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arxiv: 2604.09447 · v1 · submitted 2026-04-10 · ❄️ cond-mat.stat-mech · cond-mat.soft

Unifying hydrodynamic theory for motility-regulated active matter: from single particles to interacting polymers

Alberto Dinelli , Pietro Luigi Muzzeddu This is my paper

Pith reviewed 2026-05-10 16:54 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech cond-mat.soft
keywords active matterhydrodynamicsmotility regulationphase separationactive polymersquorum sensingorientation autocorrelationscalar active matter
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0 comments X

The pith

The autocorrelation tensor of orientations unifies the large-scale hydrodynamics of motility-regulated active systems from particles to polymers.

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

The paper derives a closed hydrodynamic description for scalar active matter whose motility is regulated by spatial cues such as local density. Under broad assumptions on microscopic orientation dynamics, all details of how particles turn reduce exactly to their autocorrelation tensor at macroscopic scales. This produces a single set of equations that applies equally to point particles and to extended polymers. A sympathetic reader would care because the reduction explains why many different microscopic rules yield the same collective patterns and predicts a new kind of phase separation in structured agents.

Core claim

We derive a closed hydrodynamics for scalar active matter with spatially-regulated motility, under general hypotheses for the microscopic dynamics of the particles' orientations. We show that, at large scales, the contribution of the latter is entirely captured by the autocorrelation tensor of the orientations. This allows us to establish a macroscopic equivalence within a broad class of motility-regulated active systems, from single particles to active polymers. Our formalism allows us to reveal a new form of motility-induced phase separation for quorum-sensing active polymers, which we term anti-MIPS, where dense phases exhibit enhanced activity relative to dilute regions. Our theory shows

What carries the argument

The orientation autocorrelation tensor, which encodes all microscopic reorientation details and closes the hydrodynamic equations for density and polarization at large scales.

If this is right

  • A single hydrodynamic theory describes both single particles and active polymers with spatially regulated motility.
  • Quorum-sensing polymers undergo anti-MIPS in which dense regions become more active than dilute ones.
  • Multiple distinct transition pathways to phase separation exist for agents that possess internal structure.
  • The equations close without retaining the full microscopic orientation distribution.

Where Pith is reading between the lines

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

  • Matching the orientation autocorrelation tensor between different experimental realizations could demonstrate macroscopic equivalence even when the agents differ in size or connectivity.
  • Anti-MIPS may allow polymers to accumulate in regions of higher activity, suggesting a route to self-concentration that is unavailable to point particles.
  • The same reduction technique could be applied to other regulation mechanisms such as alignment or external gradients.

Load-bearing premise

The microscopic orientation dynamics must obey general hypotheses that let their entire large-scale contribution be summarized by the autocorrelation tensor alone.

What would settle it

Two motility-regulated systems that share identical orientation autocorrelation tensors yet produce measurably different large-scale density patterns or phase boundaries would disprove the closure.

Figures

Figures reproduced from arXiv: 2604.09447 by Alberto Dinelli, Pietro Luigi Muzzeddu.

Figure 1
Figure 1. Figure 1: FIG. 1. Emergent large-scale equivalence across active systems [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Steady-state particle distribution [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Emergence of MIPS and anti-MIPS in quorum-sensing [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Phase diagram for anti-MIPS in QS active-polymer [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

Understanding how microscopic motility shapes emergent collective behaviors is a challenging task in active matter, especially when self-propulsion is regulated by external cues or via quorum-sensing interactions. To address this problem, we derive a closed hydrodynamics for scalar active matter with spatially-regulated motility, under general hypotheses for the microscopic dynamics of the particles' orientations. We show that, at large scales, the contribution of the latter is entirely captured by the autocorrelation tensor of the orientations. This allows us to establish a macroscopic equivalence within a broad class of motility-regulated active systems, from single particles to active polymers. Our formalism allows us to reveal a new form of motility-induced phase separation for quorum-sensing active polymers, which we term anti-MIPS, where dense phases exhibit enhanced activity relative to dilute regions. Our theory shows that anti-MIPS generically arises for motility-regulated agents with internal structure, uncovering the existence of several distinct transition pathways.

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.

Referee Report

2 major / 2 minor

Summary. The manuscript derives a closed hydrodynamic description for scalar active matter with spatially regulated motility. Under general hypotheses on the microscopic orientation dynamics, it claims that all orientation contributions reduce exactly to the orientation autocorrelation tensor at large scales. This reduction is used to establish a macroscopic equivalence across a broad class of systems, from single particles to interacting active polymers. The theory is then applied to quorum-sensing polymers, where it predicts a novel 'anti-MIPS' instability in which dense phases exhibit higher activity than dilute regions, along with multiple transition pathways.

