Irreversibility, diffusion and multifractal measures in thermostatted systems

Non-equilibrium macroscopic processes are irreversible, so that diffusion coefficients are always positive. Here we show how irreversible behaviour arises from reversible microscopic dynamics in some thermostatted systems, the Lorentz gas in an external field, colour diffusion and planar Couette flow in N-particle systems. Macroscopic irreversibility is not only shown to be consistent with reversible equations of motion, but follows directly without ad hoc assumptions. We consider thermostatted systems from the periodic orbit expansion (POE) viewpoint, where the strange attractor is approximated by a measure on the periodic orbits of the system. Although the POE techniques facilitate the explanation, we believe the mechanism is true in general for thermostatted systems.