NONLINEAR AND HAMILTONIAN EXTENDED IRREVERSIBLE THERMODYNAMICS

Our aim is to formulate hydrodynamicslike theory for the fluids for wh ich the classical hydrodynamics fails (e.g., polymeric fluids). In add ition, we limit ourselves in this paper to the fluids for which the en larged set of classical hydrodynamic fields, enlarged by the fields of the extra stress tensor and the extra energy flux, represent a dynami cally closed set of state variables. We say, roughly speaking, that a set of state variables is dynamically closed if predictions calculated from the dynamical theory that uses this set of state variables agree , to some extent, with results of hydrodynamicslike (rheological) obse rvations. Examples of such fluids can be found in Jou et al., [Extende d Irreversible Thermodynamics (Springer, Berlin, 1996)]. In this book the hydrodynamicslike theory whose consequences are compared with resu lts of observations is linear in the fields that extend the set of cla ssical hydrodynamic fields. In this paper we extend the linear theory to a fully nonlinear theory. The additional physical insight that make s the extension possible is the requirement of a generalized Hamiltoni an structure. This structure has been identified in all dynamical theo ries (on all levels of description, including, for example, kinetic th eory) that describe the time evolution of externally unforced fluids ( i.e., fluids that eventually reach equilibrium states at which they ca n be well described by equilibrium thermodynamics). A prominent new fe ature of the nonlinear theory is that the extra fields extending the s et of classical hydrodynamical fields are not exactly the fields of th e extra stress and the extra energy flux, but new fields from which th e extra stress and the extra energy flux can always be calculated. The inverse of this map exists, however, always only in the linear case. (C) 1998 American Institute of Physics.