Entropy in Human Brain Networks

Dear Colleagues,

An important area of science where a dynamical system framework of thermodynamics can prove invaluable is in neuroscience. Advances in neuroscience have been closely linked to mathematical modeling beginning with the integrate-and-fire model of Lapicque and proceeding through the modeling of the action potential by Hodgkin and Huxley to the current era of mathematical neuroscience. Neuroscience has always had models to interpret experimental results from a high-level complex systems perspective; however, expressing these models with dynamic equations rather than words fosters precision, completeness, and self-consistency. Nonlinear dynamical system theory, and in particular system thermodynamics, is ideally suited for rigorously describing the behavior of large-scale networks of neurons.

Merging the two universalisms of thermodynamics and dynamical systems theory with neuroscience can provide the theoretical foundation for understanding the network properties of the brain by rigorously addressing large-scale interconnected biological neuronal network models that govern the neuroelectronic behavior of biological excitatory and inhibitory neuronal networks. As in thermodynamics, neuroscience is a theory of large-scale systems wherein graph theory can be a very useful tool in capturing the connectivity properties of system interconnections, with neurons represented by nodes, synapses represented by edges or arcs, and synaptic efficacy captured by edge weighting giving rise to a weighted adjacency matrix governing the underlying directed graph network topology. However, unlike thermodynamics, wherein energy spontaneously flows from a state of higher temperature to a state of lower temperature, neuron membrane potential variations occur due to ion species exchanges which evolve from regions of higher concentrations to regions of lower concentrations. And this evolution does not occur spontaneously but rather requires the opening and closing of specific gates within specific ion channels. The purpose of this special issue is to use a dynamical systems framework merged with thermodynamic state notions (i.e., entropy, energy, free energy, chemical potential, etc.) to provide a fundamental understanding of the networks properties of the brain.

Prof. Dr. Wassim M. Haddad
Guest Editor

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