Nonequilibrium Distribution Functions in a Fluid

Abstract

The behavior of a nonequilibrium fluid is analyzed on a level intermediate between that of hydrodynamics, where microstructure is totally ignored, and a phase space description, where the complete N‐body problem must be solved. The study of the fluid at this level generally involves solving an appropriate transport equation. For liquids, the primary subject of this investigation, the Fokker‐Planck equation of Kirkwood is accepted as a working model and solutions are found by the methods of Chapman and Enskog and of Grad to terms linear in deviations from local equilibrium. (It is argued, however, for a different form of the pair space force than that suggested by Kirkwood and co‐workers.) The results are similar in form to distributions found with other kinetic models. Variational principles are also considered. It is shown that the one‐ and two‐ particle distribution functions have the property of maximizing the entropy subject to the constraints of given densities and fluxes. Alternatively, these distributions maximize the entropy plus entropy productions in appropriate characteristic times. These variational principles do not depend on the use of the Fokker‐Planck equation but appear to possess general validity.