Anomalous transport in strongly inhomogeneous systems. I. A kinetic theory of nonlocal hydro- and plasma dynamics

Starting from the Fokker-Planck or Boltzmann type of linearized kinetic equation, and using a projection operator technique, a general evolution equation is derived for the hydrodynamical component of the distribution function with a renormalized collision operator providing extra dissipation mechanisms. Generalized Fourier and Newtonian laws are derived leading to nonlocal transport in time and space. Explicit evaluation of the transport coefficients is performed after a discussion of various truncation procedures. The results are applied to the study of dispersion and damping of sound in a rarefied one-component gas. A comparison with experimental results shows that a 14-moment approximation is very satisfactory.