Comment on "Black Hole Entropy: A Closer Look"

TL;DR

This paper critiques Tsallis's claim that traditional entropy measures are inadequate for black hole entropy, clarifying key thermodynamic distinctions and defending the conventional entropy framework.

Contribution

It clarifies the distinction between additivity and extensivity in entropy and counters Tsallis's proposal of a non-additive entropy for black holes.

Findings

Reaffirmation of the importance of additivity in entropy

Clarification of the difference between extensivity and additivity

Critique of Tsallis's non-additive entropy proposal

Abstract

In a recent paper [Entropy 2020, 22(1), 17] C. Tsallis states that entropy -- as in Shannon's or Kullback-Leiber's definitions -- is inadequate to interpret black hole entropy and suggests that a new non-additive functional should take the role of entropy. Here we counter argue by explaining the important distinction between the properties of extensivity and additivity, the latter is fundamental for entropy while the former is a property of particular thermodynamical systems that is not expected on black holes. We also point out other debatable statements in his analysis of black hole entropy.