Neural Coherence as an Emergent Field Near Criticality: A Phase-Synchronization and Stochastic Dynamical Framework

This work introduces a novel framework in which neural coherence is formalized as an emergent dynamical field arising from stochastic interactions in coupled neural systems. Using phase synchronization as an observable, we define a coherence field (ΛN) and introduce Δ-coherence as a metric of structural stability over time. A nonlinear stochastic field equation is derived, bridging microscopic neural dynamics—modeled via stochastic FitzHugh–Nagumo systems—with macroscopic coherence patterns observed in electrophysiological data. The framework predicts that maximal coherence occurs near criticality, where integration and variability are balanced. We provide an empirical proof of concept using EEG data, demonstrating that the coherence field remains stable across runs while Δ-coherence exhibits structured temporal fluctuations. These findings support the interpretation of neural activity as a dynamically evolving coherence structure rather than a collection of independent signals. The proposed framework connects neuroscience, nonlinear dynamics, and stochastic processes, and suggests that coherence may serve as a fundamental organizing principle of brain function. Potential applications include biomarker development for neurological conditions and extensions to cognitive systems and artificial intelligence.