The statistical mechanics of the coagulation–diffusion process with a stochastic 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.

Diffusion in a potential landscape with stochastic resetting

“…In such states probability currents are non-zero and detailed balance does not hold naturally. Of late, the implication of the stochastic reset has been studied in the one dimensional reaction-diffusion systems where a finite reset rate leads to an unique non equilibrium stationary state [14]. The interface growth models described by Kardar-Parisi-Zhang and Edwards-Wilkinson equations also exhibit nonequilibrium stationary states with non-Gaussian interface fluctuations when the interface stochastically resets to a fixed initial profile at a constant rate [15].…”

Continuous-time random walks with reset events

“…Resets have also been studied in more concrete applications as in Lévy flights [33][34][35], in coagulation-diffusion processes [36] or in the modeling of RNA polymerases to describe cleavages during the so-called backtracking, where the RNA performs a random walk to scan the DNA template [37]. Also, the thermodynamic properties of resetting stochastic processes have been widely studied in [38], while in [39] general properties of restarted processes are analyzed by drawing an analogy with MichaelisMenten reactions.…”

Directed random walk with random restarts: The Sisyphus random walk

“…The present paper continues this line of research and considers a different special case of stochastic processes with a reset mechanism. See [12][13][14][15][16] for other developments in this regard.…”