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arxiv: 2606.18911 · v1 · pith:34J3RPXD · submitted 2026-06-17 · cond-mat.stat-mech · cond-mat.soft

Nonequilibrium nucleation theory for nonconserved fields: from active matter to population dynamics

Michalis Chatzittofi , Noah Ziethen , Cesare Nardini , Michael E. Cates This is my paper

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classification cond-mat.stat-mech cond-mat.soft
keywords nonequilibrium nucleation theorynonconserved order parameteractive matterpopulation dynamicsdroplet nucleationinterfacial density profile
0
0 comments X

The pith

Deviations in the interfacial density profile alter the nucleation barrier for nonconserved nonequilibrium systems, but a carefully chosen droplet-radius reaction coordinate projects them out to recover a usable barrier.

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

The paper constructs a nonequilibrium nucleation theory for systems with a single scalar nonconserved order parameter. It shows that the barrier controlling noise-driven droplet growth differs from the equilibrium case because the interfacial density profile during nucleation deviates from the profile that appears during deterministic droplet relaxation. The barrier remains computable once the reaction coordinate is defined as droplet radius in a manner that eliminates those deviations. This matters for driven systems such as active matter and population dynamics, where standard free-energy arguments do not apply, and the new expressions yield predictions that match numerical simulations.

Core claim

In nonconserved nonequilibrium systems the nucleation barrier is profoundly altered by deviations of the interfacial density profile from the deterministic relaxation profile, yet the barrier can still be analysed by defining the reaction coordinate as droplet radius so as to project out those deviations, producing explicit predictions that agree with numerical studies of population-dynamics and active-matter models.

What carries the argument

The reaction coordinate defined as droplet radius, chosen to project out deviations of the interfacial density profile from the deterministic relaxation profile.

If this is right

  • Explicit nucleation-rate formulas become available for a range of nonconserved active-matter models.
  • Explicit nucleation-rate formulas become available for population-dynamics models with nonconserved order parameters.
  • The same projection procedure recovers agreement with simulations in both classes of systems.

Where Pith is reading between the lines

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

  • The projection technique could be tested on other nonconserved driven systems not examined in the paper, such as certain reaction-diffusion models.
  • If the same logic applies when multiple fields are present, the method might extend beyond the single-scalar case treated here.

Load-bearing premise

That a reaction coordinate defined as droplet radius can be chosen so as to project out all relevant deviations of the interfacial density profile from the deterministic relaxation profile.

What would settle it

A direct numerical measurement of nucleation rates in a nonconserved active-matter or population-dynamics model that fails to match the barrier obtained after projecting the reaction coordinate onto droplet radius.

Figures

Figures reproduced from arXiv: 2606.18911 by Cesare Nardini, Michael E. Cates, Michalis Chatzittofi, Noah Ziethen.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Plot of [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) The driving force for the two population dynam [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Results for AMA in two dimensions: (a) Color map [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
read the original abstract

Classical nucleation theory (CNT) describes the formation of a stable phase from a metastable one. In equilibrium systems, it quantifies the free-energy competition between a favorable bulk gain and an unfavorable interfacial cost. For systems without detailed balance, the corresponding nonequilibrium nucleation theory (NNT) was so far developed only for cases with a conserved order parameter, such as active fluid-fluid phase separation. Here we construct the NNT for systems with a (single, scalar) nonconserved order parameter. Unlike in the conserved case, the nucleation barrier controlling (noise-driven) droplet growth is profoundly altered by deviations in the interfacial density profile from the one arising during (deterministic) droplet relaxation. The barrier can nonetheless be analysed by carefully defining the reaction coordinate (droplet radius) to project out those deviations. We give explicit NNT predictions for models drawn from population dynamics and active matter, finding excellent agreement with numerical studies.

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

1 major / 2 minor

Summary. The paper constructs a nonequilibrium nucleation theory (NNT) for nonconserved scalar order parameters. It shows that, unlike the conserved case, deviations of the interfacial density profile from the deterministic relaxation profile alter the nucleation barrier for noise-driven droplet growth. The barrier is recovered by defining the reaction coordinate as droplet radius so as to project out those deviations, yielding an explicit expression. Explicit NNT predictions are given for population-dynamics and active-matter models and reported to agree with direct numerical simulations.

Significance. If the central construction holds, the work supplies the missing nonconserved extension of NNT, directly applicable to active-matter and population-dynamics models. Credit is due for the parameter-free derivation (no free_parameters listed) and for the explicit, falsifiable predictions that are stated to match numerics. The result is of clear interest to the statistical-mechanics community working on driven phase transitions.

major comments (1)
  1. [NNT construction paragraph / reaction coordinate definition] Nonconserved NNT construction (abstract and § on reaction-coordinate definition): the claim that the droplet-radius coordinate projects out all relevant interfacial-profile deviations rests on the assertion that residual modes do not contribute to the barrier. No explicit orthogonality proof or mode decomposition is referenced that would confirm this projection is complete for the nonconserved dynamics; this is load-bearing for the barrier expression.
minor comments (2)
  1. [Results / comparison with numerics] The abstract states 'excellent agreement' but the manuscript should include a dedicated comparison section or table listing the models, the precise observables compared, error bars or confidence intervals on the numerical data, and the criteria used to select simulation runs.
  2. [Throughout] Notation for the nonconserved order parameter and the deterministic relaxation profile should be introduced once with a clear equation reference rather than re-defined inline in multiple places.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for recognizing the significance of the nonconserved NNT construction. We address the single major comment below.

read point-by-point responses

  1. Referee: Nonconserved NNT construction (abstract and § on reaction-coordinate definition): the claim that the droplet-radius coordinate projects out all relevant interfacial-profile deviations rests on the assertion that residual modes do not contribute to the barrier. No explicit orthogonality proof or mode decomposition is referenced that would confirm this projection is complete for the nonconserved dynamics; this is load-bearing for the barrier expression.

    Authors: We agree that the completeness of the projection is central to the barrier expression and that an explicit demonstration strengthens the presentation. The reaction coordinate is defined as the droplet radius precisely to integrate out interfacial deviations; the associated projection is constructed so that residual modes are orthogonal by design and do not enter the effective potential along this coordinate. The derivation in the reaction-coordinate section obtains the barrier from the projected stochastic dynamics, with residual modes shown to relax on fast timescales without altering the quasi-static barrier height. To make the orthogonality explicit, we will add a short mode decomposition and projection argument in the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained against external benchmarks

full rationale

The abstract and description present a new construction of NNT for nonconserved fields by defining a reaction coordinate (droplet radius) that projects out interfacial deviations, followed by explicit predictions for specific models that are then compared to independent numerical simulations. No equations, self-citations, or fitted parameters are shown reducing the central barrier expression to its own inputs by construction. The agreement with numerics is presented as external validation rather than a self-referential fit. This matches the most common honest finding of a self-contained derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; the theory presumably inherits standard assumptions from statistical mechanics and prior CNT/NNT literature.

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discussion (0)

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  1. Nucleation and time-reversal symmetry breaking in nonconserved scalar field theories

    cond-mat.stat-mech 2026-07 accept novelty 7.0

    Extends classical nucleation theory to nonequilibrium non-conserved scalar fields by showing the time-reversed-relaxation ansatz fails and deriving corrected quasipotentials via two independent routes, validated numerically.

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