{"id":"ca25ec3a-687e-4f89-8bb2-67ef7e3231ec","arxiv_id":"2512.17827","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"In a 2D Kawasaki lattice gas under a smooth temperature gradient, the steady state organizes into regularly spaced density stripes with convection cells, and stripe number grows with system size.","lead":"A temperature gradient turns a low-temperature lattice gas's usual phase separation into robust convection stripes with circulating particle currents. It is a clean statistical-mechanics example of weak nonequilibrium driving creating dissipative structure and destroying long-range order.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Macroscopic proof targets quasi-stationary pure states, not the true NESS; if the steady state is a stripe-position mixture, the maximum-principle argument does not apply and the N~L^{1/2} scaling may be metastable.","rationale":"The reader's weakest_assumption already identifies the central problem: the macroscopic argument is formulated for locally pure stationary profiles, while the actual NESS may be a superposition of quasi-stationary stripe states. I agree this is the most load-bearing concern. It directly attacks the logical bridge from Eqs. (12)-(16) to the conclusion that N must diverge in the true steady state. The Fick's-law assumption (Eq. 16) is also unproven, but if the mixture issue is resolved—i.e., if the NESS is shown to be pure on macroscopic scales—the Fick's-law concern would remain a quantitative gap; conversely, even a perfect Fick's law would not rescue the maximum-principle argument if the steady state is a mixture. Therefore the mixture/quasi-stationarity issue is the single most load-bearing concern. The paper is honest about this limitation, and the numerical evidence supports a real finite-time phenomenon, so I do not recommend a stronger verdict than the reader's CONDITIONAL; UNCHANGED is appropriate. The proposed ensemble-average test is a direct, computationally feasible check of whether the NESS measure violates the pure-state assumption.","tokens_in":17819,"tokens_out":16087,"duration_ms":185486,"concrete_test":"Compute the true steady-state ensemble average ⟨ρ⟩ by averaging over many (e.g., 100) independent realizations from white-noise initial conditions at fixed L=200, without selecting by stripe number or aligning stripe positions. If the resulting ⟨ρ⟩ is y-independent and takes values inside (1−ρ_c,ρ_c) in the cold region, the NESS is a mixture and the pure-state maximum-principle argument does not apply; if ⟨ρ⟩ retains a striped profile, the quasi-stationary assumption is supported and the theory's applicability to the NESS is more secure.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—stripes proliferate with L and destroy conventional long-range order—is derived from the macroscopic Observation in Sec. IV.D.a, which assumes a stationary pure-state density profile satisfying local equilibrium (12), conservation (14)-(15), and Fick's law (16). But the authors explicitly restrict the theory to 'locally pure state... not of a mixture' (Sec. IV opening) and state that it can only treat 'microscopically quasi-stationary' configurations. If the true NESS is a superposition of slowly moving stripe states—as the observed y-translation invariance and the existence of a range of stable stripe counts 8≤N≤17 suggest—then the ensemble-averaged density is y-independent and can enter the forbidden interval (1−ρ_c,ρ_c) near the cold line. In that case Eq. (12) fails for the actual NESS and the maximum-principle argument does not constrain the steady-state ensemble. The numerical N~L^{1/2} data (Fig. 5) are limited to t=1.33×10^7, L≤200, and are consistent with a slowly coarsening transient rather than a true stationary state. Compounding this, Eq. (16) with unspecified D>0 is asserted rather than derived from the microscopic current (D1), so even the quasi-stationary argument rests on an unproven constitutive relation.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies a two-dimensional conservative Kawasaki lattice gas with Ising interactions, coupled everywhere to a heat bath whose temperature varies smoothly on the macroscopic scale. For an x-dependent sinusoidal temperature profile below criticality, Monte Carlo simulations show the formation of regular high- and low-density stripes with persistent convection currents. The number of stripes grows sublinearly with system size (reported as N ~ L^{1/2}), and the structure-factor peak grows slower than the volume, which the authors interpret as destruction of conventional long-range order. The same phenomenology is seen for a Mexican-hat temperature profile but not for a single-dip profile, and the patterns differ qualitatively from a detailed-balance dynamics with the same local temperature profile. A macroscopic theory is then proposed, based on local equilibrium, conservation, and Fick's law, leading to a maximum-principle argument that stationary pure density profiles must fragment at temperature minima, so that the number of stripes must diverge with system size.","tokens_in":18127,"tokens_out":7430,"duration_ms":85546,"significance":"If the central claims hold, the paper identifies a genuinely new nonequilibrium ordering mechanism: a weakly driven symmetry-broken phase reorganizes into convection-stabilized stripes and loses conventional long-range