Abstract

Deterministic diffusive systems, such as the periodic Lorentz gas, multibaker map, as well as spatially periodic systems of interacting particles, have nonequilibrium stationary states with fractal properties when put in contact with particle reservoirs at their boundaries. We study the macroscopic limits of these systems and establish a correspondence between the thermodynamics of the macroscopic diffusion process and the fractality of the stationary states that characterize the phase-space statistics. In particular the entropy production rate is recovered from first principles using a formalism due to Gaspard [J. Stat. Phys. 88, 1215 (1997)]. This paper is the first of two; the second article considers the influence of a uniform external field on such systems. © 2009 The American Physical Society.