Mesoscopic transport equations and contemporary thermodynamics: an introduction

The local equilibrium hypothesis is a very successful basis for non-equilibrium thermodynamics over a wide range of phenomena and physical situations. However, the increasing interest in small systems in nanotechnology, in rarefied gases in high-altitude aeronautics, in high-frequency behaviour in information processing, or the search for new materials with sophisticated internal microstructures and tailored thermal properties have led one to ask about the limits of validity of this hypothesis, and to go beyond it. Here we do so in a constructive way, i.e. not only pointing out at these limits, but also embedding the local-equilibrium theory in a more general framework which explicitly exhibits these limits and suggests how to go beyond them, in search for a wider range of applications and a deeper understanding of the foundations.