Correlation between kinetic and nonlocal hydrodynamic descriptions for phonon systems

Abstract

Earlier it was shown that the description of gases, plasma, and semiconductors using kinetic theory is equivalent to the hydrodynamic description of a class of sources of a certain type. In the present work, this result is extended to the case of phonon systems. The conversion from kinetics to hydrodynamics turns out to be reversible, since a certain solution of the kinetic equation can be restored using any solution of the hydrodynamic problem. In so doing, the hydrodynamic model is nonlocal in space and time. Some general properties of the hydrodynamic nonlocality kernels are determined.