Chaos and hydrodynamics

Pierre Gaspard

Physica A: Statistical Mechanics and its Applications, 1997, vol. 240, issue 1, 54-67

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.

Date: 1997
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:240:y:1997:i:1:p:54-67

DOI: 10.1016/S0378-4371(97)00130-1

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