Overview

This section is a reference shelf: one page per paper, each a self-contained summary (thesis, key equations, results, and why it’s relevant here). It collects the criticality and collective-behaviour literature that bears on BrainlessLab’s two-scale question — how (and whether) criticality at the reservoir/network scale relates to criticality at the swarm/ensemble scale, and what either buys a system functionally. The papers below are grouped by theme; follow any link for the full note.

Reviews & foundations

• Dynamical criticality: overview (Roli et al. 2016) — the edge-of-chaos hypothesis surveyed: CA/RBN evidence, critical living systems, and the open task-dependence question.
• Criticality in living systems (Muñoz 2018) — the definitive Rev. Mod. Phys. colloquium: contact/branching process, SOC, reservoir computing, and the honest caveats.
• 25 years of self-organized criticality (Watkins et al. 2016) — what SOC is and isn’t; the necessary/sufficient conditions and the “power law ≠ criticality” caution.
• SOC induced by diversity (Corral et al. 1997) — heterogeneity among integrate-and-fire units creates criticality, over an extended region, if it touches only the slow scale.

Swarm & flock criticality

• Swarm criticality & transmission (Vanni 2011) — lookouts steer a flock at criticality via organizational collapses (temporal complexity) and flock-scale correlation length.
• Finite-size scaling in natural swarms (Attanasi & Cavagna 2014) — midge swarms are near-critical: the pair (control parameter, size) sits in the scaling region; no saturation.
• An extended critical region in swarms (González-Albaladejo & Bonilla 2024) — a scale-free-chaos alternative: apparent power laws from pooling over an extended critical region.
• Collective predator evasion (Klamser & Romanczuk 2021) — criticality is optimal via spatial structure, not information transfer, and is evolutionarily unstable.
• Criticality in collective behavior (Romanczuk & Daniels 2022) — the connective review: “near, not at” criticality, the self-tuning problem, and the evolutionary social dilemma.
• Subcritical escape waves in fish (Poel et al. 2022) — a real school sits below criticality and tunes its distance with risk, managing a false-alarm (sensitivity/robustness) trade-off.
• Turning avalanches in schooling fish (Puy et al. 2024) — the full avalanche toolkit on real fish: power laws, the $m=(\alpha-1)/(\tau-1)$ relation, data collapses, dragon kings, aftershocks.

Engineered & robotic collectives

• SOC in an aquatic robot swarm (Zhao et al. 2026) — a physical swarm self-organizes to criticality; correlated-cluster avalanches, finite-size scaling, a coupling threshold.
• Criticality in swarm robots (Lei et al. 2023) — only alignment-induced criticality maximizes collective response; a noise-induced transition gives no functional gain.

Information & thermodynamic utility

• Information flow near criticality (Meijers 2021) — the transmission rate peaks near (not at) criticality, set by matched response/input timescales.
• Criticality → collective intelligence (De Vincenzo 2017) — a decision model where the mutual information between fitness and consensus peaks at the critical front.
• Thermodynamics of collective motion (Crosato et al. 2018) — entropy-reduction-per-unit-work peaks at criticality; Fisher information as an order-parameter-free probe.
• Why self-organize to criticality (Chen & Prokopenko 2025) — thermodynamic efficiency (the “super-efficiency” principle) is the utility uniquely optimized at criticality.
• Information-based fitness & criticality (Hidalgo et al. 2014) — evolution self-tunes a collective to the Fisher-information peak to represent complex environments.
• Spectral radius, criticality & dynamic range (Larremore et al. 2011) — the largest eigenvalue $\lambda=1$ governs criticality and peak dynamic range across network topologies.

Cross-scale & active matter

• Macro-criticality from micro-critical agents (Bessone & Plantec 2026) — the closest analog to our own question: near-critical reservoirs do not yield collective criticality by themselves; connectivity is decisive.
• Activation fronts in active systems (Gascuel et al. 2024) — an internal-state→motion coupling makes a 2-state active system an effective 3-state (SIR) one, critical in 2D.

Alternative measures & framing

• Heterogeneous criticality in a fish school (Niizato et al. 2024) — Integrated Information (Φ) reveals nested criticality and finds the unit of analysis instead of assuming it.
• Cognition as search efficiency (Chis-Ciure & Levin 2025) — intelligence as $K=\log_{10}(\tau_{\text{blind}}/\tau_{\text{agent}})$ over multi-scale problem spaces.