Information supercurrents and spin waves in chiral active matter: Universality of the Landau-Lifshitz-Gilbert equation

Recent minimalist modeling indicates that overdamped polar chiral active matter can support inviscid Euler turbulence, despite the system's strictly dissipative microscopic nature. In this article, we establish the statistical mechanical foundation for this emergent inertial regime by deriving a formal isomorphism between the model's agent dynamics and the overdamped Langevin equation for disordered Josephson junctions. We identify the trapped agent state as carrying non-dissipative phase rigidity supercurrents, a mapping we confirm empirically by demonstrating a disorder-broadened Adler-Ohmic crossover in the system's slip velocity. Generalizing this framework to three dimensions $S¹→ S²$, we show that polar alignment on the unit sphere is geometrically equivalent to the Gilbert damping term in spintronics, and that the two-dimensional Kuramoto coupling term naturally appears in the tangent-plane projection of spin relaxation. This constraint generates inertial spin waves (ferromagnetic magnons) from the overdamped active bath, recovering the macroscopic transport predicted by Toner-Tu theory without invoking microscopic inertia. Our results show that all polar chiral agents who seek to align on the unit sphere strictly constitute a dissipative spintronic fluid, where phase gradient transport is ensured by the Goldstone modes of the underlying broken symmetry.