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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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The Second Law of Thermodynamics01:14

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In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Scientists refer to the measure of randomness or disorder within a system as entropy. High entropy means high disorder and low energy. To better understand entropy, think of a student’s bedroom. If no energy or work were put into it, the room would quickly become messy. It would exist in a very disordered state, one of high entropy. Energy must be...
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Entropy Change in Reversible Processes01:10

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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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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.
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Second Law of Thermodynamics02:49

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In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic...
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Random Error01:04

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Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
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Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy
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Characterizing Complex Spatiotemporal Patterns from Entropy Measures.

Luan Orion Barauna1, Rubens Andreas Sautter1, Reinaldo Roberto Rosa1,2

  • 1Applied Computing Graduate Program (CAP), National Institute for Space Research, Av. dos Astronautas, 1.758, Jardim da Granja, São José dos Campos 12227-010, SP, Brazil.

Entropy (Basel, Switzerland)
|June 26, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces a novel entropy-based method for classifying complex spatiotemporal patterns. The approach effectively distinguishes between various dynamic processes like turbulence and noise using Shannon permutation entropy (SHp) and Tsallis Spectral Permutation Entropy (Sqs).

Keywords:
Shannon entropyTsallis entropygradient pattern analysisnonlinear dynamicsspatiotemporal patternsturbulence

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Area of Science:

  • Complex Systems Analysis
  • Statistical Thermodynamics
  • Time Series Analysis

Background:

  • Probabilistic entropy measurements are vital for analyzing complex systems and time series.
  • Current entropy methods require further development for two- and three-dimensional data.
  • Spatiotemporal process classification remains a challenge.

Purpose of the Study:

  • To develop a new method for classifying spatiotemporal processes using entropy measurements.
  • To validate the method by distinguishing between five classes of random patterns.
  • To identify optimal entropy measures for enhanced classification performance.

Main Methods:

  • Selected five classes of random patterns: white noise, red noise, reaction-diffusion, hydrodynamic turbulence, and plasma turbulence (MHD).
  • Evaluated seven entropy measurement techniques from matrices.
  • Developed a parameter space using the two most effective entropy measures: Shannon permutation entropy (SHp) and Tsallis Spectral Permutation Entropy (Sqs).

Main Results:

  • The SHp×Sqs parameter space effectively segregates the five classes of spatiotemporal processes.
  • Shannon permutation entropy (SHp) and Tsallis Spectral Permutation Entropy (Sqs) showed superior combined performance.
  • Specific sectors within the SHp×Sqs space were identified for each dynamic process class.

Conclusions:

  • The proposed entropy-based method offers a robust approach for classifying complex spatiotemporal patterns.
  • The SHp×Sqs parameter space provides a powerful tool for distinguishing between different dynamic processes.
  • This method can be utilized to train machine learning models for automated spatiotemporal pattern classification.