Fractality of the nonequilibrium stationary states of open volume-preserving systems. II. Galton boards.
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.
Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla, 487-3 Santiago, Chile.
Felipe
F
Barra
Pierre
P
Gaspard
Thomas
T
Gilbert