Critical Scaling and Metabolic Regulation in a Ginzburg--Landau Theory of Cognitive Dynamics

Abstract: We formulate a phenomenological effective field theory in which biological intelligence emerges as a macroscopic order parameter sustained by continuous metabolic flux. By modeling cognition as a coarse-grained neural activity field governed by a variational free energy, we derive closed-form expressions for information capacity and structural susceptibility using a Gaussian maximum entropy approximation. The theory predicts a universal algebraic divergence of the susceptibility, $χ\sim K^{-3/2}$, as the structural stiffness $K$ approaches the instability threshold. The exponent $γ= 3/2$ is consistent with the mean-field branching process universality class, thereby providing a theoretical rationale for the observed avalanche size exponent $τ\approx 3/2$ in cortical dynamics without invoking microscopic equivalence. We identify adult cognition as a metabolically pinned non-equilibrium steady state maintained near the critical regime $Γ\equiv K/α\approx 1$ by continuous metabolic regulation, while pathological decline corresponds to a delocalization transition triggered by the violation of structural stability conditions. The framework generates concrete, falsifiable predictions for attention scaling, altered states of consciousness, and transcranial magnetic stimulation responses, each of which can be tested against existing neuroimaging and electrophysiological datasets.