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Irreversibility in the short memory approximation

Author

Listed:
  • Karlin, Iliya V.
  • Tatarinova, Larisa L.
  • Gorban, Alexander N.
  • Öttinger, Hans Christian

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) 066124) 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.

Suggested Citation

  • Karlin, Iliya V. & Tatarinova, Larisa L. & Gorban, Alexander N. & Öttinger, Hans Christian, 2003. "Irreversibility in the short memory approximation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 327(3), pages 399-424.
    • Handle: RePEc:eee:phsmap:v:327:y:2003:i:3:p:399-424
    DOI: 10.1016/S0378-4371(03)00510-7
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    Cited by:

    1. Gorban, Alexander N. & Karlin, Iliya V., 2004. "Uniqueness of thermodynamic projector and kinetic basis of molecular individualism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(3), pages 391-432.
    2. Gorban, A.N. & Packwood, D.J., 2014. "Enhancement of the stability of lattice Boltzmann methods by dissipation control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 414(C), pages 285-299.

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