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arxiv: 2604.24741 · v1 · submitted 2026-04-27 · ❄️ cond-mat.stat-mech · cond-mat.soft· math-ph· math.MP· nlin.SI

Universal tracer statistics in single-file transport

Soumyabrata Saha , Jitendra Kethepalli , Benjamin Guiselin , Jacopo De Nardis , Tridib Sadhu This is my paper

Pith reviewed 2026-05-07 17:39 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech cond-mat.softmath-phmath.MPnlin.SI
keywords single-file transporthard-rod gastracer statisticsnon-Gaussian fluctuationsuniversalitylarge deviationsannealed ensemblequenched ensemble
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The pith

Multiple tracers in a hard-rod gas show identical non-Gaussian position fluctuations under both diffusive and ballistic dynamics, up to scaling.

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

This paper shows that one-dimensional hard-rod systems produce the same one-time joint statistics for the positions of several tracer particles whether the rods move according to stochastic diffusive rules or unitary ballistic rules. A sympathetic reader would care because the result indicates that initial conditions leave a permanent imprint on these statistics even as the microscopic driving mechanism changes, while differences surface only in time-dependent correlations. The claim rests on exact solutions for both dynamics, fluctuating hydrodynamics in one case, and rare-event simulations that sample the atypical fluctuations directly. If correct, it means that single-file transport models can be unified for one-time observables across physical realizations that differ at the particle level.

Core claim

We uncover an emergent universality in the large-scale, long-time statistics of a one-dimensional hard-rod gas evolving under two fundamentally different classes of microscopic dynamics: stochastic (diffusive) and unitary (ballistic). Remarkably, despite the difference of the two systems, the one-time joint distribution of the positions of multiple tracers exhibits identical non-Gaussian fluctuations, up to a simple dynamical scaling. This universality holds in both annealed and quenched ensembles, demonstrating a persistent memory of the initial state. Differences between the dynamics manifest at large scales only in multi-time statistics. Our conclusions are based on explicit large-deviati

What carries the argument

Large-deviation functions for the one-time joint distribution of tracer-pair positions, obtained from exact microscopic solutions in both dynamics and from fluctuating hydrodynamics in the ballistic annealed case.

If this is right

  • Universality holds for both annealed and quenched initial conditions.
  • Initial-state memory persists in the one-time joint distributions.
  • Multi-time statistics of a single tracer differ between the two dynamics.
  • Current fluctuations display analogous universality in the quenched ensemble.
  • Rare-event sampling works for atypical fluctuations in both types of hard-rod gas.

Where Pith is reading between the lines

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

  • Effective hydrodynamic theories may capture one-time observables across a wider set of single-file models once scaled appropriately.
  • Experiments with colloidal particles in narrow channels could directly compare diffusive and driven cases to test the predicted matching distributions.
  • The separation between one-time universality and multi-time distinctions may apply to other conserved quantities such as energy or momentum currents.
  • Initial-condition control could become a design principle for steady-state fluctuation engineering in transport systems.

Load-bearing premise

The large-scale, long-time limit of the hard-rod gas under the two classes of dynamics produces matching statistics without further dependence on microscopic details or initial conditions beyond the dynamical scaling.

What would settle it

A simulation or measurement that finds different non-Gaussian tails or different scaled variances in the one-time joint position distribution of two tracers between the diffusive and ballistic hard-rod models at sufficiently late times would disprove the universality.

Figures

Figures reproduced from arXiv: 2604.24741 by Benjamin Guiselin, Jacopo De Nardis, Jitendra Kethepalli, Soumyabrata Saha, Tridib Sadhu.

