Journal of Statistical Physics

, Volume 114, Issue 3–4, pp 1127–1137 | Cite as

Complexity of Dynamics as Variability of Predictability

  • Ruedi Stoop
  • Norbert Stoop
  • Leonid Bunimovich


We construct a complexity measure from first principles, as an average over the “obstruction against prediction” of some observable that can be chosen by the observer. Our measure evaluates the variability of the predictability for characteristic system behaviors, which we extract by means of the thermodynamic formalism. Using theoretical and experimental applications, we show that “complex” and “chaotic” are different notions of perception. In comparison to other proposed measures of complexity, our measure is easily computable, non-divergent for the classical 1-d dynamical systems, and has properties of non-overuniversality. The measure can also be computed for higher-dimensional and experimental systems, including systems composed of different attractors. Moreover, the results of the computations made for classical 1-d dynamical systems imply that it is not the nonhyperbolicity, but the existence of a continuum of characteristic system length scales, that is at the heart of complexity.

complex systems thermodynamic formalism complexity measures entropy prediction 


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Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • Ruedi Stoop
    • 1
  • Norbert Stoop
    • 2
  • Leonid Bunimovich
    • 3
  1. 1.INI, Physics DepartementUniversity/ETH ZürichZürichSwitzerland
  2. 2.Physics Department ETH Zürich, and International School of Scientific ComputingRand Afrikaans UniversityJohannesburgSouth Africa
  3. 3.Southeast Applied Analysis CenterGeorgia Institute of TechnologyAtlanta

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