Kinetic Monte-Carlo Algorithms for Active-Matter systems

TL;DR

This paper investigates kinetic Monte-Carlo algorithms for active matter, revealing issues with their continuous-time limits and proposing new algorithms that accurately capture active particle dynamics.

Contribution

It identifies the ill-defined continuous-time limit of existing KMC algorithms for active systems and introduces new AKMC algorithms with well-defined limits for various active particle models.

Findings

Large discrete time steps accelerate active system dynamics.

Ill-defined continuous-time limit causes loss of key active matter behaviors.

New AKMC algorithms provide consistent active dynamics in the continuous-time limit.

Abstract

We study kinetic Monte-Carlo (KMC) descriptions of active particles. By relying on large discrete time steps, KMC algorithms accelerate the relaxational dynamics of active systems towards their steady-state. We show, however, that their continuous-time limit is ill-defined, leading to the vanishing of trademark behaviors of active matter such as the motility-induced phase separation, ratchet effects, as well as to a diverging mechanical pressure. We show how mixing passive steps with active ones regularizes this behavior, leading to a well-defined continuous-time limit. We propose new AKMC algorithms whose continuous-time limits lead to the active dynamics of Active-Ornstein Uhlenbeck, Active Brownian, and Run-and-Tumbles particles.