{"id":"3eb65415-7d85-4a68-95c5-bf17b0b75914","arxiv_id":"2607.14073","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"For Brownian hard-rod single-file diffusion, exact large-deviation functions for tracer position and integrated current follow from a canonical mapping to point particles.","lead":"The paper obtains exact formulas for the rare large fluctuations of the tracer position and the integrated current in a one-dimensional gas of Brownian hard rods, by mapping the interacting rods to non-interacting point particles through a canonical transformation. The closed expressions, verified by rare-event simulations, cover both annealed and quenched initial ensembles and extend to lattice gases with finite-range exclusion.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Canonical transformation is internally sound; the load-bearing gap is the unproven quenched point-particle SCGF χ_Q (2d), quoted from self-cited work rather than derived.","rationale":"The reader identified the exactness of the canonical transformation as the weakest assumption. On careful review, I find that assumption holds: the boundary term vanishes, the noise transformation is consistent, and the free-energy transform is exact. The paper's internal algebra and the mapping of observables to the point-particle system are sound. However, the reader's second concern—that the quenched point-particle SCGF (2d) is not derived in the visible text and rests on self-cited work—is the step I could not independently verify. This is a genuine gap in the paper's self-containedness, though not a demonstrated error. The simulation validation in Fig. 2 is supportive but lacks error bars, so it does not settle the exactness of (2d) to high precision. Because the central derivation is otherwise coherent and the missing step is an unproven but plausible quotation of prior results, I do not think the verdict should change from CONDITIONAL. The proposed concrete test—deriving χ_Q from the supplement's own Cole–Hopf solution—would either retire the concern or expose a concrete error in (2d). Hence UNCHANGED.","tokens_in":19379,"tokens_out":15695,"duration_ms":146855,"concrete_test":"Derive χ_Q(ξ,B) from the point-particle MFT equations (60)–(63) with the local-height boundary conditions (71)/(74): substitute the solution (64)–(68) into the action (57), evaluate the integral over X, and Legendre-transform the resulting SCGF. Verify that the result matches (2d) for ξ=0 (recovering the known quenched integrated-current SCGF) and for several ξ>0 at fixed B. Also perform the analogous derivation of χ_A (2c) as a cross-check.","verdict_should_be":"UNCHANGED","load_bearing_attack":"I scrutinized the exactness of the canonical transformation (Letter (13); Supplement §1.a, §3.a). The boundary term (55) vanishes because J_r → 0 at spatial infinity for any finite-action configuration; the noise redefinition η_ρ = η_r/√(1+ar) preserves the delta-correlation; and the free-energy integrand (58) is the exact Jacobian-scaled transform of (45), with the (1+ar) prefactor canceling the local Jacobian. Thus the mapping of the action, the free energy, and the observables is internally consistent. The real soft spot is the point-particle local-height SCGF χ, in particular the quenched expression χ_Q (2d). This formula appears without derivation in the Letter; the supplement's Cole–Hopf solution (64)–(68) provides the machinery but never evaluates the action integral to produce (2c)–(2d). The reader is correct that the provenance of χ_Q rests on self-cited work [58,84] and on [66]. If χ_Q has a missing prefactor, a sign error in the integration limit, or a subtlety in the quenched boundary conditions, then μ_tp and μ_ic in (2) are wrong for the quenched ensemble, undermining the claim of exact solvability. This is the single most load-bearing unverified step; the rest of the derivation is solid.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper claims to solve the macroscopic fluctuation theory (MFT) of a one-dimensional gas of Brownian hard rods (BHR) exactly, through a canonical transformation that maps the BHR onto point particles. The central results are closed-form expressions for the scaled cumulant-generating functions (SCGFs) of the tracer position and the integrated current, in both annealed and quenched ensembles (Eqs. (2a)-(2d)), together with explicit optimal density trajectories (Eqs. (5a)-(5c)). The construction is based on a free-volume coordinate transformation (13), which the supplement shows maps the BHR action, initial free energy, and observables onto those of the point-particle limit. The paper also extends the method to finite-size lattice exclusion processes (multi-site SEP) and validates the formulas with rare-event simulations.","tokens_in":19638,"tokens_out":19644,"duration_ms":178180,"significance":"If the central formulas are correct, this is a substantial advance: it provides one