Topological Flux on a Context Manifold Generates Nonreciprocal Collective Dynamics

TL;DR

This paper demonstrates that non-reciprocal collective dynamics can emerge from agents evolving on a topological manifold coupled to a Chern-Simons gauge field, leading to persistent chiral phenomena and memory effects.

Contribution

It introduces a novel mechanism where internal topological structures generate non-reciprocity without phenomenological assumptions.

Findings

Emergence of chiral waves and vorticity

Observation of hysteresis and memory effects

Signatures of broken reciprocity in simulations

Abstract

Non-reciprocal interactions, where the influence of agent $i$ on $j$ differs from that of $j$ on $i$, are fundamental in active and living matter. Yet, most models implement such asymmetry phenomenologically. Here we show that non-reciprocity 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: long-lived vortex cores, finite circulation, asymmetric information flow, and a nonzero reciprocity residual. 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 non-reciprocal collective behavior.