{"id":"8517a9eb-8b0c-471b-92fa-f9f94a9dfa9e","arxiv_id":"2606.18911","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":7.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Constructs nonequilibrium nucleation theory for nonconserved order parameters and reports explicit predictions that agree with numerical simulations in active matter and population dynamics models.","lead":"The paper develops a nonequilibrium nucleation theory for nonconserved scalar order parameters by redefining the droplet radius reaction coordinate to isolate the nucleation barrier from interfacial profile deviations. A smart generalist might read it to see how nonequilibrium effects change phase formation predictions in active materials and population models.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"The reader's weakest assumption correctly isolates the projection step, but the reported numerical agreement supplies independent support for that step. No additional load-bearing gap is visible once the full construction and validation are taken into account; the UNVERDICTED status therefore remains appropriate pending a closer reading of the derivation details.","tokens_in":1708,"tokens_out":268,"duration_ms":23243,"concrete_test":"Reproduce the numerical nucleation-rate measurements for one of the explicit models (e.g., the population-dynamics example) and compare the observed barrier height against the NNT formula both with and without the radius-projection step; agreement within statistical error confirms the projection suffices.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper constructs an NNT for nonconserved order parameters by showing that deviations in the interfacial profile alter the barrier relative to the conserved case, yet a reaction coordinate based on droplet radius can be defined to project those deviations out and recover an explicit barrier expression. Explicit predictions are then given for population-dynamics and active-matter models and stated to agree with direct numerical simulations. Because the construction is supported by this agreement and no internal inconsistency appears in the argument as described, the central claim does not rest on an unsecured assumption.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","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.","tokens_in":1795,"tokens_out":436,"duration_ms":18052,"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":[{"comment":"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.","section":"NNT construction paragraph / reaction coordinate definition"}],"minor_comments":[{"comment":"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.","section":"Results / comparison with numerics"},{"comment":"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.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"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.","responses":[{"response":"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_made":"yes","referee_comment":"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."}],"tokens_in":1262,"tokens_out":273,"duration_ms":19860,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"This paper constructs nonequilibrium nucleation theory for a nonconserved scalar order parameter. Earlier NNT work covered only conserved cases, so the extension itself is the main new element. They show that interfacial profile deviations from the deterministic relaxation path change the barrier height, but choosing droplet radius as the reaction coordinate projects those deviations out and yields an explicit expression.\n\nThey then derive concrete predictions for population-dynamics and active-matter models and report that these match direct numerical simulations. That match is the primary evidence offered.\n\nThe construction looks workable. The reaction-coordinate step sidesteps the extra dynamical complications that nonconserved fields introduce, and the applications are specific enough to be checked. No internal contradictions or obvious circularity appear in the argument.\n\nThe soft spot is the strength of the numerical support. The abstract claims excellent agreement, but without seeing the actual plots, error bars, or how the barrier was extracted from the runs, it is hard to judge how robust the match really is. The assumption that radius alone captures the relevant deviations may hold for the models tested but could need more scrutiny in broader cases.\n\nThis is for people working on nucleation in driven systems, active matter, or ecological models. A reader who needs a calculable rate expression beyond classical CNT would find the formulas and comparisons useful.\n\nI would send it for peer review. The extension is new, the logic is traceable, and the claims are concrete enough for referees to evaluate.","headline":"Extends NNT to nonconserved order parameters via a droplet-radius reaction coordinate, with explicit predictions for active-matter and population models that match their simulations.","tokens_in":2309,"tokens_out":370,"would_cite":false,"duration_ms":32289,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"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.","keywords":["nonequilibrium nucleation theory","nonconserved order parameter","active matter","population dynamics","droplet nucleation","interfacial density profile"],"falsifier":"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.","tokens_in":2596,"feed_emoji":"","tokens_out":580,"duration_ms":18324,"temperature":0.7,"pith_summary":"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.","feed_headline":"Interface deviations alter nucleation barriers in nonconserved systems","feed_subtitle":"Defining droplet radius to project out profile deviations recovers a usable barrier for active-matter and population models.","key_machinery":"The reaction coordinate defined as droplet radius, chosen to project out deviations of the interfacial density profile from the deterministic relaxation profile.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"fun_headline_variants":["Interface deviations alter nonconserved nucleation barriers","Defining droplet radius projects out profile deviations to recover barrier","Nonequilibrium nucleation barrier changed by interfacial density profile shifts","Nucleation theory for nonconserved fields applies to active matter models"],"cache_read_input_tokens":64,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Interface deviations alter nonconserved nucleation barriers","Defining droplet radius projects out profile deviations to recover barrier","Nonequilibrium nucleation barrier changed by interfacial density profile shifts","Nucleation theory for nonconserved fields applies to active matter models"]},"model":"grok-4.3","cost_usd":0.006394,"raw_usage":{"total_tokens":2963,"prompt_tokens":596,"num_sources_used":0,"completion_tokens":63,"cost_in_usd_ticks":63937000,"prompt_tokens_details":{"text_tokens":596,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2304,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":596,"tokens_out":63,"duration_ms":26925,"temperature":1.0,"reasoning_tokens":2304,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-26T19:16:45.011627+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"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.","supporting_citations":[],"review_version":1}