Entropy flux in non-equilibrium thermodynamics

An important problem in thermodynamics is the link between the entropy flux and the heat flux, for phenomena far from equilibrium. As an illustration we consider here the case of a rigid heat conductor subject to heating. The expression of the entropy flux is determined by the expressions of the evolution equations of the basic variables. It is shown that the coefficient relating entropy and heat fluxes differs far from equilibrium from the inverse of the non-equilibrium temperature θ. The particular case in which these two quantities are identical is examined in detail. A simple but intuitive physical illustration of the results is proposed. A comparison with information theory is also made: it is shown that agreement with Boltzmann's distribution function requires the introduction of non-local terms.