The modified group expansions for construction of solutions to the BBGKY hierarchy

TL;DR

This paper introduces modified group expansions to solve the BBGKY hierarchy, explicitly incorporating nonequilibrium distribution functions and conservation laws, leading to generalized kinetic equations for dense particle systems.

Contribution

It proposes a novel approach with modified boundary conditions and group expansions for deriving kinetic equations in nonequilibrium statistical mechanics.

Findings

Derived a generalized kinetic equation for hard spheres.

Formulated a generalized Bogolubov-Lenard-Balescu equation for dense electron gases.

Demonstrated the effectiveness of the modified expansions in nonequilibrium scenarios.

Abstract

A solution to the BBGKY hierarchy for nonequilibrium distribution functions is obtained within modified boundary conditions. The boundary conditions take into account explicitly both the nonequilibrium one-particle distribution function as well as local conservation laws. As a result, modified group expansions are proposed. On the basis of these expansions, a generalized kinetic equation for hard spheres and a generalized Bogolubov-Lenard-Balescu kinetic equation for a dense electron gas are derived within the polarization approximation.