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Gorban AN, Karlin IV. Macroscopic dynamics through coarse-graining: a solvable example. Phys Rev E Stat Nonlin Soft Matter Phys. 2002;65(2):026116doi: 10.1103/PhysRevE.65.026116.
Gorban, A. N., & Karlin, I. V. (2002). Macroscopic dynamics through coarse-graining: a solvable example. Physical review. E, Statistical, nonlinear, and soft matter physics, 65(2), 026116. https://doi.org/10.1103/PhysRevE.65.026116
Gorban, Alexander N, and Karlin, Iliya V. "Macroscopic dynamics through coarse-graining: a solvable example." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 65,2 (2002): 026116. doi: https://doi.org/10.1103/PhysRevE.65.026116
Gorban AN, Karlin IV. Macroscopic dynamics through coarse-graining: a solvable example. Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Feb;65(2):026116. doi: 10.1103/PhysRevE.65.026116. Epub 2002 Jan 18. PMID: 11863596.
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Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Feb;65(2):026116. doi: 10.1103/PhysRevE.65.026116. Epub 2002 Jan 18.

Macroscopic dynamics through coarse-graining: a solvable example.

Physical review. E, Statistical, nonlinear, and soft matter physics

Alexander N Gorban, Iliya V Karlin

Affiliations

  1. Institute of Computational Modeling RAS, 660036 Krasnoyarsk, Russia.

PMID: 11863596 DOI: 10.1103/PhysRevE.65.026116

Abstract

The recently derived fluctuation-dissipation formula [A. N. Gorban et al., Phys. Rev. E 63, 066124 (2001)] is illustrated by the explicit computation for McKean's kinetic model [H. P. McKean, J. Math. Phys. 8, 547 (1967)]. It is demonstrated that the result is identical, on the one hand, to the sum of the Chapman-Enskog expansion, and, on the other hand, to the exact solution of the invariance equation. The equality between all three results holds up to the crossover from the hydrodynamic to the kinetic domain.

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