Statistical mechanics of the coagulation-diffusion process with a stochastic reset

TL;DR

This paper investigates how stochastic resetting influences the stationary states of a one-dimensional coagulation-diffusion process, revealing complex behaviors driven by the interplay of reset and input rates.

Contribution

It provides an exact analysis of the coagulation-diffusion process with stochastic reset, highlighting the resulting non-equilibrium stationary states and their dependence on reset and input rates.

Findings

Reset modifies large-scale behavior of particle distributions.

Competition between reset and input rates creates non-trivial stationary states.

Small-scale correlations remain dominated by the original process without reset.

Abstract

The effects of a stochastic reset, to its initial configuration, is studied in the exactly solvable one-dimensional coagulation-diffusion process. A finite resetting rate leads to a modified non-equilibrium stationary state. If in addition the input of particles at a fixed given rate is admitted, a competition between the resetting and the input rates leads to a non-trivial behaviour of the particle-density in the stationary state. From the exact inter-particle probability distribution, a simple physical picture emerges: the reset mainly changes the behaviour at larger distance scales, while at smaller length scales, the non-trivial correlation of the model without a reset dominates.