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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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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...
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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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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 models, the...
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Second Law of Thermodynamics00:53

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The Second Law of Thermodynamics states that entropy, or the amount of disorder in a system, increases each time energy is transferred or transformed. Each energy transfer results in a certain amount of energy that is lost—usually in the form of heat—that increases the disorder of the surroundings. This can also be demonstrated in a classic food web. Herbivores harvest chemical energy from plants and release heat and carbon dioxide into the environment. Carnivores harvest the...
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Related Experiment Video

Updated: Jan 13, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Entropy-Based Uncertainty Quantification in Linear Consecutive k-out-of-n:G Systems via Cumulative Residual Tsallis

Boshra Alarfaj1, Mohamed Kayid1, Mashael A Alshehri2

  • 1Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia.

Entropy (Basel, Switzerland)
|October 28, 2025
PubMed
Summary

This study introduces a new framework using cumulative residual Tsallis entropy (CRTE) to quantify uncertainty in complex systems. The findings offer practical tools for reliability analysis and engineering applications.

Keywords:
consecutive k-out-of-n:G systemscumulative residual Tsallis entropydispersive ordering testentropy-based uncertainty quantificationinformation-theoretic reliabilitylifetime data analysisreliability modelingstochastic ordering

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Area of Science:

  • Engineering
  • Information Theory
  • Reliability Analysis

Background:

  • Quantifying uncertainty is crucial in complex systems for reliability analysis.
  • Existing methods face challenges in large-scale or nonstandard lifetime scenarios.

Purpose of the Study:

  • To develop an information-theoretic framework for analyzing linear consecutive k-out-of-n:G systems.
  • To introduce cumulative residual Tsallis entropy (CRTE) as a tool for uncertainty quantification.

Main Methods:

  • Derived a general analytical expression for CRTE.
  • Investigated CRTE behavior under stochastic ordering relations.
  • Established analytical bounds for uncertainty quantification and reliability assessment.

Main Results:

  • Developed a CRTE-based nonparametric test for dispersive ordering with established asymptotic distribution.
  • Validated statistical properties via Monte Carlo simulations.
  • Demonstrated practical application using real lifetime data.

Conclusions:

  • CRTE offers a versatile and computationally feasible approach for reliability modeling and uncertainty quantification.
  • The framework provides effective tools for bounding analysis, characterization, and inference in critical systems.