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Entropy

Entropy

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...

Entropy and the Second Law of Thermodynamics

Entropy and the Second Law of Thermodynamics

The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The relation between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...

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 and Solvation

Entropy and Solvation

The process of surrounding a solute with solvent is called solvation. It involves evenly distributing the solute within the solvent. The rule of thumb for determining a solvent for a given compound is that like dissolves like. A good solvent has molecular characteristics similar to those of the compound to be dissolved. For example, polar solutions dissolve polar solutes, and apolar solvents dissolve apolar solutes. A polar solvent is a solvent that has a high dielectric constant (ϵ...

Third Law of Thermodynamics

Third Law of Thermodynamics

A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single microstate, as its purity, perfect crystallinity,and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.

The Second Law of Thermodynamics

The Second Law of Thermodynamics

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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Related Experiment Video

Updated: May 24, 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

On generalized bidimensional ensemble permutation entropy.

M Muñoz-Guillermo¹

¹Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, 30202 Cartagena (Murcia), Spain.

Chaos (Woodbury, N.Y.)

|March 6, 2025

Summary

This summary is machine-generated.

This study introduces modified ensemble permutation entropy measures for analyzing image and time series data. These new methods overcome previous limitations, enhancing data discrimination for machine learning applications.

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Area of Science:

Data analysis and machine learning
Information theory and signal processing

Background:

Entropy measurements are crucial for data analysis and feature extraction in machine learning.
Permutation entropy and its ensemble versions are effective for time series and image analysis.
Existing ensemble permutation entropy methods have limitations on image size, restricting applicability.

Purpose of the Study:

To address the limitations of current bidimensional ensemble permutation entropy methods.
To propose generalized versions of bidimensional ensemble permutation entropy.
To extend the applicability of ensemble permutation entropy to a wider range of data.

Main Methods:

Development of modified bidimensional ensemble permutation entropy algorithms.
Generalization of the ensemble approach to overcome size restrictions.
Application of the proposed measures to diverse datasets.

Main Results:

The modified methods successfully generalize the original bidimensional ensemble permutation entropy.
Overcoming the image size restriction significantly broadens the applicability of the technique.
Enhanced data discrimination capabilities were observed across various databases.

Conclusions:

Modified bidimensional ensemble permutation entropy offers a more versatile and applicable approach to data analysis.
The generalized methods improve information content and discrimination power for machine learning.
This work expands the utility of entropy-based feature extraction in diverse fields.