Symmetric exclusion process under stochastic power-law resetting

Abstract

We study the behaviour of a symmetric exclusion process in the presence of non-Markovian stochastic resetting, where the configuration of the system is reset to a step-like profile at power-law waiting times with an exponent α. We find that the power-law resetting leads to a rich behaviour for the currents, as well as density profile. We show that, for any finite system, for α < 1, the density profile eventually becomes uniform while for α > 1, an eventual non-trivial stationary profile is reached. We also find that, in the limit of thermodynamic system size, at late times, the average diffusive current grows ∼ t θ with θ = 1 / 2 for α ⩽ 1 / 2 , θ = α for 1 / 2 < α ⩽ 1 and θ = 1 for α > 1. We also analytically characterize the distribution of the diffusive current in the short-time regime using a trajectory-based perturbative approach. Using numerical simulations, we show that in the long-time regime, the diffusive current distribution follows a scaling form with an α − dependent scaling function. We also characterise the behaviour of the total current using renewal approach. We find that the average total current also grows algebraically ∼ t ϕ where ϕ = 1 / 2 for α ⩽ 1 , ϕ = 3 / 2 − α for 1 < α ⩽ 3 / 2 , while for α > 3 / 2 the average total current reaches a stationary value, which we compute exactly. The standard deviation of the total current also shows an algebraic growth with an exponent Δ = 1 2 for α ⩽ 1 , and Δ = 1 − α 2 for 1 < α ⩽ 2 , whereas it approaches a constant value for α > 2. The total current distribution remains non-stationary for α < 1, while, for α > 1, it reaches a non-trivial and strongly non-Gaussian stationary distribution, which we also compute using the renewal approach.

Stationary state of harmonic chains driven by boundary resetting

“…In this paper, the boundary walls perform free diffusion with Poisson resetting where the waiting time between the two resetting events is drawn from an exponential distribution. However, the dynamics of the boundary walls can be generalized where the waiting time between two consecutive resetting events follow a power-law distribution [34,59,60] or the resetting mechanism becomes non-instantaneous [45,[61][62][63]. It is expected that such changes in the dynamics of the boundary walls will affect the NESS of the ordered harmonic chain and it is intriguing to explore the transport properties of such NESS.…”

“…This leads to some striking features like a nonequilibrium stationary state, finite mean first-passage time, and anomalous relaxation behavior. The effect of stochastic resetting on well-known equilibrium and nonequilibrium processes has been observed theoretically [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43] as well as experimentally [44][45][46]. Stochastic resetting drives a system out-of-equilibrium irrespective of the underlying dynamics of the system.…”