Irreversibility in the short memory approximation

Karlin, Iliya V.; Tatarinova, Larisa L.; Gorban, Alexander N.; Ottinger, Hans Christian

Irreversibility in the short memory approximation

Authors

Karlin, Iliya V.

Tatarinova, Larisa L.

Gorban, Alexander N.

Ottinger, Hans Christian

Description

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