Irreversibility in the short memory approximation

Karlin, I.V, Tatarinova, L.L., Gorban, A.N. and Ottinger, H.C. (2003) Irreversibility in the short memory approximation. Physica A: Statistical Mechanics and its Applications, 327 (3-4), 399-424. (doi:10.1016/S0378-4371(03)00510-7).

Record type: Article

Abstract

A recently introduced systematic approach to derivations of the macroscopic dynamics from the underlying microscopic equations of motions in the short-memory approximation (Phys. Rev. E 63 (2001) 066 124) 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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