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Natural systems often show complex dynamics. The quantification of such complex dynamics is an important step in, e.g., characterization and classification of different systems or to investigate the effect of an external perturbation on the dynamics. Promising routes were followed in the past using concepts based on (Shannon’s) entropy. Here, we propose a new, conceptually sound measure that can be pragmatically computed, in contrast to pure theoretical concepts based on, e.g., Kolmogorov complexity. We illustrate the applicability using a toy example with a control parameter and go on to the molecular evolution of the HIV1 protease for which drug treatment can be regarded as an external perturbation that changes the complexity of its molecular evolutionary dynamics. In fact, our method identifies exactly those residues which are known to bind the drug molecules by their noticeable signal. We furthermore apply our method in a completely different domain, namely foreign exchange rates, and find convincing results as well.