Energy transport in a mesoscopic thermo-hydrodynamics

We analyse the question of transport of energy in fluids, done, for specificity, for the case of a system of fermions interacting with a boson system. Resorting to a generalized thermo-hydrodynamics based on a nonequilibrium ensemble formalism, the so-called MaxEnt-NESOM, we derive the equations of evolution for the energy density and its first and second fluxes in a truncated description. We obtain a generalized Fourier's law, relating the flux of energy with extended thermodynamic forces which include contributions of the Guyer-Krumhansl-type. An extended evolution equation for the density of energy is derived, and the conditions when it goes over restricted forms of the type of the telegraphist equation and the traditional Fourier heat diffusion equation are discussed.