Comment on "Essential discreteness in generalized thermostatistics with non-logarithmic entropy" by S. Abe

TL;DR

This paper refutes Abe's claim by demonstrating that the q-entropy of nonextensive statistical mechanics can be generalized to continuous variables similarly to Boltzmann-Gibbs entropy, allowing its use in both discrete and continuous cases.

Contribution

The paper provides a clear demonstration that q-entropy can be extended to continuous variables, countering previous claims that it is only applicable to discrete systems.

Findings

q-entropy can be generalized to continuous variables

Contradicts Abe's claim about the limitations of q-entropy

Supports broader applicability of nonextensive statistical mechanics

Abstract

Recently Abe (arXiv:cond-mat/1005.5110v1) claimed that the q-entropy of nonextensive statistical mechanics cannot be generalized for the continuous variables and therefore can be used only in the discrete case. In this letter, we show that the discrete q-entropy can be generalized to continuous variables exactly in the same manner as Boltzmann-Gibbs entropy, contrary to the claim by Abe, so that q-entropy can be used with discrete as well as continuous variables.