English

Topological Flux on a Context Manifold Generates Nonreciprocal Collective Dynamics

Adaptation and Self-Organizing Systems 2025-12-23 v1 Mathematical Physics math.MP Biological Physics Physics and Society

Abstract

Non-reciprocal interactions, where the influence of agent ii on jj differs from that of jj on ii, 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.

Keywords

Cite

@article{arxiv.2512.19598,
  title  = {Topological Flux on a Context Manifold Generates Nonreciprocal Collective Dynamics},
  author = {Jyotiranjan Beuria and Venkatesh H. Chembrolu},
  journal= {arXiv preprint arXiv:2512.19598},
  year   = {2025}
}

Comments

11 pages, 4 figures