The Maxwell-Boltzmann Equation as a Constitutive Equation of Continuum Mechanics

Abstract

While speculations that gross matter is a vast assembly of tiny grains of a few distinct kinds are of great age, the first mathematical theories sufficient to yield quantities rather than pictures are those of NAVIER, POISSON, and CAUCHY, in which fluids and solids are represented as static or nearly static arrays of point centers of force. Although correct if somewhat special equations were drawn from such hypotheses by those mathematicians, physicists later rejected the molecular models on which they rest, entirely in the case of fluids, and with such qualifications for solids as to bury the starting point. Scientists should use these theories as examples to show that one man’s molecules may be another man’s poison.