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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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Related Experiment Video

Updated: Nov 27, 2025

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy
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Range Entropy: A Bridge between Signal Complexity and Self-Similarity.

Amir Omidvarnia1,2, Mostefa Mesbah3, Mangor Pedersen1

  • 1The Florey Institute of Neuroscience and Mental Health, Austin Campus, Heidelberg, VIC 3084, Australia.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary
This summary is machine-generated.

Approximate entropy (ApEn) and sample entropy (SampEn) are linked to the Hurst exponent. A new method, RangeEn, offers improved robustness and a linear relationship with the Hurst exponent for temporal complexity analysis.

Keywords:
Hurst exponentapproximate entropycomplexity, self-similarityrange entropysample entropy

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Area of Science:

  • Complexity Science
  • Time Series Analysis
  • Biomedical Signal Processing

Background:

  • Approximate entropy (ApEn) and sample entropy (SampEn) are standard metrics for assessing temporal complexity.
  • Existing entropy measures exhibit limitations, including susceptibility to signal amplitude variations and an unclear relationship with self-similarity (Hurst exponent).
  • Standard practice involves amplitude correction, which may not fully resolve these issues.

Purpose of the Study:

  • To investigate the relationship between ApEn, SampEn, and the Hurst exponent.
  • To develop a novel entropy measure, RangeEn, that addresses the limitations of existing methods.
  • To evaluate the performance of RangeEn in terms of robustness and linearity with the Hurst exponent.

Main Methods:

  • Simulations were used to explore the relationship between ApEn, SampEn, and the Hurst exponent, focusing on parameters like tolerance (r) and embedding dimension (m).
  • A new entropy measure, Range entropy (RangeEn), was developed.
  • RangeEn was compared against ApEn and SampEn for robustness to nonstationary signals and linearity with the Hurst exponent. Its bounded nature (0-1) and independence from amplitude correction were also assessed.

Main Results:

  • ApEn and SampEn demonstrate a relationship with the Hurst exponent influenced by tolerance (r) and embedding dimension (m).
  • RangeEn exhibits greater robustness to nonstationary signal changes compared to ApEn and SampEn.
  • RangeEn shows a more linear relationship with the Hurst exponent and does not require signal amplitude correction.

Conclusions:

  • RangeEn offers an improved approach to temporal complexity analysis, overcoming limitations of ApEn and SampEn.
  • The robustness and linear relationship with the Hurst exponent make RangeEn suitable for analyzing complex, real-world data.
  • The study highlights the clinical utility of RangeEn for characterizing physiological signals, exemplified by its application to epileptic EEG data.