Statistical mechanics of dissipative transport in crystals

We present a microscopic derivation of dissipative (nonideal) hydrodynamic-like equations for crystals. The local density changes and the lattice displacement (distortion) are treated as independent. In this way we take into account all the eight slow modes predicted by the phenomenological theory, including the so-called vacancy diffusion mode. However, microscopically derived hydrodynamic-like equations are simpler than those postulated in the phenomenological theory. We also derive the exact formal expressions for the solid-state transport coefficients in terms of the Green-Kubo integrals.