  Active matter research focuses on the emergent behavior among interacting
self-propelled particles. Unification of seemingly disconnected paradigms --
active phase-separation of repulsive discs and collective motion of
self-propelled rods -- is a major challenge in contemporary active matter.
Inspired by the quanto-mechanical wave-particle duality, we develop an approach
based on the representation of active particles by smoothed continuum fields.
On the basis of the collision kinetics, we demonstrate analytically and
numerically how nonequilibrium stresses acting among self-driven, anisotropic
objects hinder the formation of phase-separated states as observed for
self-propelled discs and facilitate the emergence of orientational order.
Besides particle shape, the rigidity of self-propelled objects controlling the
symmetry of emergent ordered states is as a crucial parameter: impenetrable,
anisotropic rods are found to form polar, moving clusters, whereas large-scale
nematic structures emerge for soft rods, notably separated by a bistable
coexistence regime. These results indicate that the symmetry of the ordered
state is not dictated by the symmetry of the interaction potential but is
rather a dynamical, emergent property of active systems. This unifying
theoretical framework can represent a variety of active systems: living cell
tissues, bacterial colonies, cytoskeletal extracts as well as shaken granular
media.
