Maxent-Nesom-Based Kinetic Theory

Abstract

Nonlinear transport phenomena in far-from-equilibrium systems is a subject of importance in many areas besides the physics of condensed matter, like in physical chemistry, biology, engineering, and others. One type of nonlinear transport theory is connected with the handling of higher order approximations of the solutions of the Boltzmann equation via the Hilbert-Chapman-Enskog method [368]. For arbitrarily far-from-equilibrium systems several methods, based on different approaches, are used to derive nonlinear transport equations [417, 418]. Some of them are built upon the generalization of ideas originated in the theory of Brownian motion [262], and others on the extension of Gibbs’ algorithm to nonequilibrium situations based either on intuitive approaches or complemented with projection operator techniques [117, 229, 243, 260, 289, 324, 325, 327]. The transport equations that are obtained following the latter approach are considered a far-reaching generalization of the Hilbert-Chapman-Enskog point of view [418].