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.
Barra
Felipe
F
Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla, 487-3 Santiago, Chile.
Gaspard
Pierre
P
Gilbert
Thomas
T