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Two facts are pointed out: (1) Only when the diffusion equation is inadmissibly applied, outside its defined range of validity, does it lead to acausal predictions; (2) although there are many instances in which usually diffusive hydrodynamic variables propagate wave-like in condensed systems, none of them are connected with this appearance of acausality.
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Kostädt et al. (2001) studied this question.
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