Simple Exclusion Processes with Local Resetting

Abstract

We investigate the stationary state of Symmetric and Totally Asymmetric Simple Exclusion Processes with local resetting, on a one-dimensional lattice with periodic boundary conditions, using mean-field approximations, which appear to be exact in the thermodynamic limit, and kinetic Monte Carlo simulations. In both cases we find that in the thermodynamic limit the models exhibit three different regimes, depending on how the resetting rate scales with the system size. The Totally Asymmetric version of the model has a particularly rich behaviour, especially in an intermediate resetting regime where the resetting rate vanishes as the inverse of the system size, exhibiting 4 different phases, including phase separation.

Aggregation with constant kernel under stochastic resetting

“…We have solved the master equation instead of relying on renewal equations. This approach is natural in many-body systems whose constituents are reset independently, and has already been used for local resetting in [17,18]. The steady state of the model is independent of the initial conditions and contains aggregates of all sizes, whose average density is a decreasing function of the size of the aggregate.…”

“…Moreover, stochastic resetting induces non-equilibrium steady states: the steady state of the diffusive random walker with resetting to the origin has been shown to be an exponentially decaying function of the distance to the origin [1]. These rich features of stochastic resetting have found numerous applications to active matter [6,7], predator-prey dynamics [8,9], population dynamics [10][11][12], as well as stochastic processes [13][14][15][16][17][18] (see [19] for a recent review, and references therein).…”