order, in marked contrast to the equilibrium phase-separated state with the same local temperature. The connection to Rayleigh-Bénard-like dissipative structures is conceptually appealing. The numerical work is substantial: multiple diagnostics (density profiles, currents, structure factors, local-equilibrium checks), several temperature profiles, filling factors, initial conditions, and a symmetry-breaking boundary perturbation. The authors are also unusually explicit about the limitations of their macroscopic theory. However, the theoretical proof is conditional on assumptions that are not fully established, and those assumptions are close to the load-bearing conclusions.","major_comments":[{"comment":"The domain of the macroscopic theory is narrower than the conclusion drawn from it. The opening of Sec. IV states that the density refers to a 'locally pure state... not of a mixture' and that the theory 'can treat as stationary configurations that are microscopically quasi-stationary.' Section IV.D.b nevertheless concludes that 'the number of stripes must indeed increase with system size' for the NESS. If the true stationary measure is a y-translation-invariant superposition of slowly moving stripe states—which the paper leaves open (Sec. III.A: 'consistent with the existence of a unique steady state that is invariant under translations along y'; Sec. III.D: stable stripe counts 8≤N≤17)—then the ensemble-averaged density is homogeneous in y and can enter the forbidden interval (1−ρ_c,ρ_c). In that case Eq. (12) fails for the actual NESS and the maximum-principle Observation does not con","section":"Sec. IV (opening), Sec. IV.D.b"},{"comment":"Fick's law is asserted rather than derived. The microscopic current is computed in (D1), but the authors explicitly say they 'do not expect the diffusion coefficient to be read directly from this expression' and replace it by J=−D∇ρ with D finite and positive and otherwise unspecified. Equations (17) and the maximum-principle proof use only this constitutive relation. Thus the theoretical conclusion is conditional on an unverified hydrodynamic postulate; in particular D could be density-dependent in a more complicated way, or nonlocal terms could matter near interfaces. The paper should either derive the macroscopic current (even in a scaling limit or at leading order in a low-temperature expansion), or state Eq. (16) as an explicit phenomenological assumption and validate it locally from the measured current and density gradient inside stripe interiors.","section":"Sec. IV.A.c, Eq. (16)"},{"comment":"The paper reports an unexplained breakdown of the local-equilibrium prediction in the coldest region: for ρ=0.8, ρ̃(x) 'systematically exceeds the spontaneous density ρc in the coldest part by a few percent' and 'this effect does not diminish with increasing system size.' This is precisely the region where Eq. (12) is used in the proof of the Observation. The deviation does not by itself invalidate the numerics, but it is a load-bearing unresolved discrepancy: if it persists, the local-equilibrium condition is either incomplete or the identification of bulk stripe sites is biased, and the maximum-principle argument needs to be revisited.","section":"Sec. III.G and Fig. 8"},{"comment":"The numerical support for the central scaling claim is limited to moderate sizes and a single time horizon: L_x≤200 at t=1.33×10^7 for Fig. 5, with strong integer-threshold effects; the current data in Fig. 6 show that the expected 1/L regime has not been reached; Fig. 7 shows subextensive S(k_peak) only for a few sizes and a selected subset of realizations. Since the macroscopic proof is conditional (see above), the extrapolation N∼L^{1/2} and the destruction of long-range order carry more weight than they would otherwise. A test against slow coarsening—e.g., showing that N(t) is flat for times well beyond the nucleation time at each L, or that the structure-factor peak grows slower than V with controlled error bars—would materially strengthen the claim.","section":"Sec. III.D, III.F and Figs. 5, 7"}],"minor_comments":[{"comment":"Typographical errors: 'wether' should read 'whether' and 'Dykin' should be 'Dynkin'.","section":"Appendix D"},{"comment":"The decomposition L=L_eq+L_non-eq at a fixed macroscopic point and the assertion that local equilibrium 'follows from the structure of microscopic dynamics' is heuristic; if it is not intended as a proof, the wording should be softened.","section":"Sec. IV.A.a"},{"comment":"The sentence 'the lower panel of Fig. 1 would have to be modified so that stripes extend continuously toward the center' is difficult to parse without an overlay; please clarify the hypothetical construction.","section":"Sec. III.B"},{"comment":"The notation N∼L^a should specify that L is L_x at fixed aspect ratio, and the fitted exponent should be quoted with an uncertainty estimate.","section":"Sec. III.D"},{"comment":"'over a proportion of40 realizations' should be 'over a proportion of the 40 realizations'; also check the spacing in 'of40'.","section":"Fig. 7 caption"}],"recommendation":"major_revision","confidential_remarks":"This is a stimulating paper with extensive and careful numerics, and the pattern-formation phenomenology is likely to attract interest. However, the key theoretical statement ('the number of stripes must increase with system size') is proved only for locally pure, quasi-stationary profiles, not for the full NESS ensemble. I would advise the editor that acceptance should be conditional on the authors either supplying an argument that the invariant measure is not a translation-invariant mixture of stripe states, or reframing the central claim as a metastability/pattern-formation statement supported by the numerics. The unexplained density excess in the coldest region should also be addressed before publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Worth a read. The paper reports robust convection stripes in a Kawasaki lattice gas under a smooth macroscopic temperature gradient, with the number of stripes growing roughly as L^{1/2}. That is a clean, new phenomenon, and the simulations look careful.