Instability of q-expectation value

TL;DR

This paper demonstrates that the q-expectation value, used in nonextensive statistical mechanics, is generally unstable under small probability distribution changes, unlike the stable ordinary expectation value.

Contribution

It reveals the instability of the q-expectation value under small probability deformations, highlighting a fundamental limitation in its application.

Findings

q-Expectation value is unstable under small distribution changes

Ordinary expectation value remains stable under similar deformations

Implications for the use of q-expectation in statistical mechanics

Abstract

q-Expectation value of a physical quantity is widely used in nonextensive statistical mechanics. Here, it is shown that the q-expectation value is not stable under small deformations of a probability distribution function, in general, whereas the ordinary expectation value is always stable.