Second law of thermodynamics and phonon-boundary conditions in nanowires

The restrictions placed by the second law of thermodynamics on the boundary conditions have a special interest in nanosystems, where the Knudsen boundary layer, whose width is of the order of the mean-free path of heat carriers, becomes comparable to the size of the whole system. Here we explore second-order boundary conditions and show that the constraints of the classical irreversible thermodynamics are too restrictive, and that other formalisms going beyond local-equilibrium approach yield more realistic constraints for hydrodynamic phonon flow along nanowires. Furthermore, our analysis suggests a transition to zero thermal conductivity for very thin nanowires due to phonon backscattering.