Boundary-Guided Topological Entropy Production in Confined Active Nematics

Active nematic flows in two dimensions, largely driven by motile +1/2 disclinations, mix themselves efficiently and exhibit chaos in the bulk steady state. What constraints does this efficient mixing tendency place on the ordered, periodic flows that could be stabilized in confined active nematics? We use Beris-Edwards nematodynamics simulations to study two-dimensional active nematics in strongly confined systems by systematically identifying ordered flows via internal topological charge modulation. We find ordered flows for systems of three and four defects, and use tools from braid theory to identify that spontaneously preferred periodic defect motions produce maximal topological entropy. We generalize an experimentally verified technique of using sharp cusps to pin negative defects (Memarian, Fereshteh L., et al. Physical Review Letters 132.22: 228301 (2024)) to realize higher-charge braiding in experimentally testable geometries. We demonstrate a general geometrical mapping between a desired net topological defect charge in the active nematic bulk and a smooth boundary shape with tangential anchoring. This mapping equivalently generates an active force that prevents periodicity for systems of more than four defects. Our results identify the parameter regime outside of which periodicity is lost, and let us probe the limits of topological entropy production.