A crucial assumption in the conventional description of thermal conduction is the existence of local thermal equilibrium. We test this assumption in two simple models of heat conduction. Our first model is a linear chain of planar spins with nearest neighbour couplings, and the second model is that of a Lorentz gas. We look at the steady state of the system when the two ends are connected to he...

Within the framework of relativistic quantum field theory, a novel method is established which allows to distinguish non-equilibrium states admitting locally a thermodynamic interpretation. The basic idea is to compare these states with global equilibrium states (KMS states) by means of local thermal observables. With the help of such observables, the states can be ordered into classes of incre...

In light of a local thermal non-equilibrium model, fully developed forced convection in an annulus filled with a porous medium is treated to elucidate its exact temperature solutions for both fluid and solid phases. In this study, the plug-flow approximation is assumed since Darcian velocity over the cross-section is uniform except in a small region very close to the walls. The inner wall is he...