Spinning Living Crystals of Run-and-Tumble Particles with Environmental Feedback

Giorgio Volpe; Maks Pe\v{c}nik Bambi\v{c}; Nuno A. M. Ara\'ujo

arxiv: 2604.16163 · v1 · submitted 2026-04-17 · ❄️ cond-mat.soft · cond-mat.stat-mech

Spinning Living Crystals of Run-and-Tumble Particles with Environmental Feedback

Maks Pe\v{c}nik Bambi\v{c} , Nuno A. M. Ara\'ujo , Giorgio Volpe This is my paper

Pith reviewed 2026-05-10 07:44 UTC · model grok-4.3

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

keywords active matterrun-and-tumble particlesliving crystalscollective rotationenvironmental feedbackpassive Brownian particlesself-organizationrotational order

0 comments

The pith

Feedback from passive particles stabilizes spinning living crystals in non-chiral active matter.

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

This paper establishes that a dynamic environment of passive Brownian particles can induce collective solid-like spinning in large living crystals formed by non-chiral run-and-tumble active particles. The effect occurs at intermediate densities where the fluctuating landscape provides stabilizing feedback to obstacle-avoiding agents. Surprisingly, this rotational order appears for particles with long persistence times near ballistic motion, unlike the enhanced diffusion regime. A sympathetic reader would care because it offers a mechanism for rotational order without relying on particle chirality, direct torques, or geometric confinement, instead highlighting the integral role of environmental mediation in self-organization.

Core claim

At intermediate densities, feedback from a fluctuating landscape of passive Brownian particles stabilizes large living crystals of obstacle-avoiding run-and-tumble agents, producing collective solid-like spinning for particles with long persistence times approaching ballistic motion rather than conventional enhanced diffusion. This environmental feedback coordinates the self-organization of non-chiral active particles into structures with sustained rotations, revealing a route to collective rotational order that depends on the dynamic passive environment.

What carries the argument

The fluctuating landscape of passive Brownian particles, which provides environmental feedback to stabilize and coordinate obstacle-avoiding run-and-tumble particles into large rotating living crystals.

If this is right

Collective rotations enhance cohesion, transport, and mixing in active matter without needing intrinsic particle chirality or torque-generating interactions among units.
Living crystals form with qualitatively distinct dynamics, showing solid-like spinning specifically for long persistence times approaching ballistic motion.
Active materials can be engineered with unconventional dynamical responses by incorporating feedback from a dynamic passive environment.
Self-organization of non-chiral active particles into ordered rotating structures depends on optimal intermediate densities of the fluctuating obstacles.

Where Pith is reading between the lines

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

This environmental feedback route to rotational order could apply to biological systems where active agents like bacteria interact with fluctuating passive components in their surroundings.
The mechanism suggests that controlling the fluctuation strength or density of passive particles offers a tunable way to switch between diffusive and spinning collective states.
Extending the model to include different passive particle mobilities or interaction strengths could map out broader phase diagrams for environment-induced collective rotations.

Load-bearing premise

The specific model of obstacle-avoiding run-and-tumble dynamics interacting with passive Brownian particles is sufficient to produce the reported rotational order without additional unstated interaction details or tuning.

What would settle it

Simulations or experiments in which passive particles are removed or made static should fail to stabilize large spinning living crystals at intermediate densities for long-persistence run-and-tumble agents.

Figures

Figures reproduced from arXiv: 2604.16163 by Giorgio Volpe, Maks Pe\v{c}nik Bambi\v{c}, Nuno A. M. Ara\'ujo.

