Jove
Visualize
Contact Us

Related Concept Videos

Entropy02:39

Entropy

35.1K
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...
35.1K
Entropy01:18

Entropy

3.5K
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...
3.5K
Standard Entropy Change for a Reaction03:00

Standard Entropy Change for a Reaction

24.1K
Entropy is a state function, so the standard entropy change for a chemical reaction (ΔS°rxn) can be calculated from the difference in standard entropy between the products and the reactants.
24.1K
Entropy and Solvation02:05

Entropy and Solvation

8.3K
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...
8.3K
Entropy within the Cell01:22

Entropy within the Cell

12.8K
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...
12.8K
Entropy and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

4.8K
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...
4.8K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Widespread deep-sea microorganisms in subseafloor geochemical cycling.

Frontiers in microbiology·2026
Same author

ComplexityMeasures.jl: Scalable software to unify and accelerate entropy and complexity timeseries analysis.

PloS one·2025
Same author

Mapping Microbial Abundance and Prevalence to Changing Oxygen Concentration in Deep-Sea Sediments Using Machine Learning and Differential Abundance.

Frontiers in microbiology·2022
Same author

On how the power supply shapes microbial survival.

Mathematical biosciences·2021
Same author

Nitrifier abundance and diversity peak at deep redox transition zones.

Scientific reports·2019
Same author

Forcing of late Pleistocene ice volume by spatially variable summer energy.

Scientific reports·2018
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Video

Updated: Jan 24, 2026

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy
11:15

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

Published on: June 27, 2013

34.4K

Transfer entropy computation using the Perron-Frobenius operator.

David Diego1, Kristian Agasøster Haaga1, Bjarte Hannisdal1

  • 1Department of Earth Science, University of Bergen, PO Box 7803, NO-5020 Bergen, Norway.

Physical Review. E
|May 22, 2019
PubMed
Summary

This study introduces a novel transfer entropy estimation method using Ulam's approximation of the Perron-Frobenius operator. The new approach improves coupling direction detection in sparse time series data.

More Related Videos

Bulk and Thin Film Synthesis of Compositionally Variant Entropy-stabilized Oxides
09:41

Bulk and Thin Film Synthesis of Compositionally Variant Entropy-stabilized Oxides

Published on: May 29, 2018

10.0K
Using Wavelet Entropy to Demonstrate how Mindfulness Practice Increases Coordination between Irregular Cerebral and Cardiac Activities
08:08

Using Wavelet Entropy to Demonstrate how Mindfulness Practice Increases Coordination between Irregular Cerebral and Cardiac Activities

Published on: May 10, 2017

15.2K

Related Experiment Videos

Last Updated: Jan 24, 2026

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy
11:15

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

Published on: June 27, 2013

34.4K
Bulk and Thin Film Synthesis of Compositionally Variant Entropy-stabilized Oxides
09:41

Bulk and Thin Film Synthesis of Compositionally Variant Entropy-stabilized Oxides

Published on: May 29, 2018

10.0K
Using Wavelet Entropy to Demonstrate how Mindfulness Practice Increases Coordination between Irregular Cerebral and Cardiac Activities
08:08

Using Wavelet Entropy to Demonstrate how Mindfulness Practice Increases Coordination between Irregular Cerebral and Cardiac Activities

Published on: May 10, 2017

15.2K

Area of Science:

  • Dynamical Systems
  • Information Theory
  • Time Series Analysis

Background:

  • Transfer entropy is a key measure for quantifying information flow between time series.
  • Existing transfer entropy estimators can struggle with sparse data and low embedding dimensions.
  • Accurate estimation of invariant measures is crucial for reliable transfer entropy calculations.

Purpose of the Study:

  • To develop a novel method for computing transfer entropy using Ulam's approximation of the Perron-Frobenius operator.
  • To improve the estimation of invariant measures for transfer entropy calculations, especially from sparse data.
  • To evaluate the performance and robustness of the proposed method against existing estimators.

Main Methods:

  • Utilizing Ulam's approximation to estimate the Perron-Frobenius operator and its invariant distribution.
  • Employing a triangulation approach for sparse time series and a grid-based approach for data-rich time series.
  • Comparing the proposed method with k-nearest neighbors and kernel density estimation using coupled chaotic systems.

Main Results:

  • The proposed method provides an alternative way to estimate invariant measures for transfer entropy.
  • The triangulation estimator demonstrates improved detection of coupling directionality in sparse time series (n < 100) and low embedding dimensions.
  • The estimators show robustness against moderate levels of noise.

Conclusions:

  • The Ulam approximation-based transfer entropy method offers a viable alternative, particularly for challenging sparse data scenarios.
  • This approach enhances the ability to infer causal relationships and information flow direction in complex systems.
  • The method's robustness to noise suggests practical applicability in real-world time series analysis.