Condensed Matter Physics, 2016, vol. 19, No. 4, 43705
DOI:10.5488/CMP.19.43705
arXiv:1612.07219
Title:
BBGKY chain of kinetic equations, nonequilibrium statistical operator method and collective variable method in the statistical theory of nonequilibrium liquids
Author(s):

I.R. Yukhnovskii
(Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii St., 79011 Lviv, Ukraine)
,


P.A. Hlushak
(Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii St., 79011 Lviv, Ukraine)
,


M.V. Tokarchuk
(Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii St., 79011 Lviv, Ukraine)

A chain of kinetic equations for nonequilibrium oneparticle, twoparticle and sparticle distribution functions of particles which take into account nonlinear hydrodynamic fluctuations is proposed. The method of Zubarev nonequilibrium statistical operator with projection is used. Nonlinear hydrodynamic fluctuations are described with nonequilibrium distribution function of collective variables that satisfies generalized FokkerPlanck equation. On the basis of the method of collective variables, a scheme of calculation of nonequilibrium structural distribution function of collective variables and their hydrodynamic speeds (above Gaussian approximation) contained in the generalized FokkerPlanck equation for the nonequilibrium distribution function of collective variables is proposed. Contributions of short and longrange interactions between particles are separated, so that the shortrange interactions (for example, the model of hard spheres) are described in the coordinate space, while the longrange interactions — in the space of collective variables. Shortranged component is regarded as basic, and corresponds to the BBGKY chain of equations for the model of hard spheres.
Key words:
nonlinear fluctuations, nonequilibrium statistical operator, distribution function, Fokker–Planck equation, simple fluid
PACS:
74.40.Gh, 05.70.L, 64.70.F
