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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

Entropy

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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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Entropy and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

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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...
4.0K
The Second Law of Thermodynamics01:14

The Second Law of Thermodynamics

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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

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.
3.0K
Third Law of Thermodynamics02:38

Third Law of Thermodynamics

21.0K
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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Approximate Entropy and Sample Entropy: A Comprehensive Tutorial.

Alfonso Delgado-Bonal1,2, Alexander Marshak1

  • 1NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA.

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

Approximate Entropy and Sample Entropy are powerful algorithms for analyzing data patterns. This guide clarifies their distinct theories and applications across various scientific fields.

Keywords:
approximate entropychaos theoryinformation theorysample entropy

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Area of Science:

  • Data Science
  • Information Theory
  • Chaos Theory

Background:

  • Approximate Entropy (ApEn) and Sample Entropy (SampEn) are widely used for time series regularity analysis.
  • Despite similarities, their underlying theoretical frameworks differ, often leading to misunderstandings.
  • These algorithms, initially for physiological data, now find applications in diverse fields.

Purpose of the Study:

  • To provide a comprehensive tutorial on the theory and application of Approximate Entropy and Sample Entropy.
  • To elucidate the distinct theoretical underpinnings of ApEn and SampEn.
  • To guide researchers in applying these entropy measures correctly across disciplines.

Main Methods:

  • Explanation of theoretical concepts from Information Theory and Chaos Theory.
  • Provision of simple source codes for calculating ApEn and SampEn.
  • Step-by-step examples demonstrating the proper application of the algorithms.

Main Results:

  • Detailed theoretical explanations of Approximate Entropy and Sample Entropy.
  • Accessible source code for practical implementation.
  • Illustrative examples clarifying algorithm usage.

Conclusions:

  • This tutorial clarifies the theoretical differences and practical applications of ApEn and SampEn.
  • Researchers can confidently apply these entropy measures with the provided guidance.
  • The paper serves as a foundational resource for understanding time series regularity analysis.