Yu. L. Klimontovich

Quantum kinetic equations in systems with bound states

Starting from the quantum mechanical BBGKY-hierarchy kinetic equations in systems with two particles bound states are given in this paper. With this equation it is possible to consider transport properties in nonideal gases with three particles reactions.

Turbulent Motion. The Structure of Chaos

Turbulence even to this day remains one of the most complicated and enigmatic kinds of motion. The phenomenon of turbulence was first discovered in connection with the studies of piped flows of incompressible fluids, and for a long time had been treated as a subject of fluid mechanics. It seems that a chapter on turbulence as a physical phenomenon was for the first time included into a course of statistical physics by the author in 1982 (Klimontovich, iv).

Ito, stratonovich and kinetic forms of stochastic equations

The well known Ito and Stratonovich forms of presentation of stochastic equations are not, in general, physically equivalent. From the point of view of the statistical theory of nonequilibrium processes the third is most natural-the “kinetic form” of presentation of the Langevin and corresponding Fokker-Planck equations. Only in this case exist fluctuation- dissipation relations (the Einstein formula) for nonlinear systems. For the confirmation of this point of view the following different concrete systems are considered: Brownian motion of particles in a medium with nonlinear friction, of the Van der Pol oscillators and others. The connection between the master equation and the Fokker-Planck one is also considered.

On the need for and the possibility of a unified description of kinetic and hydrodynamic processes

The aim of the paper is to demonstrate the possibility of a unified description of kinetic and hydrodynamic processes on the basis of a generalized kinetic equation without the use of perturbation theory with respect to the Knudsen number. The derivation of the generalized kinetic equation is based on a concrete definition of a continous medium in the kinetic and hydrodynamic description of nonequilibrium processes in a Boltzmann gas and in a fully ionized plasma. The concept of a “point” of a continuous medium is introduced through the definition of corresponding physically infinitesimally small volumes. On this basis we also give a definition of a Gibbs ensemble to the description of nonequilibrium processes in statistical theory. Besides the usual “collision integral,” which takes into account the dissipation through the redistribution of the particles with respect to the velocities, the generalized kinetic equation contains in the case of the physical definition of the “continuous medium” an additional term of diffusion type. For this reason, it becomes possible to describe kinetic and hydrodynamic processes at all admissible Knudsen numbers. BoltzmannsH theorem is proved for the generalized kinetic equation. The entropy production is determined by the sum of two positive contributions, which are due, respectively, to the redistribution of the particles in the velocity space and in ordinary space. The entropy flux also consists of two terms, one proportional to the entropy and one proportional to the entropy gradient. The presence of the second term makes it possible to give a general definition of a heat flux for arbitrary Knudsen numbers. For small Knudsen numbers and slow processes, it reduces to Fouriers law. The equations of gas dynamics follow from the generalized kinetic equation without the use of perturbation theory with respect to the Knudsen number. They take into account not only processes of viscosity and heat conduction but also self-diffusion. The region of applicability of the equations of gas dynamics is discussed. Generalized kinetic equations are obtained for the distribution functions of the states of the electrons and ions of a partly ionized plasma. Kinetic equations for active media, and also in the theory of Brownian motion, are discussed.

Criteria of self-organization

As we have already said in the Introduction, one of the main tasks of statistical theory of open systems consists in establishing the criteria of self-organization. We touched upon this problem now and then in the course of our discussion. Now is the time to draw conclusions, to compare various criteria of self-organization, to illustrate their efficiency with concrete examples.

Statistical theory of plasma-molecular systems

Abstract The basic principles of kinetic theory are formulated for combined plasma-molecular systems consisting of both free and bound charged particles. The description of the subsystem of bound particles is bassed on the classical model of atomic oscillators (this makes it impossible to take into account ionization and recombination processes, byt the general formalism is still quite useful). In the framework of such a model, collective electromagnetic processes in infinite and bounded plasma-molecular matter are studied. The influence of boundaries on the collision integrals, on the kinetic coefficients and on the space distributions of particles is investigated in detail. The theory of electromagnetic fluctuations in bounded plasma-molecular systems is developed as well. This theory is used to obtain the correlation functions of electron density fluctuations and spontaneous emission spectra. A numerical analysis of spontaneous emission spectra is presented for systems with plane-parallel boundaries. The generalization of the fluctuation theory of bremsstrahlung radiation in a plasma to the case of plasma-molecular matter is also discussed.

Natural flicker noise («1/f noise») in music

A large class of musical selections exhibits a spectral density of audio power fluctuations characterized by a low-frequency behaviour typical of lif noise. We show that this lif behaviour follows from natural flicker noise theory.

The unified description of kinetic and hydrodynamic processes in gases and plasmas

Abstract The unified description of kinetic and hydrodynamic processes in gases and plasmas for all values of the Knudsen number is proposed. The generalized kinetic equation consists of the additional dissipative term and is defined by the diffusion of the distribution function in the coordinate space. This equation is used for the description of nonequilibrium processes in passive and active media.

Fluctuation Dissipation Relations

This chapter is the second longest in the book. The reader might ask whether so much attention to fluctuation dissipation relations is justified in a monograph devoted to the statistical theory of open systems.

Evolution of the entropy of stationary states in selforganization processes in the control parameter space

The behaviour of entropy (Shannon-information) and renormalized entropy (based on theS-theorem [3]) is investigated for systems with an exponential stationary probability distribution function (1). Analytical results for the derivatives with respect to the control parameters are derived. One class of systems (3) is separated for which the renormalized entropy is a monotonously decreasing function of the control parameters.