Dynamical systems theory and transport coefficients: A survey with applications to Lorentz gases

Recent developments in the applications of ideas from dynamical systems theory to transport phenomena in non-equilibrium fluids are reviewed. We discuss methods for expressing transport coefficients for fluid systems in terms of dynamical quantities that characterize the chaotic behavior of the phase-space trajectories of such systems. We describe two such methods: the escape rate method of Gaspard and co-workers, and the Gaussian thermostat method of Hoover, Posch and co-workers, and of Evans and Morriss and co-workers. Related issues such as the properties of repellers and attractors and of entropy production in such systems will be discussed. As examples of these formal developments, we describe recent work on Lorentz gases where the escape rate and Gaussian thermostat approaches to transport can be implemented in detail and the results compared with both numerical simulations and with the results of kinetic theory of gases.