Emergence and Electrophysiological Analogies in Jellium Models for Cortical Brain Matter

Abstract

The complicated and puzzling neuronal structure of human and animal brains is responsible for mental abilities. Concerning a mechanistic understanding of brain activities, the crucial question refers to the properties of a single neuron versus neurons' spatial arrangement and interconnection as a whole. In this paper we adopt the point of view that a significant share of neurons in a being can be modeled by (in our approach complex-valued) dynamical systems based on a manageable number of phase-space dimensions, thus representing a macroscopic overall description of the totality of highly redundant neuronal processes. This agrees with the general theory of interacting many-particle systems that usually undergo a dramatic reduction of complexity in the spirit of the Kolmogorov entropy, due to collective behavior. Then, emergence is understood as a complexity increase in the dynamics under consideration, where the K-entropy characterizes and summarizes the time evolution of many physiological details. Analogies and their limits with respect to the dynamics of selected physical many-particle systems are investigated.