\n\nWhat the paper does well: it checks robustness across initial conditions, filling factors, temperature profiles, and boundary flips. The comparison with an equilibrium dynamics engineered to produce the same local Gibbs weights is a smart way to demonstrate that the stripes are genuinely nonequilibrium. The macroscopic framework—local equilibrium, conservation, Fick's law—is a useful organizing principle, and the maximum-principle argument on quasi-stationary profiles is elegant.\n\nThe soft spots are real but not disqualifying. The macroscopic theory is explicitly restricted to locally pure, quasi-stationary configurations, not to the true steady-state ensemble. The paper is open about this, but it has a direct consequence: if the NESS is a mixture of slowly drifting stripe positions, the ensemble-averaged density is y-independent, Eq. (12) can fail, and the maximum-principle observation does not constrain the infinite-time state. So the central claim—stripe number grows with L and destroys conventional long-range order—is supported by simulations of long-lived striped states, not by a proof about the NESS. The scaling data, with L<=200 and t=1.3e7, are consistent with a slow coarsening transient as well as with true stationarity. Separately, Eq. (16) is an unproven Fick-law assumption with an unspecified diffusion coefficient, and Fig. 4 shows unexplained density deviations in the coldest region.\n\nNone of this is a red flag. The authors disclose these limitations clearly, and the phenomenon is likely real even if the theory needs refinement. But the paper would be stronger if it distinguished what is proven about quasi-stationary states from what is conjectured about the NESS, and if it provided more direct evidence of stationarity.\n\nWho should read it: anyone working on driven lattice gases, macroscopic fluctuation theory, or nonequilibrium pattern formation. It deserves a serious referee. A good referee should push on the quasi-stationary versus true steady-state distinction and ask for either longer-time data or a more careful statement of what the macroscopic theory is allowed to assert.\n\nRecommendation: send it to peer review. It is a genuine advance in a minimal model, and the flaws are addressable in revision.","headline":"Good numerics and an honest paper, but the central claim is only proven for quasi-stationary striped states, not for the true NESS.","tokens_in":18615,"tokens_out":3457,"would_cite":true,"duration_ms":34522,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["82C22","82C20","82B20"],"pacs":[],"model":"deepseek-v4-flash","headline":"A conservative lattice gas driven by a smooth macroscopic temperature gradient develops convection-driven density stripes whose number grows with system size, replacing conventional long-range order.","keywords":["nonequilibrium steady state","Kawasaki dynamics","lattice gas","convection patterns","stripe formation","local equilibrium","long-range order","phase separation"],"falsifier":"Measure the stationary probability distribution of the local density at the point of minimal temperature in a large subcritical system. The framework predicts a locally pure phase there (density near 0 or 1), whereas a bimodal histogram indicating a mixture over phases would falsify the premise. A second decisive check is the scaling of the stripe number N(L) at fixed aspect ratio for L up to 1000: if N saturates or grows slower than any positive power of L, the claim of stripe proliferation with system size is false.","tokens_in":17695,"feed_emoji":"🌀","tokens_out":8034,"duration_ms":78104,"temperature":0.7,"pith_summary":"This paper studies a two-dimensional lattice gas with conserved particles and Ising interactions, kept in contact with a heat bath whose temperature varies smoothly across the sample. Below the critical temperature such a gas normally phase-separates into high- and low-density regions, but the paper shows that a macroscopic temperature gradient destroys that familiar order. Instead, the steady state organizes into regularly spaced density stripes with circulating particle currents, and the number of stripes grows with system size, so no stripe survives as a macroscopic phase. The authors argue from local equilibrium, particle conservation, and Fickian diffusion that a temperature minimum cannot lie in the interior of a single phase, which forces stripe proliferation. They also show that the nonequilibrium steady state differs sharply from the equilibrium state with the same local temperatures, demonstrating that free-energy minimization is not a valid global