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

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.

arXiv comment21 pages, 11 figures

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• Sample-to-sample fluctuations of transport coefficients in the totally asymmetric simple exclusion process with quenched disorder
• Role of interactions in a closed quenched system
• Nonequilibrium steady states in coupled asymmetric and symmetric exclusion processes
• Non-self-averaging of current in a totally asymmetric simple exclusion process with quenched disorder
• Totally asymmetric simple exclusion process with local resetting and open boundary conditions
• Unexpected Effects of Disorder on Current Fluctuations in the Symmetric Simple Exclusion Process
• Symmetry Breaking of Current Response in Disordered Exclusion Processes