Irreversibility in the short memory approximation

TL;DR

This paper details a systematic method for deriving macroscopic equations from microscopic dynamics in the short-memory approximation, emphasizing irreversibility and stability in hydrodynamic models.

Contribution

It introduces a consistent coarse-graining approach using matched expansions, applied to derive nonlinear Vlasov-Fokker-Planck, diffusion, and hydrodynamic equations.

Findings

Stable post-Navier-Stokes hydrodynamics derived

Method effectively captures irreversibility

Applications demonstrate accuracy and stability

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.