A generalized $q$ growth model based on nonadditive entropy

TL;DR

This paper introduces a unified growth model derived from non-extensive statistical physics using nonadditive $q$ entropy, capable of reproducing various classical growth laws and revealing a universal early-time power law behavior.

Contribution

The paper develops a generalized growth equation based on nonadditive entropy that encompasses many known growth laws and highlights a universal early-time power law growth.

Findings

The model reproduces power law, exponential, logistic, and other growth laws.

Early-time growth follows a power law with exponent related to $q$.

The model connects growth dynamics with nonadditive entropy concepts.

Abstract

We present a general growth model based on non-extensive statistical physics is presented. The obtained equation is expressed in terms of nonadditive $q$ entropy. We show that the most common unidimensional growth laws such as power law, exponential, logistic, Richards, Von Bertalanffy, Gompertz can be obtained. This model belongs as a particular case reported in (Physica A 369, 645 (2006)). The new evolution equation resembles the "universality" revealed by West for ontogenetic growth (Nature 413, 628 (2001)). We show that for early times the model follows a power law growth as $ N(t) \approx t ^ D $, where the exponent $D \equiv \frac{1}{1-q}$ classifies different types of growth. Several examples are given and discussed.