Topological flux on a context manifold generates nonreciprocal collective dynamics
Phys. Rev. E 113, 065401 – Published 1 June, 2026
DOI: https://doi.org/10.1103/kn6c-nb4l
Abstract
Nonreciprocal interactions, where the influence of agent on differs from that of on , are fundamental in active and living matter. Yet, most models implement such asymmetry phenomenologically. Here, we show that nonreciprocity can emerge from internal topology alone. Agents evolve on an internal “context manifold” coupled to a Chern–Simons gauge field. Because the gauge field is first order in time, it relaxes rapidly; eliminating it yields an effective transverse, antisymmetric interaction kernel that generically produces chiral waves, persistent vorticity, and irreversible state transitions. Numerical simulations reveal clear signatures of broken reciprocity characterized by long-lived vortex cores, nonzero total rotational energy of the flow, and signed circulation dominance. The dynamics further exhibit pronounced hysteresis under parameter sweeps, demonstrating memory effects that cannot occur in reciprocal or potential-driven systems. These results identify Chern–Simons gauge fields as a minimal and universal source of directional influence and robust nonreciprocal collective behavior.