SELF-ORGANIZATION AND NONEQUILIBRIUM STRUCTURES IN THE PHASE SPACE

Abstract

We consider the possibilities of the formation of quasistationary distributions of particles over energy with power asymptotics in nonequilibrium systems and dynamical systems with couplings. It is shown that the Tsallis distribution is related to the exact solutions of a kinetic equation of the Boltzmann type and those of covariant kinetic equations of the Vlasov nonlocal statistical mechanics. We have studied the connection of the power-like solutions of kinetic equations with the eigenfunctions of fractional integro-differential operators and Jackson operators within quantum analysis, and that of nonextensiveness parameters in the framework of the Tsallis thermostatics, with flows in the phase space. It is shown that the processes running in a nonequilibrium nonconservative medium can be described by the solutions of the equation with fractional derivatives or Jackson derivatives for oscillations.