With reference to systems obeying conservation of flow, for which a probability density function may be used in their description, it is shown that the interesting relationship established by Nikolov and Frieden (NF) between entropy increase and Fisher information [Phys. Rev. E 49, 4815 (1994)] holds only in special cases. We will here (i) exhibit a counterexample (to the hypothetical NF relationship) and (ii) derive a valid, Fisher's information-related upper bound to entropy increases.