RESUMO
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.
RESUMO
Galton boards are models of deterministic diffusion in a uniform external field, akin to driven periodic Lorentz gases, here considered in the absence of dissipation mechanism. Assuming a cylindrical geometry with axis along the direction of the external field, the two-dimensional board becomes a model for one-dimensional mass transport along the direction of the external field. This is a purely diffusive process which admits fractal nonequilibrium stationary states under flux boundary conditions. Analytical results are obtained for the statistics of multibaker maps modeling such a nonuniform diffusion process. A correspondence is established between the local phase-space statistics and their macroscopic counterparts. The fractality of the invariant state is shown to be responsible for the positiveness of the entropy production rate.