An extension of the local equilibrium hypothesis

In order to extend the range of application of classical irreversible thermodynamics far from equilibrium, an extension of the Gibbs equation is presented. The new Gibbs equation is assumed to contain, besides its usual contributions, supplementary terms equal to the thermodynamic fluxes. The entropy flux and the entropy production also take more general forms than in classical non-equilibrium thermodynamics. As an illustration of the formalism, an isotropic viscous and non-isothermal two-fluid mixture is considered. The results are shown to be in agreement with the Boltzmann kinetic theory.