Criticality Concentrates Extensive Sensing Information into a Local Readout

Abstract

We show that criticality concentrates extensive sensing information into a local trajectory. In the rapid-readout limit of an all-to-all dissipative feedback network, a single binary trajectory has a Fisher-information rate linear in $N$ for a common weak field, as does the full record. Critical slowing does not remove this gain because the local weight of the slow mode decreases with $N$. An analytic bound guarantees that the local record retains more than half of the full information across the entire channel-parameter range. We also identify how parameter drives and observation dynamics determine local access to collective information beyond permutation symmetry. Furthermore, our sparse-readout theorem establishes a $k^{-1}$ decay of fractional information loss: only $\Theta ({\epsilon }^{-1})$ trajectories are needed to retain a fraction $1-\epsilon$ of the full information rate. Any growing readout set, even of vanishing density, asymptotically recovers the full common-field Fisher-information rate.