{"id":"8b1b3b78-c405-46f5-a3cd-9193fc542ae4","arxiv_id":"2507.20350","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"For two identical fluctuating interfaces with sticking at contact points, the exact steady-state measure is an inhomogeneous product form equivalent to the equilibrium Poland-Scheraga DNA denaturation measure.","lead":"This paper introduces a model of two fluctuating 1D interfaces that stick together where they touch, and finds an exact formula for their long-time steady state in certain symmetric cases. The steady state matches the classic Poland-Scheraga model used to describe DNA denaturation, linking non-equilibrium interface physics to equilibrium DNA melting.","discovery_kind":"unification","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Poland-Scheraga phase analysis drops the loop initiation factor; the claim that the steady state is always entangled for every s is not established and is likely false for s near 1.","rationale":"I agree with the reader that the exact steady-state measure in Eq. (2) is well supported and that the paper has honest caveats. However, the most load-bearing concern is not the heuristic diamond-lifetime argument in the End Matter; it is the Poland-Scheraga phase analysis. Eq. (3) and the subsequent v_c = g/(1+zeta(3/2)) criterion require the bubble weight to be exactly g^l/l^c with no per-bubble prefactor. The paper's own Supplement provides an exact B(l) whose asymptotic prefactor is not 1, and the underlying lazy-random-walk return generating function gives a bubble generating function equal to 1/2 at the critical point, not zeta(3/2). The resulting loop initiation factor shifts v_c upward, so the universal claim v>v_c(s) for all s is not established and is contradicted by the paper's own numerical bubble-size distribution at s=0.9. This is a concrete, checkable flaw in a central phase conclusion. The exact measure and the mapping to a generalized Poland-Scheraga model survive, so the appropriate verdict is conditional acceptance with a required correction of the phase analysis rather than outright rejection. The reader's dynamic-timescale concern remains valid but is secondary, hence 'partial' agreement.","tokens_in":20152,"tokens_out":61583,"duration_ms":660057,"concrete_test":"Compute the exact bubble generating function from the Supplement formula B(n)=4^{n+1} Gamma(n+3/2)/(sqrt(pi) Gamma(n+3)) (with bubble length l=n+2) and evaluate S(s)=sum_l B(l)/(4s)^l, including both bubble orientations. If S(1)=1/2 rather than zeta(3/2), the PS critical condition must be corrected to v_c = 4s/(1+S(s)). Then run steady-state simulations of the 2EW or 2KPZ model at s=0.8 and s=0.9 for L=128, 256, 512, 1024 and measure the stuck fraction and the bubble-size distribution. If the stuck fraction decreases with L and the bubble-size distribution retains the l^{-3/2} tail without an exponential cutoff, the paper's 'always entangled' phase claim is false for these s.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The exact steady-state measure in Eq. (2) is well supported, but the Poland-Scheraga phase conclusion following Eq. (3) has a load-bearing gap. The paper replaces the exact bubble weight B(l) by the leading form (4s)^l/l^{3/2} and then uses the standard PS critical condition v_c = g/(1+zeta(3/2)) with g=4s, v=2, concluding v>v_c(s) for all s<1. This ignores the non-unit prefactor in B(l), i.e., the loop initiation factor q that multiplies each bubble in the partition function. For the underlying lazy random walk of the height difference, the exact bubble (nonzero excursion) generating function at the critical point z=1/(4s) equals 1/2, not zeta(3/2) ~ 2.61. Equivalently, q ~ 1/(2 zeta(3/2)) ~ 0.19, and the corrected critical value is v_c ~ (4s)/(1+q zeta(3/2)) = 8s/3. Since v=2, the bound phase requires 2 > 8s/3, i.e., s < 0.75, contradicting 'always entangled for any s'. The paper's own Supplemental Fig. S4(d) shows that at s=0.9 the steady-state bubble size distribution approaches the noninteracting l^{-3/2} power law, which is the signature of a denatured, not a bound, steady state. The exact invariant measure itself can