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Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
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Quantifying entropy using recurrence matrix microstates.

Gilberto Corso1, Thiago de Lima Prado2, Gustavo Zampier Dos Santos Lima3

  • 1Departamento de Biofísica e Farmacologia, Universidade Federal do Rio Grande do Norte, Natal 59078-970, Brazil.

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Summary
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A novel recurrence quantifier using information entropy offers a robust method for time series analysis. This new entropy calculation correlates well with system dynamics and is efficient for various data lengths.

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Area of Science:

  • Complex Systems Analysis
  • Information Theory
  • Time Series Analysis

Background:

  • Traditional entropy quantifiers for time series analysis often have limitations.
  • Existing methods can be computationally intensive and sensitive to parameters.
  • There is a need for robust and efficient entropy measures for diverse time series data.

Purpose of the Study:

  • To introduce a new recurrence quantifier for time series analysis based on information entropy.
  • To demonstrate the advantages of this novel method over traditional entropy quantifiers.
  • To validate the method's performance across different types of systems and data lengths.

Main Methods:

  • Defining probabilities based on microstates within a recurrence matrix (small binary submatrices).
  • Calculating information entropy using these microstate-defined probabilities.
  • Applying the method to both discrete and continuous time series data.

Main Results:

  • The new entropy quantifier shows a good correlation with the maximum Lyapunov exponent.
  • The method exhibits weak dependence on the vicinity threshold parameter.
  • Consistent and accurate results are obtained for both short and long time series segments.
  • The approach is computationally efficient, even for large datasets.

Conclusions:

  • The proposed recurrence quantifier offers a significant advancement in time series entropy analysis.
  • Its robustness, efficiency, and applicability to various systems make it a valuable tool.
  • This method provides a precise and computationally feasible alternative for analyzing complex systems.