IRREVERSIBILITY, DIFFUSION AND MULTIFRACTAL MEASURES IN THERMOSTATTEDSYSTEMS

Non-equilibrium macroscopic processes are irreversible, so that diffus ion coefficients are always positive. Here we show how irreversible be haviour arises from reversible microscopic dynamics in some thermostat ted systems, the Lorentz gas in an external field, colour diffusion an d planar Couette flow in N-particle systems. Macroscopic irreversibili ty is not only shown to be consistent with reversible equations of mot ion, but follows directly without ad hoc assumptions. We consider ther mostatted systems from the periodic orbit expansion (POE) viewpoint, w here the strange attractor is approximated by a measure on the periodi c orbits of the system. Although the POE techniques facilitate the exp lanation, we believe the mechanism is true in general for thermostatte d systems. (C) 1997 Elsevier Science Ltd.