The q-nonadditivity of nonextensive statistics is not a true physical property

TL;DR

This paper argues that the commonly assumed nonadditivity in nonextensive statistics is not a fundamental physical property, as the parameter defining nonadditivity depends on the mathematical division of the system and is inconsistent.

Contribution

It challenges the notion that q-nonadditivity is a true physical property, showing that the nonadditivity parameter is not unique and depends on the mathematical partitioning.

Findings

The nonadditivity parameter lphaannot be uniquely defined for a given system.

lphaepends on how the system is mathematically divided.

The use of lphas a characterization of nonadditivity is mathematically inconsistent.

Abstract

This is a note showing that, contrary to our lasting belief, the nonadditivity X(1+2)=X(1)+X(2)+\alpha X(1)X(2) is not a true physical property. \alpha in this expression cannot be unique for a given system. It unavoidably depends on how one mathematically divides the system and cannot be used to characterize nonadditivity. As a matter of fact, its use is mathematically inconsistent.