{"id":"fffe3d49-3322-4090-a628-fea37ed024a0","arxiv_id":"2505.16824","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Mesoscopic fluxes in chemically driven phase-separated fluids originate from non-equilibrium interfacial statistics, and a FLEX-based hybrid theory predicts coexistence curves, flux localization, and droplet size scaling.","lead":"Simulations and theory show that in chemically driven fluids, the steady-state flows of molecules are generated at the interface between condensed and dilute phases, not in the bulk. This means interfacial properties, not bulk thermodynamics, control how non-equilibrium droplets form and what size they reach.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"FLEX boundary conditions use an equilibrium p(nB) that the paper's own Fig. S5 shows is perturbed by the drive; sensitivity of the parameter-free coexistence curves to this wrong input is never tested.","rationale":"The reader's weakest_assumption correctly identified the FLEX timescale separation and the neglect of condensed-phase fluxes, but the more pointed issue is internal: the theory's boundary conditions use an equilibrium p(nB) while the same paper shows p(nB) is perturbed by the drive (Fig. S5). This is not a matter of large-mobility degradation; it occurs at the main simulation conditions. The paper only addresses the impact on capillary fluctuations, not on the coexistence curves, which are the theory's headline parameter-free predictions. If the coexistence predictions are insensitive to the p(nB) perturbation, the theory is robust and the paper's claims hold; if they are sensitive, the agreement is partly accidental. This is directly testable from data already in the paper. The reader's conditional verdict remains appropriate: the theory is promising but needs this robustness check, plus the already-noted limits on droplet-size-scaling fits (σ as a fitting parameter). I therefore recommend no change to the reader's CONDITIONAL verdict, but with the condition explicitly tied to the p(nB) sensitivity test.","tokens_in":36626,"tokens_out":3358,"duration_ms":30894,"concrete_test":"Recompute the flat-interface coexistence curves (Fig. 4A) and the droplet size-scaling predictions (Fig. 5A,B) using the measured nonequilibrium p(nB) from Fig. S5 (rather than the equilibrium p(nB)) in the FLEX boundary conditions BC(3) and BC(4), while keeping everything else unchanged. If the predicted curves shift by more than the simulation symbol sizes, the theory's agreement depends on using a demonstrably false input, and the first-principles claim fails; if the curves remain within error, the assumption is benign and the central claim stands.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that Eqs. (4) and (5) provide a first-principles theory of nonequilibrium phase coexistence. A load-bearing input to those boundary conditions is the marginal distribution p(nB) over local environments at the interface: FLEX explicitly assumes 'the marginal distribution, p(nB), is unperturbed by the chemical drive' (main text, paragraph before Eq. 4), and the SI states that BC(3) uses p(nB) 'obtained from an equilibrium simulation.' However, the paper's own Fig. S5 shows that p(nB) deviates measurably from equilibrium at the very conditions used for the main results: at βΔμ = 2 and Λ = 10², the populations of nB = 1 and nB = 3 sites decrease while nB = 2 increases relative to equilibrium. This is not a small-Lambda breakdown; it is a direct violation of the approximation at the parameter values where the parameter-free coexistence curves (Fig. 4A) are validated. The paper acknowledges the p(nB) deviation only to explain underpredictions of capillary fluctuations (Fig. 4D), but never examines whether the coexistence predictions in Figs. 4A and 5 are sensitive to this deviation. Since BC(4) depends on ⟨pB⟩ and BC(3) depends on a flux averaged over p(nB), the wrong p(nB) could in principle shift the predicted coexistence conditions by amounts comparable to the simulation error bars. If the predictions are robust, that is an important and interesting result; if they shift, the 'first-principles' label is unjustified and the agreement is partly fortuitous. Because this is an internal inconsistency rather than a disagreement with an external consensus, it is the most load-bearing concern about the central claim.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper presents a lattice-gas model of a chemically driven fluid in which molecules interconvert between bonding (B) and inert (I) states through passive and fuel-driven reaction pathways. Using kinetic Monte Carlo simulations, the authors show that steady-state mesoscopic diffusive and reactive fluxes localize near condensate interfaces, that interfacial compositional and capillary fluctuations deviate from equilibrium, and that these deviations are coupled to the chemical drive. They then develop a microscopic–mesoscopic theory: the dilute phase is described by linearized reaction–diffusion equations, while the interface is treated with a Fixed Local Environment approximation (FLEX) encoded in boundary conditions Eqs. (4) and (5). Flat-interface coexistence curves are compared with simulations over a range of Δμ and Λ, along with the