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.Comment: 19 pages, 4 figures, research pape