How does noise induce order?

TL;DR

This paper establishes a general condition under which additive noise causes a transition from chaos to order in certain dynamical systems, illustrating the Noise Induced Order phenomenon with mathematical rigor.

Contribution

It provides a new, easily checkable criterion for noise-induced order in random dynamical systems, with applications to nonuniformly expanding maps.

Findings

Noise can induce order in chaotic systems under specific conditions

The paper demonstrates the phenomenon in one-dimensional dynamical systems

A general mathematical criterion for noise-induced order is established

Abstract

In this paper we present a general result with an easily checkable condition that ensures a transition from chaotic regime to regular regime in random dynamical systems with additive noise. We show how this result applies to a prototypical family of nonuniformly expanding one dimensional dynamical systems, showing the main mathematical phenomenon behind Noise Induced Order. Accepted at Journal of Statistical Physics