Comment on "Troublesome aspects of the Renyi-MaxEnt treatment" by A. Plastino, M.C. Rocca and F. Pennini

Plastino, Rocca and Pennini [Phys. Rev. E \textbf{94} (2016) 012145] recently stated that the R\'enyi entropy is not suitable for thermodynamics by using functional calculus, since it leads to anomalous results unlike the Tsallis entropy. We first show that the Tsallis entropy also leads to such anomalous behaviours if one adopts the same functional calculus approach. Second, we note that one of the Lagrange multipliers is set in an \textit{ad-hoc} manner in the functional calculus approach of Plastino, Rocca and Pennini. Finally, the explanation for these anomalous behaviours is provided by observing that the generalized distributions obtained by Plastino, Rocca and Pennini does not yield the ordinary canonical partition function in the appropriate limit and therefore cannot be considered as genuine generalized distributions.