Cortical phase transitions, non-equilibrium thermodynamics and the time-dependent Ginzburg-Landau equation

TL;DR

This paper explores the thermodynamics of non-equilibrium phase transitions in brain activity, deriving a time-dependent Ginzburg-Landau equation to understand the formation of neural assemblies and their topological structures.

Contribution

It introduces a microscopic basis for brain phase transitions and derives a non-stationary Ginzburg-Landau equation relevant to neural dynamics and structure formation.

Findings

Derivation of the time-dependent Ginzburg-Landau equation for brain dynamics

Identification of vortex solutions as topologically non-trivial structures

Discussion of power laws in brain activity related to coherent states

Abstract

The formation of amplitude modulated and phase modulated assemblies of neurons is observed in the brain functional activity. The study of the formation of such structures requires that the analysis has to be organized in hierarchical levels, microscopic, mesoscopic, macroscopic, each with its characteristic space-time scales and the various forms of energy, electric, chemical, thermal produced and used by the brain. In this paper, we discuss the microscopic dynamics underlying the mesoscopic and the macroscopic levels and focus our attention on the thermodynamics of the non-equilibrium phase transitions. We obtain the time-dependent Ginzburg-Landau equation for the non-stationary regime and consider the formation of topologically non-trivial structures such as the vortex solution. The power laws observed in functional activities of the brain is also discussed and related to coherent states characterizing the many-body dissipative model of brain.