| A detailed comparison is made between single and double generator formalisms for the thermodynamics and mechanics of complex fluids, expressed in either bracket or operator form. In the first part of this paper (Part I), we found a complete equivalence between single and double generator formalisms applied to macroscopic systems with respect to the physics described and the practical utility of the formalisms. For microscopic systems the conclusion is different: the double generator formalism is more natural to implement, and for some physical systems may be absolutely essential to the system description. As in Part I, the interrelationships between these two alternate approaches are examined and direct connections are determined for some specific examples of fluid systems: a nonisothermal dilute polymer solution, with and without a polymer contribution to the heat transport, and Boltzmann's kinetic equation. The splitting of the GENERIC dissipation matrix into mechanical and thermodynamic submatrices in the linear regime, as described in Part I, remains valid at the microscopic level. Furthermore, this splitting allows for the mathematical statement of a double generator dissipation bracket, which may subsequently be transformed to one involving only a single generator for many systems of interest. The Boltzmann equation appears to require the use of two generators since no thermodynamic potential can be defined for the system.
for LaTeX users @article{BJEdwards1998-23,
author = {B. J. Edwards and A. N. Beris and H. C. \"Ottinger},
title = {An Analysis of Single and Double Generator Thermodynamic Formalisms for Complex Fluids. II. The Microscopic Description},
journal = {J. Non-Equilib. Thermodyn.},
volume = {23},
pages = {334-350},
year = {1998}
}
\bibitem{BJEdwards1998-23} B.J. Edwards, A.N. Beris, H.C. \"Ottinger,
An Analysis of Single and Double Generator Thermodynamic Formalisms for Complex Fluids. II. The Microscopic Description,
J. Non-Equilib. Thermodyn. {\bf 23} (1998) 334-350.BJEdwards1998-23
B.J. Edwards, A.N. Beris, H.C. \"Ottinger
An Analysis of Single and Double Generator Thermodynamic Formalisms for Complex Fluids. II. The Microscopic Description
J. Non-Equilib. Thermodyn.,23,1998,334-350 |
mk@mat.ethz.ch
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