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Permutation group entropy: A new route to complexity for real-valued processes.

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This study unifies permutation entropy and group entropy for time series analysis. The approach extends complexity measures to random processes, offering a framework for chaotic and random behaviors.

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Area of Science:

  • Complexity Science
  • Time Series Analysis
  • Information Theory

Background:

  • Permutation entropy is a key measure for time series complexity.
  • Group entropy offers complementary insights into system dynamics.
  • Existing methods struggle to unify analysis of deterministic and random processes.

Purpose of the Study:

  • To review and extend group entropy for permutation complexity.
  • To develop a unified framework for analyzing chaotic and random time series.
  • To bridge the gap between deterministic dynamics and stochastic processes in complexity measures.

Main Methods:

  • Revisiting the application of group entropy to permutation complexity.
  • Extending permutation entropy rate from deterministic to random processes.
  • Developing a unified theoretical framework for complexity analysis.

Main Results:

  • The proposed approach successfully extends permutation entropy to random processes.
  • Group entropy provides a robust foundation for a unified complexity framework.
  • The unified framework accommodates both chaotic and random behaviors.

Conclusions:

  • The integration of group entropy and permutation entropy offers a powerful new tool for time series analysis.
  • This unified approach enhances our ability to characterize complex systems.
  • The framework provides a more comprehensive understanding of time series dynamics.