English

Irreversibility in the short memory approximation

Statistical Mechanics 2007-05-23 v1 Soft Condensed Matter Mathematical Physics math.MP Fluid Dynamics

Abstract

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.

Keywords

Cite

@article{arxiv.cond-mat/0305419,
  title  = {Irreversibility in the short memory approximation},
  author = {Iliya V. Karlin and Larisa L. Tatarinova and Alexander N. Gorban and Hans Christian Ottinger},
  journal= {arXiv preprint arXiv:cond-mat/0305419},
  year   = {2007}
}

Comments

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