BBGKY chain of kinetic equations, non-equilibrium statistical operator method and collective variable method in the statistical theory of non-equilibrium liquids

Abstract

A chain of kinetic equations for non-equilibrium one-particle, two-particle and s-particle distribution functions of particles which take into account nonlinear hydrodynamic fluctuations is proposed. The method of Zubarev non-equilibrium statistical operator with projection is used. Nonlinear hydrodynamic fluctuations are described with non-equilibrium distribution function of collective variables that satisfies generalized Fokker-Planck equation. On the basis of the method of collective variables, a scheme of calculation of non-equilibrium structural distribution function of collective variables and their hydrodynamic speeds (above Gaussian approximation) contained in the generalized Fokker-Planck equation for the non-equilibrium distribution function of collective variables is proposed. Contributions of short-and long-range interactions between particles are separated, so that the short-range interactions (for example, the model of hard spheres) are described in the coordinate space, while the long-range interactions -in the space of collective variables. Short-ranged component is regarded as basic, and corresponds to the BBGKY chain of equations for the model of hard spheres.

To the kinetic theory of dense gases and liquids. Calculation of quasi-equilibrium particle distribution functions by the method of collective variables

“…In the next section, the method of collective variables Yukhnovskii [96][97][98][99][100] will be used to calculate the pair quasi-equilibrium distribution function and higher-order distribution functions.…”

“…The calculation of the statistical sum of the quasi-equilibrium distribution will be performed using the method of collective variables [96][97][98][99][100]. In doing so, we will take into account the nature of short-range and long-range interactions of particles, therefore Z rel (t) is given in the form:…”

“…The structural function W G (ρ; t) in the Gaussian approximation makes it possible to calculate full structural function (25) in higher approximations by Gaussian moments [99,100]:…”

Kinetic description of ion transport in the system "ionic solution – porous environment"

“…In particular, in the case of simple fluids in the works [45][46][47], when considering the corresponding models of the collision integral for this distribution function we used the generalization of the virial decomposition by the density chosen for the time-dependent density. Another way is suggested in the recent work [44], in which the paired quasi-equilibrium coordinate distribution function of a simple liquid is calculated from the statistical sum of the corresponding quasi-equilibrium particle distribution in the method of collective variables [48][49][50][51][52]. In addition, it is important to note that the use of the Ornstein-Zernicke equation, which depends on the time [53][54][55][56], is promising to calculate g 2 (r 1 , r 2 |n, β; t).…”

Vapour-liquid phase diagram for an ionic fluid in a random porous medium

“…Following the formalism originally proposed by Madden and Gland for a one-component system in a disordered porous matrix [8], we consider our matrix-fluid system as a partlyquenched model. Combining the collective variable (CV) method [24][25][26][27] with the SPT, we develop a theoretical approach which allows us to formulate the perturbation theory and to treat the model of an uncharged hard-sphere fluid in an uncharged hard-sphere matrix as a reference system. It should be noted that the CV method is a useful tool for the study of phase transitions in systems with Coulomb interactions [7,28,29].…”