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Related Concept Videos

Entropy02:39

Entropy

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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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Weighted Mean00:57

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While taking the arithmetic, geometric, or harmonic mean of a sample data set, equal importance is assigned to all the data points. However, all the values may not always be equally important in some data sets. An intrinsic bias might make it more important to give more weightage to specific values over others.
For example, consider the number of goals scored in the matches of a tournament. While computing the average number of goals scored in the tournament, it may be more important to...
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Entropy and the Second Law of Thermodynamics01:20

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The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The relation  between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
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Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

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In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
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Standard Entropy Change for a Reaction03:00

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Entropy is a state function, so the standard entropy change for a chemical reaction (ΔS°rxn) can be calculated from the difference in standard entropy between the products and the reactants.
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Third Law of Thermodynamics02:38

Third Law of Thermodynamics

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A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single microstate, as its purity, perfect crystallinity,and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.
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Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy
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Generalized weighted permutation entropy.

Darko Stosic1, Dusan Stosic1, Tatijana Stosic2

  • 1Centro de Informática, Universidade Federal de Pernambuco, Av. Luiz Freire s/n, 50670-901 Recife, PE, Brazil.

Chaos (Woodbury, N.Y.)
|November 1, 2022
PubMed
Summary
This summary is machine-generated.

A new method, Generalized Weighted Permutation Entropy, analyzes time series data by generalizing permutation entropy and weighted permutation entropy. It uses a scaling parameter to reveal unique complexity and disorder signatures in various data types.

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Area of Science:

  • Complexity Science
  • Time Series Analysis
  • Information Theory

Background:

  • Permutation Entropy (PE) and Weighted Permutation Entropy (WPE) are established methods for time series analysis.
  • Existing methods may not fully capture the complexity across different fluctuation scales.

Purpose of the Study:

  • To introduce Generalized Weighted Permutation Entropy (GWPE) as a novel heuristic approach for time series analysis.
  • To generalize the complexity-entropy causality plane into a complexity-entropy-scale causality box.
  • To analyze and differentiate time series based on complexity and disorder across various scales.

Main Methods:

  • Developed Generalized Weighted Permutation Entropy (GWPE) by incorporating a scaling parameter.
  • Extended the complexity-entropy causality plane to a three-dimensional complexity-entropy-scale causality box.
  • Applied GWPE to synthetic data (stochastic, chaotic, random) and real-world time series.

Main Results:

  • GWPE successfully amalgamates and generalizes PE and WPE.
  • The scaling parameter effectively distinguishes ordinal patterns with small and large fluctuations.
  • Unique signatures were observed for different data types within the 3D causality box.

Conclusions:

  • GWPE offers a more comprehensive approach to time series complexity analysis.
  • The complexity-entropy-scale causality box provides enhanced insights into time series dynamics.
  • This method has potential applications in diverse fields requiring time series analysis.