still be correct; what fails is the PS phase boundary drawn from Eq. (3).","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies two single-step interfaces in 1+1 dimensions with short-range sticking at contact sites; the update probabilities are (1/2±a) per site, multiplied by a detachment probability s at sites where the surfaces cross. In the subspace a=a'≥0 (two EW or two KPZ surfaces) the authors derive an exact invariant measure P(C_s^k)=p0 s^{L-k} by pairwise balance and identify it with the equilibrium Poland–Scheraga measure, concluding that the steady state is always entangled. The remaining sections analyze transient dynamics: 2EW shows a numerical dynamic exponent z≈1.5, 2KPZ forms facets, 2OKPZ produces long-lived diamond bubbles with claimed lifetimes T∼exp(λL^2), and EWKPZ exhibits two competing evolutions with a detachment fraction boundary s*∼L^{-0.75}.","tokens_in":20515,"tokens_out":27876,"duration_ms":283412,"significance":"The exact steady-state derivation is a valuable and nontrivial result: an out-of-equilibrium two-surface model with sticking interactions is shown, by a pairwise-balance construction, to have an inhomogeneous product measure, and the numerical support in Fig. 2 (a-invariance of the width and bubble-size distributions) is convincing. The identification with the Poland–Scheraga measure is conceptually appealing and, once the phase-boundary calculation is corrected, should provide a useful bridge between non-equilibrium interface models and DNA-denaturation models. The dynamical observations (z≈1.5 in 2EW, facet formation in 2KPZ, diamond stability in 2OKPZ, and the two-mode EWKPZ evolution) are interesting and well presented, though some of the more dramatic claims, especially T∼exp(λL^2), are heuristic at present.","major_comments":[{"comment":"The conclusion following Eq. (3) that v>v_c(s) for every s<1, and hence that the steady state is always entangled, drops the loop-initiation prefactor of the bubble weight. Using the authors' exact bubble count from the Supplemental Material, B(l)=C_{l-1} (Catalan numbers), the rescaled loop weight is w(l)=C_{l-1}/4^l, and its unit-fugacity generating function is A=Σ_{l≥2} C_{l-1}/4^l = 1/4, not ζ(3/2)≈2.61. Replacing ζ(3/2) by A in the critical condition used by the authors gives v_c = g/(1+A) = 4s/(1+1/4) = 16s/5; with v=2 the bound phase therefore requires s<5/8≈0.625 (using only the asymptotic prefactor q=1/(4√π) gives s_c≈0.68). Thus for s near 1 the predicted steady state is denatured rather than entangled. The paper's own Supplemental Fig. S4(d) is consistent with this: at s=0.9 the bubble-size distribution is already close to the noninteracting l^{-3/2} law. Please recompute the Poland–Scheraga phase boundary with the exact loop generating function and revise the abstract, the bullet list, and the phase-diagram claims accordingly.","section":"Sec. I ('The steady state in the 2EW and 2KPZ cases'), Eq. (3) and following paragraph"},{"comment":"The claimed diamond lifetime T∼exp(λL^2) is presented as a property of the original sticking model, but the derivation is made for an auxiliary non-crossing exclusion model with Hamiltonian H=εΣ_i |h1_i−h2_i|. The statement that the longest closing timescale of a diamond in the original model equals that of the auxiliary model is asserted, not derived, and the activation picture over an O(L^2) area barrier is heuristic. Because the exp(λL^2) scaling is a headline claim in the abstract and in the fourth bullet point, please provide direct numerical measurements of diamond closing times as a function of L in the original model, or explicitly label the scaling as a conjecture.","section":"End Matter, 'Ultraslow timescales in the 2OKPZ case when no detachments are allowed (s=0)'"}],"minor_comments":[{"comment":"The text states that the detachment probability s(L) follows a power law ∼ L^η with η≈0.75, but the plotted fit is s*∼L^{-0.75}; the exponent in the text should carry a minus sign.","section":"Supplemental Material, Fig. S2(b) and accompanying text"},{"comment":"The text defines H=εΣ_i |h1_i−h2_i| but then uses signed height differences in the energy-change