Complexity measures, emergence, and multiparticle correlations.
We study correlation measures for complex systems. First, we investigate some recently proposed measures based on information geometry. We show that these measures can increase under local transformations as well as under discarding particles, thereby questioning their interpretation as a quantifier for complexity or correlations. We then propose a refined definition of these measures, investigate its properties, and discuss its numerical evaluation. As an example, we study coupled logistic maps and study the behavior of the different measures for that case. Finally, we investigate other local effects during the coarse graining of the complex system.
Theoretical Physics, School of Physics and Astronomy, The University of Manchester, Manchester, United Kingdom. tobias.galla@manchester.ac.uk
Tobias
T
Galla
Otfried
O
Gühne
D000465:Algorithms; D001703:Biophysics / Q000379:methods; D003142:Communication; D003625:Data Collection; D019277:Entropy; D006801:Humans; D016247:Information Storage and Retrieval / Q000379:methods; D015233:Models, Statistical; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D015588:Observer Variation; D010825:Physics / Q000379:methods*; D011336:Probability; D015203:Reproducibility of Results