Self-Consistent Approximations in Kinetic Theory

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Abstract
A method is explained for obtaining generalizations of Boltzmann's equation which are consistent with the macroscopic conservation equations to any desired order in the density. The important feature of the method is the use of correlated stream velocity functions and temperatures, which can be derived from the statistical mechanics of equilibrium. Generalized conservation equations are obtained which serve as consistency conditions in the determination of the generalized velocity distribution functions. A self‐consistent method of approximation to these functions is developed, and illustrated by the derivation of a form of Boltzmann's equation, correct to terms quadratic in the density, and valid even when bound states are possible.