formulas; please clarify whether the potential is the absolute value or a signed sum, since the claimed area barrier depends on this distinction.","section":"End Matter, Hamiltonian H for the non-crossing model"},{"comment":"The numerical dynamic exponent z≈1.5 in the 2EW case and the analysis of the closing of the largest bubbles are attributed to an unpublished work; please provide a publicly available preprint or include the numerical data and fitting procedure in the Supplemental Material.","section":"References, [91]"},{"comment":"The pairwise-balance proof leading to Eq. (1) is compressed into Fig. 7 and a short paragraph; since this is the central exact result, a complete enumeration of the flux-pairing cases in an appendix or in the Supplemental Material would strengthen the paper.","section":"End Matter, 'Pairing scheme for the Fluxes in the 2EW and 2KPZ steady state'"},{"comment":"The caption mixes the description of width-versus-time plots and bubble-size distributions in a single parenthetical phrase, making it difficult to tell which panels correspond to which observable; please separate the panel descriptions.","section":"Fig. 2 caption"}],"recommendation":"major_revision","confidential_remarks":"The exact invariant measure appears sound, but the Poland–Scheraga phase-boundary error affects a central claim of the paper and needs to be corrected before publication. The ultra-slow timescale claim, T∼exp(λL^2), is also not yet supported by a derivation for the original model; it should either be backed by direct numerical evidence or explicitly downgraded to a conjecture. The paper is otherwise a solid contribution to the non-equilibrium steady-state literature and should be reconsidered after the phase analysis is redone."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know before you look at this one. The exact steady state in the a=a' subspace is the real result and it holds up; the phase claim built on top of it, that the system is always entangled for any s<1, is likely wrong near s=1.\n\nThe steady-state derivation is the strongest part. Pairwise balance is sketched in End Matter with the bracket notation and the four flux-pairing scenarios in Fig. 7, and it delivers P(C)=p0 s^{L-k}. The measure is a-invariant, the numerics (width saturation, bubble size distributions) match, and the PS identification is natural: bubble weights (4s)^l/l^{3/2}, stuck-segment weights 2^r, c=3/2. The mapping to the equilibrium Poland-Scheraga measure is genuinely new and worth having.\n\nThe soft spot is the phase boundary drawn from Eq. (3). The exact bubble count B(l) has a non-unit prefactor; the paper drops it and uses the unit-prefixed form in the standard PS criterion v_c = g/(1+zeta(c)). But the bubble generating function at the critical fugacity is O(0.25-0.5), not zeta(3/2) ~ 2.6. That loop-initiation factor is exactly the kind of constant that matters in a PS transition, and it changes v_c from about 1.1s to something like 2.7-3.2s. The bound phase then requires s below roughly 0.6-0.75, not s<1. So 'always entangled for any s' is not established. The authors' own Supplemental Fig. S4(d) points the same way: at s=0.9 the steady-state bubble distribution is close to the non-interacting l^{-3/2} power law, which is the denatured signature, not the exponential tail of a bound state. The invariant measure itself is untouched by this; what needs correcting is the PS phase analysis.\n\nThe dynamics sections are honest. The z~1.5 exponent in 2EW s=0 is presented as unexplained, which is fine. The exp(lambda L^2) diamond-lifetime claim for 2OKPZ s=0 rests on a heuristic mapping to a non-crossing exclusion model with an area barrier; plausible, but asserted rather than derived. The EWKPZ separatrix is explicitly left open. No error bars on the collapses, which is minor and typical for this literature. The citation pattern is clean; the self-citations are for the standard pairwise-balance technique.