Large Deviations in Single File Diffusion

TL;DR

This paper uses macroscopic fluctuation theory to analyze large deviations in the position of a tracer particle within a one-dimensional single-file diffusion system, deriving key statistical functions for both simple and complex interactions.

Contribution

It provides a unified framework to compute the cumulant generating function and large deviation function for tracer positions, extending to arbitrary interactions and initial conditions.

Findings

Derived the cumulant generating function for Brownian particles.

Expressed tracer variance in terms of diffusion coefficient and mobility.

Applicable to both annealed and quenched initial configurations.

Abstract

We apply macroscopic fluctuation theory to study the diffusion of a tracer in a one-dimensional interacting particle system with excluded mutual passage, known as single-file diffusion. In the case of Brownian point particles with hard-core repulsion, we derive the cumulant generating function of the tracer position and its large deviation function. In the general case of arbitrary inter-particle interactions, we express the variance of the tracer position in terms of the collective transport properties, viz. the diffusion coefficient and the mobility. Our analysis applies both for fluctuating (annealed) and fixed (quenched) initial configurations.