The entropy production paradox for fractional diffusion

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.