Nonequilibrium statistical mechanics of swarms of driven particles
Werner Ebeling, Udo Erdmann
TL;DR
The paper develops a nonequilibrium statistical mechanics framework for swarms of driven particles using active Brownian dynamics with depot-based velocity-dependent friction. It analyzes confinement, self-confinement via Morse interactions, and Morse-driven clusters from two-particle to many-particle swarms, deriving stationary distributions and identifying translational and rotational attractors as well as rotating ring lattices under strong driving. Through analytical treatment and simulations, it reveals how energy input, dissipation, and interactions shape mode stability and clustering, even in the presence of noise and anharmonicity. The work provides a theoretical basis for understanding qualitative swarm modes observed in biological systems and connects to established classifications of collective motion.
Abstract
As a rough model for the collective motions of cells and organisms we develop here the statistical mechanics of swarms of self-propelled particles. Our approach is closely related to the recently developed theory of active Brownian motion and the theory of canonical-dissipative systems. Free motion and motion of a swarms confined in an external field is studied. Briefly the case of particles confined on a ring and interacting by repulsive forces is studied. In more detail we investigate self-confinement by Morse-type attracting forces. We begin with pairs N = 2; the attractors and distribution functions are discussed, then the case N > 2 is discussed. Simulations for several dynamical modes of swarms of active Brownian particles interacting by Morse forces are presented. In particular we study rotations, drift, fluctuations of shape and cluster formation.