reaction–diffusion length, integrated flux, and capillary fluctuations. Finite-droplet size scaling is analyzed through a Gibbs–Thomson-like correction, with the interfacial tension σ as the sole fitting parameter. The paper concludes that equilibrium interface models are generically invalid for chemically driven fluids and that nonequilibrium interfacial effects control coexistence and droplet size scaling.","tokens_in":36999,"tokens_out":5689,"duration_ms":49169,"significance":"If the flat-interface coexistence predictions are quantitatively robust, this is an important step: it offers a route from microscopic reaction rates to nonequilibrium phase diagrams without fitting to the target coexistence data, and it makes the falsifiable prediction of Λ-dependent coexistence curves that qualitatively distinguish the theory from equilibrium boundary-condition approaches. The simulation effort is substantial, the code is provided, and the authors test alternative reaction schemes, which strengthens the generality claims. The main caveats are that the droplet-size-scaling comparison relies on a fitted interfacial tension and that the central FLEX input p(nB) is demonstrably perturbed at the conditions used. A sensitivity check on the latter is needed before the 'first-principles' designation can be fully credited.","major_comments":[{"comment":"The FLEX boundary conditions use the equilibrium marginal distribution p(nB), while the paper's own Fig. S5 shows that p(nB) is measurably perturbed under the same conditions used for the main coexistence results (βΔμ = 2, Λ = 10^2, with nB = 1 and nB = 3 depleted and nB = 2 enhanced relative to equilibrium). Because BC(3) and BC(4) average over p(nB), this is a load-bearing input rather than a cosmetic one. The manuscript never tests how the coexistence curves in Fig. 4A shift if the simulated nonequilibrium p(nB) is used instead of the equilibrium distribution. Please add such a sensitivity analysis; if the predictions are robust, that should be stated explicitly, and if they shift by amounts comparable to the simulation error bars, the 'parameter-free' description should be qualified.","section":"Main text, paragraph before Eq. (4); SI BC(3); Fig. S5"},{"comment":"The droplet size-scaling comparison is not an independent prediction, because the interfacial tension σ is extracted by fitting the same finite-R simulation data that the theory is then compared with. This is acknowledged in the figure caption and methods, but the abstract and discussion present droplet size scaling as a prediction of the theory. To support the claim, the authors should either obtain σ independently (for example from the flat-interface capillary fluctuation spectrum, with appropriate caveats given Fig. S8) or explicitly label the size-scaling curves as one-parameter fits and adjust the wording accordingly. The correlation in Fig. 5C is suggestive, but the non-unity slope indicates that the interpretation of σ is not quantitatively settled.","section":"Fig. 5A,B; Materials and Methods, final paragraph"},{"comment":"The manuscript acknowledges that FLEX underpredicts capillary fluctuations, especially at large Λ, and that the timescale-separation assumption breaks down in this regime. Since the central claim is a first-principles description of nonequilibrium phase behavior, the paper should state the regime of quantitative validity more precisely. In particular, the capillary-fluctuation predictions are only qualitative (Fig. 4D and the surrounding text), and the theory is restricted to strongly phase-separated conditions by SI BC(1) and BC(2). A concise statement of the expected domain of applicability would prevent overgeneralization of the conclusions.","section":"Discussion, paragraph on FLEX limitations; Fig. 4D"}],"minor_comments":[{"comment":"In the upper row of Fig. 4D, only the theoretical prediction for Λ = 10^2 is shown; to allow the reader to judge the claimed qualitative trend in Λ, the authors should show predictions for the same Λ values as the simulation points.","section":"Fig. 4D"},{"comment":"The deviations of p(nB) from equilibrium are presented without error bars or statistical significance. Since this figure is now load-bearing for the sensitivity discussion, uncertainty estimates should be added.","section":"SI Fig. S5"},{"comment":"The theory is described as 'first-principles' and 'parameter-free' in the abstract and main text. Given that p(nB) is taken from an equilibrium simulation and σ is fitted for droplet scaling, the wording should be sharpened (for example, 'parameter-free for flat-interface coexistence curves').","section":"Abstract and main text"},{"comment":"The predicted reaction–diffusion length ξ uses the ideal-limit expression, while the SI shows that measured self-diffusion coefficients differ from the ideal value; the main text should note that the predicted ξ in Fig. 4B is the ideal-limit value and that empirical ξ is used for the concentration-profile fits.","section":"Main text, paragraph after Eq. (3)"}],"recommendation":"major_revision","confidential_remarks":"This is a strong and interesting paper, but the missing sensitivity analysis for the perturbed p(nB) input and the fitted-σ caveat for droplet size scaling are important for the journal's readership. I would like to see a revised version that addresses these points; the central idea is likely correct, but the 'first-principles' claim currently overreaches in places. The manuscript is well within scope for cond-mat.soft and will be of considerable interest to the active-condensate community."