  Many biomolecular systems can be viewed as ratchets that rectify
environmental noise through measurements and information processing. As
miniaturized robots cross the scale of unicellular organisms, on-board sensing
and feedback open new possibilities for propulsion strategies that exploit
fluctuations rather than fight them. Here, we study extended media in which
many constituents display a feedback control loop between measurement of their
microstates and the capability to bias their noise-induced transitions. We dub
such many body systems informational active matter and show how information
theoretic arguments and kinetic theory derivations yield their macroscopic
properties starting from microscopic agent strategies. These include the
ability to self-propel without applying work and to print patterns whose
resolution improves as noise increases. We support our analytical results with
extensive simulations of a fluid of `thinker' type particles that can
selectively change their diameters to bias scattering transitions. This minimal
model can be regarded as a non-equilibrium analogue of entropic elasticity that
exemplifies the key property of this class of systems: self-propulsive forces
grow ever stronger as environmental noise increases thanks to measurements and
control actions undertaken by the microscopic constituents. We envision
applications of our ideas ranging from noise induced patterning performed by
collections of microrobots to reinforcement learning aided identification of
migration strategies for collections of organisms that exploit turbulent flows
or fluctuating chemotactic fields.