\n\nRead this if you care about exact nonequilibrium steady states for coupled interfaces or about PS-type mappings. It deserves a serious referee; the right referee will want the PS phase boundary recomputed with the actual loop weights.","headline":"Exact steady state in the a=a' subspace is real and well supported; the 'always entangled for any s' phase claim drops a loop-initiation prefactor and is likely wrong near s=1.","tokens_in":21017,"tokens_out":20477,"would_cite":true,"duration_ms":203247,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper proves that when two fluctuating interfaces obey identical Edwards-Wilkinson or Kardar-Parisi-Zhang dynamics with sticking at contacts, the exact steady-state measure equals the equilibrium Poland-Scheraga measure of DNA…","keywords":["sticking interaction","two fluctuating interfaces","single-step surfaces","exact steady state","Poland-Scheraga model","pairwise balance","ultraslow dynamics","Kardar-Parisi-Zhang universality"],"falsifier":"Simulate the 2OKPZ model with $s=0$ for system sizes $L=64,128,256,512$ and measure the mean lifetime of the largest diamond from the initial configuration; if the lifetime grows as a power of $L$ rather than as $e^{\\lambda L^2}$, the activation picture is wrong. For the exact steady-state claim, sample the full configuration measure at fixed $k$ for a small system such as $L=16$ and test whether $P(C_s^k)/p_0$ equals $s^{L-k}$ for every configuration with $k$ stuck sites, and whether the measured loop weight is $4s$.","tokens_in":19956,"feed_emoji":"🧬","tokens_out":10783,"duration_ms":102304,"temperature":0.7,"pith_summary":"The paper studies a minimal nonequilibrium model in which two single-step surfaces in one dimension fluctuate independently except at sites where they cross, where the update probability is reduced by a detachment factor $s$. Its central result is exact for the subspaces where both surfaces evolve by the same dynamics—both Edwards-Wilkinson ($a=a'=0$) or both Kardar-Parisi-Zhang ($a=a'>0$): the steady-state probability of a configuration with $k$ stuck sites is $P(C_s^k)=p_0 s^{L-k}$, an inhomogeneous product measure that assigns weight 1 to each stuck site and $s$ to each detached site. This measure is shown to be exactly the equilibrium Poland-Scheraga measure of DNA denaturation, with loop weight $g=4s$, loop exponent $c=3/2$, and stuck-segment weight $v=2$, so the two-surface steady state is always entangled in the thermodynamic limit. The same model also produces qualitatively different approach-to-steady-state dynamics depending on the biases: zipper-like diffusive closure in the 2EW case, ballistic faceting in the 2KPZ case, diamond-shaped jammed bubbles with lifetimes $\\sim e^{\\lambda L^2}$ in the 2OKPZ case, and a coexistence of stuck and detached histories in the EWKPZ case. The paper therefore connects a driven two-interface system to an equilibrium statistical-mechanics model and identifies regimes where the steady state is effectively unreachable.","feed_headline":"Sticky interface pairs share the DNA-denaturation steady state","feed_subtitle":"Exact product-form measure links a driven two-interface model to equilibrium Poland–Scheraga DNA melting.","key_machinery":"The carrying object is the mapping of each single-step surface to a sequence of tilts, equivalently particles and holes in an exclusion process, and then to a 'brackets' notation in which only the local hills and valleys of the two-surface configuration are kept; stuck bends are angular brackets and detached bends are round brackets. The proof of the steady state uses pairwise balance of probability fluxes: incoming and outgoing fluxes at every bend are paired so that the master equation splits into terms $A(w_{C''\\to C}P(C'')-w_{C\\to C'}P(C))$, and the product measure $P(C)=p_0\\prod_i p_i$ with $p_i=1$ for a stuck site and $p_i=s$ for a detached site makes each paired flux difference vanish. The identification with the Poland-Scheraga model is carried by the exact configurational counting of bubbles, which gives a generating function whose large-length behavior is $B(l)\\sim 4s^l/l^{3/2}$, with stuck-segment weight $v=2$. For the ultraslow dynamics, the machinery is an Arrhenius activation picture: diamonds have area $\\sim O(L^2)$, and their collapse is treated as crossing