Corrections and enhancements of quasi-equilibrium states
Gorban A. N., Karlin I. V., Ilg P. Ottinger H. C.
J. Non-Newtonian Fluid Mech. 2001, 96, P. 203–219.
Full text of the article [pdf, 190 Kb, in english]
We give a compact non-technical presentation of two basic principles for reducing the description of nonequilibrium systems based on the quasi-equilibrium approximation. These two principles are: construction of invariant manifolds for the dissipative microscopic dynamics, and coarse-graining for the entropy-conserving microscopic dynamics. Two new results are presented: first, an application of the invariance principle to hybridization of micro-macro integration schemes is introduced, and is illustrated with non-linear dumbbell models; second, Ehrenfest's coarse-graining is extended to general quasi-equilibrium approximations, which gives the simplest way to derive dissipative equations from the Liouville equation in the short memory approximation.