Journal of Statistical Physics, Vol. 46, Nos. 3/4, 1987. p. 709-727.
Although the Chapman Enskog treatment of the Boltzmann equation is one of the first examples of the elimination of fast variables, it is not usually presented consistently from that point of view. Here it is developed systematically as a special case of the general method for eliminating fast variables from nonlinear equations. As a result certain ambiguities can be remedied. First, it is inconsistent with the separation of time scales to extend the phenomenological description of the gas by including some of the higher moments of the distribution function (such as the heat flow). In the application to the relativistic Boltzmann equation, the dilemma concerning the choice of the lowest order approximation is resolved. In the final section it is demonstrated that unsystematic elimination of fast variables leads to secular terms.