Statistical Mechanics of finite arrays of coupled bistable elements

TL;DR

This paper investigates the equilibrium behavior of finite arrays of coupled bistable elements, revealing differences from infinite systems and providing a Langevin equation approach to understand their collective dynamics.

Contribution

It introduces a method to analyze finite coupled bistable systems and compares finite size effects to the infinite case, offering a practical Langevin equation approximation.

Findings

Finite size effects significantly alter system behavior compared to the infinite limit.

A procedure to construct approximate Langevin equations for finite arrays.

Identification of distinct parameter regions with different collective behaviors.

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. The results obtained in prior works in the asymptotic infinite size limit are significantly different from the finite size results. A procedure to construct approximate 1-dimensional Langevin equation is adopted. This equation provides a useful tool to understand the collective behavior even in the presence of an external driving force.