Nonreciprocal alignment as a minimal mechanism for tunable collective chirality

Nonreciprocal interactions where forces between particles are asymmetric, drive many unusual collective behaviors in active matter that have no counterpart in equilibrium systems. We study a simple system of two species of point-like self-propelled agents: individuals align with neighbors of their own species symmetrically, but interact with the other species asymmetrically. We show that this asymmetry naturally drives collective rotation, and that introducing a smooth constraint on each agent’s turning rate stabilizes this chiral motion, allowing continuous control of the rotation speed. Beginning with just two interacting agents, we derive all possible steady states and their stability, obtaining exact conditions for when the system develops persistent rotation with a fixed angular offset between species. In larger groups, collective interactions substantially increase the probability of entering this rotating state, producing a robust chiral phase across a wide parameter range between flocking and antiflocking motion. These results establish a mathematically solvable framework for tunable collective rotation in active systems, with applications to biological swarms, robotic collectives, and synthetic active materials.