Chaos and hydrodynamics

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.