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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

Entropy

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...

Standard Entropy Change for a Reaction

Standard Entropy Change for a Reaction

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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...

Entropy within the Cell

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A living cell's primary tasks of obtaining, transforming, and using energy to do work may seem simple. However, the second law of thermodynamics explains why these tasks are harder than they appear. None of the energy transfers in the universe are completely efficient. In every energy transfer, some amount of energy is lost in a form that is unusable. In most cases, this form is heat energy. Thermodynamically, heat energy is defined as the energy transferred from one system to another that...

Entropy and the Second Law of Thermodynamics

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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.
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...

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Related Experiment Video

Updated: Jan 22, 2026

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

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Underwater time delay estimation method based on spectral entropy-driven multipath separation.

Xuerong Cui¹, Lurui Chao¹, Juan Li²

¹College of Oceanography and Space Informatics, China University of Petroleum (East China), Qingdao, 266000, China.

The Journal of the Acoustical Society of America

|January 21, 2026

Summary

This study introduces a novel spectral entropy-driven method for underwater time delay estimation. It effectively separates multipath signals, improving localization accuracy in noisy, complex acoustic environments.

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Area of Science:

Acoustics
Signal Processing
Oceanography

Background:

Underwater acoustic channels suffer from multipath effects, causing signal aliasing.
Non-stationary ocean noise further degrades existing time delay estimation algorithms.
High-precision underwater localization relies heavily on accurate time delay estimation.

Purpose of the Study:

To develop a robust time delay estimation method for complex underwater environments.
To address signal aliasing and noise interference issues.
To enhance the accuracy of underwater localization.

Main Methods:

Proposed a spectral entropy-driven multipath separation technique.
Utilized a spectral entropy-driven bandwidth overlap criterion for mode selection.
Implemented a time-domain energy detection mechanism incorporating energy gradient and information entropy.

Main Results:

Achieved dynamic selection of effective multipath modes and discarding of noise-dominated modes.
Successfully separated time-frequency aliased signals.
Demonstrated significant improvements in multipath separation accuracy (52.1%-61.4%) and reduced time delay RMSE (36.6%-47.2%) in simulations.

Conclusions:

The proposed method overcomes limitations of fixed-parameter modal decomposition.
It enables high-precision time delay estimation even in low signal-to-noise ratio conditions.
Offers a theoretical advancement for multipath localization in challenging underwater acoustic environments.