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Non-stationary current fluctuations in 1D boundary-driven diffusive systems via Macroscopic Fluctuation Theory

T0 review · 2 major / 2 minor · reviewed 2026-07-01 · grok-4.3

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Pith's one-line read Macroscopic Fluctuation Theory yields exact current variance during relaxation in one-dimensional boundary-driven diffusive systems.

desk verdict MFT gets pushed to relaxation dynamics here with exact variance and CGF results, but only for constant diffusion and a couple of solvable models. read the letter →

arxiv 2605.27275 v2 pith:FTHQTHWH submitted 2026-05-26 cond-mat.stat-mech

Daisuke Suzuki , Tomohiro Sasamoto This is my paper · ORCID
classification cond-mat.stat-mech
keywords MacroscopicFluctuationTheorycurrentfluctuationsnon-stationaryprocessesdiffusivesystemsboundary-drivenrelaxationdynamicsReflectiveBrownianMotion
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

Macroscopic Fluctuation Theory extended to time-dependent relaxation, used to compute exact current statistics.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

Macroscopic Fluctuation Theory, developed for steady states, extends directly to the relaxation regime and still produces exact closed-form results for constant diffusion coefficient.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 2 minor

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.

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 (2)
  1. [§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'.
  2. [§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.
minor comments (2)
  1. The abstract and introduction should clarify the precise hydrodynamic scaling limit under which the MFT equations are applied to the relaxation process.
  2. Notation for the mobility function and the time-dependent current should be introduced consistently before the first derivation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment and the detailed comments on our manuscript. We address each major comment below.

read point-by-point responses

  1. Referee: [§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'.

    Authors: 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: no

  2. Referee: [§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.

    Authors: 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: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity in derivation chain

full rationale

The paper applies MFT to derive exact closed-form expressions for current variance (constant D, arbitrary mobility) and CGF for RBM in the relaxation regime. No load-bearing steps reduce by construction to inputs, fitted parameters renamed as predictions, or self-citation chains that substitute for independent derivation. The results are positioned as following directly from the MFT framework under the stated solvability conditions for this restricted class of systems, with no evidence of self-definitional equivalence or smuggling of ansatzes via prior work.

Assumptions & free parameters 0 free parameters · 0 assumptions · 0 invented entities

Abstract-only access prevents identification of specific free parameters, axioms, or invented entities; no details on fitting, background assumptions, or new postulated quantities are provided.

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Pith. "Pith review of Non-stationary current fluctuations in 1D boundary-driven diffusive systems via Macroscopic Fluctuation Theory." pith.science (2026). https://pith.science/paper/FTHQTHWH

@misc{pith2026260527275,
  author       = {Pith},
  title        = {Pith review of: Non-stationary current fluctuations in 1D boundary-driven diffusive systems via Macroscopic Fluctuation Theory},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FTHQTHWH}},
  note         = {Machine review of arXiv:2605.27275}
}
read the original abstract

While Macroscopic Fluctuation Theory (MFT) has been highly successful in analyzing non-equilibrium steady states, its application to non-steady-state processes remains limited. In this study, we apply MFT to the relaxation process of one-dimensional boundary-driven diffusive systems coupled to particle reservoirs at both ends. We exactly derive the current variance for systems with a constant diffusion coefficient and arbitrary mobility, as well as the cumulant generating function for the current in Reflective Brownian Motion (RBM). Our results demonstrate that non-steady current fluctuations during the approach to a steady state can be quantitatively described within the MFT framework.

Figures

Figures reproduced from arXiv: 2605.27275 by the authors.

Figure 1
Figure 1. An example of the time evo￾lution of the expected integrated cur￾rent ⟨QT ⟩ in boundary-driven RBM. QT crosses over from O( √ T) growth to linear O(T) growth in time. Macroscopic Fluctuation Theory (MFT), recently proposed by Bertini et al., has emerged as a pow￾erful theoretical framework for analyzing large deviations of density and current fields in these diffusive systems [14, 15]. MFT describes fluctuations in … view at source ↗
Figure 2
Figure 2. (a)Calculated results for the integrated current variance [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. An example of RBM trajectories The boundary behavior is defined analogously to the stochastic lattice gases introduced in Section 2. The system is connected to two particle reservoirs: a reservoir L with density ρL at the left boundary (x = 0) and a reservoir R with density ρR at the right boundary (x = L). At the left reservoir, particles are injected at rate a and extracted at rate c. Similarly, at the right reser… view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Integrated current with param￾eters L = 5, ρL = 0.8, ρR = 0.2, ρ¯ = 0.5, A = B = 10 The integrated current initially scales as O(T) before crossing over to O( √ T) at T ∼ ρ 2 L A2 . It even￾tually returns to O(T) scaling at T ∼ L 2 at the diffusive time scale. The marg…
Figure 5
Figure 5. Figure 5: Large deviation function I(q) for the annealed initial condition, obtained via the Legendre transformation of the SCGF in (4.17). The plots illustrate the dependence on the boundary cou￾pling strengths (A, B), comparing the case (1, 1), (10, 10) and (100, 100). Other p…
Figure 6
Figure 6. Figure 6: The plots compare the LDFs under an￾nealed and quenched initial conditions across three distinct scaling regimes: (a)the initial O(T) regime at t = 0.008, (b)the intermediate diffusive O( √ T) regime at t = 1, (c)O(T) steady-state regime at t = 15. Under the parameters…
Figure 7
Figure 7. Figure 7: Calculated results for the large deviation function from Legendre trans￾formation of (4.17) with parameters L = 5, ρL = 2.0, ρR = 0.5, ρ¯ = 1.25. (at t = 0.008, 1, 15) Consistency with previous research In this section, we verify whether the current SCGF for the finite…

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Nonisospectral Integrability and Exact Current Fluctuations in the Two-Dimensional SSEP

    cond-mat.stat-mech 2026-08 conditional novelty 8.0 of 10

    The scaled cumulant generating function for annealed current fluctuations across a disk in the two-dimensional SSEP is obtained in closed form via a nonisospectral integrable reduction.

  2. An integrable approach to macroscopic fluctuation theory for the multispecies SSEP

    cond-mat.stat-mech 2026-06 conditional novelty 7.0 of 10

    Multispecies MFT saddle-point equations for SSEP are integrable and solved via inverse scattering to recover the current fluctuation cumulant generating function for arbitrary species number.

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