开放保体积系统非平衡态stationary states的分形性：II。高尔顿板
Fractality of the non-equilibrium stationary states of open volume-preserving systems: II. Galton boards
摘要：
高尔顿板是在均匀外场中确定性扩散的模型，类似于驱动周期性洛伦兹气体，在这里考虑的耗散机制的情况下。假设一个圆柱形的几何形状与轴沿外场的方向，二维板成为一个模型的一维质量输运沿外场的方向。这是一个纯粹的扩散过程，允许分形非平衡定态下的流量边界条件。分析结果得到的统计多面包师映射建模这样一个非均匀扩散过程。建立了局部相空间统计与宏观相空间统计之间的对应关系。不变状态的分形是负责的熵产生率的积极性。
英文摘要：
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.
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