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Entropy Change in Reversible Processes

Entropy Change in Reversible Processes

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.

Entropy

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Sampling Continuous Time Signal

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Sampling Theorem

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Related Experiment Video

Updated: Oct 6, 2025

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

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

Published on: June 27, 2013

Variational Embedding Multiscale Sample Entropy: A Tool for Complexity Analysis of Multichannel Systems.

Hongjian Xiao¹, Danilo P Mandic¹

¹Department of Electrical and Electronic Engineering, Imperial College London, London SW7 2AZ, UK.

Entropy (Basel, Switzerland)

|January 21, 2022

Summary

This summary is machine-generated.

We introduce variational embedding multiscale sample entropy (veMSE), a novel method for quantifying system complexity. veMSE effectively analyzes shorter data series than traditional sample entropy, offering robust and computationally efficient structural complexity quantification.

Keywords:

complexity science multi-channel system multivariate data physical signal analysis sample entropy variational embedding entropy

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Area of Science:

Complex Systems Analysis
Information Theory
Signal Processing

Background:

Entropy-based methods are crucial for quantifying structural complexity in real-world systems.
Existing conditional entropy methods, like sample entropy, require extensive data lengths for accurate analysis.
Limitations in data requirements hinder the scalability and applicability of current entropy measures.

Purpose of the Study:

To propose a novel entropy-based method, variational embedding multiscale sample entropy (veMSE), for robust complexity quantification.
To demonstrate veMSE's ability to function effectively with significantly shorter data series compared to existing methods.
To highlight veMSE's advantages in terms of data efficiency, robustness, and computational performance.

Main Methods:

Development of the variational embedding multiscale sample entropy (veMSE) algorithm.
Application of veMSE to both simulated and real-world signals.
Comparative analysis of veMSE against existing multivariate multiscale sample entropy methods.

Main Results:

veMSE demonstrates robust performance with substantially shorter data lengths than conventional methods.
The method exhibits resilience to variations in embedding dimension and noise.
veMSE offers computational advantages over existing amplitude distance-based entropy methods.
Independent channel permutation analysis enhances the rigor of multivariate data interpretation.

Conclusions:

veMSE provides a more efficient and robust approach to quantifying structural complexity.
The method overcomes data length limitations inherent in traditional sample entropy.
veMSE presents a promising advancement for analyzing complex systems across various scientific domains.