Topology of Fluctuation Bands in Chiral Active Matter

While band topology is usually associated with the deterministic dynamics of a system, we show that it can instead reside in its fluctuations. Using a reciprocal lattice driven by nonequilibrium chiral active noise, we find that the displacement spectrum—which quantifies displacement fluctuations—admits bands with nonzero Chern numbers despite a Chern-trivial deterministic mechanics. A Haldane-like effective coupling in the correlation spectrum explains this topology and produces topological transitions controlled by both the stochastic driving and the observation frequency. Through the bulk–boundary correspondence, we find boundary-localized fluctuation modes that are distinct from the usual propagating mechanical edge states.