of the few fully explicit MFT solutions for a continuum single-file model, going beyond the handful of previously solved lattice cases. The derivation of the canonical transformation in the supplement is careful and internally consistent: the action mapping, the free-energy transform, the noise convention, and the observable maps all pass direct check. The agreement with importance-sampling simulations for both ensembles and observables is a genuine strength, and the formulas contain no fitted parameters. The main weakness is that the point-particle SCGF χ — in particular the quenched expression χ_Q — is asserted rather than derived in this paper; the supplement stops short of evaluating the saddle-point action. Because all quenched results in (2) and (5) depend on χ_Q, this is a load-bearing gap that needs to be closed or precisely traced to prior work.","major_comments":[{"comment":"The SCGFs χ_A and χ_Q are the building blocks of the main results, but their derivation is not included. The Cole-Hopf solution (64)-(68) gives the optimal fields r and ˆr, yet the action integral that would produce (2c)-(2d) is never evaluated. This is most consequential for the quenched expression (2d), which is quoted from the literature: all quenched SCGFs (2a)-(2b), the variance relations (E.13), and the optimal profiles (5b) inherit its correctness. Please add a self-contained derivation of (2c)-(2d) in the supplement, or if they are taken from [66], state the precise theorem/equation there and explicitly verify that the renormalized densities and the H(u) convention coincide. Without this, the exact-solvability claim for the quenched ensemble cannot be checked from the manuscript.","section":"Eqs. (2c)-(2d); Supplement §3.a"},{"comment":"The SCGFs are defined through extrema over (ξ,B), but the paper does not address uniqueness or the identification of the physical branch. The later discussion of exponential tails (λ^{3/2}) and the finite support of μ_tp_A indicates non-trivial λ-dependence; a spurious stationary point could change the result. Since the Legendre transform is used to produce the large-deviation functions in Fig. 2, an argument for the convexity of (2a)-(2b) in λ, or at least a statement that the extremum is a maximum, is needed for the claim of a complete explicit computation. The numerical checks cover a limited region and do not rule out multiple stationary points.","section":"Eqs. (2a)-(2b)"}],"minor_comments":[{"comment":"As printed, μ_A and μ_Q are identical: both are written as (1/√t) ln −̅{e^{λ O_t}}. Please fix the typesetting to distinguish the annealed average −̅{⟨e^{λ O_t}⟩} from the quenched average −̅{ln ⟨e^{λ O_t}⟩}, or otherwise clarify the placement of the disorder average.","section":"Eq. (1)"},{"comment":"The notation Ṣ_t[ρ] for the transformed observable is not defined in the Letter; it appears as 'Ṣ_t' in the sentence 'O_t[ρ] ≡ Ṣ_t[r]'. Please define it (e.g., τ̃ O_t) and use it consistently, as in the supplement.","section":"Point-particle mapping"},{"comment":"The caption lists parameters and ensembles but does not clearly identify which curve in panels (c) and (d) is annealed versus quenched. The text mentions upper/lower panels, but the caption should state it explicitly.","section":"Fig. 2 caption"},{"comment":"The claimed coincidence of the annealed integrated-current SCGF with the Hamiltonian hard-rod result [84] is stated without demonstration. A one-sentence indication of how it follows from (2b)-(2c) and the cited work would help the reader assess this connection.","section":"End Matter, SSTEP"}],"recommendation":"major_revision","confidential_remarks":"The central mapping derivation appears sound; the main risk is the unproven quenched point-particle SCGF χ_Q. This is fixable by adding a derivation to the supplement or by a precise, convention-matching citation. I would not reject, but the manuscript should not be accepted until that gap is closed. The self-citation to [58] is acceptable, and [66] is an appropriate source for point-particle results."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nRead this one. It adds the Brownian hard-rod gas to the short list of exactly solvable MFTs, and it does it with a genuinely new construction: the free-volume coordinate plus field transformation (13) that maps the interacting variational problem onto the point-particle MFT. The payoff is real — explicit a-dependent SCGFs for tracer position and integrated current in both ensembles, plus optimal density trajectories, where even for SSEP the optimal profiles were known only at initial and final times. The supplement carries the weight, and the derivation is careful. I checked the reported internal consistency: the a→0 limits reduce to the point-particle forms, the SSTEP mobility maps to SSEP's σ(r)=2r(1−r), and the boundary term in the kinetic part vanishes for finite-action configurations. The noise redefinition and the free-energy transform also work through without leftover corrections. So the central mapping is solid, not hand-waving.