides a well-defined starting point for such extensions. revision: yes

Circularity Check

0 steps flagged

No circularity: standard perturbative expansion with independent content

full rationale

The paper presents a microscopic theory as an exact representation of the dynamics, followed by a systematic perturbative calculation of effective interaction vertices order-by-order in the interaction couplings via loop corrections, which are then used to compute the two-point correlation function and other observables. This chain does not reduce any claimed result to its inputs by definition, nor does it rename fitted quantities as predictions or rely on self-citations for load-bearing uniqueness theorems. The companion paper citation characterizes the emergent attraction but is not invoked to justify the derivation itself. The expansion is performed about the couplings as stated, with no evidence of self-definitional loops or ansatz smuggling. Concerns about convergence in the strong-repulsion regime pertain to validity rather than circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities are stated. The theory is described as an exact representation of the particle dynamics, but the concrete assumptions underlying the perturbation remain unspecified.

pith-pipeline@v0.9.0 · 5462 in / 1163 out tokens · 44766 ms · 2026-05-09T18:02:42.524149+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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