organizing principle out of equilibrium.","feed_headline":"Temperature gradient turns phase separation into convection stripes","feed_subtitle":"Weak heat drive makes a lattice gas form convection stripes whose count grows with size, erasing long-range order.","key_machinery":"The load-bearing object is the set of macroscopic constraints — local equilibrium (no metastable densities), the continuity equation with a Stefan condition at interfaces, and Fick's law J = -D(T,rho) grad rho — from which the paper derives an observation: a stationary density profile satisfying these constraints cannot have a minimal-temperature point in the interior of a high- or low-density region, because the maximum principle would then force the density to be constant there, contradicting the boundary values. This 'no extremum inside a phase' constraint is what drives stripe proliferation with system size. Microscopically, the currents arise because thermally created defects are cheape","core_discovery":"Under a smooth macroscopic temperature gradient, a conservative lattice gas with Ising interactions forms regularly spaced density stripes with circulating particle currents. The number of stripes grows sublinearly with system size, consistent with N ~ L^{1/2}, so the steady state has no conventional long-range order. Locally the state looks like a Gibbs state at the local temperature, but globally it differs from the equilibrium state with the same temperature profile: vacancies accumulate in the hot region in equilibrium, while the nonequilibrium dynamics produces stripes in the cold region. A macroscopic argument based on local equilibrium, conservation, and Fick's law shows that a temper","pith_inferences":["The same 'no extremum inside a phase' reasoning may apply to other conserved dynamics with Fick-type transport, suggesting stripe or modulated states whenever temperature has interior minima; this could be tested by varying the temperature landscape.","The unexplained density excess above the spontaneous value in the coldest region may be a real nonequilibrium correction to local equilibrium; measuring its system-size dependence would indicate whether the macroscopic theory needs refinement.","Because the theory describes quasi-stationary pure profiles rather than the full stationary ensemble, a sharper test is to measure the distribution of stripe positions over very long times; a translationally mixed stationary state would fall outside the theory's assumptions."],"forward_implications":["Free-energy minimization fails as a global organizing principle: the same local temperature profile gives qualitatively different steady states in equilibrium and nonequilibrium dynamics.","The number of stripes must diverge with system size, so the macroscopic limit has no fixed phase boundary; order exists only over intermediate distances.","Local equilibrium can hold while global long-range order is destroyed, so measuring local Gibbs behavior does not reveal the global steady state.","Interface shapes are governed by particle currents, not mean-curvature relaxation, explaining elongated and dumbbell-shaped domains.","The theory yields specific scaling predictions — stripe number growing as L^{1/2} and current decaying as 1/L — that can be checked in larger simulations."],"fun_headline_variants":["Heat gradient turns lattice gas into convection stripes","Temperature gradient drives lattice gas to form stripes","Nonequilibrium heat flow makes lattice gas stripe","Kawasaki dynamics under heat flux yields striped convection","Driven lattice gas loses order, gains convection stripes"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The macroscopic argument treats the steady state as a locally pure, quasi-stationary density profile satisfying Fick's law with a positive diffusion coefficient; if the true NESS is a mixture over slowly moving stripe configurations, or if Fick's law fails near the coldest region, the maximum-principle observation and the predicted stripe scaling do not follow.","fun_headline_variants_meta":{"raw":{"variants":["Heat gradient turns lattice gas into convection stripes","Temperature gradient drives lattice gas to form stripes","Nonequilibrium heat flow makes lattice gas stripe","Kawasaki dynamics under heat flux yields striped convection","Driven lattice gas loses order, gains convection stripes"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000141,"raw_usage":{"total_tokens":928,"prompt_tokens":595,"completion_tokens":333,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":339,"completion_tokens_details":{"reasoning_tokens":262}},"tokens_in":339,"tokens_out":333,"duration_ms":4348,"temperature":1.0,"reasoning_tokens":262,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T15:07:59.120066+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the stationary probability distribution of the local density at the point of minimal temperature in a large subcritical system. The framework predicts a locally pure phase there (density near 0 or 1), whereas a bimodal histogram indicating a mixture over phases would falsify the premise. A second decisive check is the scaling of the stripe number N(L) at fixed aspect ratio for L up to 1000: if N saturates or grows slower than any positive power of L, the claim of stripe proliferation with system size is false.","supporting_citations":[],"review_version":1}