Extended irreversible thermodynamics of heat transport A brief introduction

Current frontiers of technology require generalized transport equations incorporating memory, non-local effects, and non-linear effects. Extended Irreversible Thermodynamics provides Such transport equations in a form compatible with the second law of thermodynamics, and that, for low frequency and short mean-free paths, reduce to the classical transport equations. Here we present the basic concepts of extended irreversible thermodynamics, namely, the fluxes as independent variables, and their evolution equations as generalized transport equations obeying the second law of thermodynamics. We show that these equations cover a rich phenomenology in heat transport, including thermal waves, phonon hydrodynamics, ballistic transport, and saturation in the fluxes for high values of the thermodynamic forces.