An entropical characterization for complex systems becoming out of control

• We study complex systems whose components have a hierarchical sub-structure.
• The system is partitioned into cells to which a generalized entropy SS is associated.
• The different regimes of SS define an entropical classification of the components.
• This classification is independent of the observer’s criteria.
• The normalized SS can be associated to an evolution in the absence of control.

General properties of NN-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)S(D) that is shown to be a universal function of the fractal dimension DD of the configurations, exhibiting self-similarity properties which are independent of the dimensionality NN. 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)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).