Statistical mechanics of finite arrays of coupled bistable elements

Abstract

We discuss the equilibrium of a single collective variable characterizing a finite set of coupled, noisy, bistable systems as the noise strength, the size and the coupling parameter are varied. We identify distinct regions in parameter space. Our finite size results indicate important qualitative differences with respect to those obtained in the asymptotic infinite size limit. We also discuss how to construct approximate 1-dimensional Langevin equations. This equation provides a useful tool to understand the collective behavior even in the presence of an external driving force.