Nonlinear Higher-Order Thermo-Hydrodynamics: Generalized Approach in a Nonequilibrium Ensemble Formalism

Construction of a nonlinear higher-order thermo-hydrodynamics, including correlations, in the framework of a Generalized Nonequilibrium Statistical Grand-Canonical Ensemble is presented. In that way it is provided a particular formalism for the coupling and simultaneous treatment of the kinetics and hydrodynamic levels of description. It is based on a complete thermostatistical approach in terms of the densities of energy and of matter and their fluxes of all orders, as well as on their direct and cross correlations, covering systems arbitrarily driven-away-from equilibrium. The set of coupled nonlinear integro-differential hydrodynamic equations is derived. Illustrations of the application of the theory are described in the follow up article.