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Generalized Derangetropy Functionals for Modeling Cyclical Information Flow.

Masoud Ataei1, Xiaogang Wang2

  • 1Department of Mathematical and Computational Sciences, University of Toronto, Mississauga, ON L5L 1C6, Canada.

Entropy (Basel, Switzerland)
|June 26, 2025
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Summary
This summary is machine-generated.

This study introduces derangetropy operators to model cyclical information flow. These operators analyze information topography and dynamics, revealing long-term behavior in complex systems.

Keywords:
cyclical information flowentropyfunctional information theoryinformation dynamicsnonlinear differential equationsprobability distributions

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Area of Science:

  • Information theory
  • Non-equilibrium statistical mechanics
  • Dynamical systems

Background:

  • Traditional entropy measures like Shannon entropy are scalar and do not capture topographical information.
  • Modeling cyclical and feedback-driven information flow requires advanced analytical tools.
  • Understanding information evolution in complex systems is crucial for various scientific fields.

Purpose of the Study:

  • To introduce a generalized functional framework for modeling cyclical and feedback-driven information flow.
  • To develop derangetropy operators that act directly on probability densities for topographical information representation.
  • To provide analytical tools for understanding the long-term dynamics of information in periodically structured and stochastic systems.

Main Methods:

  • Development of a generalized family of derangetropy operators.
  • Application of functional transformations governed by nonlinear differential equations.
  • Recursive application of operators to induce a spectral diffusion process governed by the heat equation.

Main Results:

  • Derangetropy operators provide a topographical representation of information across probability distribution support.
  • The framework captures periodic and self-referential aspects of information evolution.
  • Recursive application leads to spectral diffusion converging toward a Gaussian characteristic function, establishing an analytical foundation for long-term dynamics.

Conclusions:

  • The proposed framework offers novel tools for analyzing temporal information evolution in systems with periodic structure, stochastic feedback, and delayed interaction.
  • Potential applications include artificial neural networks, communication theory, and non-equilibrium statistical mechanics.
  • The convergence result provides a theoretical basis for understanding information dynamics under cyclic modulation.