\n\nWhat gives me pause is not the mapping but the input to it. The quenched point-particle SCGF χ_Q (2d) is quoted from the authors' own recent work and from [66]; it is not derived in the supplement. The Cole–Hopf machinery in Supplement §3 is set up, but the action integral that would produce (2c)-(2d) is never evaluated. If χ_Q has a missing prefactor or a subtlety in the boundary conditions, both μ^tp and μ^ic in the quenched ensemble are wrong. That is the load-bearing unverified step. The annealed results are on firmer ground because χ_A is standard and the mapping derivation is self-contained.\n\nSecondary issues: the simulation comparisons in Fig. 2 have no error bars and no deposited data, so the \"validation\" is visually convincing but not numerically auditable. The quenched lattice results are restricted to half-filling. Neither touches the core derivation, but they are the kind of thing a referee will ask for.\n\nVerdict: this deserves a serious referee. The paper is not finished as is — the quenched χ_Q needs a derivation or a clear pointer to a derivation in a venue that is not the same group's unpublished preprint — but the central result is important enough and the derivation of the mapping is strong enough that peer review should engage with it, not desk-reject it. If I were the editor, I'd send it out with a request to pin down χ_Q and add error bars. I'd cite this work for the annealed results as soon as the quenched gap is closed.","headline":"The canonical transformation is the real new thing, and it checks out; the quenched SCGF is the one piece I wouldn't sign off without seeing the derivation.","tokens_in":20194,"tokens_out":3198,"would_cite":true,"duration_ms":29106,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["82C22","82C31","60F10"],"pacs":[],"model":"deepseek-v4-flash","headline":"A single canonical transformation turns the Brownian hard-rod gas into non-interacting point particles, making its macroscopic fluctuation theory exactly solvable.","keywords":["Brownian hard rods","single-file diffusion","macroscopic fluctuation theory","canonical transformation","large deviations","tracer position","integrated current","annealed and quenched ensembles"],"falsifier":"Measure the SCGFs for Brownian hard rods via rare-event simulation for a specific case (e.g., $a=1$, $\\bar\\rho_\\mp=0.25$) and compare the empirical large-deviation function with the Legendre transform of (2) over a range of $\\lambda$; a systematic discrepancy in the curvature or in the predicted $\\lambda^{3/2}$ tails would falsify the exactness claim. A second check: simulate both Brownian rods and ballistic hard rods with matched densities and compare the annealed integrated-current SCGF, which the paper predicts to be identical.","tokens_in":19176,"feed_emoji":"⚛️","tokens_out":8820,"duration_ms":80715,"temperature":0.7,"texified_at":"2026-08-05T21:22:33.129114+00:00","pith_summary":"This paper works with Brownian hard rods, the natural continuum model of single-file diffusion, and tries to show that the macroscopic fluctuation theory (MFT) describing their large-scale fluctuations is exactly solvable. The route is a canonical change of variables from rod coordinates to free-volume point-particle coordinates. With that map, the full large-deviation statistics of the tracer position and integrated current can be written down explicitly in both the annealed and quenched initial ensembles. If correct, continuum single-file systems join the very small class of interacting models for which the entire large-deviation function, not just typical fluctuations, is known exactly. The same transformation extends to lattice exclusion models with finite-size particles, linking them to the standard symmetric exclusion process.","texify_model":"deepseek-v4-flash","texify_usage":{"total_tokens":6547,"prompt_tokens":797,"completion_tokens":5750,"prompt_tokens_details":{"cached_tokens":0},"prompt_cache_hit_tokens":0,"prompt_cache_miss_tokens":797,"completion_tokens_details":{"reasoning_tokens":5024}},"feed_headline":"One coordinate swap makes single-file diffusion exactly solvable","feed_subtitle":"A canonical map to point particles yields exact large-deviation laws for tracer position and current in both ensembles.","key_machinery":"The load-bearing object is the canonical transformation (13): free-volume coordinate $X = x - a\\int_{z(s)}^{x} \\rho dx$, renormalized density $r = \\rho/(1-a\\rho)$, and conjugate response field $\\hat{r}$. It maps the BHR action and free energy onto the point-particle MFT exactly. There, the exponential change of variables $Q = r e^{-\\hat{r}}, P = e^{\\hat{r}}$ turns the MFT equations into linear diffusion equations solved by Gaussian convolution. Observables transform non-trivially: tracer position keeps its functional