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

Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

3.0K
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.
3.0K
Entropy and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

3.7K
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...
3.7K
Entropy01:18

Entropy

3.2K
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...
3.2K
Entropy02:39

Entropy

33.3K
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...
33.3K
Entropy and Solvation02:05

Entropy and Solvation

7.9K
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...
7.9K
Entropy within the Cell01:22

Entropy within the Cell

12.3K
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...
12.3K

You might also read

Related Articles

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

Sort by
Same author

Superstatistics approach to turbulent circulation fluctuations.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same author

Diversity as an entropic measure derived from entropiclike functionals.

Physical review. E·2026
Same author

Multiclass portfolio optimization via variational quantum Eigensolver with Dicke state ansatz.

Scientific reports·2026
Same author

Central limit behavior at the edge of chaos in the z-logistic map.

Physical review. E·2026
Same author

Composing α-Gauss and logistic maps: Gradual and sudden transitions to chaos.

Physical review. E·2025
Same author

On the mathematical divergences emerging in the theory of critical phenomena within Boltzmann-Gibbs statistical mechanics.

Chaos (Woodbury, N.Y.)·2025

Related Experiment Video

Updated: Nov 21, 2025

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

2.5K

Connecting complex networks to nonadditive entropies.

R M de Oliveira1, Samuraí Brito2, L R da Silva1,3

  • 1Departamento de Física Teórica e Experimental, Federal University of Rio Grande do Norte, Natal, RN, 59078-900, Brazil.

Scientific Reports
|January 14, 2021
PubMed
Summary

Generalized statistical mechanics using q-entropies successfully models complex, scale-invariant networks. This approach replaces Boltzmann-Gibbs statistics, revealing a connection between random geometric and thermal problems.

More Related Videos

Modeling the Functional Network for Spatial Navigation in the Human Brain
05:55

Modeling the Functional Network for Spatial Navigation in the Human Brain

Published on: October 13, 2023

1.4K
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

34.1K

Related Experiment Videos

Last Updated: Nov 21, 2025

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

2.5K
Modeling the Functional Network for Spatial Navigation in the Human Brain
05:55

Modeling the Functional Network for Spatial Navigation in the Human Brain

Published on: October 13, 2023

1.4K
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

34.1K

Area of Science:

  • Statistical Mechanics
  • Complex Systems
  • Network Science

Background:

  • Boltzmann-Gibbs statistical mechanics is widely applicable but fails for complex systems with nonlocal entanglement.
  • Generalized thermostatistics using nonadditive q-entropies can model such complex systems.

Purpose of the Study:

  • To investigate the applicability of generalized thermostatistics to scale-invariant networks.
  • To establish a connection between random geometric network problems and thermal problems.

Main Methods:

  • Numerical study of a d-dimensional geographically located network with weighted links.
  • Analysis of the 'energy' distribution per site at its quasi-stationary state.

Main Results:

  • Scale-invariant networks were shown to belong to the class of systems handled by generalized thermostatistics.
  • A correspondence was found between the random geometric network problem and thermal problems under generalized thermostatistics.
  • The Boltzmann-Gibbs exponential factor was shown to be substituted by its q-generalization, recovering the standard form in a specific limit.

Conclusions:

  • Generalized statistical mechanics provides a framework for understanding complex, scale-invariant networks.
  • The findings suggest a cross-fertilization potential between research in random geometric networks and generalized thermostatistics.