Canonical active Brownian motion

TL;DR

This paper develops a comprehensive theory of active Brownian motion by incorporating couplings to potential energy, analyzing both stationary and dynamic behaviors, including bifurcations, through analytical and numerical methods.

Contribution

It extends existing models by integrating potential energy couplings into the active Brownian motion framework, forming a general theory of canonical dissipative systems.

Findings

Identification of stationary solutions

Discovery of bifurcation phenomena in non-equilibrium dynamics

Analytical and numerical characterization of particle motion in harmonic potentials

Abstract

Active Brownian motion is the complex motion of active Brownian particles. They are active in the sense that they can transform their internal energy into energy of motion and thus create complex motion patterns. Theories of active Brownian motion so far imposed couplings between the internal energy and the kinetic energy of the system. We investigate how this idea can be naturally taken further to include also couplings to the potential energy, which finally leads to a general theory of canonical dissipative systems. Explicit analytical and numerical studies are done for the motion of one particle in harmonic external potentials. Apart from stationary solutions, we study non-equilibrium dynamics and show the existence of various bifurcation phenomena.