The uncertainty measure for q-exponential distribution function

TL;DR

This paper derives a new uncertainty measure based on the q-exponential distribution, applicable to complex physical systems, exhibiting non-additivity and converging to Boltzmann-Gibbs entropy as q approaches 1.

Contribution

It introduces a novel entropic form for q-exponential distributions, capturing non-additive properties and ensuring concavity and maximization across different systems.

Findings

The entropy is non-additive for independent subsystems.

It converges to Boltzmann-Gibbs entropy as q approaches 1.

The entropy is concave and maximizable for all q.

Abstract

Based on the q-exponential distribution which has been observed in more and more physical systems, the varentropy method is used to derive the uncertainty measure of such an abnormal distribution function. The uncertainty measure obtained here can be considered as a new entropic form for the abnormal physical systems with complex interaction. The entropy obtained here also presents non-additive property for two independent subsystems and it will tend to the Boltzmann-Gibbs entropy when the nonextensive parameter q->1. It is very important to find that for different systems with any q, this entropic form is always concave and the systemic entropy is maximizable.