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Role of interactions in a closed quenched system

We study the non-equilibrium steady states in a closed system consisting of interacting particles obeying exclusion principle with quenched hopping rate. Cluster mean field approach is utilized to theoretically analyze the system dynamics in terms of phase diagram, density profiles, current, etc. with respect to interaction energy $E$. It turns out that on increasing the interaction energy beyond a critical value, $E_c$, shock region shows non-monotonic behavior and contracts until another critical value $E_{c_1}$ is attained; a further increase leads to its expansion. Moreover, the phase diagram of an interacting system with specific set of parameters has a good agreement with its non-interacting analogue. For interaction energy below $E_c$, a new shock phase displaying features different from non-interacting version is observed leading to two distinct shock phases. We have also performed Monte Carlo simulations extensively to validate our theoretical findings.