{"id":"a2b38654-d954-4d63-b073-c824f2c05b0a","arxiv_id":"2605.27275","paper_version":2,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Exact derivations of non-stationary current variance (constant diffusion, arbitrary mobility) and cumulant generating function (Reflective Brownian Motion) via MFT for 1D boundary-driven diffusive systems.","lead":"The paper applies Macroscopic Fluctuation Theory to derive exact expressions for current variance and the cumulant generating function during relaxation in one-dimensional boundary-driven diffusive systems. This extends prior MFT work, which focused mainly on steady states, to time-dependent non-equilibrium processes.","discovery_kind":"unclear","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"Reader correctly flags the MFT extension as the pivotal assumption but notes the limitation of abstract-only review. With the claim restricted to exactly solvable cases and no contradictory elements visible, the assessment requires no adjustment; a concrete numerical check on the derived formulas would still be informative even if no flaw is suspected.","tokens_in":1628,"tokens_out":286,"duration_ms":33887,"concrete_test":"For the constant-D case, substitute a concrete mobility function (e.g., σ(ρ)=ρ(1-ρ) for SSEP) into the derived variance expression and compare the time-dependent result against direct Monte Carlo sampling of the microscopic process on a lattice of size L=100 for times up to the relaxation scale; agreement within sampling error confirms the exactness claim.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that MFT yields exact closed-form results for current variance (constant D, arbitrary mobility) and the CGF for RBM in the relaxation regime. The provided abstract and strongest claim describe a restricted class where this is asserted to hold; no internal inconsistency, unstated approximation, or violated assumption is apparent from the summary. The extension of MFT is the key step, but the paper positions the results as exact derivations rather than approximations, consistent with the specific solvability conditions stated.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper applies Macroscopic Fluctuation Theory (MFT) to the relaxation dynamics of 1D boundary-driven diffusive systems coupled to reservoirs. It claims exact closed-form derivations of the time-dependent current variance for constant diffusion coefficient D and arbitrary mobility, together with the cumulant generating function for the current in Reflective Brownian Motion (RBM). The central result is that non-stationary current fluctuations during relaxation are quantitatively captured by the MFT framework without additional approximations beyond the standard hydrodynamic scaling.","tokens_in":1721,"tokens_out":458,"duration_ms":16792,"significance":"If the derivations hold, the work provides a concrete extension of MFT from steady states to the transient regime for a solvable class of models. The exact variance and CGF expressions constitute falsifiable predictions that can be tested against microscopic simulations or exact solutions in the constant-D limit, strengthening the case for MFT as a tool for non-stationary fluctuations.","major_comments":[{"comment":"§3 (or the section deriving the variance): the reduction of the MFT action to a closed-form variance for arbitrary mobility appears to rely on the specific choice of constant D; it is unclear whether the same steps remain exact when D is position-dependent, which would limit the generality of the claim that the result holds for 'arbitrary mobility'.","section":"§3"},{"comment":"The derivation of the CGF for RBM (likely §4): the boundary conditions and the reflective nature of the process must be shown to map exactly onto the MFT saddle-point equations without residual boundary terms; the manuscript should explicitly verify that the time-dependent optimal density and current profiles satisfy the Euler-Lagrange equations with the reflective constraint.","section":"§4"}],"minor_comments":[{"comment":"The abstract and introduction should clarify the precise hydrodynamic scaling limit under which the MFT equations are applied to the relaxation process.","section":null},{"comment":"Notation for the mobility function and the time-dependent current should be introduced consistently before the first derivation.","section":null}],"recommendation":"minor_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the positive assessment and the detailed comments on our manuscript. We address each major comment below.","responses":[{"response":"We agree with the referee that the closed-form expression for the time-dependent current variance is derived under the assumption of constant diffusion coefficient D. The manuscript explicitly states this restriction (see abstract and §3), and the claim of arbitrary mobility applies only within the constant-D class. We do not claim or derive the same closed-form result for position-dependent D, where the MFT action reduction does not close in the same manner. The scope of the paper is therefore accurately delimited, and no revision is required.","revision_made":"no","referee_comment":"[§3] §3 (or the section deriving the variance): the reduction of the MFT action to a closed-form variance for arbitrary mobility appears to rely on the specific choice of constant D; it is unclear whether the same steps remain exact when D is position-dependent, which would limit the generality of the claim that the result holds for 'arbitrary mobility'."},{"response":"We thank the referee for this suggestion. In the revised version we will add an explicit verification step showing that the time-dependent optimal density and current profiles obtained from the MFT saddle-point equations for Reflective Brownian Motion satisfy the Euler-Lagrange equations together with the reflective boundary conditions, confirming the absence of residual boundary terms.","revision_made":"yes","referee_comment":"[§4] The derivation of the CGF for RBM (likely §4): the boundary conditions and the reflective nature of the process must be shown to map exactly onto the MFT saddle-point equations without residual boundary terms; the manuscript should explicitly verify that the time-dependent optimal density and current profiles satisfy the Euler-Lagrange equations with the reflective constraint."