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A generalized permutation entropy for noisy dynamics and random processes.

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We introduce multivariate group entropies, novel information-theoretical measures extending group entropies. These measures are suitable for complex systems and enable the creation of solvable dynamical models.

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Area of Science:

  • Information Theory
  • Complex Systems Science
  • Mathematical Physics

Background:

  • Group entropies are established information-theoretical measures.
  • Complex systems often exhibit universal behaviors, such as the super-exponential class.
  • Dynamical models are crucial for understanding system evolution.

Purpose of the Study:

  • To define and explore a new class of multivariate group entropies.
  • To propose information measures applicable to the super-exponential universality class.
  • To demonstrate the utility of group-theoretical structures in constructing solvable dynamical models.

Main Methods:

  • Definition of multivariate group entropies.
  • Application of these entropies to complex systems.
  • Utilizing group theory to derive discrete dynamical models.

Main Results:

  • Introduction of multivariate group entropies, extending existing families.
  • Proposal of a general entropy measure for the super-exponential universality class.
  • Demonstration that group-theoretical structures yield exactly solvable discrete dynamical models.

Conclusions:

  • Multivariate group entropies offer a powerful new framework in information theory.
  • These entropies provide suitable measures for specific complex system classes.
  • The connection between group theory and dynamical systems opens new avenues for research.