Measurement-Induced Phase Transitions in Informational Active Matter

Various biological and synthetic media out of equilibrium can be viewed as many-ratchet systems that rectify environmental noise through local measurements and information processing, like in Maxwell's prototypical demon. These systems pose a challenge to standard coarse-graining approaches because they are better described in terms of decision-making protocols similar to computer programs rather than force laws. Here, we study a many-body generalization of the Maxwell demon problem: a fluid composed of adaptive particles that achieve collective behavior by biasing noise-driven scattering events subject to measurements. Using a combination of information-theoretic, kinetic, and hydrodynamic tools, we elucidate how microscopic decision-making protocols, rather than microscopic forces, generate macroscopic active states sustained by continuous measurements. These include an informational version of flocking whose order parameter is bounded by the information measured, and the onset of which may be viewed as a measurement-induced phase transition. We find that the signature of such microscopic choices is an `informational activity' that selectively compresses phase space, without work, and causes deviations from equilibrium scaling with the magnitude of environmental noise. We envision applications to noise-induced patterning performed by collections of microrobots guided by reinforcement learning or programmable phoretic colloids in turbulent flows that exploit local measurements and control actions to counteract the scrambling of information by chaos.