}],"tokens_in":1262,"tokens_out":401,"duration_ms":19696,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main point is that they apply Macroscopic Fluctuation Theory to current fluctuations while the system relaxes to steady state in 1D boundary-driven diffusive setups, and they get closed-form expressions for the variance when diffusion is constant (arbitrary mobility) plus the cumulant generating function for reflective Brownian motion.\n\nWhat is new is the explicit extension of MFT beyond steady states to the time-dependent regime. The abstract frames this as filling a gap where prior MFT work stayed mostly at stationarity, and the derivations are presented as following directly from the MFT equations applied to the relaxation process. That is a clean, incremental advance within the subfield.\n\nThe paper does well by staying inside the solvable window: constant D plus the RBM case lets them avoid approximations and deliver exact results. This keeps the claims grounded rather than vague.\n\nThe soft spot is the reliance on the direct extension of MFT to non-stationary dynamics still producing exact closed forms. The abstract asserts this works for the chosen class, but the strength of that claim depends on whether the intermediate steps in the full text really close without extra assumptions or restrictions that only appear later. Scope is also narrow—strictly 1D diffusive with reservoirs at the ends—so the method may not travel far without more work.\n\nThis is for people already using MFT on driven diffusive systems who want concrete expressions for transient current statistics. It is worth a serious referee because the central claim is a precise, falsifiable extension with exact results rather than hand-waving, even if the audience stays specialized.","headline":"MFT gets pushed to relaxation dynamics here with exact variance and CGF results, but only for constant diffusion and a couple of solvable models.","tokens_in":2208,"tokens_out":390,"would_cite":false,"duration_ms":19807,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Macroscopic Fluctuation Theory yields exact current variance during relaxation in one-dimensional boundary-driven diffusive systems.","keywords":["Macroscopic Fluctuation Theory","current fluctuations","non-stationary processes","diffusive systems","boundary-driven systems","relaxation dynamics","Reflective Brownian Motion"],"falsifier":"Measure or simulate the time-dependent current variance in a one-dimensional diffusive system with constant diffusion during relaxation and compare it to the MFT-derived formula; systematic deviation would show the extension fails.","tokens_in":2528,"feed_emoji":"📈","tokens_out":546,"duration_ms":21649,"temperature":0.7,"pith_summary":"The paper applies Macroscopic Fluctuation Theory to the time-dependent relaxation of one-dimensional diffusive systems driven by particle reservoirs at the boundaries. It obtains an exact expression for the current variance when the diffusion coefficient is constant (with arbitrary mobility) and the cumulant generating function for current in Reflective Brownian Motion. These derivations establish that fluctuations in the non-steady regime, as the system approaches a steady state, fall within the quantitative reach of the MFT framework.","feed_headline":"MFT yields exact current variance in relaxing diffusive systems","feed_subtitle":"Closed-form results for constant diffusion and Reflective Brownian Motion cover fluctuations before steady state.","key_machinery":"Macroscopic Fluctuation Theory extended to time-dependent relaxation, used to compute exact current statistics.","core_discovery":"Applying Macroscopic Fluctuation Theory to the relaxation process produces an exact current variance for constant diffusion coefficient and arbitrary mobility, together with the cumulant generating function for Reflective Brownian Motion, showing that non-steady current fluctuations are quantitatively described by MFT.","pith_inferences":["Time-resolved current measurements in mesoscopic systems could test the formulas before steady state is reached.","The constant-diffusion restriction suggests checking whether similar exact results hold when diffusion varies weakly with density.","The derivations may generalize to other boundary-driven transport models once the mobility-diffusion relation is fixed."],"forward_implications":["Current variance follows a closed-form time dependence throughout the approach to steady state.","The cumulant generating function for current is obtained exactly in Reflective Brownian Motion.","Non-steady fluctuations are captured quantitatively by the same MFT equations used for steady states.","The framework applies to arbitrary mobility when diffusion is constant."],"fun_headline_variants":["MFT derives exact current variance in 1D relaxing diffusion","Exact variance via MFT for relaxing boundary-driven systems","MFT quantifies non-steady current fluctuations in 1D diffusion","Current variance and RBM cumulants from MFT in relaxation"],"cache_read_input_tokens":64,"weakest_assumption_plain":"Macroscopic Fluctuation Theory, developed for steady states, extends directly to the relaxation regime and still produces exact closed-form results for constant diffusion coefficient.","fun_headline_variants_meta":{"raw":{"variants":["MFT derives exact current variance in 1D relaxing diffusion","Exact variance via MFT for relaxing boundary-driven systems","MFT quantifies non-steady current fluctuations in 1D diffusion","Current variance and RBM cumulants from MFT in relaxation"]},"model":"grok-4.3","cost_usd":0.005757,"raw_usage":{"total_tokens":2669,"prompt_tokens":517,"num_sources_used":0,"completion_tokens":69,"cost_in_usd_ticks":57574500,"prompt_tokens_details":{"text_tokens":517,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2083,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":517,"tokens_out":69,"duration_ms":22626,"temperature":1.0,"reasoning_tokens":2083,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-01T15:52:06.311793+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Measure or simulate the time-dependent current variance in a one-dimensional diffusive system with constant diffusion during relaxation and compare it to the MFT-derived formula; systematic deviation would show the extension fails.","supporting_citations":[],"review_version":1}