Figure 1
Figure 1. Figure 1: Schematic trajectories of the (a) diffusive and (b) view at source ↗
Figure 2
Figure 2. Figure 2: Results for both gases in the quenched ensemble with view at source ↗
read the original abstract

We uncover an emergent universality in the large-scale, long-time statistics of a one-dimensional hard-rod gas evolving under two fundamentally different classes of microscopic dynamics: stochastic (diffusive) and unitary (ballistic). Remarkably, despite the difference of the two systems, the one-time joint distribution of the positions of multiple tracers exhibits identical non-Gaussian fluctuations, up to a simple dynamical scaling. This universality holds in both annealed and quenched ensembles, demonstrating a persistent memory of the initial state. Differences between the dynamics manifest at large scales only in multi-time statistics. Our conclusions are based on explicit large-deviation results for the one-time statistics of tracer pairs and the two-time statistics of a single tracer. Similar physics extends to current fluctuations, demonstrated explicitly in the quenched ensemble. We obtain these results from exact microscopic solutions for both dynamics and, independently, from fluctuating hydrodynamics in the ballistic case in the annealed ensemble. Our rare-event simulations further corroborate these findings and provide a novel demonstration of sampling atypical fluctuations in both types of hard-rod gas.

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 / 3 minor

Summary. The paper claims an emergent universality in the one-time joint position statistics of multiple tracers in a 1D hard-rod gas. Despite the systems evolving under fundamentally different microscopic dynamics (stochastic diffusive vs. unitary ballistic), the non-Gaussian fluctuations are identical up to a simple dynamical scaling. This holds for both annealed and quenched ensembles, indicating persistent memory of the initial state. The result is obtained from exact microscopic solutions for both dynamics, an independent fluctuating-hydrodynamics derivation in the ballistic annealed case, and rare-event simulations; differences between the dynamics appear only in multi-time statistics. Similar universality is shown for current fluctuations in the quenched ensemble.

Significance. If the results hold, the work establishes a striking universality in single-file transport that is independent of the microscopic dynamics class, supported by multiple independent routes (exact solutions, hydrodynamics, and simulations). The exact large-deviation functions for tracer pairs and the demonstration that initial-state memory persists in one-time but not multi-time observables are notable contributions to non-equilibrium statistical mechanics. The extension to current fluctuations and the novel sampling of atypical events in both dynamics add further value.

minor comments (3)
  1. In the fluctuating-hydrodynamics section, the mapping to the large-deviation function for the annealed ballistic case should explicitly state the hydrodynamic scaling variable used and confirm it matches the microscopic rescaling factor derived for the stochastic case.
  2. The rare-event simulation section would benefit from a brief description of the bias or importance-sampling protocol employed and a quantitative comparison (e.g., overlap of the sampled tails) with the analytic large-deviation curves.
  3. Notation for the dynamical scaling factor and the large-deviation rate functions should be unified across the exact-solution and hydrodynamic derivations to avoid any ambiguity in the universality statement.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive and detailed assessment of our manuscript, including the recognition of the emergent universality in one-time tracer statistics across diffusive and ballistic dynamics, the supporting evidence from multiple methods, and the recommendation for minor revision. We appreciate the constructive feedback and will incorporate all suggested changes in the revised version.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained via independent methods

full rationale

The paper obtains its universality results for one-time tracer joint distributions from explicit large-deviation functions computed via exact microscopic solutions for both stochastic and unitary hard-rod dynamics, plus a separate fluctuating-hydrodynamics derivation in the ballistic annealed ensemble. These routes are stated to converge after a single dynamical rescaling, with simulations providing independent corroboration and multi-time statistics showing differences. No equation or claim reduces a derived quantity to a fitted parameter from the same data, a self-citation chain, or a definition that presupposes the target result; the central large-scale statistics are derived directly from the microscopic models under stated assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Based solely on the abstract; no explicit free parameters or invented entities are mentioned. The listed axioms are standard domain assumptions for the single-file model.

axioms (2)
  • domain assumption Particles in one dimension cannot pass each other
    Defines the single-file constraint for the hard-rod gas.
  • domain assumption Dynamics belong to either stochastic diffusive or unitary ballistic classes
    The two fundamentally different microscopic rules being compared.

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