Corrections and enhancements of quasi-equilibrium states

we give a compact non-technical presentation of two basic principles for re ducing the description of nonequilibrium systems based on the quasi-equilib rium approximation. These two principles are: construction of invariant man ifolds for the dissipative microscopic dynamics, and coarse-graining for th e entropy-conserving microscopic dynamics. Two new results are presented: f irst, 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 genera l quasi-equilibrium approximations, which gives the simplest way to derive dissipative equations from the Liouville equation in the short memory appro ximation (C) 2001 Elsevier Science B.V. All rights reserved.