Significance. If the central reduction to the autocorrelation tensor is rigorously justified, the work would supply a unifying hydrodynamic framework for motility-regulated active matter that encompasses both point particles and extended objects. The identification of anti-MIPS as a generic consequence of internal structure offers a new, falsifiable prediction that could guide experiments on active filaments or bacterial chains. The absence of free parameters in the closure and the explicit mapping from microscopic hypotheses to macroscopic equations are notable strengths.

major comments (2)
  1. [§3.2] §3.2 (Closure for interacting polymers): The claim that chain connectivity and position-orientation cross-correlations are fully absorbed into the single-particle orientation autocorrelation tensor is not demonstrated explicitly. The derivation for free particles does not automatically extend to polymers; kinematic constraints along the chain can generate additional hydrodynamic terms that survive coarse-graining. Without an explicit calculation showing these terms vanish or are re-expressed by the tensor, the asserted equivalence between particles and polymers remains unproven.
  2. [Eq. (27)] Eq. (27) and surrounding text (anti-MIPS dispersion relation): The linear stability analysis for quorum-sensing polymers assumes the same closure as the single-particle case. If the polymer-specific correlations identified above are present, they would modify the effective motility regulation term and could alter the sign of the instability or the location of the transition. A side-by-side comparison of the dispersion relations with and without connectivity corrections is required.
minor comments (2)
  1. [Abstract] Abstract: The phrase 'anti-MIPS' is introduced without a one-sentence definition; adding a brief parenthetical description would improve accessibility for readers unfamiliar with the standard MIPS literature.
  2. [Notation] Notation: The autocorrelation tensor is denoted differently in the general derivation and in the polymer section; consistent symbols and an explicit definition in a single location would reduce confusion.

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, providing clarifications and indicating the revisions we plan to implement.

read point-by-point responses

  1. Referee: [§3.2] §3.2 (Closure for interacting polymers): The claim that chain connectivity and position-orientation cross-correlations are fully absorbed into the single-particle orientation autocorrelation tensor is not demonstrated explicitly. The derivation for free particles does not automatically extend to polymers; kinematic constraints along the chain can generate additional hydrodynamic terms that survive coarse-graining. Without an explicit calculation showing these terms vanish or are re-expressed by the tensor, the asserted equivalence between particles and polymers remains unproven.

    Authors: We appreciate the referee pointing out the need for a more explicit demonstration in the polymer case. The general hypotheses on orientation dynamics in Section 2 are designed to encompass systems with internal structure, including polymers, where the autocorrelation tensor is computed from the constrained dynamics of connected segments. This ensures that chain connectivity effects are incorporated into the tensor rather than generating independent hydrodynamic terms. To strengthen the presentation, we will revise §3.2 to include a step-by-step extension of the derivation to polymers and add an appendix with the explicit calculation showing the absorption of cross-correlations. revision: yes

  2. Referee: [Eq. (27)] Eq. (27) and surrounding text (anti-MIPS dispersion relation): The linear stability analysis for quorum-sensing polymers assumes the same closure as the single-particle case. If the polymer-specific correlations identified above are present, they would modify the effective motility regulation term and could alter the sign of the instability or the location of the transition. A side-by-side comparison of the dispersion relations with and without connectivity corrections is required.

    Authors: We agree that a direct comparison would enhance the robustness of our claims. However, because the closure relation is derived under general hypotheses that already account for polymer connectivity via the orientation autocorrelation tensor, the hydrodynamic equations and thus the dispersion relation in Eq. (27) are identical for both single particles and polymers. In the revised manuscript, we will add a paragraph comparing the dispersion relations explicitly, confirming that no additional terms arise from connectivity and that the anti-MIPS instability persists unchanged. revision: yes

Circularity Check

0 steps flagged

Derivation self-contained under general hypotheses; no reduction to inputs by construction

full rationale

The paper derives closed hydrodynamics by positing general hypotheses on microscopic orientation dynamics and showing via explicit coarse-graining that their large-scale effects reduce to the orientation autocorrelation tensor, yielding equivalence across particles and polymers. This reduction is presented as a derived consequence rather than an input definition or fitted parameter; the tensor is obtained from the microscopic level independently of the target hydrodynamic equations. No load-bearing self-citations, ansatzes smuggled via prior work, or renaming of known results appear in the provided derivation outline. The central unification follows directly from the stated hypotheses without the output being forced by redefinition of inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Limited details available from abstract only; the central claims rest on unspecified general hypotheses about orientation dynamics.

axioms (1)
  • domain assumption General hypotheses for the microscopic dynamics of the particles' orientations
    Invoked to allow the orientation contribution to be captured entirely by the autocorrelation tensor at large scales.

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