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Related Concept Videos

Entropy02:39

Entropy

35.3K
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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Standard Entropy Change for a Reaction03:00

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Entropy is a state function, so the standard entropy change for a chemical reaction (ΔS°rxn) can be calculated from the difference in standard entropy between the products and the reactants.
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Transfer Function to State Space01:23

Transfer Function to State Space

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State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an RLC...
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State Space to Transfer Function01:21

State Space to Transfer Function

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The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
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Transfer function and Bode Plots-II01:23

Transfer function and Bode Plots-II

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In the standard form, the transfer function is shown in constant gain, poles/zeros at origin, simple poles/zeros, and quadratic poles/zeros; each contributing uniquely to the system's overall response. The term represents the magnitude of the simple zero:
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Related Experiment Video

Updated: Jan 27, 2026

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy
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Transfer Spectral Entropy and Application to Functional Corticomuscular Coupling.

Xiaoling Chen, Yuanyuan Zhang, Shengcui Cheng

    IEEE Transactions on Neural Systems and Rehabilitation Engineering : a Publication of the IEEE Engineering in Medicine and Biology Society
    |March 26, 2019
    PubMed
    Summary

    A new Transfer Spectral Entropy (TSE) method enhances the analysis of functional corticomuscular coupling (FCMC) by accurately measuring neural communication. TSE reveals detailed frequency band interactions between EEG and EMG signals, improving upon traditional methods.

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    Area of Science:

    • Neuroscience
    • Biomedical Engineering
    • Signal Processing

    Background:

    • Functional corticomuscular coupling (FCMC) involves neural communication between the central and peripheral nervous systems via rhythmic oscillations.
    • Existing methods like coherence and Granger causality (GC) have limitations in capturing signal complexity and directionality.
    • Information theory methods, particularly transfer entropy (TE), offer advantages in analyzing complexity and directionality.

    Purpose of the Study:

    • To propose and validate a novel method, Transfer Spectral Entropy (TSE), for analyzing local frequency band characteristics in coupled signals.
    • To explore functional corticomuscular coupling (FCMC) by analyzing electroencephalogram (EEG) and electromyogram (EMG) signals.
    • To compare the performance of TSE against the Granger causality (GC) method.

    Main Methods:

    • Extended the transfer entropy (TE) method to develop Transfer Spectral Entropy (TSE).
    • Utilized Henon and neural mass models to generate simulation signals for method verification.
    • Applied TSE to analyze EEG-EMG signal correlations during steady-state force output.

    Main Results:

    • TSE accurately described information interaction in local frequency bands and reduced 'false coupling' compared to GC.
    • TSE demonstrated sensitivity to coupling strength but not data length.
    • Analysis of EEG-EMG data revealed prominent FCMC in beta1 (15-25 Hz) and beta2 (25-35 Hz) bands, with higher EEG-to-EMG coupling.
    • EMG-to-EEG coupling was higher in the gamma1 band (35-45 Hz).

    Conclusions:

    • The novel TSE method effectively quantifies information interaction in local frequency bands between coupled time series.
    • TSE provides a more nuanced understanding of functional corticomuscular coupling (FCMC), refining previous findings primarily focused on the beta band.
    • The study validates TSE's effectiveness using both simulated and experimental data, extending research on FCMC.