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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.
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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.
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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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Certain mathematical functions exhibit unpredictable or highly variable behavior near specific input values, making direct evaluation of their limits challenging. This complexity may arise from rapid oscillations or irregular patterns that obscure the function’s trend. In such cases, the Squeeze Theorem offers a reliable method for determining limits.According to the Squeeze Theorem, if a function is confined between two other functions near a particular point, and both outer functions...
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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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Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy
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Entropy-Based Evidence Functions for Testing Dilation Order via Cumulative Entropies.

Mashael A Alshehri1

  • 1Department of Quantitative Analysis, College of Business Administration, King Saud University, Riyadh 11362, Saudi Arabia.

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Summary

This study introduces new non-parametric entropy-based methods to assess probability distribution order. These entropy-driven tools offer robust statistical evidence and outperform traditional methods, especially for heavy-tailed distributions.

Keywords:
HNBUEL-statisticscumulative entropycumulative residual entropydilation orderevidence functionsnon-parametric methodsstatistical inferencetest power

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Area of Science:

  • Statistics
  • Information Theory

Background:

  • Traditional statistical methods for comparing probability distributions can be limited, particularly with complex or heavy-tailed data.
  • Existing approaches like Kullback-Leibler discrepancies may not always capture nuanced distributional differences effectively.

Purpose of the Study:

  • To develop novel non-parametric entropy-based evidence functions and test statistics.
  • To assess the dilation order of probability distributions using cumulative residual entropy and cumulative entropy.
  • To provide a robust, entropy-driven alternative for quantifying statistical evidence and stochastic ordering.

Main Methods:

  • Introduction of non-parametric entropy-based evidence functions and test statistics.
  • Development within a rigorous evidential framework.
  • Establishment of asymptotic distributions for large-sample inference.
  • Utilizing cumulative residual entropy and cumulative entropy.

Main Results:

  • The proposed methods are explicitly tuned for distributional variability and stochastic ordering.
  • Demonstrated robustness and high statistical power through Monte Carlo simulations.
  • Effective performance across diverse distributional scenarios, including heavy-tailed models.
  • Real-data example showcasing practical utility and sharper statistical evidence.

Conclusions:

  • The novel entropy-based procedures offer a compelling non-parametric alternative for statistical inference.
  • These methods advance the theoretical foundation of evidential statistics.
  • Opens new avenues for applying cumulative entropies to a wider range of stochastic inference problems.