Irreversibility in the short memory approximation

Details Irreversibility in the short memory approximation Irreversibility in the short memory approximation

2003-05-18

arxiv.org/abs/cond-mat/0305419v1

Physica A, Volume 327, Issues 3-4, 15 September 2003, Pages 399-424

Physics

Condensed Matter

Statistical Mechanics

32 pages, 2 figures, elsart, Physica A, to appear

Scientific paper

10.1016/S0378-4371(03)00510-7

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, Phys. Rev. E, 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.

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