A generalized $q$ growth model based on non-additive entropy

Rond'on, I.; Sotolongo-Costa, O.; Gonz'alez, J. A.

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 \textquotedblleft universality \textquotedblright 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 $D \equiv \frac{1}{1-q}$ classify different growth. Several examples are presented and discussed.