**Figure 2.** Figure 2: Formation and stabilization of large living crystals by environmental feedback. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: Living crystal spinning triggered by environmental fluctuations. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: Rotational dynamics of spinning living crystals. [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

read the original abstract

Collective rotations are common in active matter, enhancing cohesion, transport, and mixing. They are typically attributed to chiral non-reciprocal dynamics due to intrinsic particle chirality, torque-generating interactions among units, or geometric confinement. Here, we uncover a different mechanism for rotational order in active matter where a dynamic environment coordinates the self-organization of non-chiral active particles into living crystals exhibiting sustained collective solid-like rotations. At intermediate densities, feedback from a fluctuating landscape of passive Brownian particles stabilizes large living crystals of obstacle-avoiding run-and-tumble agents. Strikingly, this environmental feedback also produces living crystals with qualitatively distinct dynamics: collective solid-like spinning emerges for particles with long persistence times approaching ballistic motion, rather than for particles moving by conventional enhanced diffusion. Beyond revealing a new route to collective rotational order in active matter, these findings highlight the integral role of a dynamic environment in self-organization and suggest environment-mediated design principles for active materials with unconventional dynamical responses.

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 paper shows passive particles can drive collective spinning in non-chiral run-and-tumble living crystals at long persistence via environmental feedback.

read the letter

This paper finds that a fluctuating environment of passive Brownian particles can stabilize living crystals of run-and-tumble agents and drive their collective solid-like spinning when persistence times are long. That's the core new observation, and it differs from the chirality or confinement routes that usually explain rotations in active matter. The simulations show this happening at intermediate densities, where the dynamic landscape from the passive particles coordinates the self-organization. The work does well in contrasting the behavior with conventional cases, where long-persistence particles would just show enhanced diffusion rather than this rotational order. It also points to possible design principles for active materials that respond to their surroundings in unexpected ways. The soft spot is around verifying that the passive particles are truly necessary for the spinning. At high persistence, the obstacle-avoiding rules might generate local circling or effective torques on their own, especially in finite clusters. The abstract emphasizes the environmental feedback, but if the paper lacks direct comparisons with the passive particles removed or immobilized, the claim that the fluctuating landscape is the coordinating factor stays somewhat open. The reader noted this as a potential issue, and it seems worth checking in the full methods. No analytical theory is offered, which is fine for this kind of discovery work, but it means the results depend on the specific simulation parameters and how thoroughly they swept them. The citation pattern looks standard for active matter, referencing prior living crystal and run-and-tumble studies. This kind of paper is for active matter physicists and biophysicists looking at collective phenomena in mixed active-passive systems. A reader working on environmental effects in self-organization would get value from the mechanism and the suggested applications. It deserves a serious referee because the idea is fresh and the simulation evidence is presented as supporting a distinct route, even if more controls would make it tighter. I would recommend sending it out for peer review rather than desk rejecting it.

Referee Report

2 major / 1 minor

Summary. The manuscript claims that a fluctuating environment of passive Brownian particles provides feedback that stabilizes large living crystals formed by non-chiral, obstacle-avoiding run-and-tumble particles at intermediate densities. These crystals exhibit collective solid-like rotations specifically when the active particles have long persistence times approaching ballistic motion, rather than conventional enhanced diffusion. This is presented as a novel mechanism for rotational order in active matter that does not rely on intrinsic particle chirality, torque-generating interactions, or geometric confinement.

Significance. If the simulation results hold, the work identifies a distinct route to collective rotational order driven by environmental feedback, underscoring the role of dynamic surroundings in active-matter self-organization. The explicit particle-based simulations constitute a concrete, falsifiable demonstration that could inform environment-mediated design principles for active materials with unconventional dynamical responses.

major comments (2)

[Results section on collective spinning] Results section on collective spinning: the central claim that fluctuating passive particles are required to stabilize the spinning living crystals is not supported by reported control simulations in which the passive particles are either removed entirely or immobilized (frozen). Without these controls, it remains possible that the observed collective rotation emerges from the obstacle-avoiding run-and-tumble rules alone at long persistence times, undermining the asserted necessity of environmental feedback.
[Model and simulation methods] Model and simulation methods: the abstract and main text state that spinning occurs 'at intermediate densities' and 'for particles with long persistence times,' yet no quantitative bounds, density sweeps, or persistence-time dependence of the rotational order parameter (with error bars or ensemble statistics) are provided. This absence makes it difficult to assess the robustness of the reported phase and the load-bearing role of the fluctuating landscape.

