FROM THE HAMILTONIAN-MECHANICS TO A CONTINUOUS MEDIA - DISSIPATIVE STRUCTURES - CRITERIA OF SELF-ORGANIZATION

The paper is aimed at presenting some main ideas and results of the mo dern statistical theory of macroscopic open systems. We begin from the demonstration of the necessity and the possibility of the unified des cription of kinetic, hydrodynamic, and diffusion processes in nonlinea r macroscopic open systems based on generalized kinetic equations. A d erivation of the generalized kinetic equations is based on the concret e physical definition of continuous media. A ''point'' of a continuous medium is determined by definition of physically infinitesimal scales . On the same basis, the definition of the Gibbs ensemble for nonequli brium process is given. The Boltzmann gas and a fully ionized plasma a s the test systems are used. For the transition from the reversible Ha milton equations to the generalized kinetic equations the dynamic inst ability of the motion of particles plays the constructive role. The ge neralized kinetic equation for the Boltzmann gas consists of the two d issipative terms: 1) the ''collision integral,'' defined by the proces ses in a velocity space; 2) an additional dissipative term of the diff usion type in the coordinate space. Owing to the latter the unified de scription of the kinetic, hydrodynamic, and diffusion processes for al l values of the Knudsen number becomes possible. The H-theorem for the generalized kinetic equation is proved. The entropy production is def ined by the sum of two independent positive terms corresponding to red istribution of the particles in velocity and coordinate space respecti vely. An entropy flux also consists of two paris. One is proportional to the entropy, and the other is proportional to the gradient of entro py. The existence of the second term allows one to give a general defi nition of the heat flux for any values of the Knudsen number, which is proportional to the gradient of entropy. This general definition for small Knudsen number and constant pressure leads to the Fourier law. T he equations of gas dynamic for a special class of distribution functi ons follow from the generalized kinetic equation without the perturbat ion theory for the Knudsen number. These equations differ from the tra ditional ones by taking the self-diffusion processes into account. The generalized kinetic equation for describing the Brownian motion and o f autowave processes in active media is considered. The connection wit h reaction diffusion equations, the Fisher-Kolmogorov-Petrovski-Piskun ov and Ginzburg-Landau equations, is established. We discuss the conne ction between the diffusion of particles in a restricted system with t he natural flicker (1/f) noise in passive and active systems. The crit eria of the relative degree of order of the states of open system - th e criteria of self-organization, are presented.