Identification of chaotic and stochastic processes by permutation entropy analysis

The dynamical nature of time signals can be determined by the simultaneous use of entropy and statistical complexity [O. A. Rosso, \textit{et al.}, \textit{Phys. Rev. Lett. }99 154102 (2007)]. These key measures can be implemented using the amplitude permutation probability introduced by Bandt and Pompe [C. Bandt and B. Pompe, \textit{Phys. Rev. Lett.}, 88 174102 (2002)]. Stochastic and chaotic processes are distinguished because they occupy different regions of the entropy-complexity plane. Permutation entropy analysis is used to demonstrate that temperature fluctuations observed in a basic heat transport experiment arise from chaotic dynamics [J. E. Maggs and G. J. Morales, \textit{Plasma Phys. and Control. Fusion}, 55 085015 (2013)]. Locations of various known stochastic and chaotic processes in the entropy-complexity plane are presented and the important technique of 'sub-sampling' for the amelioration of noise is discussed. The permutation entropy analysis can be applied to any time signal as no pre-processing or \textit{a priori} conditions are required. This signal analysis technique has the potential to uncover new features in a wide range of fusion and basic plasma experiments.