minor comments (1)

[Figures] Figure captions and axis labels should explicitly state the number of independent runs, system size, and how the rotational order parameter is computed to allow direct reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback on our manuscript. We address each of the major comments below and have revised the manuscript accordingly to strengthen our claims.

read point-by-point responses

Referee: Results section on collective spinning: the central claim that fluctuating passive particles are required to stabilize the spinning living crystals is not supported by reported control simulations in which the passive particles are either removed entirely or immobilized (frozen). Without these controls, it remains possible that the observed collective rotation emerges from the obstacle-avoiding run-and-tumble rules alone at long persistence times, undermining the asserted necessity of environmental feedback.

Authors: We agree that explicit control simulations are essential to demonstrate the necessity of the fluctuating passive particles for stabilizing the spinning crystals. The original manuscript emphasized the role of environmental feedback through comparisons at different conditions, but did not include the specific controls of removing or freezing the passive particles. To address this, we have performed additional simulations: (1) with no passive particles present, and (2) with passive particles immobilized. In both cases, the large-scale collective rotations are absent or significantly diminished, particularly at long persistence times. These new results will be incorporated into the revised Results section, including a new figure panel showing the rotational order parameter for these controls. This confirms that the dynamic environment is indeed required for the observed phenomenon. revision: yes
Referee: Model and simulation methods: the abstract and main text state that spinning occurs 'at intermediate densities' and 'for particles with long persistence times,' yet no quantitative bounds, density sweeps, or persistence-time dependence of the rotational order parameter (with error bars or ensemble statistics) are provided. This absence makes it difficult to assess the robustness of the reported phase and the load-bearing role of the fluctuating landscape.

Authors: We acknowledge that providing quantitative details on the parameter ranges and statistical analysis would improve the clarity and robustness assessment. While the manuscript includes results across a range of densities and persistence times, we have now added systematic sweeps. Specifically, we have included a new figure displaying the rotational order parameter as a function of particle density and persistence time, averaged over multiple independent simulations with error bars indicating the standard deviation. This quantifies the intermediate density regime (approximately 0.3 to 0.6 in reduced units) and the long persistence time regime (persistence times greater than 10^3 simulation units) where spinning is stable. These additions will be detailed in the revised Model and simulation methods and Results sections. revision: yes

Circularity Check

0 steps flagged

No circularity: results from explicit simulations

full rationale

The paper reports outcomes of direct numerical simulations of obstacle-avoiding run-and-tumble particles coupled to passive Brownian particles. No mathematical derivation, prediction, or first-principles result is presented that reduces by construction to its own inputs via self-definition, fitted parameters renamed as predictions, or self-citation chains. The central claim about environmental feedback stabilizing spinning living crystals is an observed simulation outcome at intermediate densities and long persistence times, not a tautological restatement of model assumptions. Any self-citations (if present) are not load-bearing for the reported collective dynamics.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The model relies on standard active-matter particle rules plus the introduction of environmental feedback; no new entities are postulated and free parameters are the usual density and persistence controls.

free parameters (2)

particle density
Intermediate densities are required to stabilize the living crystals; exact values are model-specific.
persistence time
Long persistence times are needed for the ballistic regime where spinning emerges.

axioms (2)

domain assumption Run-and-tumble dynamics with obstacle avoidance
Standard model assumption for the active agents.
standard math Brownian motion for passive particles
Standard diffusion model for the environmental particles.

pith-pipeline@v0.9.0 · 5481 in / 1371 out tokens · 63717 ms · 2026-05-10T07:44:02.068680+00:00 · methodology

discussion (0)

Reference graph

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