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A statistical derivation of the hydrodynamic equations of change for a system of ionized molecules. I. General equation of change and the Maxwell equations

Abstract

Nonrelativistic, classical statistical mechanics is used to describe a dense fluid of molecules composed of nuclei and electrons with purely Coulomb interaction potentials. A general equation of change is derived for the time rate of change of any macroscopic (ensemble averaged) dynamical variable. From this general equation, Maxwell's equations in a medium are derived and expressed in terms of molecular properties, e.g., polarization and magnetization densities.

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This research was carried out in part under Grant NsG-275-62 from the National Aeronautics and Space Administration and in part under a grant from the National Science Foundation. This paper is based on a thesis submitted by R. J. B. to the Graduate School of the University of Wisconsin in partial fulfillment of the requirements for the Ph.D. degree.

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Beshinske, R.J., Curtiss, C.F. A statistical derivation of the hydrodynamic equations of change for a system of ionized molecules. I. General equation of change and the Maxwell equations. J Stat Phys 1, 163–174 (1969). https://doi.org/10.1007/BF01007248

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  • DOI: https://doi.org/10.1007/BF01007248

Key words

  • Maxwell equations
  • Hydrodynamic equation
  • Magnetohydrodynamic equations
  • Polarization
  • Magnetization
  • Ionized systems