Wave-function formalism for evolving neural dynamics: a mathematical framework informed by EEG

Abstract

The organization of distributed neural activity remains one of the central challenges in computational neuroscience. Contemporary frameworks, including Integrated Information Theory, Global Workspace Theory, entropy-based approaches, and electromagnetic field theories, have advanced our understanding of neural coordination but employ different mathematical descriptions of large-scale brain dynamics. This study investigates whether wave-function formalism provides a useful mathematical framework for representing evolving neural dynamics measured using electroencephalography (EEG). Rather than introducing a new electrophysiological measure or proposing a new mechanism of consciousness, the framework represents complementary EEG observables within a common state-space description of neural activity. Mathematical inspiration is drawn from Everett’s representation of evolving state spaces, although no claims are made regarding quantum computation or quantum processes in the brain. Electroencephalographic recordings from interictal, preictal, and ictal seizure states (150 EEG segments) were analyzed using complementary measures of signal amplitude, spectral organization, entropy, phase dynamics, cross-frequency coupling, and recurrence quantification. Statistical comparisons employed nonparametric analyses, effect-size estimation, confidence intervals, and post hoc testing. Significant differences were observed across all major electrophysiological domains. Ictal recordings exhibited increased signal amplitude, redistribution of spectral power toward lower frequencies, reduced entropy, altered phase organization, changes in cross-frequency coupling, and increased recurrence structure, indicating coordinated changes in evolving neural dynamics during seizure progression. These findings are interpreted within a mathematical framework that treats established EEG observables as complementary descriptors of a single evolving neural state. The principal contribution of this work is the proposal of a mathematically grounded and experimentally testable representation of evolving neural dynamics. Whether this formalism provides new insight into cognition or conscious experience remains an empirical question for future investigation.