Statistical mechanics of multiple scales of neocortical interactions

Abstract

INTRODUCTION General philosophy In many complex systems, as spatial-temporal scales of observation are increased, new phenomena arise by virtue of synergistic interactions among smaller-scale entities--perhaps more properly labeled "quasientities"--which serve to explain much observed data in a parsimonious, usually mathematically aesthetic, fashion. For example, in classical thermodynamics of equilibrium systems, it is possible to leap from microscopic molecular scales to macroscopic scales, to use the macroscopic concept of temperature to describe the average kinetic energy of microscopic molecular activity, or to use the macroscopic concept of pressure to describe the average rate of change of momentum per unit area of microscopic molecules bombarding the wall of a cavity. However, many complex systems are in nonequilibrium, being driven by nonlinear and stochastic interactions of many external and internal degrees of freedom. For these systems, classical thermodynamics typically does not apply. For example, the description of weather and ocean patterns, which attempt to include important features such as turbulence, rely on semiphenomenological mesoscopic models, those in agreement with molecular theories but not capable of being rigorously derived from them. Phase transitions in magnetic systems, and many systems similarly modeled, require careful treatment of a continuum of scales near critical points. In general, rather than having a general theory of nonequilibrium nonlinear process, there are several overlapping approaches, typically geared to classes of systems, usually expanding on nonlinear treatments of stochastic systems. Many biological systems give rise to phenomena at overlapping spatial-temporal scales. For example, the coiling of DNA is reasonably approached by blending microscopic molecular-dynamics calculations with mesoscopic diffusion equations to study angular winding. These approaches have been directed to study electroencephalography (EEG), as well as other biological systems. Therefore, it should not be surprising that the complex human brain supports many phenomena arising at different spatial-temporal scales. What is perhaps surprising is that it seems possible to study truly macroscopic neocortical phenomena such as EEG by appealing to a chain of arguments dealing with overlapping microscopic and mesoscopic scales. A series of papers has developed this statistical mechanics of neocortical interactions (SMNI). This approach permits us to find models of EEG whose variables and parameters are reasonably identified with ensembles of synaptic and neuronal interactions. This approach has only recently been made possible by developments in mathematical physics since the late 1970s, in the field of nonlinear nonequilibrium statistical mechanics. The origins of this theory are in quantum and gravitational field theory.