  The time-independent projection-operator formalism of Brey et al. [Physica
109A, 425-444 (1981)] for the derivation of Burnett equations is extended and
considered in the context of multispecies and magnetized plasmas. The procedure
provides specific formulas for the transport coefficients in terms of two-time
correlation functions involving both two and three phase-space points. It is
shown how to calculate those correlation functions in the limit of weak
coupling. The results are used to demonstrate, with the aid of a particular
nontrivial example, that previously derived formulas from the two-time
formalism [J. J. Brey, J. Chem. Phys. 79, 4585-598 (1983)] are consistent with
the Chapman-Enskog methodology employed later by Catto & Simakov (CS) [Phys.
Plasmas 11, 90-102 (2004)] for the contributions to the parallel viscosity
driven by temperature gradients. The work serves to unify various previous work
on plasma kinetic theory with formalism usually applied to turbulence theory.
Additional contributions include discussions of (i) Braginskii-order
interspecies momentum exchange from the point of view of two-time correlations;
and (ii) a simple stochastic model, unrelated to many-body theory, that
exhibits Burnett effects. Insights from that model emphasize the role of
non-Gaussian statistics in the evaluation of Burnett transport coefficients,
including the effects calculated by CS that stem from the nonlinear collision
operator. Together, Parts I and II of this series provide a tutorial
introduction to projection-operator methods that should be broadly useful in
theoretical plasma physics. A Supplement (bundled at the end of Part II)
provides some technical details of the reduction of the general Burnett
equations of Brey et al. (1981) to a one-component neutral fluid in order to
support the result quoted by Brey (1983).
