# Symmetric Exclusion Process under Stochastic Resetting

## TL;DR

This paper investigates how stochastic resetting influences the symmetric exclusion process, revealing non-trivial stationary states, altered current growth, and distinct fluctuation behaviors, with exact analytical results for density profiles and current distributions.

## Contribution

It provides the first exact analysis of SEP under stochastic resetting, showing inhomogeneous stationary states and detailed current distribution characterizations.

## Key findings

- Stationary state becomes inhomogeneous due to resetting.
- Average diffusive current grows linearly with time for r>0.
- Total current distribution exhibits non-Gaussian behavior.

## Abstract

We study the behaviour of a Symmetric Exclusion Process (SEP) in presence of stochastic resetting where the configuration of the system is reset to a step-like profile with a fixed rate $r.$ We show that the presence of resetting affects both the stationary and dynamical properties of SEP strongly. We compute the exact time-dependent density profile and show that the stationary state is characterized by a non-trivial inhomogeneous profile in contrast to the flat one for $r=0.$ We also show that for $r>0$ the average diffusive current grows linearly with time $t,$ in stark contrast to the $\sqrt{t}$ growth for $r=0.$ In addition to the underlying diffusive current, we identify the resetting current in the system which emerges due to the sudden relocation of the particles to the step-like configuration and is strongly correlated to the diffusive current. We show that the average resetting current is negative, but its magnitude also grows linearly with time $t.$ We also compute the probability distributions of the diffusive current, resetting current and the total current (sum of the diffusive and the resetting currents) using the renewal approach. We demonstrate that while the typical fluctuations of both the diffusive and reset currents around the mean are typically Gaussian, the distribution of the total current shows a strong non-Gaussian behaviour.