Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2009-03-20
Phys. Rev. E 80, 021127 (2009) [15 pages]
Physics
Condensed Matter
Statistical Mechanics
Second of two papers, 17 double column pages, 10 figures
Scientific paper
10.1103/PhysRevE.80.021127
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 non-equilibrium stationary states under flux boundary conditions. Analytical results are obtained for the statistics of multi-baker maps modeling such a non-uniform diffusion process. A correspondence is established between the local phase-space statistics and their macroscopic counter-parts. The fractality of the invariant state is shown to be responsible for the positiveness of the entropy production rate.
Barra Felipe
Gaspard Pierre
Gilbert Thomas
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