I will derive the Green-Kubo expressions for linear transport
coefficients with the aid of the Mori-Zwanzig projection operator
formalism. The essential physical step in this procedure consists in
the identification of the slow variables that are required for a closed
macroscopic description of the dynamics. For solid systems, besides
energy and momentum density, these include displacement fields,
describing the deviations of particle positions from their equilibrium
averages. As a result of this the shear modes
describing momentum relaxation in fluids, are replaced by pairs of
transverse sound modes. I will discuss the consequences of this for the
long time behavior of the current-current time correlation functions
occurring in the Green-kubo expressions.

As part of these derivations I will discuss the proper equilibrium (or
metastable state) description of solids under anisotropic and/or
nonuniform stress and the slight differences in the common definitions
of hydrodynamic or elastodynamic modes in fluids and solids
respectively, plus the ways to relate these. Finally I will show how to
include processes such as hopping diffusion in the Green-Kubo formalism.