Zwanzig-Mori projection operators and EEG dynamics: deriving a simple equation of motion

TL;DR

This paper develops a macroscopic EEG dynamics model using Zwanzig-Mori projection operators, resulting in a simple generalized Langevin equation that relies solely on experimentally accessible macroscopic properties.

Contribution

The paper introduces two variational principles for extracting macroscopic properties from data within the Zwanzig-Mori formalism, advancing the theoretical framework for EEG modeling.

Findings

Derivation of a simple GLE for EEG dynamics

Introduction of variational principles for data-driven parameter extraction

Potential applications in brain critical phenomena and causality analysis

Abstract

We present a macroscopic theory of electroencephalogram (EEG) dynamics based on the laws of motion that govern atomic and molecular motion. The theory is an application of Zwanzig-Mori projection operators. The result is a simple equation of motion that has the form of a generalized Langevin equation (GLE), which requires knowledge only of macroscopic properties. The macroscopic properties can be extracted from experimental data by one of two possible variational principles. These variational principles are our principal contribution to the formalism. Potential applications are discussed, including applications to the theory of critical phenomena in the brain, Granger causality and Kalman filters.