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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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Entropy01:18

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The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
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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 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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Third Law of Thermodynamics02:38

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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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Entropy within the Cell01:22

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A living cell's primary tasks of obtaining, transforming, and using energy to do work may seem simple. However, the second law of thermodynamics explains why these tasks are harder than they appear. None of the energy transfers in the universe are completely efficient. In every energy transfer, some amount of energy is lost in a form that is unusable. In most cases, this form is heat energy. Thermodynamically, heat energy is defined as the energy transferred from one system to another that...
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Related Experiment Video

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Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180&#176; Curved Artery Test Section
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The Entropy Universe.

Maria Ribeiro1,2, Teresa Henriques3,4, Luísa Castro3

  • 1Institute for Systems and Computer Engineering, Technology and Science (INESC-TEC), 4200-465 Porto, Portugal.

Entropy (Basel, Switzerland)
|March 6, 2021
PubMed
Summary
This summary is machine-generated.

This review explores diverse entropy measures for time-series analysis, detailing their origins, mathematical definitions, and applications. It highlights Shannon, Tsallis, sample, permutation, and approximate entropies as most cited, crucial for selecting appropriate methods.

Keywords:
application areasentropy measuresinformation theorytime-series

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Area of Science:

  • Entropy measures are applied across diverse scientific fields, including computer science, physics, mathematics, and engineering.
  • The study focuses on time-series analysis, a common application area for various entropy variants.

Background:

  • The concept of entropy, introduced by Rudolf Clausius, has evolved significantly over 160 years.
  • Entropy has been extended and applied in fields such as information theory, chaos theory, data mining, and mathematical linguistics.

Purpose of the Study:

  • To review and explain various entropy measures used in time-series analysis.
  • To detail the emergence, mathematical definitions, relationships, and applications of different entropy variants.
  • To guide researchers in selecting the most suitable entropy measure for their specific data.

Main Methods:

  • A comprehensive review of entropy variants applied to time-series data.
  • Analysis of citation counts over sixteen years for papers introducing new entropy measures.
  • Identification of the most applied scientific fields using bibliometric data from Web of Science and Scopus.

Main Results:

  • Shannon/differential, Tsallis, sample, permutation, and approximate entropies are the most frequently cited.
  • Computer science, physics, mathematics, and engineering are the primary fields utilizing these entropy measures.
  • The application landscape of entropy is continuously expanding with new variants and uses.

Conclusions:

  • Understanding the strengths and limitations of each entropy measure is vital for advancing research.
  • The selection of an appropriate entropy variant is critical for effective time-series data analysis.
  • The field of entropy research is dynamic, necessitating ongoing exploration of new developments and applications.