A Smoothing-Channel Model of Cognition: Linking Coherence, Spectral Entropy, and Complexity

Abstract

This paper proposes a formal framework for modeling cognition as a smoothing process acting on an accessible subsystem of a larger Hilbert-space state. The biological system is represented as a reduced density matrix coupled to a broader universal state, while cognition and perception are modeled as a parameterized, non-unital coarse-graining Completely Positive Trace-Preserving (CPTP) map Sα. Under standard assumptions, this smoothing process is approximated as an effective Gaussian noise channel, where the parameter α controls the suppression of fine-grained structure into stable macroscopic observables. To connect the formal model to measurable data without equating distinct categories, we introduce a bridge chain linking coherence-based structure in the formalism to spectral entropy (Hspec) and macroscopic Lempel-Ziv complexity (CLZ) in EEG/MEG-style signals. We further define an operational Refusal to Zero (RTZ) constraint as a lower bound on accessible structural complexity under a standardized preprocessing pipeline. A preliminary toy model shows that increasing Gaussian smoothing monotonically reduces both spectral entropy and Lempel-Ziv complexity, supporting the internal consistency of the proposed bridge chain at the signal level. The framework generates testable predictions for altered states modeled as reductions in smoothing strength, including increased spectral entropy and increased signal complexity under pharmacological perturbation.