Criterion for noise-induced synchronization: application to colloidal alignment

TL;DR

This paper establishes a criterion based on statistical entropy to predict noise-induced synchronization in dynamical systems, demonstrated through colloidal particle alignment under programmed forcing.

Contribution

It introduces a general entropy-based bound on synchronization rate applicable to systems with stable periodic motion under impulsive perturbations.

Findings

Derived an upper limit on entropy change using phase maps.

Showed that negative entropy change guarantees synchronization.

Applicable to colloidal alignment and similar dynamical systems.

Abstract

Colloidal bodies of irregular shape rotate as they descend under gravity in solution. This rotational response provides a means of bringing a dispersion of identical bodies into a synchronized rotation with the same orientation using programmed forcing. We use the notion of statistical entropy to derive bounds on the rate of synchronization. These bounds apply generally to dynamical systems with stable periodic motion with a phase $\phi(t)$, when subjected to an impulsive perturbation. The impulse causes a change of phase expressible as a phase map $\psi(\phi)$. We derive an upper limit on the average change of entropy $\left<\Delta H\right>$ in terms of this phase map; when this limit is negative, alignment must occur. For systems that have achieved a low entropy, the $\left<\Delta H\right>$ approaches this upper limit.