A Comment on Nonextensive Statistical Mechanics

TL;DR

This paper clarifies a misconception in statistical mechanics, showing that long tail distributions are present in equilibrium thermodynamics and are not exclusive to nonextensive entropies like Tsallis entropy.

Contribution

It corrects a common misconception by demonstrating that long tail distributions exist in classical equilibrium thermodynamics, challenging the belief that they only arise from nonextensive statistics.

Findings

Long tail distributions are present in equilibrium thermodynamics.

The misconception about the origin of long tails is addressed and corrected.

Classical thermodynamics can produce long tail distributions without nonextensive entropies.

Abstract

There is a conception that Boltzmann-Gibbs statistics cannot yield the long tail distribution. This is the justification for the intensive research of nonextensive entropies (i.e. Tsallis entropy and others). Here the error that caused this misconception is explained and it is shown that a long tail distribution exists in equilibrium thermodynamics for more than a century.