Thermodynamics of Irreversible Processes: Fundamental Constraints, Representations, and Formulation of Boundary Conditions

Starting from the analysis of the lack of positivity of the Cattaneo heat equation, the article addresses the thermodynamic relevance of the positivity constraint in irreversible thermodynamics, than is at least as important as the entropic constraints. The fulfillment of this condition in hyperbolic models leads to the parametrization of the concentration fields with respect to internal variables associated with the microscopic dynamics. Using Brownian motion theory as a landmarking example for deriving macroscopic transport equations from the equations of motion at the particle/molecular level, we discuss two typical problems involving hydrodynamic interactions at microscale: surface chemical reactions at a solid interface of a diffusing reactant, and mass-balance equations in a complex viscoelastic fluid, in which the physics of the interaction leads either to the overcome the parabolic diffusion model or to consider the parametrization of the concentration with respect to the degrees of freedom associated with the relaxation dynamics of the solvent fluid.