Nonequilibrium thermodynamics and heat transport at nanoscale

Current frontiers in nanotechnology and materials science require generalized transport equations beyond the local-equilibrium theory. In particular, heat-transport equations for miniaturized systems whose size is comparable to (or smaller than) the mean-free path of the heat carriers nowadays have become an important topic in science and technology. Analogously, the behavior of systems submitted to high-frequency perturbations which are comparable to the reciprocal of internal relaxation times is studied to optimize the operation of high-frequency devices. Equations for heat, mass, charge, and momentum transport have been actively explored in several situations: in miniaturized electronic devices, in nanotubes and nanowires, in theoretical models of energy transport in one-dimensional chains, in rarefied gases, etc. As a consequence, new thermodynamic formalisms are necessary in this endeavor because thementioned situations clearly exceed the limits of validity of the classical local-equilibrium thermodynamics. This constitutes a formidable challenge for nonequilibrium thermodynamics to better understand its basic concepts, its limits of application, and its frontiers.