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: this is a real step forward for chemically driven condensates, but the headline “first-principles” needs a qualifier. The paper's own SI shows that one of the theory's inputs is not what the approximation says it is, and the authors never test how much that matters.\n\nWhat's genuinely new: the FLEX boundary conditions from the authors' earlier papers are turned into coexistence curves in the Δμ–Λ plane, and these curves match direct-coexistence simulations without adjustable parameters. That's a meaningful result, not a trivial extension. The observation that steady-state mesoscopic fluxes are concentrated at the interface, and that the dilute-phase gradient plus interfacial reaction flux form a closed cycle, is clearly demonstrated and mechanistically useful. The paper also shows the equilibrium-interface alternative fails generically, which is worth having on record. The simulation work is careful, the code is public, and the SI is thorough.\n\nThe soft spots, in order of importance. First, the p(nB) problem. The FLEX approximation assumes the marginal distribution of local environments at the interface is unperturbed by the drive. BC(3) uses p(nB) from an equilibrium simulation. But Fig. S5 shows p(nB) at βΔμ=2, Λ=10² is clearly different from equilibrium: nB=1 and 3 decrease, nB=2 increases. The paper mentions this only to explain why capillary-fluctuation predictions underperform. It never asks whether the coexistence curves in Fig. 4A, or the droplet-size scaling in Fig. 5, are sensitive to this deviation. That is a genuine gap. It doesn't necessarily sink the paper—the agreement may be robust to the error—but the “first-principles” claim is too strong until this is tested. The reader's conditional verdict captures this well.\n\nSecond, the droplet-size scaling: σ is a fitting parameter, and the paper is honest about that. It's a useful empirical extraction, but it is not a prediction. Combined with the p(nB) issue, the droplet-size section is the weakest part.\n\nThird, capillary fluctuations are only qualitatively captured, and the authors say so. That's a minor issue, not a flaw.\n\nMy overall take: the central claim that equilibrium interface models fail generically for these fluids is supported. The precise quantitative framework needs one more loop of self-consistency checking—specifically, re-solving the theory with the nonequilibrium p(nB) or carrying out a sensitivity analysis. This is a solid paper that deserves a serious referee, but the referee should push on the p(nB) point before publication.","headline":"Real progress on nonequilibrium coexistence, but the 'first-principles' label is undercut by an untested equilibrium input in the boundary conditions.","tokens_in":37498,"tokens_out":2217,"would_cite":true,"duration_ms":18299,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"In chemically driven fluids, the condensate interface—not the bulk—sets phase coexistence, fluxes, and droplet sizes.","keywords":["chemically driven fluids","nonequilibrium phase coexistence","biomolecular condensates","interfacial fluctuations","capillary waves","reaction-diffusion","lattice kinetic Monte Carlo","FLEX approximation"],"falsifier":"The cleanest test is the paper's own control scheme: driving the fluid with concentration-independent reaction rate constants is predicted to produce zero net mesoscopic fluxes and Boltzmann interfacial statistics despite dissipation everywhere. Running the same lattice simulation with uniform rate constants and detecting a persistent steady-state flux loop, a non-Boltzmann interface population, or a shift in the coexistence curve would refute the claim that interfacial fluctuations are the mechanism coupling the chemical drive to mesoscopic phase behavior.","tokens_in":36435,"feed_emoji":"💧","tokens_out":14591,"duration_ms":110843,"temperature":0.7,"pith_summary":"This paper asks where nonequilibrium effects actually act in a fluid that burns chemical fuel while phase-separating into droplets, and answers: at the interface. Simulations of a two-dimensional lattice fluid show that net diffusive and reactive fluxes appear only within a reaction–diffusion length of the condensate boundary, and that the molecular state populations at the boundary stray from the Boltzmann distribution whenever a steady concentration gradient exists in the surrounding dilute phase. The authors then build a first-principles theory that grafts a microscopic treatment of the interface (the Fixed Local Environment approximation, FLEX) onto a reaction–diffusion description of the dilute phase, and show it predicts the simulated nonequilibrium coexistence curves, the flux location, the reaction–diffusion length, and the droplet size scaling. Their conclusion is that equilibrium interface models are generically wrong for chemically driven fluids, recovering accuracy only