Complexity measures, emergence, and multiparticle correlations

Abstract

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.

13 pages, 5 figures, accepted by Phys. Rev. E

References in corpus (5)

• Entanglement detection
• Geometric phase of an atom in a magnetic storage ring
• Symbolic Synchronization and the Detection of Global Properties of Coupled Dynamics from Local Information
• Irreducible multiparty correlation can be created by local operations
• Quantifying structure in networks

Cited by in corpus (8)

• Quantifying genuine multipartite correlations and their pattern complexity
• Information-theoretical analysis of topological entanglement entropy and multipartite correlations
• Computing complexity measures for quantum states based on exponential families
• Aging and Reliability of Quantum Networks
• A superstatistical measure of distance from canonical equilibrium
• Weaving and neural complexity in symmetric quantum states
• Analysing multiparticle quantum states
• Cooperation and dependencies in multipartite systems