9 - Mechanisms for noise-induced transitions in chemical systems

Summary

Introduction

The state of chemical equilibrium is endowed with stability: perturbations away from equilibrium always decay to this state. This is a fundamental feature of the statistical mechanics of relaxation processes near equilibrium. The situation is not so simple in the far-from-equilibrium regime. Bifurcations can lead to the appearance of more exotic system states, ranging from simple stationary states akin to the equilibrium state, to periodic, quasiperiodic or even chaotic states. In addition, the asymptotic state may not be unique; given different initial conditions, different final states may be reached. While these phenomena are widespread in nature, chemically reacting fluids, driven to the nonequilibrium regime by external constraints, constitute a ubiquitous and important class of systems of this type (Nicolis and Prigogine, 1977).

The presence of noise can have significant effects on nonlinear systems. It can modify the nature of existing states, create new states, or induce transitions between coexisting states (Horsthemke and Lefever, 1984). Noise may enter the description through internal fluctuations that have their origin in the molecular nature of the system, or through external means due to the inability to control system constraints. In fact, external noise may be intentionally applied to the system in order to achieve a given transition process.

The principal focus of this article is on transitions between bistable states, induced by external noise. The use of external noise sources to promote noiseinduced transitions has several convenient features.