An entropical characterization for complex systems becoming out of control

Abstract

General properties of N-dimensional multi-component or many-particle systems exhibiting self-similar hierarchical structure are presented. The entire system is partitioned into cells, which have an associated generalized entropy S(D) that is shown to be a universal function of the fractal dimension D of the configurations, exhibiting self-similarity properties which are independent of the dimensionality N. This provides a general way to classify the components of the system according to entropical reasons, independently of the observer's criteria. For certain complex systems, the normalized S(D) may also be associated with the large time stationary profile of the fractal density distribution in the absence of external fields (or control).