Universal tracer statistics in single-file transport

TL;DR

This paper reveals a universal statistical behavior in the large-scale, long-time dynamics of one-dimensional hard-rod gases under both diffusive and ballistic microscopic rules, showing identical tracer fluctuation distributions.

Contribution

It demonstrates an emergent universality in tracer statistics across different microscopic dynamics using exact solutions and large-deviation analysis.

Findings

Tracer position distributions are identical up to a simple scaling in both dynamics.

Large-scale differences only appear in multi-time statistics.

Simulation results support the theoretical universality.

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.