Mesoscopic derivation of hyperbolic transport equations

In this paper we present a derivation of the hyperbolic type of Fokker-Planck equations governing the dynamics of the numerical values associated to a set of observables of a many body system. The ensuing transport equations for the appropriate averages of such variables, namely the gross variables, are also obtained. In both cases we simply extend the ideas set forth by M. S. Green in his work on the statistical mechanics of transport phenomena [J. Chem. Phys. 20, 1281 (1952)]. These types of equations have been recently used to cope with a large class of transport phenomena. We thus discuss at length the generalized thermodynamic frame to which these equations belong and compare the results with other recent approaches to irreversible thermodynamics.