Gorban, Alexander N., Karlin, Iliya V., Ilg, Patrick and Öttinger, Hans Christian
Corrections and enhancements of quasi-equilibrium states
Journal of Non-Newtonian Fluid Mechanics, 96, (1-2), . (doi:10.1016/S0377-0257(00)00135-X).
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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.
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