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Chaos and hydrodynamics

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  • Gaspard, Pierre

Abstract

We present a general approach to transport properties based on the dynamics of statistical ensembles of trajectories, the so-called Liouvillian dynamics. An approach is developed for time-reversal symmetric and volume-preserving systems like Hamiltonian systems or billiards with elastic collisions. The crucial role of boundary conditions in the modeling of nonequilibrium systems is emphasized. A general construction of hydrodynamic modes using quasiperiodic boundary conditions is proposed based on the Frobenius-Perron operator and its Pollicott-Ruelle resonances, which can be defined in chaotic systems. Moreover, we obtain a simple derivation of the Lebowitz-McLennan steady-state measures describing a nonequilibrium gradient of density in diffusion. In a large-system limit, the singular character of such steady states is shown to have important implications on entropy production.

Suggested Citation

  • Gaspard, Pierre, 1997. "Chaos and hydrodynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 240(1), pages 54-67.
    • Handle: RePEc:eee:phsmap:v:240:y:1997:i:1:p:54-67
    DOI: 10.1016/S0378-4371(97)00130-1
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    Cited by:

    1. Lazare Osmanov & Ramaz Khomeriki, 2022. "Regular and chaotic motion of two bodies swinging on a rod," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(11), pages 1-7, November.
    2. Cang, Shijian & Li, Yue & Kang, Zhijun & Wang, Zenghui, 2020. "Generating multicluster conservative chaotic flows from a generalized Sprott-A system," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).

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