| A recently introduced systematic approach to derivations of the macroscopic dynamics from the underlying microscopic equations of motions in the short-memory approximation [Gorban et al, {\it Phys. Rev. E} {\bf 63}, 066124 (2001)] is presented in detail. The essence of this method is a consistent implementation of Ehrenfest's idea of coarse-graining, realized via a matched expansion of both the microscopic and the macroscopic motions. Applications of this method to a derivation of the nonlinear Vlasov-Fokker-Planck equation, diffusion equation and hydrodynamic equations of the fluid with a long-range mean field interaction are presented in full detail. The advantage of the method is illustrated by the computation of the post-Navier-Stokes approximation of the hydrodynamics which is shown to be stable unlike the Burnett hydrodynamics.
for LaTeX users @article{IVKarlin2003-327,
author = {I. V. Karlin and L. L. Tatarinova and A. N. Gorban and H. C. \"Ottinger},
title = {Irreversibility in the short memory approximation},
journal = {Physica A},
volume = {327},
pages = {399-424},
year = {2003}
}
\bibitem{IVKarlin2003-327} I.V. Karlin, L.L. Tatarinova, A.N. Gorban, H.C. \"Ottinger,
Irreversibility in the short memory approximation,
Physica A {\bf 327} (2003) 399-424.IVKarlin2003-327
I.V. Karlin, L.L. Tatarinova, A.N. Gorban, H.C. \"Ottinger
Irreversibility in the short memory approximation
Physica A,327,2003,399-424 |
mk@mat.ethz.ch
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