Smooth or shock: universality in closed inhomogeneous driven single file motions

TL;DR

This paper classifies steady states in driven single file particle systems into two universal types based on current-density dependence, revealing topology and phase diagram features independent of system specifics.

Contribution

It introduces a universal classification of nonequilibrium steady states in driven single file motions based on current dependence on density, applicable to various systems.

Findings

Two classes of steady states identified, depending on current-density relation.

Universal phase diagrams and fundamental diagrams determined by control parameters.

Theory applicable to laboratory experiments with driven particles in closed systems.

Abstract

We study the nonequilibrum steady states in a unidirectional {or driven} single file motion (DSFM) of a collection of particles with hard-core repulsion in a closed system. For driven propulsion that is {spatially} smoothly varying with a few discontinuities, we show that the steady states are broadly classified into two classes, independent of any system detail: (i) when the steady state current depends explicitly on the {conserved} number density $n$, and (ii) when it is independent of $n$. This manifests itself in the universal topology of the phase diagrams {and fundamental diagrams (i.e., the current versus density curves) } for DSFM, which are determined solely by the interplay between {two control parameters} $n$ and the minimum propulsion speed along the chain. Our theory can be tested in laboratory experiments on driven particles in a closed geometry.