arxiv: 2604.23808 · v1 · submitted 2026-04-26 · ⚛️ physics.bio-ph

Recognition: unknown

Information transfer enhanced by non-reciprocity in a model of turning flocks

Mario Sandoval

Authors on Pith no claims yet

Pith reviewed 2026-05-08 04:45 UTC · model grok-4.3

classification ⚛️ physics.bio-ph

keywords flock dynamicsinformation transfernon-reciprocityactive torquesturning eventscontinuum modelscollective behaviorbird flocks

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The pith

Active torques added to turning flock models create non-reciprocity that makes information transfer speed depend on turning rate.

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

The paper establishes that adding active torques to a one-dimensional model of bird-like objects, motivated by adaptive rotational energy use, renders the system non-reciprocal and raises the speed and efficiency of information transfer during turns. A sympathetic reader would care because this links the model directly to real flocks that must exchange information faster when turning sharply under threat to stay cohesive. In the continuum limit the governing equation takes a form that makes transfer speed a direct function of turning angular velocity.

Core claim

By incorporating active torques motivated by birds' adaptive injection of rotational energy, the model leads to a non-reciprocal modified Korteweg-de Vries equation with dissipation in the continuum limit. This equation's structure allows the information transfer speed to be expressed as a function of the turning angular velocity, thereby improving transfer during turns and aligning with the biological requirement for rapid information exchange when flocks turn sharply.

What carries the argument

The non-reciprocal modified Korteweg-de Vries equation with dissipation obtained in the continuum limit, which encodes how active torques tie information propagation speed to the flock's turning angular velocity.

If this is right

Information transfer speed and efficiency increase during turning events.
The interactions become non-reciprocal due to the active torques.
Transfer speed becomes a function of the turning angular velocity.
The model reproduces the faster information exchange required when real flocks turn under threat.
Cohesion is better maintained through the enhanced propagation.

Where Pith is reading between the lines

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

Models without active torques would likely underestimate the transfer speeds needed for rapid collective responses.
The same non-reciprocal mechanism could be tested in other groups that adjust rotation adaptively, such as fish schools.
Controlled simulations that vary turning rate while holding other parameters fixed would directly check the predicted speed dependence.

Load-bearing premise

The added active torques accurately capture birds' adaptive rotational energy injection while the one-dimensional continuum limit still represents information transfer in real flocks.

What would settle it

A measurement in live bird flocks of whether information transfer speed scales with turning angular velocity exactly as predicted by the derived non-reciprocal equation.

Figures

Figures reproduced from arXiv: 2604.23808 by Mario Sandoval.

**Figure 1.** Figure 1: FIG. 1. Schematic of view at source ↗

**Figure 2.** Figure 2: FIG. 2. Efficiency ( view at source ↗

**Figure 3.** Figure 3: FIG. 3. Turning of view at source ↗

**Figure 4.** Figure 4: FIG. 4. Average dimensionless propagation signal speed vs view at source ↗

**Figure 5.** Figure 5: FIG. 5. Average dimensionless propagation signal speed vs view at source ↗

read the original abstract

Seminal works on animal collectives started proposing a diffusive model (overdamped) for the information transfer occurring in it \cite{Vicsek}. Afterwards, the introduction of self-rotational inertia brought into play an underdamped model able to better describe the information flux occurring in a real tuning flock event \cite{Atta}. That model was recently improved by adding nonlinear torques which allowed to match experiments \cite{cavagna2025}. The current work extends the latter model by adding active torques to a one-dimensional flock of boids (bird-like objects) while keeping key ingredients such as self-rotational inertia and nonlinearity. Those active torques are seen to enhance the system's information transfer speed and efficiency during a turning event, as well as rendering it a non-reciprocal status. The proposed internal active torques are motivated by the adaptive injection of rotational energy (active system) of birds in a real flock while turning. The continuum limit of the proposed model leads to a non-reciprocal modified Korteweg-de Vries (mKdV) equation with dissipation, whose structure allows the information transfer speed to be a function of the turning angular velocity. This feature occurs in real birds since under threat, birds turn faster and are required to get the information more rapid to keep cohesion.

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 adds active torques to a turning flock model to break reciprocity and produce an mKdV whose information speed depends on angular velocity.

