Generalized hydrodynamics from relativistic kinetic theory

The problem is considered of extending the Chapman-Enskog solution of the linearized transport equation for a relativistic quantum gas to the transition regime. The particular system studied is composed of various kinds of particles between which reactive processes are allowed. Following the classical approach of Ernst and Bixon, Dorfman and Mo, we construct a normal solution, as in the Chapman-Enskog procedure, but without any restriction on the wave lengths of the macroscopic disturbances. The method makes use of Zwanzig's projection-operator technique and yields a closed set of hydrodynamic equations with dissipative terms expressed as memory kernels. For small frequencies and wave vectors we recover the linearized Navier-Stokes equations with static transport coefficients given by the usual Chapman-Enskog expressions. Special attention is paid to the thermodynamic fluctuations as described by the static susceptibility matrix.