Entropy–complexity analysis in some globally-coupled systems

•The entropy–complexity plane enables to assess the chaotic or noisy nature of time series.•This frame is applied to analyze the mean-field time series in a globally-coupled model.•A Poincaré section analysis provides a natural sampling time for this analysis.•Permutation entropy is shown to detect dynamical anomalies related to coherent structures.

Globally-coupled NN-body systems are well known to possess an intricate dynamics. When NN is large, collective effects may drastically lower the effective dimension of the dynamics breaking the conditions on ergodicity necessary for the applicability of statistical mechanics. These problems are here illustrated and discussed through an entropy–complexity analysis of the repulsive Hamiltonian mean-field model. Using a Poincaré section of the mean-field time series provides a natural sampling time in the entropy–complexity treatment. This approach is shown to single-out the out-of-equilibrium dynamical features and to uncover a transition of the system dynamics from low-energy non-Boltzmann quasi-stationary states to high-energy stochastic-like behavior.