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 Θ(ε−1) trajectories are needed to retain a fraction 1−ε of the full information rate. Any growing readout set, even of vanishing density, asymptotically recovers the full common-field Fisher-information rate.
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BibTeX
@misc{wang2026criticality,
title = {{Criticality Concentrates Extensive Sensing Information into a Local Readout}},
author = {Peng Wang and Yu-Xuan Zhang and Hai-Tao Ding and Leong-Chuan Kwek},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15364},
eprint = {2610.15364},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15364},
}
RIS
TY - UNPB
TI - Criticality Concentrates Extensive Sensing Information into a Local Readout
AU - Peng Wang
AU - Yu-Xuan Zhang
AU - Hai-Tao Ding
AU - Leong-Chuan Kwek
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15364
UR - https://arxiv.org/abs/2610.15364
AB - 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 Θ(ε^−1) trajectories are needed to retain a fraction 1−ε of the full information rate. Any growing readout set, even of vanishing density, asymptotically recovers the full common-field Fisher-information rate.
ER -