  Recent experiments show that both natural and artificial microswimmers in
narrow channel-like geometries will self-organise to form steady, directed
flows. This suggests that networks of flowing active matter could function as
novel autonomous microfluidic devices. However, little is known about how
information propagates through these far-from-equilibrium systems. Through a
mathematical analogy with spin-ice vertex models, we investigate here the
input-output characteristics of generic incompressible active flow networks
(AFNs). Our analysis shows that information transport through an AFN is
inherently different from conventional pressure or voltage driven networks.
Active flows on hexagonal arrays preserve input information over longer
distances than their passive counterparts and are highly sensitive to bulk
topological defects, whose presence can be inferred from marginal input-output
distributions alone. This sensitivity further allows controlled permutations on
parallel inputs, revealing an unexpected link between active matter and group
theory that can guide new microfluidic mixing strategies facilitated by active
matter and aid the design of generic autonomous information transport networks.
