Comment on "Route from discreteness to the continuum for the Tsallis q-entropy"

TL;DR

This paper critiques a recent modification of Tsallis q-entropy for discrete variables, arguing it violates fundamental entropy properties and supports the view that q-entropy cannot be applied to continuous systems.

Contribution

It provides a critical analysis showing that the proposed modification of q-entropy breaks the expandability property, reinforcing the idea that q-entropy is unsuitable for continuous variables.

Findings

The modification violates the expandability property of entropy.

Supports the absence of q-entropy for continuous systems.

Highlights fundamental limitations of non-logarithmic entropies.

Abstract

Several years ago, it has been discussed that non-logarithmic entropies such as the Tsallis q-entropy cannot be applied to systems with continuous variables. Now, in their recent paper [Phys. Rev. E 97, 012104 (2018)], Oikonomou and Bagci have modified the form of the q-entropy for discrete variables in such a way that its continuum limit exists. Here, it is shown that this modification violates the expandability property of entropy, and their work is actually a supporting evidence for the absence of the q-entropy for systems with continuous variables.