in the fast-diffusion limit where the whole system approaches an effective equilibrium.","feed_headline":"Droplet interfaces set phase behavior in chemically driven fluids","feed_subtitle":"Fluxes, coexistence, and droplet sizes are governed by the condensate interface, not the bulk.","key_machinery":"The load-bearing machinery is the Fixed Local Environment approximation (FLEX), which treats the microscopically sharp interface as a boundary between the two bulk descriptions. FLEX solves the steady-state balance of reactions and diffusive exchange at a tagged interface site for each local environment $n_B$, assuming the marginal environment distribution $p(n_B)$ is unperturbed by the drive; from this it computes the conditional species distribution $p_{B/I}(n_B)$ and the interfacial flux. The dilute phase is described by a linearized reaction–diffusion equation with a reaction–diffusion length $\\xi$, and the two descriptions are joined by the flux-matching boundary condition (Eq. 4) and the coexistence condition (Eq. 5) with the Gibbs–Thomson term $\\beta\\sigma R^{-1}$ for finite droplets. The coupling of these two conditions is what forces the non-Boltzmann statistics: stationarity plus flux conservation plus a Boltzmann ansatz is an overdetermined system unless the flux-to-mobility ratio vanishes.","core_discovery":"The central claim is that steady-state mesoscopic fluxes in a phase-separated chemically driven fluid originate at the condensate interface, and that these interfacial effects determine the conditions for phase coexistence and the size scaling of droplets. Within the theory, the flux-matching boundary condition (Eq. 4) and the particle–hole-symmetric phase-coexistence condition with a Gibbs–Thomson correction (Eq. 5) replace the usual equilibrium requirements of equal chemical potentials and pressures at a sharp interface. These conditions are mutually consistent only if the interfacial conditional distribution $p_{B/I}(n_B)$ is non-Boltzmann whenever $j_B(R^+)/\\Lambda \\neq 0$; a Boltzmann distribution on the interface would overdetermine the system unless the entire fluid is governed by a single effective equilibrium, which occurs only when the dilute-phase concentration gradient vanishes. The droplet-size data further imply a nonequilibrium interfacial tension $\\sigma$ that departs systematically from the equilibrium value and correlates with the measured capillary fluctuation amplitude. The simulations also isolate a control case: a reaction scheme whose rates do not depend on local concentration dissipates energy everywhere yet produces no mesoscopic fluxes and no interfacial deviations from equilibrium.","pith_inferences":["A concrete test the paper does not spell out: because coexistence concentrations are predicted to move with mobility at fixed reaction rates, experiments or simulations that change viscosity or crowding—while holding fuel chemical potential fixed—should shift droplet coexistence and size distributions, a purely nonequilibrium signature.","Nucleation is the natural probe: the barrier height scales with interfacial tension, so the predicted drive-dependent $\\sigma$ implies nucleation rates that classical theory with $\\sigma_{\\rm eq}$ would misestimate; counting nucleation events versus driving strength and sign would measure the nonequilibrium tension directly.","The homogeneous-reaction control doubles as an in vivo diagnostic: if steady flux loops or altered capillary fluctuations near condensate surfaces are observed, they indicate that the relevant enzymatic activity is concentrated or concentration-dependent, whereas uniform catalysis would leave interfaces near equilibrium-like behavior.","Whether interfacial control persists near critical points is open: the theory's quantitative reach is limited where capillary fluctuations are large, so the near-critical regime is the natural place to test whether the interface remains the dominant seat of nonequilibrium effects."],"forward_implications":["Equilibrium-interface theories for chemically driven condensates—which impose equal chemical potentials and pressures across a sharp interface with no reactions on the interface—agree with the simulations only for weak driving or in the fast-diffusion limit $\\Lambda \\to \\infty$, where the system approaches a global effective equilibrium.","Nonequilibrium coexistence becomes mobility-dependent: at fixed reaction rates, the far-field concentration at coexistence shifts with $\\Lambda$, a signature that equilibrium boundary conditions cannot produce.","Droplet size scaling reports a nonequilibrium interfacial tension: $\\ln(\\rho^v/\\rho^v_{\\rm flat})$ is linear in $R^{-1}$ in the regime $\\xi \\ll R$ with slope set by $\\sigma \\neq \\sigma_{\\rm eq}$, and becomes nonlinear when $\\xi \\gtrsim R$ because the flux boundary condition itself acquires $R$-dependence.","Driving with concentration-independent reaction rate constants produces no mesoscopic fluxes and no non-Boltzmann interfacial statistics, so molecular-scale dissipation alone does not imply observable nonequilibrium phase behavior.","The inferred nonequilibrium interfacial tension tracks the capillary fluctuation amplitude in a consistent linear trend across both size-scaling