Chain of kinetic equations for the distribution functions of particles in simple liquid taking into account nonlinear hydrodynamic fluctuations

TL;DR

This paper develops a chain of kinetic equations incorporating nonlinear hydrodynamic fluctuations for particles in simple liquids, using a generalized Fokker-Planck framework and Zubarev's statistical operator method.

Contribution

It introduces a novel approach to account for nonlinear hydrodynamic fluctuations in kinetic equations of particles in liquids, extending beyond Gaussian approximations.

Findings

Derived a chain of kinetic equations including nonlinear fluctuations.

Formulated a generalized Fokker-Planck equation for hydrodynamic fluctuations.

Proposed a method to calculate structural distribution functions of collective variables.

Abstract

Chain of kinetic equations for non-equilibrium single, double and s-particle distribution functions of particles is obtained taking into account nonlin- ear hydrodynamic fluctuations. Non-equilibrium distribution function of non-linear hydrodynamic fluctuations satisfies a generalized Fokker-Planck equation. The method of non-equilibrium statistical operator by Zubarev is applied. A way of calculating of the structural distribution function of hydrodynamic collective variables and their hydrodynamic velocities (above Gaussian approximation) contained in the generalized Fokker-Planck equa- tion for the non-equilibrium distribution function of hydrodynamic collective variables is proposed.