Dispersive diffusion and wave propagation seem to be unconnected and fundamentally different evolution equations. In the context of anomalous diffusion however modeling approaches based on fractional diffusion equations have been presented, which allow to build a continuous bridge between the two regimes. The transition from irreversible dispersive diffusion to reversible wave propagation shows an unexpected increase in entropy production. This seemingly paradoxical behavior of fractional diffusion is reviewed and compared to the behavior of a tree-based diffusion model.

中文翻译：

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分数扩散的熵产生悖论

色散扩散和波传播似乎是互不相关且根本不同的演化方程。然而，在反常扩散的背景下，已经提出了基于分数扩散方程的建模方法，它允许在两种状态之间建立一个连续的桥梁。从不可逆色散扩散到可逆波传播的转变显示出熵产生的意外增加。对分数扩散的这种看似矛盾的行为进行了审查，并将其与基于树的扩散模型的行为进行了比较。