Basic principles of statistical theory of dusty plasmas are formulated with regard for electron and ion absorption by dust particles. Rigorous microscopic equations are introduced and employed to derive the BBGKY hierarchy and kinetic equations. The charging processes are shown to induce a considerable modification of both microscopic and kinetic equations for plasma particles and grains. In the approximation of dominant influence of charging collisions, explicit kinetic equations are derived and applied to calculate stationary distributions of grain velocities and charges.

Kinetic treatment of the Jeans gravitational instability, with collisions taken into account, is presented. The initial-value problem for the distribution function which obeys the kinetic equation, with the collision integral conserving the number of particles, is solved. Dispersion relation is obtained and analyzed. New modes are found. Collisions are shown not to affect the Jeans instability criterion. Although the instability growth rate diminishes, the collisions they cannot quench the instability. However, the oscillation spectrum is modified significantly: even in the neighborhood of the threshold frequency =0 (separating stable and unstable modes) the spectrum of oscillations can strongly depend on the collision frequency. Propagating (rather than aperiodic) modes are also found. These modes, however, are strongly damped.

The distance-resolved effective forces between two spherical, highly charged colloidal macroions are calculated by computer simulation within the primitive model of strongly asymmetric electrolytes. In particular we consider the case of two asymmetric macroions, i.e., two particles with different charges and different radii, as well as the case of added salt ions. Different parameter sets corresponding to typical experimental samples are investigated. The results are compared with the predictions of traditional linear screening theory of Derjaguin and Landau ͓Acta Physicochim. URSS 14, 633 ͑1941͔͒ and of Verwey and Overbeek ͓Theory of the Stability of Lyophobic Colloids ͑Elsevier, Amsterdam, 1948͔͒. For moderate charge asymmetries we find a semiquantitative agreement and verify different scaling laws obtained from Derjaguin-Landau-Verwey-Overbeek ͑DLVO͒ theory justifying the DLVO description of binary mixtures and of charge-and sizepolydisperse macroion samples. However for very large asymmetry, particularly for the mixture of charged and uncharged colloid particles, we obtain a nonzero repulsive interaction contrarily to DLVO theory.

A Fokker-Planck equation with velocity-dependent coefficients is considered for various isotropic systems on the basis of probability transition (PT) approach. This method provides a self-consistent and universal description of friction and diffusion for Brownian particles. Renormalization of the friction coefficient is shown to occur for two-dimensional and three-dimensional cases, due to the tensorial character of diffusion. The specific forms of PT are calculated for Boltzmann-type and absorption-type collisions (the latter are typical in dusty plasmas and some other systems). The validity of the Einstein's relation for Boltzmann-type collisions is analyzed for the velocity-dependent friction and diffusion coefficients. For Boltzmann-type collisions in the region of very high grain velocity as well as it is always for non-Boltzmann collisions, such as, absorption collisions, the Einstein relation is violated, although some other relations (determined by the structure of PT) can exist. The generalized friction force is investigated in dusty plasmas in the framework of the PT approach. The relation among this force, the negative collecting friction force, and scattering and collecting drag forces is established. The concept of probability transition is used to describe motion of active particles in an ambient medium. On basis of the physical arguments, the PT for a simple model of the active particle is constructed and the coefficients of the relevant Fokker-Planck equation are found. The stationary solution of this equation is typical for the simplest self-organized molecular machines.

Information-theoretic entropy measures are useful tools for quantifying the spreading of quantum states in phase space. In the present paper, we compare the time evolution of the joint entropy for three simple quantum systems: ͑i͒ a free Gaussian wave packet, ͑ii͒ a wave packet in a monochromatic electromagnetic field, and ͑iii͒ a wave packet tunneling through a ␦ barrier. As initial condition maximal classical states are used, which minimize the Heisenberg uncertainty and the entropy. It is found that, in all three cases, the joint entropy increases in time.