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Irreversibility in the short memory approximation

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

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Iliya V. Karlin, Larisa L. Tatarinova, Alexander N. Gorban, Hans Christian Ottinger. 2003-05-18. Irreversibility in the short memory approximation. https://doi.org/10.1016/s0378-4371(03)00510-7

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