Mesoscopic Non-Equilibrium Thermodynamics: Application to Radiative Heat Exchange in Nanostructures

Abstract

Systems in conditions of equilibrium strictly follow the rules of thermodynamics (Callen, 1985). In such cases, despite the intricate behaviour of large numbers of molecules, the system can be completely characterized by a few variables that describe global average properties. The extension of thermodynamics to non-equilibrium situations entails the revision of basic concepts such as entropy and its related thermodynamic potentials as well as temperature that are strictly defined in equilibrium. Non-equilibrium thermodynamics proposes such an extension (de Groot & Mazur, 1984) for systems that are in local equilibrium. Despite its generality, this theory is applicable only to situations in which the system manifests a deterministic behaviour where fluctuations play no role. Moreover, nonequilibrium thermodynamics is formulated in the linear response domain in which the fluxes of the conserved local quantities (mass, energy, momentum, etc.) are proportional to the thermodynamic forces (gradients of density, temperature, velocity, etc.). While the linear approximation is valid for many transport processes, such as heat conduction and mass diffusion, even in the presence of large gradients, it is not appropriate for activated processes such as chemical and biochemical reactions in which the system immediately enters the non-linear domain or for small systems in which fluctuations may be relevant. To circumvent these limitations, one has to perform a probabilistic description of the system, which in turn has to be compatible with thermodynamic principles. We have recently proposed such a description aimed at obtaining a simple and comprehensive explanation of the dynamics of non-equilibrium systems at the mesoscopic scale. The theory, mesoscopic non-equilibrium thermodynamics, has provided a deeper understanding of the concept of local equilibrium and a framework, reminiscent of non-equilibrium thermodynamics, through which fluctuations in non-linear systems can be studied. The probabilistic interpretation of the density together with conservation laws in phase-space and positiveness of global entropy changes set the basis of a theory similar to non-equilibrium thermodynamics but of a much broader range of applicability. In particular, the fact of its being based on probabilities instead of densities allows for the consideration of mesoscopic systems and their fluctuations. The situations that can be studied with this formalism