read the letter

This paper adds active torques to an existing one-dimensional boid model of turning flocks. The torques represent adaptive rotational energy injection by birds, which renders the system non-reciprocal and raises information transfer speed and efficiency. The continuum limit yields a non-reciprocal dissipative modified Korteweg-de Vries equation whose structure makes propagation speed depend on turning angular velocity, matching the idea that threatened birds turn faster and need quicker coordination to stay together. The work extends the line from Vicsek through Atta and the recent nonlinear-torque model by keeping self-rotational inertia and nonlinearity while adding this minimal active term. The speed dependence emerges from the equation rather than from fitting, and the motivation ties directly to observed bird behavior. The derivation is presented cleanly in one dimension, which lets the authors isolate the turning event and extract the claimed dependence without extra parameters. The soft spots are modest. The explicit steps from discrete rules to the PDE are only outlined, so the precise way the active torque enters the non-reciprocal terms would need checking in the full text. The one-dimensional reduction is a deliberate modeling choice that simplifies analysis but leaves open how results carry to two- or three-dimensional flocks where turning has more directional freedom. The link to real flocks stays qualitative, with no quantitative comparison to specific data sets. No internal contradictions appear in the setup or claims. This is for researchers working on active matter or collective animal behavior who want a concrete mechanism connecting non-reciprocity to information flow. It is a straightforward, grounded extension that deserves peer review to verify the continuum limit and assess possible higher-dimensional generalizations.

Referee Report

1 major / 2 minor

Summary. The manuscript extends a one-dimensional boid model for turning flocks by incorporating active torques, motivated by adaptive rotational energy injection in birds, while retaining self-rotational inertia and nonlinear torques from prior work. The central claim is that the continuum limit of this discrete model produces a non-reciprocal dissipative modified Korteweg-de Vries (mKdV) equation whose structure makes the information transfer speed a function of the turning angular velocity. This is argued to enhance the speed and efficiency of information propagation during turning events, render the dynamics non-reciprocal, and align with real flock behavior where faster turns under threat require quicker information transfer to maintain cohesion.

Significance. If the derivation holds, the work supplies a mechanistic hydrodynamic description in which non-reciprocity and angular-velocity-dependent information speed emerge directly from the active-torque terms rather than from parameter fitting. This strengthens the link between microscopic active-matter rules and macroscopic collective information dynamics, offers a testable prediction for flock experiments, and contributes to the broader study of non-reciprocal active systems.

major comments (1)

Continuum-limit derivation: the manuscript must supply the explicit intermediate steps from the discrete equations (including the active-torque contributions) to the final non-reciprocal dissipative mKdV equation, together with a demonstration that the information-transfer speed depends on angular velocity through the equation structure and not through an auxiliary parameter choice. This step is load-bearing for the central claim.

minor comments (2)

Abstract: the description of the model extension, continuum limit, and biological motivation is compressed; separating these elements would improve readability.
References: verify that all cited works (Vicsek, Atta, cavagna2025) appear with complete bibliographic details.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript, positive assessment of its significance, and recommendation for minor revision. We agree that clarifying the continuum-limit derivation is essential to support the central claims and will revise the manuscript accordingly.

read point-by-point responses

Referee: Continuum-limit derivation: the manuscript must supply the explicit intermediate steps from the discrete equations (including the active-torque contributions) to the final non-reciprocal dissipative mKdV equation, together with a demonstration that the information-transfer speed depends on angular velocity through the equation structure and not through an auxiliary parameter choice. This step is load-bearing for the central claim.

Authors: We will expand the derivation section in the revised manuscript to include all explicit intermediate steps. Beginning from the discrete equations of motion for the boids (including self-rotational inertia, nonlinear torques, and the newly introduced active-torque terms), we will show the continuum limit procedure step by step, identifying precisely how the active-torque contributions generate the non-reciprocal terms in the resulting dissipative modified KdV equation. We will also add an explicit demonstration that the information-transfer speed is determined by the angular velocity through the structure of the derived PDE itself, without dependence on auxiliary parameter tuning. These additions will be incorporated into the main text (with possible supplementary material for lengthy algebra) to make the mechanistic origin transparent. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper introduces active torques as an explicit modeling extension to a prior boid model (with self-rotational inertia and nonlinearity), performs a continuum limit to obtain a non-reciprocal dissipative mKdV equation, and states that the information-transfer speed then follows as a function of turning angular velocity from the resulting PDE structure. This is a standard forward derivation from discrete rules to continuum equation; the angular-velocity dependence is not presupposed by definition or by fitting a parameter that is later relabeled as a prediction. Prior citations (Vicsek, Atta, cavagna2025) supply background but are not invoked as uniqueness theorems or load-bearing justifications for the new result. No self-definitional loop, fitted-input-as-prediction, or ansatz-smuggling via self-citation is present in the claimed chain.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 1 invented entities

Abstract-only review provides no explicit free parameters, axioms, or independent evidence for new entities; active torques are introduced as a modeling choice motivated by biology.

invented entities (1)

active torques no independent evidence
purpose: Model adaptive rotational energy injection by birds during turns
Introduced to extend prior models; no independent falsifiable prediction or data verification is mentioned in the abstract.

pith-pipeline@v0.9.0 · 5527 in / 1263 out tokens · 64158 ms · 2026-05-08T04:45:10.864830+00:00 · methodology

discussion (0)

Reference graph

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It is also worth mentioning that a spin model with added non-reciprocity in the way of a step function has been reported very re- cently [15]

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