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

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.

arXiv comment19 pages, 4 figures, research paper

References in corpus (12)

• A nonequilibrium equality for free energy differences
• Equilibrium free energy differences from nonequilibrium measurements: a master equation approach
• Cosmological Experiments in Condensed Matter Systems
• Nonlinear brain dynamics as macroscopic manifestation of underlying many-body field dynamics
• Dissipation and memory capacity in the quantum brain model
• Vortex String Formation in a 3D U(1) Temperature Quench
• Dissipation and spontaneous symmetry breaking in brain dynamics
• Quantum noise induced entanglement and chaos in the dissipative quantum model of brain
• The Ginzburg regime and its effects on topological defect formation
• Classical chaotic trajectories in quantum field theory
• Domain formation in noninstantaneous symmetry breaking phase transitions
• On topological defect formation in the process of symmetry breaking phase transitions

Cited by in corpus (3)

• Fractals, coherent states and self-similarity induced noncommutative geometry
• On the molecular dynamics in the hurricane interactions with its environment
• Time and a Temporally Statistical Quantum Geometrodynamics