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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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Expected Frequencies in Goodness-of-Fit Tests01:19

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A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (n)  to the number of categories (k).
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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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Entropy and Solvation02:05

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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...
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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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Updated: Nov 27, 2025

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy
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Estimating Topic Modeling Performance with Sharma-Mittal Entropy.

Sergei Koltcov1, Vera Ignatenko1, Olessia Koltsova1

  • 1St. Petersburg School of Physics, Mathematics, and Computer Science, National Research University Higher School of Economics, Kantemirovskaya Ulitsa, 3A, St. Petersburg 194100, Russia.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces a novel method using Sharma-Mittal entropy for topic modeling, enhancing parameter optimization and semantic stability in text clustering. It addresses key limitations in probabilistic Latent Semantic Analysis and Latent Dirichlet Allocation models.

Keywords:
Sharma–Mittal entropyoptimal number of topicsstabilitytopic modeling

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Area of Science:

  • Computational Linguistics
  • Machine Learning Theory
  • Statistical Physics Applications

Background:

  • Topic modeling is widely used for text document clustering.
  • Existing tools suffer from parameter instability and lack selection criteria.
  • Current metrics address only single parameters, neglecting semantic stability.

Purpose of the Study:

  • To propose a novel method for optimizing topic model parameters.
  • To enhance semantic stability in text clustering.
  • To leverage statistical physics concepts for machine learning theory.

Main Methods:

  • Developed a method based on Sharma-Mittal entropy.
  • Applied the approach to probabilistic Latent Semantic Analysis (pLSA) and Latent Dirichlet Allocation (LDA) with Gibbs sampling.
  • Tested on diverse datasets in multiple languages.

Main Results:

  • Demonstrated Sharma-Mittal entropy's effectiveness in selecting the number of topics and hyper-parameters.
  • Showcased simultaneous control over semantic stability, a capability lacking in existing metrics.
  • Validated the approach against standard metrics on different datasets and models.

Conclusions:

  • Sharma-Mittal entropy offers a unified approach for topic model parameter optimization and semantic stability.
  • Statistical physics provides a valuable theoretical foundation for advancing machine learning.
  • The proposed method offers a more robust and stable solution for text clustering challenges.