Statistical Mechanics of Neocortical Interactions. I. Basic Formulation

An approach to collective aspects of the neocortical system is formulated by methods of modern nonlinear nonequilibrium statistical mechanics. Microscopic neuronal synaptic interactions, consistent with anatomical observations, are first spatially averaged over columnar domains. These spatially ordered domains retain contact with the original physical synaptic parameters, are consistent with observed columnar physiology, and are a suitable substrate for macroscopic spatial-temporal regions described by a Lagrangian formalism. Long-ranged influences from extrinsic and inter-regional afferents drive these short-ranged interactions, giving rise to several columnar mechanisms affecting macroscopic activity.