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Construction, in the framework of a Nonequilibrium Statistical EnsembleFormalism, of a Mesoscopic Hydro-Thermodynamics, that is, covering phenomenainvolving motion displaying variations short in space and fast in time-unrestricted values of Knudsen numbers-, is presented. In that way, it isprovided an approach enabling for the coupling and simultaneous treatment ofthe kinetics and hydrodynamic levels of descriptions. It is based on a completethermo-statistical approach in terms of the densities of matter and energy andtheir fluxes of all orders covering systems arbitrarily driven away fromequilibrium. The set of coupled nonlinear integro-differential hydrodynamicequations is derived. They are the evolution equations of the Grad-like momentsof all orders, derived from a kinetic equation built in the framework of theNonequilibrium Statistical Ensemble Formalism. For illustration, the case of asystem of particles embedded in a fluid acting as a thermal bath is fullydescribed. The resulting enormous set of coupled evolution equations is ofunmanageable proportions, thus requiring in practice to introduce anappropriate description using the smallest possible number of variables. Wehave obtained a hierarchy of Maxwell-times, which can be considered a kind ofBogoliubov's characteristic times in hydrodynamics and which have a particularrelevance in the creteria for stablishing a contraction of description.

Nonlinear Higher-Order Hydrodynamics. Unification of kinetic and hydrodynamic approaches within a nonequilibrium statistical ensemble formalism