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Information transfer between dynamical system components.

X San Liang1, Richard Kleeman

  • 1Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA. sanliang@cims.nyu.edu

Physical Review Letters
|December 31, 2005
PubMed
Summary

We developed a new method to quantify information transfer in dynamical systems. This approach accurately measures how information moves between system components, applicable to both continuous and discrete systems.

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Area of Science:

  • Statistical Mechanics
  • Dynamical Systems Theory
  • Information Theory

Background:

  • Understanding information flow is crucial in complex systems.
  • Existing measures of information transfer have limitations.
  • Quantifying entropy change in multi-component systems requires a robust framework.

Purpose of the Study:

  • To develop a rigorous formalism for information transfer in systems with known dynamics.
  • To accurately classify entropy change mechanisms into self-evolution and transfer.
  • To provide a versatile measure applicable to continuous flows and discrete maps.

Main Methods:

  • Formalism based on classifying entropy change.
  • Decomposition of entropy change into self-evolution and transfer components.

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  • Validation using canonical dynamical systems (Baker transformation, Hénon map).

    • Main Results:

    • A novel, rigorous formalism for information transfer is presented.
    • The formalism accurately distinguishes between self-entropy change and transferred entropy.
    • The derived transfer measure exhibits asymmetry and aligns with classical measures.

    Conclusions:

    • The presented formalism offers a precise method for quantifying information transfer.
    • This approach enhances the understanding of information dynamics in various systems.
    • The validated measure provides a reliable tool for analyzing complex system interactions.