Thermal waves in an extended hydrodynamic approach

A study of the question of heat propagation in an extended quantum hydrodynamic approach is presented. We consider a fluid of Fermi particles in interaction with a thermal bath of bosons. The equation of evolution for the flux of energy, which is incorporated as a basic thermodynamic variable thus extending the space of variables of linear thermodynamics, is derived via the nonequilibrium statistical operator method. We obtain an equation of propagation of thermal waves with damping. This hyperbolic equation, which replaces Fourierʹs heat law removing associated inconsistencies, depends on several thermodynamic forces that include the space variation of the flux itself. The equation allows for the propagation of damped thermal excitations that are of the type of a second sound. The dispersion relation is derived with the transport coefficients given at a microscopic (mechano-statistical)level. The limiting conditions that allow to go from the damped-wave regime of propagation to the diffusive regime are discussed.