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.
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