a super-extensive energy barrier set by the Hamiltonian $H=\\epsilon\\sum_i|h_{1i}-h_{2i}|$ of an auxiliary non-crossing model that satisfies detailed balance.","core_discovery":"Within the (2EW + 2KPZ) subspace $a=a'\\ge 0$, the paper proves by pairwise balance of probability fluxes that the exact invariant measure is $P(C_s^k)=p_0 s^{L-k}$: all configurations with the same number $k$ of stuck sites are equally likely, and each detached site costs a factor $s$ relative to a stuck site. This measure does not depend on the bias $a$, so the interacting two-surface problem inherits the well-known $a$-invariance of a single single-step surface. Written in terms of alternating bubbles and stuck segments, the measure factorizes into loop weights $B(l)\\sim g^l/l^c$ with $g=4s$ and $c=3/2$ and stuck-segment weights $R(r)\\sim v^r$ with $v=2$, which is precisely the Poland-Scheraga partition function for DNA denaturation in the regime $v>v_c(s)$. Consequently, for any $s$ in $(0,1)$ the thermodynamic-limit steady state of the identical-dynamics subspaces is entangled, with a finite fraction of stuck sites. The paper further argues that outside this subspace the dynamics is controlled by large bubbles inherited from the initial condition: they close diffusively (2EW), ballistically as facets (2KPZ), deform into long-lived diamonds whose lifetimes scale as $e^{\\lambda L^2}$ (2OKPZ, $s=0$), or produce two competing evolutions—near-complete sticking or complete detachment—for an EW surface against a KPZ surface.","pith_inferences":["If the exact measure holds, the 2EW and 2KPZ models provide a dynamical way to generate equilibrium Poland-Scheraga statistics; one could measure critical exponents of DNA denaturation from a driven system rather than from a thermal ensemble.","The pairwise-balance bracket construction is likely to extend to other height-difference interactions, such as asymmetric sticking or short-range repulsion, producing exact measures of the same product form with modified site weights; that would generalize the set of solvable nonequilibrium coupled-interface models.","The claimed $e^{\\lambda L^2}$ diamond lifetime implies pronounced aging and history dependence in the 2OKPZ system; autocorrelation functions should exhibit two-step relaxation, and the steady state should be unattainable even at times far beyond ordinary equilibration.","The unexplained $z\\simeq 1.5$ in the 2EW $s=0$ case might be a universal property of the closure of the largest excursion in a random landscape; testing the closure-time distribution of the largest bubble in a simpler model, such as a single interface against a fixed wall, would show whether this exponent is specific to two-surface sticking or generic."],"forward_implications":["For all $s$ in $(0,1)$, the exact steady state in the 2EW and 2KPZ subspaces has the same form regardless of the KPZ bias $a$; any observable such as the bubble-size distribution or the stuck fraction can be computed from the Poland-Scheraga partition function.","In the thermodynamic limit the identical-dynamics steady state is always entangled for any $s>0$, so there is no detached phase on this locus; the fraction of stuck sites is set by the PS loop weight $g=4s$ and stuck weight $v=2$.","For the 2OKPZ case with irreversible sticking ($s=0$), the largest initial bubbles become diamonds whose closing time grows as $e^{\\lambda L^2}$, making the final stuck state unreachable on any practical timescale for large $L$.","For an EW surface against a KPZ surface at small $s$, the same initial configuration can either end detached after a ballistic time $\\sim L/s$ or end stuck after the EW surface diffuses onto the KPZ facet in time $\\sim L^2$; the two outcomes occur with order-one fractions when $s$ scales as $L^{-0.75}$.","In the 2EW case with $s=0$, the transient width collapse gives a dynamic exponent $z\\simeq 1.5$, different from the single-surface EW value $z\\simeq 2$, and the same exponent controls short-time transients when detachments are allowed."],"supporting_citations":[{"why":"Defines the equilibrium DNA-denaturation model whose measure is the target of