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Related Concept Videos

Entropy Changes Accompanying Specific Processes01:21

Entropy Changes Accompanying Specific Processes

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Entropy, a measure of disorder in a system, changes during phase transitions like freezing or boiling. At the transition temperature Ttrs, where two phases are in equilibrium, the phase transition is a reversible process. The entropy change can be calculated from a substance's enthalpy of transition using the equation ΔStrs = ΔtrsH /Ttrs.When a perfect gas expands isothermally from one volume to another, entropy increases logarithmically with volume. Conversely, isothermal compression...
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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

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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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Entropy and the Second Law of Thermodynamics01:26

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Consider an isolated system in which a hot object is placed in contact with a cold one. This is an irreversible process that eventually leads both objects to reach the same equilibrium temperature. It is crucial to note that the constituents of any substance exhibit increased disorder at higher temperatures. As a cold substance absorbs heat, its constituents become more disordered. The energy transfer from a hotter object to a cooler one increases the system's disorder or randomness. This...
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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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Related Experiment Video

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Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy
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Optimized Kernel Entropy Components.

Emma Izquierdo-Verdiguier, Valero Laparra, Robert Jenssen

    IEEE Transactions on Neural Networks and Learning Systems
    |March 2, 2016
    PubMed
    Summary
    This summary is machine-generated.

    Optimized Kernel Entropy Component Analysis (OKECA) enhances feature extraction by maximizing data entropy, outperforming standard KECA. OKECA also proves more robust in kernel parameter selection for density estimation tasks.

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    Area of Science:

    • Machine Learning
    • Data Analysis
    • Statistical Modeling

    Background:

    • Standard Kernel Entropy Component Analysis (KECA) sorts kernel eigenvectors by entropy, unlike Kernel Principal Component Analysis (KPCA) which uses variance.
    • KECA and KPCA face challenges in optimizing kernel decomposition and Gaussian kernel parameter selection.
    • Effective feature extraction is crucial for accurate data representation and analysis.

    Purpose of the Study:

    • To introduce an optimized KECA (OKECA) method for enhanced feature extraction.
    • To improve information compaction into fewer, more expressive features.
    • To address and analyze kernel parameter selection in KECA and OKECA.

    Main Methods:

    • Proposed Optimized KECA (OKECA) method based on Independent Component Analysis (ICA).
    • Incorporated an optimized rotation into the eigen decomposition via gradient-ascent search.
    • Analyzed common kernel length-scale selection criteria for Gaussian kernels.

    Main Results:

    • OKECA extracts optimal features that retain maximum data entropy, compacting information into one or two features.
    • OKECA features demonstrate higher expressive power compared to KECA.
    • Maximum likelihood emerged as the most successful rule for kernel parameter estimation.
    • OKECA exhibits greater robustness to kernel length-scale parameter selection in density estimation.

    Conclusions:

    • OKECA offers superior feature extraction with enhanced expressive power over standard KECA.
    • Maximum likelihood is recommended for kernel parameter selection.
    • OKECA provides a more robust approach to kernel density estimation, especially concerning parameter sensitivity.