自相似台球中的稳态传导
Steady-state conduction in self-similar billiards
摘要：
自相似Lorentz台球信道是一个空间扩展的确定性动力学系统，它由一维无限多个单元组成，这些单元的大小根据它们的指数单调增加。这种特殊的几何形状诱导了一个非平衡定态，粒子从小尺度到大尺度稳定地流动。相应的不变测度具有分形性质，反映在相空间收缩率的动力学限制在一个细胞与适当的边界条件。在近平衡极限，我们发现这个量和热力学指定的熵产生率之间的数值协议。
英文摘要：
The self-similar Lorentz billiard channel is a spatially extended deterministic dynamical system which consists of an infinite one-dimensional sequence of cells whose sizes increase monotonically according to their indices. This special geometry induces a nonequilibrium stationary state with particles flowing steadily from the small to the large scales. The corresponding invariant measure has fractal properties reflected by the phase-space contraction rate of the dynamics restricted to a single cell with appropriate boundary conditions. In the near-equilibrium limit, we find numerical agreement between this quantity and the entropy production rate as specified by thermodynamics.
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