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Multiscale entropy (MSE) and Allan variance, though developed independently, share information-theoretic foundations. They exhibit similar properties in natural systems like chaotic lasers and heartbeat data, but diverge in artificial random sequences.

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Area of Science:

  • Complex Systems Analysis
  • Nonlinear Dynamics
  • Statistical Signal Processing

Background:

  • Multiscale entropy (MSE) analyzes nonlinear systems across multiple time scales.
  • Allan variance assesses oscillator stability over various time scales.
  • Both methods examine multiscale temporal structures in physical phenomena.

Purpose of the Study:

  • To explore the information-theoretic foundations and shared properties of MSE and Allan variance.
  • To experimentally verify the consistency of MSE and Allan variance in natural systems.
  • To identify conditions governing the consistency between MSE and Allan variance.

Main Methods:

  • Information-theoretic comparison of Multiscale Entropy (MSE) and Allan variance.
  • Experimental analysis of low-frequency fluctuations (LFF) in chaotic lasers.
  • Analysis of physiological heartbeat data.
  • Calculation of conditions for consistency based on conditional probabilities.

Main Results:

  • MSE and Allan variance share underlying information-theoretic principles and exhibit similar tendencies.
  • Experimental confirmation of similar properties in chaotic laser LFF and heartbeat data.
  • Identification of a specific condition, related to conditional probabilities, for consistency.
  • Demonstration of differing trends between MSE and Allan variance in an artificial random sequence.

Conclusions:

  • Natural physical systems often satisfy the condition for consistency between MSE and Allan variance.
  • MSE and Allan variance can be considered complementary or interchangeable in certain natural system analyses.
  • The distinction between natural and artificial systems highlights the importance of the identified consistency condition.