Time Evolution of Relative Entropies for Anomalous Diffusion
Time Evolution of Relative Entropies for Anomalous Diffusion
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DOI：
10.3390/e15082989
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发表时间：
2013-08-01
期刊：
影响因子：
2.7
通讯作者：
Hoffmann, Karl Heinz
中科院分区：
文献类型：
--
作者：
Prehl, Janett;Boldt, Frank;Hoffmann, Karl Heinz
反常扩散过程的熵产生佯谬描述了一种现象，即介于扩散方程和波动方程之间的单参数动力学方程族的熵产生率（香农，Tsallis或Renyi）意外地向波动方程极限增加。此外，同样令人惊讶的是，熵根本不对扩散和波之间的桥接状态进行排序。然而，已经发现，相对熵，与适当选择的参考分布，做。因此，相对熵提供了一种物理上合理的方式来设置哪个过程比另一个过程更“接近”纯扩散，将纯波传播理想地放置在离纯扩散“最远”的地方。在这里，我们研究的时间行为的相对熵下的基本的单参数家庭的动力学方程的基础上空间分数阶导数的演化动力学。
The entropy production paradox for anomalous diffusion processes describes a phenomenon where one-parameter families of dynamical equations, falling between the diffusion and wave equations, have entropy production rates (Shannon, Tsallis or Renyi) that increase toward the wave equation limit unexpectedly. Moreover, also surprisingly, the entropy does not order the bridging regime between diffusion and waves at all. However, it has been found that relative entropies, with an appropriately chosen reference distribution, do. Relative entropies, thus, provide a physically sensible way of setting which process is "nearer" to pure diffusion than another, placing pure wave propagation, desirably, "furthest" from pure diffusion. We examine here the time behavior of the relative entropies under the evolution dynamics of the underlying one-parameter family of dynamical equations based on space-fractional derivatives.