In a recent paper (Commun. Phys. 3, 100) Znidaric studies the growth of higher Renyi entropies in diffusive systems and claims that they generically grow ballistically in time, except for spin-1/2 models in d=1 dimension. Here, we point out that the necessary conditions for sub-ballistic growth of Renyi entropies are in fact much more general, and apply to a large class of systems, including experimentally relevant ones in arbitrary dimension and with larger local Hilbert spaces.
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