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arxiv: 2405.00654 · v3 · submitted 2024-05-01 · ❄️ cond-mat.stat-mech · math-ph· math.MP

Large deviations of current for the symmetric simple exclusion process on a semi-infinite line, and on an infinite line with a slow bond

Kapil Sharma , Soumyabrata Saha , Sandeep Jangid , Tridib Sadhu This is my paper

Pith reviewed 2026-05-24 01:49 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech math-phmath.MP
keywords symmetric simple exclusion processlarge deviationsmacroscopic fluctuation theorysemi-infinite linecurrent statisticscloning algorithmdefect bond
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The pith

The exact large deviation function for the current in the symmetric simple exclusion process on a semi-infinite line is obtained using macroscopic fluctuation theory.

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

The paper derives the large deviation function for current fluctuations in the symmetric simple exclusion process on a semi-infinite line attached to a single reservoir. This geometry sits between the previously solved cases of finite lines with two reservoirs and infinite lines. The derivation uses the fluctuating hydrodynamics method from macroscopic fluctuation theory and is verified with cloning algorithm simulations for rare events. The result is applied to compute current statistics in systems with a defect bond, localized injection, and to find the survival probability of a tagged particle near an absorbing boundary.

Core claim

The large deviation function for the integrated current in the symmetric simple exclusion process on a semi-infinite line coupled with a single reservoir is obtained exactly from the variational problem in macroscopic fluctuation theory.

What carries the argument

fluctuating hydrodynamics approach of macroscopic fluctuation theory, which computes the exact rate function for current large deviations.

If this is right

  • The full counting statistics is solved in the presence of a defect bond.
  • Current statistics are obtained for the exclusion process with localized injection.
  • The survival of a tagged particle is determined in the presence of an absorbing boundary.
  • The stretched exponential decay is characterized in a kinetically constrained model.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same hydrodynamic derivation likely extends to the infinite line with a slow bond referenced in the title.
  • The approach may apply to other boundary-driven diffusive systems where macroscopic fluctuation theory holds.
  • Tagged particle survival results could connect to absorption problems in related kinetically constrained models.

Load-bearing premise

The fluctuating hydrodynamics approach of macroscopic fluctuation theory applies directly to give the exact large deviation function for the semi-infinite line with a single reservoir.

What would settle it

A cloning algorithm simulation computing the probability of atypical currents in the semi-infinite symmetric simple exclusion process that deviates from the predicted large deviation function would falsify the result.

Figures

Figures reproduced from arXiv: 2405.00654 by Kapil Sharma, Sandeep Jangid, Soumyabrata Saha, Tridib Sadhu.

Figure 1
Figure 1. Figure 1: FIG. 1. SSEP on a semi-infinite lattice coupled with a reser [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Dynamics of spins [ [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1. The solid red line represents the theoretical value of the [PITH_FULL_IMAGE:figures/full_fig_p012_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Scgf for semi-infinite SSEP with fast boundary coupli [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The large deviation function indicated in solid red line [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
read the original abstract

Two influential exact results in classical one-dimensional diffusive transport are about current statistics for the symmetric simple exclusion process: one in the stationary state on a finite line coupled with two unequal reservoirs at the boundaries, and the other in the non-stationary state on an infinite line. We present the corresponding result for the intermediate geometry of a semi-infinite line coupled with a single reservoir. This result is obtained using the fluctuating hydrodynamics approach of macroscopic fluctuation theory and confirmed by rare event simulations using a cloning algorithm. We apply our exact result for solving several related challenging problems, namely, the full counting statistics in presence of a defect bond, exclusion process with localized injection, survival of a tagged particle in presence of an absorbing boundary, and the stretched exponential decay in a kinetically constrained model.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The paper derives the exact large-deviation function for the integrated current in the symmetric simple exclusion process (SSEP) on a semi-infinite line coupled to a single reservoir, using the fluctuating hydrodynamics of macroscopic fluctuation theory (MFT). It extends the result to an infinite line with a slow bond, confirms both via cloning-algorithm rare-event simulations, and applies the semi-infinite result to full counting statistics with a defect bond, exclusion with localized injection, tagged-particle survival with an absorbing boundary, and stretched-exponential decay in a kinetically constrained model.

Significance. If the central MFT derivation holds, the work supplies the missing intermediate geometry between the known stationary finite-line and non-stationary infinite-line cases, yielding parameter-free exact large-deviation functions that are directly usable for several open problems in one-dimensional diffusive transport. The combination of an established hydrodynamic framework with independent numerical confirmation, together with the explicit applications, adds concrete value to the literature on non-equilibrium current statistics.

minor comments (2)
  1. The abstract and introduction would benefit from a brief statement of the precise boundary conditions imposed on the density and current fields at the reservoir and at infinity, to make the MFT variational problem fully self-contained for readers.
  2. Figure captions for the cloning-simulation comparisons should include the number of clones, the observation time window, and a quantitative measure of statistical uncertainty on the sampled rate function.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their careful reading and positive evaluation of the manuscript. We are grateful for the recommendation to accept and for recognizing the result as filling the intermediate geometry between the stationary finite-line and non-stationary infinite-line cases, together with the numerical confirmation and applications.

Circularity Check

0 steps flagged

No significant circularity; derivation relies on established external MFT framework

full rationale

The paper obtains its large-deviation result for the semi-infinite SSEP via the fluctuating hydrodynamics of macroscopic fluctuation theory, an independent, pre-existing framework whose validity for SSEP is established outside this work. The cloning-algorithm simulations serve as numerical confirmation rather than input to the derivation. No self-definitional steps, fitted parameters renamed as predictions, or load-bearing self-citations appear in the abstract or described chain. The central claim is therefore self-contained against external benchmarks and does not reduce to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based on abstract only; the central result rests on applicability of macroscopic fluctuation theory to the new geometry with no free parameters or invented entities mentioned.

axioms (1)
  • domain assumption Macroscopic fluctuation theory yields the exact large deviation function for current in the semi-infinite SSEP geometry
    The result is obtained using the fluctuating hydrodynamics approach of this theory.

pith-pipeline@v0.9.0 · 5686 in / 1114 out tokens · 22620 ms · 2026-05-24T01:49:58.659748+00:00 · methodology

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Forward citations

Cited by 2 Pith papers

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  2. Macroscopic fluctuation theory of interacting Brownian particles

    cond-mat.stat-mech 2025-12 unverdicted novelty 7.0

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Reference graph

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