Cognitive decline is usually described as gradual. Memory dims, processing slows, attention narrows — all by degrees, year by year. The language of decline is the language of erosion: slow, continuous, proportional to time.
A field-theoretic model of cognition (Kim, 2026) predicts something different. In this framework, neural activity is an order parameter sustained by metabolic flux — the brain's energy supply actively maintains the system near a critical point where information processing is most flexible. The key ratio is Γ ≡ K/α, structural stiffness divided by dissipation. When Γ is near 1, the system sits at criticality: neural avalanches follow power laws, susceptibility to stimulation is high, and the system can reorganize quickly. Adult cognition, in this model, is a metabolically pinned non-equilibrium steady state.
The prediction: when the metabolic pump fails — when the brain can no longer supply enough energy to maintain criticality — the system doesn't gradually weaken. It undergoes a phase transition. The order parameter delocalizes. The exponent governing this transition, γ = 3/2, matches data from cortical avalanche measurements, placing the system in the mean-field branching process universality class.
The distinction matters practically. If decline were continuous, early intervention at any stage would produce proportional benefit — slightly more metabolic support yields slightly better cognition. But near a phase transition, the system is either organized or it isn't. There is a threshold below which the metabolic pump can't maintain order, and crossing it produces collapse rather than proportional weakening. The same small change in metabolic capacity that had no effect above the threshold is catastrophic at the threshold.
The word “gradual” in “gradual decline” may be doing hidden work. Population-level data shows smooth curves because different individuals transition at different times. The average of many sharp transitions looks continuous. The individual experience — the abrupt bad week, the sudden inability to recall — may be closer to the physics than the epidemiological summary. Smoothness is an artifact of averaging over a population where each member breaks sharply.