Comment on "Critique of q-entropy for thermal statistics" by M. Nauenberg

TL;DR

This paper responds to M. Nauenberg's criticisms of nonextensive statistical mechanics, defending its physical validity and addressing concerns about fundamental thermodynamic principles.

Contribution

It provides a counter-argument to Nauenberg's objections, clarifying the theoretical foundations of nonextensive entropy and its consistency with thermodynamics.

Findings

Reaffirms the validity of q-entropy in thermal statistics

Addresses misconceptions about thermodynamic principles

Supports nonextensive mechanics as a consistent generalization

Abstract

It was recently published by M. Nauenberg [1] a quite long list of objections about the physical validity for thermal statistics of the theory sometimes referred to in the literature as {\it nonextensive statistical mechanics}. This generalization of Boltzmann-Gibbs (BG) statistical mechanics is based on the following expression for the entropy: S_q= k\frac{1- \sum_{i=1}^Wp_i^q}{q-1} (q \in {\cal R}; S_1=S_{BG} \equiv -k\sum_{i=1}^W p_i \ln p_i) . The author of [1] already presented orally the essence of his arguments in 1993 during a scientific meeting in Buenos Aires. I am replying now simultaneously to the just cited paper, as well as to the 1993 objections (essentially, the violation of "fundamental thermodynamic concepts", as stated in the Abstract of [1]).