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

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.