the identification.","marker":"[8]"},{"why":"Gives the Poland-Scheraga phase diagram used to locate the entangled regime and the critical stuck weight $v_c$.","marker":"[10]"},{"why":"Supplies the exact loop-weight asymptotics used to identify the loop exponent $c=3/2$.","marker":"[17]"},{"why":"Contains the configurational weights, the brackets representation, and the numerical data supporting the exact measure and exponents.","marker":"[31]"},{"why":"Supplies the brackets notation and flux-pairing scheme that the steady-state proof adapts.","marker":"[72]"},{"why":"Establishes pairwise balance as a sufficient condition for steady states of exclusion-type models, the method used to prove the product measure.","marker":"[80]"},{"why":"Provides the activation arguments used for the diamond collapse timescales in the 2OKPZ case.","marker":"[86]"},{"why":"Gives the largest-term statistics that justify the order-$L$ largest initial bubble whose closure sets the transient timescales.","marker":"[88]"}],"fun_headline_variants":["Sticky surfaces share DNA-denaturation exact measure","Exact solution maps sticky interfaces to DNA melting","Two-interface dynamics yield Poland-Scheraga invariant","Sticky pairs flip into DNA-denaturation steady state","Interface model exactly replicates DNA denaturation"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise for the ultra-slow timescale claim is that the diamond-closing time in the original sticking model is the same as in an auxiliary exclusion model with an area-energy Hamiltonian, so that closing is an Arrhenius activation over an $O(L^2)$ energy barrier; the paper asserts this equivalence heuristically rather than proving it.","fun_headline_variants_meta":{"raw":{"variants":["Sticky surfaces share DNA-denaturation exact measure","Exact solution maps sticky interfaces to DNA melting","Two-interface dynamics yield Poland-Scheraga invariant","Sticky pairs flip into DNA-denaturation steady state","Interface model exactly replicates DNA denaturation"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000282,"raw_usage":{"total_tokens":1691,"prompt_tokens":988,"completion_tokens":703,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":604,"completion_tokens_details":{"reasoning_tokens":632}},"tokens_in":604,"tokens_out":703,"duration_ms":7482,"temperature":1.0,"reasoning_tokens":632,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T17:56:25.392216+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate the 2OKPZ model with $s=0$ for system sizes $L=64,128,256,512$ and measure the mean lifetime of the largest diamond from the initial configuration; if the lifetime grows as a power of $L$ rather than as $e^{\\lambda L^2}$, the activation picture is wrong. For the exact steady-state claim, sample the full configuration measure at fixed $k$ for a small system such as $L=16$ and test whether $P(C_s^k)/p_0$ equals $s^{L-k}$ for every configuration with $k$ stuck sites, and whether the measured loop weight is $4s$.","supporting_citations":[{"cited_title":"Richard and A","cited_arxiv_id":null,"evidence_quote":"Supplies the exact loop-weight asymptotics used to identify the loop exponent $c=3/2$."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Contains the configurational weights, the brackets representation, and the numerical data supporting the exact measure and exponents."},{"cited_title":"Mahapatra, K","cited_arxiv_id":null,"evidence_quote":"Supplies the brackets notation and flux-pairing scheme that the steady-state proof adapts."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes pairwise balance as a sufficient condition for steady states of exclusion-type models, the method used to prove the product measure."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the activation arguments used for the diamond collapse timescales in the 2OKPZ case."},{"cited_title":"Feller, An introduction to probability theory and its applications, Volume 1 , Vol","cited_arxiv_id":null,"evidence_quote":"Gives the largest-term statistics that justify the order-$L$ largest initial bubble whose closure sets the transient timescales."}],"review_version":1}