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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.
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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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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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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Even and Odd Signals01:17

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An even signal, whether in continuous-time or discrete-time, is defined by its symmetry with its time-reversed version. Mathematically, this is represented as
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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

Updated: Jan 2, 2026

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy
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Reverse Dispersion Entropy: A New Complexity Measure for Sensor Signal.

Yuxing Li1, Xiang Gao1, Long Wang2

  • 1School of Automation and Information Engineering, Xi'an University of Technology, Xi'an 710048, China.

Sensors (Basel, Switzerland)
|December 1, 2019
PubMed
Summary

Reverse dispersion entropy (RDE) is a new complexity measure for time series analysis. RDE enhances signal detection and noise robustness, outperforming existing methods like permutation entropy (PE) and dispersion entropy (DE).

Keywords:
complexitypermutation entropy (PE)reverse dispersion entropy (RDE)reverse permutation entropy (RPE)sensor signaltime series analysisweighted-permutation entropy (W-PE)

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Area of Science:

  • Time Series Analysis
  • Complexity Measures
  • Signal Processing

Background:

  • Permutation entropy (PE) is a powerful yet limited tool for time series complexity analysis.
  • Existing improvements like Weighted-Permutation Entropy (W-PE) and Dispersion Entropy (DE) incorporate amplitude and distance information.
  • Reverse Permutation Entropy (RPE) offers stability for varying time series lengths.

Purpose of the Study:

  • To introduce a novel complexity measure, Reverse Dispersion Entropy (RDE), for enhanced time series analysis.
  • To combine the strengths of DE and RPE, leveraging amplitude and distance information.
  • To evaluate RDE's performance against established methods in various signal analysis tasks.

Main Methods:

  • Developed Reverse Dispersion Entropy (RDE) based on Permutation Entropy (PE) principles.
  • Integrated amplitude information (via NCDF) and distance metrics.
  • Conducted simulation experiments on synthetic and real-world sensor data, including mutation detection, noise robustness, and stability tests.

Main Results:

  • RDE demonstrated superior performance in abrupt signal detection and noise robustness compared to PE, W-PE, RPE, and DE.
  • RDE exhibited enhanced stability for both simulated and sensor signals across different signal-to-noise ratios (SNRs).
  • RDE showed a higher distinguishing ability for sensor signals, particularly in classifying ship types and fault data.

Conclusions:

  • Reverse Dispersion Entropy (RDE) represents a significant advancement in time series complexity analysis.
  • RDE offers improved accuracy, robustness, and stability, making it suitable for complex real-world applications.
  • The proposed RDE method provides a more effective tool for analyzing sensor signals and detecting anomalies.