The Lasting Effect of Initial Conditions on Single File Diffusion

TL;DR

This paper investigates how initial conditions affect the long-term dynamics of a single-file diffusion system, revealing that initial states influence transport properties and violate classical relations like Einstein's, with lasting effects.

Contribution

It demonstrates that initial conditions have a lasting impact on single-file diffusion dynamics, affecting mean-square-displacement, correlation functions, and transport coefficients, contrasting with typical thermal systems.

Findings

Initial conditions significantly influence long-term particle dynamics.

The Einstein relation is violated depending on initial conditions.

Transport coefficients depend on the initial state and do not equilibrate.

Abstract

We study the dynamics of a tagged particle in an environment of point Brownian particles with hard-core interactions in an infinite one dimensional channel (a single-file model). In particular we examine the influence of initial conditions on the dynamic of the tagged particle. We compare two initial conditions: equal distances between particles and uniform density distribution. The effect is shown by the differences of mean-square-displacement and correlation function for the two ensembles of initial conditions. We discuss the violation of Einstein relation, and its dependence on the initial condition, and the difference between time and ensemble averaging. More specifically, using the Jepsen line, we will discuss how transport coefficients, like diffusivity, depend on the initial state. Our work shows that initial conditions determine the long time limit of the dynamic, and in this sense the system never forgets its initial state in complete contrast with thermal systems (i.e a closed system which attains equilibrium independent of the initial state).