In systems which exhibit deterministic diffusion, the gross parameter dependence of the diffusion coefficient can often be understood in terms of random walk models. Provided the decay of correlations is fast enough, one can ignore memory effects and approximate the diffusion coefficient according to dimensional arguments. By successively including the effects of one and two steps of memory on this approximation, we examine the effects of ``persistence'' on the diffusion coefficients of extended two-dimensional billiard tables and show how to properly account for these effects, using walks in which a particle undergoes jumps in different directions with probabilities that depend on where they came from.
Entropy production of diffusion in spatially periodic deterministic systems
本文用{ \it ab initio}方法推导了不可逆热力学给出的各类扩散过程的熵产生率表达式。第一类是洛伦兹气体，其中非相互作用的粒子在空间周期性晶格上运动，并与固定的散射体弹性碰撞。第二类是周期性系统，其中$N$粒子彼此相互作用，并且其中之一是在晶格的单元之间扩散的示踪粒子。我们假设，在任何一种情况下，系统的动力学是确定性的和双曲的，与积极的李雅普诺夫指数。这项工作扩展的方法最初开发的混沌二维模型的扩散，多面包师映射，更高的维度，连续时间动力系统，适合于一个或多个移动粒子的系统。在这里，我们表示的熵产生率的流体动力学措施，是由微观流体动力学模式，描述了最慢的衰减系统的平衡态的分形特性。
Graduate School of Information Science and Technology, The University of Osaka, Osaka, Japan（信息科学与技术研究生学校，大阪大学，大阪，日本）；International Research Center for Neurointelligence, The University of Tokyo, Tokyo, Japan（神经智能国际研究中心，东京大学，东京，日本）
