Classic hydrodynamic and kinetic formalism as averaging of   delta-functional particle images
  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. 
L. S. Kuz'menkov, P. A. Andreev
physics.plasm-ph