It is shown, that the configurational partition function for a classical system of molecules interacting with nonspherical pair potential is proportionals to the configurational partition function for a system of particles interacting with temperature-dependent spherical k-body potentials (k...

The convergence properties of the integral corresponding to the three-body cyclic collisions in the two-dimensional density expansion of transport coefficients are investigated. It is shown exactly that the integral considered by Oppenheim et al. and by Eu diverges logarithmically in the...

The common formal features of classical and quantum statistical mechanics are investigated at three separate levels: at the level of L2 spaces of wave-packets on Γ-space, of Liouville spaces B2 consisting of density operators constructed from such wave-packets, and of phase-space representation...

An extension of the usual system-size expansion method is given to study the relaxation and fluctuation from unstable and metastable states. The short-time and the long-time behavior of the moments y(t) and Mn(t) and of the distribution function P(x, t) of a macroscopic variable x are...

The general method of paper I of this series is applied to derive kinetic equations (KE's), i.e. closed exact equations governing the time evolution of the single-particle density matrix. The short-memory approximation of these non-Markowian equations is formulated in such a way that it is valid...

The method of Y.L.Klimontovich is explained by a perturbation expansion technique concerning an appropriate norm determined by the considered physical problems. It can be demonstrated, that the approximations of Klimontovich are equivalent with those used by N. Rostoker who treats the...

Some new methods are discussed for the calculation of the velocity correlation function in the Ring approximation. Theory and computer “experiments” are compared, with reasonable success, for the case of the Lorentz gas.

A unified derivation of the classical and quantum Boltzmann equation for the one-particle Γ and Γs distribution functions, respectively, is presented. The starting point is a Boltzmann-like equation for density operators in B2(Γ). In the context of classical mechanics this equation turns into...

We investigate the effect of a small dissipation on the turbulent motion in a nonlinear dispersive medium governed by the Kortewegde Vries (KdV) equation. A closed equation for the energy spectrum function is derived by making use of the derivative expansion method. From the solution of this...

The Navier-Stokes equations with random stirring forces studied by Forster et al. are analyzed in the formalism developed recently. It is shown that without an Einstein relation detailed balance is violated. In detailed balance zero-frequency non-renormalization theorems are used to define a...