Chaos and hydrodynamics

✍ Scribed by Pierre Gaspard

• Book ID: 104341623
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 707 KB
• Volume: 240
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/s0378-4371(97)00130-1

✦ Synopsis

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.