Criticality
Criticality is the state of a system at a phase transition — the boundary between qualitatively distinct dynamical regimes. At criticality, the system exhibits scale-free fluctuations, diverging correlation lengths, and maximal sensitivity to perturbation. The concept originated in statistical physics, where it describes the behavior of systems at their critical temperature or critical pressure, but it has been extended to complex systems, biology, and social dynamics.
Physical Criticality
In thermodynamics, criticality occurs at the point where a continuous phase transition takes place. The correlation length — the distance over which fluctuations in one part of the system influence another — diverges, meaning that local perturbations propagate across the entire system. Physical quantities obey power laws, and the system's behavior becomes independent of microscopic details, depending only on dimensionality and symmetry — a property known as universality.
Criticality in Complex Systems
Beyond physics, criticality has been invoked to describe systems that spontaneously organize to a critical state without external tuning. Self-organized criticality (SOC), introduced by Bak, Tang, and Wiesenfeld in 1987, describes driven dissipative systems — sandpiles, earthquakes, forest fires — that naturally evolve to a critical point where event sizes follow power-law distributions. The claim is that criticality is not an exceptional state requiring fine-tuning but an attractor of the dynamics itself.
In biology, the claim that gene regulatory networks and neural networks operate at criticality has been both influential and contested. Proponents argue that criticality maximizes information processing, sensitivity, and adaptability. Critics argue that biological systems are not random and that the evidence for criticality is indirect and model-dependent.