Jove
Visualize
Contact Us
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 Concept Videos

Entropy02:39

Entropy

36.4K
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...
36.4K
Entropy01:18

Entropy

3.6K
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...
3.6K
Standard Entropy Change for a Reaction03:00

Standard Entropy Change for a Reaction

25.0K
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.
25.0K
Entropy and Solvation02:05

Entropy and Solvation

8.5K
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...
8.5K
Entropy within the Cell01:22

Entropy within the Cell

13.0K
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...
13.0K
Entropy and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

5.0K
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...
5.0K

You might also read

Related Articles

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

Sort by
Same author

Chaotic ghosts in systems with parameter drift: Delay and control critical transitions.

Physical review. E·2026
Same author

Multiscale spatiotemporal neural network with multi-attention mechanism using brain partitioning for motor imagery recognition.

Journal of neuroscience methods·2026
Same author

Complex bifurcation structures in a Hodgkin-Huxley model of thermally sensitive neurons under periodic perturbation.

Physical review. E·2025
Same author

Adaptive Whole-Brain Dynamics Predictive Method: Relevancy to Mental Disorders.

Research (Washington, D.C.)·2025
Same author

Unsupervised Domain Adaptation With Synchronized Self-Training for Cross- Domain Motor Imagery Recognition.

IEEE journal of biomedical and health informatics·2025
Same author

Transcriptomic Evidence Reveals the Dysfunctional Mechanism of Synaptic Plasticity Control in ASD.

Genes·2025
Same journal

Gap junction architecture and synchronization clusters in the thalamic reticular nuclei.

Chaos (Woodbury, N.Y.)·2026
Same journal

Exact computation of Lyapunov exponents via system parameters in multi-triangle chaotic maps: Bifurcation analysis and circuit realization.

Chaos (Woodbury, N.Y.)·2026
Same journal

Integrating score-based generative modeling and neural ODEs for accurate representation of multiscale chaotic dynamics.

Chaos (Woodbury, N.Y.)·2026
Same journal

A data-driven tuberculosis model with behavioral changes and saturated treatment: Optimal control and cost-effectiveness study.

Chaos (Woodbury, N.Y.)·2026
Same journal

Breathers, rational solutions, and their exact physical spectra in F = 1 spinor Bose-Einstein condensates.

Chaos (Woodbury, N.Y.)·2026
Same journal

Finite invariant sets with bridging points in logistic IFS.

Chaos (Woodbury, N.Y.)·2026
See all related articles

Related Experiment Video

Updated: Feb 12, 2026

Substrate Generation for Endonucleases of CRISPR/Cas Systems
11:53

Substrate Generation for Endonucleases of CRISPR/Cas Systems

Published on: September 8, 2012

28.0K

Entropy-based generating Markov partitions for complex systems.

Nicolás Rubido1, Celso Grebogi2, Murilo S Baptista2

  • 1Instituto de Física de Facultad de Ciencias (IFFC), Universidad de la República (UdelaR), Iguá 4225, Montevideo, Uruguay.

Chaos (Woodbury, N.Y.)
|April 2, 2018
PubMed
Summary
This summary is machine-generated.

This study presents a novel method for creating symbolic sequences from complex system data, preserving essential properties. This approach enables accurate calculation of invariant probability measures and complexity for real-world phenomena.

More Related Videos

Glass-Based Devices to Generate Drops and Emulsions
08:45

Glass-Based Devices to Generate Drops and Emulsions

Published on: April 5, 2022

3.2K
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

Related Experiment Videos

Last Updated: Feb 12, 2026

Substrate Generation for Endonucleases of CRISPR/Cas Systems
11:53

Substrate Generation for Endonucleases of CRISPR/Cas Systems

Published on: September 8, 2012

28.0K
Glass-Based Devices to Generate Drops and Emulsions
08:45

Glass-Based Devices to Generate Drops and Emulsions

Published on: April 5, 2022

3.2K
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

Area of Science:

  • Dynamical Systems and Network Science
  • Information Theory
  • Computational Physics

Background:

  • Encoding dynamical system trajectories into symbolic sequences is challenging due to the need to preserve invariant properties.
  • Generating Markov Partitions (GMPs) theoretically solve this but require infinite precision knowledge of system dynamics, which is often unattainable in real-world experiments with finite resolution and time spans.
  • Analyzing high-dimensional complex systems, like networks of interacting units, further complicates trajectory encoding.

Purpose of the Study:

  • To develop a method for the approximate construction of Generating Markov Partitions (GMPs) for complex systems using finite-resolution and finite-time trajectory data.
  • To encode trajectories of complex systems into optimal symbolic sequences that minimize information loss and spurious information.
  • To enable the calculation of invariant probability measures and complexity measures from observed data in complex systems.

Main Methods:

  • Developed a novel method to approximate Generating Markov Partitions (GMPs) from finite-resolution and finite-time trajectories of complex systems.
  • Applied the method to networks of coupled maps, generating symbolic sequences from their trajectories.
  • Validated the optimality of the generated symbolic sequences by demonstrating minimized information loss and spurious information.

Main Results:

  • Successfully constructed approximate GMPs for complex systems from experimental data.
  • Generated symbolic sequences that are optimal in terms of information preservation.
  • Demonstrated the ability to calculate invariant probability measures of complex systems using the derived symbolic sequences.

Conclusions:

  • The developed method provides an effective way to encode complex system dynamics into symbolic sequences, overcoming limitations of finite data resolution and time.
  • This approach facilitates the accurate calculation of invariant probability measures and the definition of complexity measures for diverse complex phenomena.
  • The method has potential applications in analyzing real-world data, such as electroencephalogram signals for brain activity and temperature anomalies for climate variability.