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

TL;DR

This paper critiques the use of functional calculus in Rènyi entropy thermodynamics, showing it produces anomalies similar to Tsallis entropy and arguing the derived distributions are not genuine generalized distributions.

Contribution

It demonstrates that the anomalies are not unique to Rènyi entropy and highlights issues with the functional calculus approach and the validity of the resulting distributions.

Findings

Tsallis entropy also shows anomalies with the same approach

The Lagrange multiplier is set in an ad-hoc manner in the method

The derived distributions do not recover the standard partition function

Abstract

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.