  The local equilibrium approach previously developed by the Authors [J.
Mabillard and P. Gaspard, J. Stat. Mech. (2020) 103203] for matter with broken
symmetries is applied to crystalline solids. The macroscopic hydrodynamics of
crystals and their local thermodynamic and transport properties are deduced
from the microscopic Hamiltonian dynamics. In particular, the Green-Kubo
formulas are obtained for all the transport coefficients. The eight
hydrodynamic modes and their dispersion relation are studied for general and
cubic crystals. In the same twenty crystallographic classes as those compatible
with piezoelectricity, cross effects coupling transport between linear momentum
and heat or crystalline order are shown to split the degeneracy of damping
rates for modes propagating in opposite generic directions.
