Classic hydrodynamic and kinetic formalism as averaging of delta-functional particle images

TL;DR

This paper presents a novel method to derive hydrodynamic and kinetic equations directly from microscopic mechanics by explicit averaging, revealing additional physical moments like electric and magnetic dipoles.

Contribution

It introduces a new averaging approach from classical mechanics that derives hydrodynamic equations without kinetic intermediates, including higher moments.

Findings

Derivation of hydrodynamic equations directly from microscopic motion.

Inclusion of electric and magnetic dipole moments in hydrodynamics.

Ability to derive evolution equations for new physical quantities.

Abstract

Critical analyses of well-known methods of derivation of kinetic and hydrodynamic equations is presented. Another method of derivation of kinetic and hydrodynamic equations from classic mechanics is described. It is shown that equations of classic hydrodynamics can be derived directly from microscopic picture of motion, without using of kinetic equations as an intermediate step. New method of derivation of equation of macroscopic motion includes explicit averaging of microscopic motion on infinitesimally small piece of medium. This averaging leads to presence of electric dipole, magnetic dipole, and higher moments along with the charge density and the current density in hydrodynamic equations. The method under consideration allows to derive equations of evolution for new quantities.