regimes, indicating that the chemical drive acts on condensation through interfacial softening or stiffening."],"supporting_citations":[{"why":"Supplies the FLEX closure and the particle–hole-symmetric coexistence condition that the boundary conditions (Eqs. 4–5) build on, plus the earlier observation of a nonequilibrium interfacial tension in nucleation.","marker":"[39]"},{"why":"Introduces the concentration-dependent reaction scheme of Eq. (1) and the FLEX framework for nonequilibrium interfacial properties that this paper extends to phase coexistence and droplet scaling.","marker":"[40]"},{"why":"A sharp-interface theory of chemically controlled droplets whose equilibrium-like assumptions are the baseline the paper's coexistence and size-scaling predictions are measured against.","marker":"[20]"},{"why":"Provides the equilibrium-boundary-condition sharp-interface theory whose coexistence curves (dotted lines in Fig. 4A) fail away from the fast-diffusion limit.","marker":"[38]"},{"why":"Defines the stochastic-thermodynamic entropy production used to map where dissipation occurs in the simulated steady states.","marker":"[45]"},{"why":"Gives the capillary-wave equipartition spectrum used to detect nonequilibrium shifts in interfacial tension and fluctuation amplitude.","marker":"[46]"},{"why":"Supplies the Young–Laplace and Gibbs–Thomson relations that the curved-interface coexistence condition (Eq. 5) generalizes to nonequilibrium tension.","marker":"[47]"},{"why":"The equilibrium solid-on-solid capillary model used to convert the FLEX effective bond energy into a prediction of mean-squared interfacial height fluctuations.","marker":"[48]"}],"fun_headline_variants":["Droplet surfaces control phase behavior in fuel-driven fluids","Interfaces set the rules for nonequilibrium condensation","Chemical fuel drives droplets but interfaces decide fate","Nonequilibrium phase maps hinge on droplet interfaces","Mesoscale fluxes localize at interfaces in active fluids"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that each interface site's local environment is frozen while single-site reactions and diffusion relax—so the drive reshuffles state populations but not the distribution of neighbor counts—and that the condensed phase is strongly phase-separated, with negligible internal fluxes and an unperturbed concentration; when diffusion is fast or conditions approach criticality, that timescale separation fails and the theory's quantitative prediction of capillary fluctuations degrades.","fun_headline_variants_meta":{"raw":{"variants":["Droplet surfaces control phase behavior in fuel-driven fluids","Interfaces set the rules for nonequilibrium condensation","Chemical fuel drives droplets but interfaces decide fate","Nonequilibrium phase maps hinge on droplet interfaces","Mesoscale fluxes localize at interfaces in active fluids"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000182,"raw_usage":{"total_tokens":1317,"prompt_tokens":957,"completion_tokens":360,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":573,"completion_tokens_details":{"reasoning_tokens":286}},"tokens_in":573,"tokens_out":360,"duration_ms":3501,"temperature":1.0,"reasoning_tokens":286,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T14:53:43.705614+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"The cleanest test is the paper's own control scheme: driving the fluid with concentration-independent reaction rate constants is predicted to produce zero net mesoscopic fluxes and Boltzmann interfacial statistics despite dissipation everywhere. Running the same lattice simulation with uniform rate constants and detecting a persistent steady-state flux loop, a non-Boltzmann interface population, or a shift in the coexistence curve would refute the claim that interfacial fluctuations are the mechanism coupling the chemical drive to mesoscopic phase behavior.","supporting_citations":[{"cited_title":"Cho and W","cited_arxiv_id":null,"evidence_quote":"Introduces the concentration-dependent reaction scheme of Eq. (1) and the FLEX framework for nonequilibrium interfacial properties that this paper extends to phase coexistence and droplet scaling."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"A sharp-interface theory of chemically controlled droplets whose equilibrium-like assumptions are the baseline the paper's coexistence and size-scaling predictions are measured against."},{"cited_title":"Bauermann, C","cited_arxiv_id":null,"evidence_quote":"Provides the equilibrium-boundary-condition sharp-interface theory whose coexistence curves (dotted lines in Fig. 4A) fail away from the fast-diffusion limit."},{"cited_title":"Van den Broeck and M","cited_arxiv_id":null,"evidence_quote":"Defines the stochastic-thermodynamic entropy production used to map where dissipation occurs in the simulated steady states."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the capillary-wave equipartition spectrum used to detect nonequilibrium shifts in interfacial tension and fluctuation amplitude."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the Young–Laplace and Gibbs–Thomson relations that the curved-interface coexistence condition (Eq. 5) generalizes to nonequilibrium tension."}],"review_version":1}