Title: Anomalous heat conduction under far from equilibrium conditions

Author: **Sergey Sobolev**

Abstract:

Classical irreversible thermodynamics is based on the local equilibrium assumption, which leads to the classical parabolic diffusion equation. But the question arises: how to describe the heatmass transfer process under far from equilibrium conditions? Can temperature, which is an equilibrium concept, still be invoked in this situation? We consider the heat-mass transfer models, which go beyond the local equilibrium assumption, and apply them to study rapid alloy solidification, ultrafast laser heating of metals, and heat conduction in nano-films .If the heat flux tends to its maximum value when all the heat carriers moves in the same directions, the effective temperature and corresponding nonequilibrium entropy go to zero

even at nonzero value of T, which implies a third-law-like behavior under nonequilibrium conditions. The discrete variable model (DVM) predicts the temperature jump at the boundary between the nano film and the thermal reservoirs and lead to the size-dependant effective thermal

conductivities and extrapolation length. These correspond to the problems of a first passage time and a Milne extrapolation length in anomalous diffusion theory. The nonlocal 2T model describes the heat conduction in metals under ultrashort laser irradiation and demonstrates a

multi-stage relaxation to local equilibrium, which corresponds to aging in terms of anomalous diffusion theory. Thus, there are strong parallels between the thermodynamically based nonlocal heat-mass transfer models and the anomalous diffusion theory, which implies that there can be fruitful cross-fertilization of ideas and techniques between the approaches.