form in $r$, while integrated current becomes a local-height observable constrained at $Z = a Q_t[r]$ — the source of the extra $a$-terms in (2b).","core_discovery":"Central claim: the MFT of the Brownian hard-rod gas is exactly solvable through the coordinate-field transformation (13a)-(13c). Under this free-volume map the dynamical action and initial free energy become exactly those of zero-length Brownian particles, rod length absorbed into renormalized densities $\\bar r_\\mp = \\bar\\rho_\\mp/(1-a\\bar\\rho_\\mp)$. A further exponential change of variables linearizes the point-particle MFT. The SCGFs (2a)-(2d) then give exact large-deviation statistics of tracer position and integrated current in both ensembles, and (5) gives the optimal density trajectory for a prescribed fluctuation. The tracer and current SCGFs differ in rod-length dependence: only the cur","pith_inferences":["The same transformation may yield explicit multi-time and conditional statistics in the Brownian setting, since the map effectively linearizes the MFT equations; the paper points toward but does not prove this.","Because optimal trajectories are now given at every intermediate time, they become measurable in colloidal-rod experiments: record the density profile of a channel conditioned on a large tracer displacement and compare with (5).","For multi-site exclusion in the quenched ensemble, the paper's explicit results stop at the uniform half-filled case; closing that gap likely requires a quenched local-height SCGF for the symmetric simple exclusion process at arbitrary density.","The predicted equality of annealed integrated-current statistics between Brownian and ballistic rods suggests that the MFT may exhibit universality across different microscopic dynamics for other observables as well; this is a testable conjecture rather than a proven result."],"forward_implications":["The full large-deviation functions for tracer position and integrated current become available for arbitrary step density profiles, not just typical Gaussian fluctuations.","The annealed integrated-current SCGF is predicted to coincide exactly with that of ballistic hard rods, extending a recently observed universality between Brownian and ballistic single-file dynamics.","The annealed tracer SCGF has finite support, while the current SCGFs and the quenched tracer SCGF display λ^{3/2} tails, giving quantitatively distinct far-tail statistics.","The same canonical transformation solves the annealed tracer and current statistics for multi-site exclusion processes by reducing them to the symmetric simple exclusion process, including a previously open integrated-current result.","Optimal density trajectories are explicit at all intermediate times, not only at initial and final times, so the route by which the system produces a rare fluctuation can be visualized and quantitatively described."],"fun_headline_variants":["One coordinate map cracks single-file diffusion","Free-volume swap yields exact tracer and current stats","Canonical transform unlocks hard-rod large deviations","A single change of variables solves single-file gas"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"Everything rests on the canonical transformation (13) being exact at the path-integral level: the spatial boundary term of the kinetic part must vanish at infinity, the noise must transform with no extra stochastic-correction term from the coordinate-dependent rescaling, and the free-energy integrand must reduce to $(r-w)/w$ without residue; if any of these steps acquire corrections, formulas (2) are approximate rather than exact.","fun_headline_variants_meta":{"raw":{"variants":["One coordinate map cracks single-file diffusion","Free-volume swap yields exact tracer and current stats","Canonical transform unlocks hard-rod large deviations","A single change of variables solves single-file gas"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000134,"raw_usage":{"total_tokens":962,"prompt_tokens":716,"completion_tokens":246,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":460,"completion_tokens_details":{"reasoning_tokens":200}},"tokens_in":460,"tokens_out":246,"duration_ms":3673,"temperature":1.0,"reasoning_tokens":200,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-02T02:51:51.128537+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the SCGFs for Brownian hard rods via rare-event simulation for a specific case (e.g., $a=1$, $\\bar\\rho_\\mp=0.25$) and compare the empirical large-deviation function with the Legendre transform of (2) over a range of $\\lambda$; a systematic discrepancy in the curvature or in the predicted $\\lambda^{3/2}$ tails would falsify the exactness claim. A second check: simulate both Brownian rods and ballistic hard rods with matched densities and compare the annealed integrated-current SCGF, which the paper predicts to be identical.","supporting_citations":[],"review_version":1}