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

32.2K
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...
32.2K
Entropy01:18

Entropy

3.0K
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...
3.0K
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

2.8K
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.
2.8K
Entropy and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

3.4K
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...
3.4K
Third Law of Thermodynamics02:38

Third Law of Thermodynamics

20.1K
A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single microstate, as its purity, perfect crystallinity,and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.
20.1K
The Second Law of Thermodynamics01:14

The Second Law of Thermodynamics

6.1K
In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Scientists refer to the measure of randomness or disorder within a system as entropy. High entropy means high disorder and low energy. To better understand entropy, think of a student’s bedroom. If no energy or work were put into it, the room would quickly become messy. It would exist in a very disordered state, one of high entropy. Energy must be...
6.1K

You might also read

Related Articles

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

Sort by
Same author

Discontinuous transition in explosive percolation via local suppression.

Physical review. E·2026
Same author

Recent Progress on Hybrid Percolation Transitions.

Entropy (Basel, Switzerland)·2026
Same author

Discontinuous percolation via suppression of neighboring clusters in a network.

Physical review. E·2025
Same author

Local suppression by link rewiring reveals discontinuous percolation transitions.

Science advances·2025
Same author

Percolation critical exponents in cluster kinetics of pulse-coupled oscillators.

Chaos (Woodbury, N.Y.)·2023
Same author

Concurrent formation of nearly synchronous clusters in each intertwined cluster set with parameter mismatches.

Physical review. E·2019

Related Experiment Video

Updated: Oct 23, 2025

Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans
09:23

Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans

Published on: August 16, 2017

8.3K

Scaling behavior of information entropy in explosive percolation transitions.

Yejun Kang1, Young Sul Cho1,2

  • 1Department of Physics, Jeonbuk National University, Jeonju 54896, Korea.

Physical Review. E
|August 20, 2021
PubMed
Summary

Information entropy in explosive percolation models does not peak at the threshold. This study explains this by analyzing differing cluster-size distribution scaling forms above and below the threshold.

More Related Videos

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

34.0K
Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy
06:37

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Published on: June 15, 2022

3.8K

Related Experiment Videos

Last Updated: Oct 23, 2025

Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans
09:23

Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans

Published on: August 16, 2017

8.3K
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

34.0K
Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy
06:37

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Published on: June 15, 2022

3.8K

Area of Science:

  • Statistical Physics
  • Complex Systems
  • Network Science

Background:

  • Explosive percolation transitions feature abrupt giant cluster formation at a critical threshold.
  • Information entropy of cluster-size distributions has been observed not to maximize at the percolation threshold, contrary to some prior findings.

Purpose of the Study:

  • To investigate the information entropy of cluster-size distributions in explosive percolation models.
  • To reconcile the observed behavior of information entropy with power-law distributions and maximum cluster-size diversity at the threshold.

Main Methods:

  • Analysis of the information entropy of cluster-size distributions.
  • Examination of the scaling forms of cluster-size distributions below and above the percolation threshold.
  • Derivation of scaling behaviors for the first and second derivatives of information entropy near the threshold.

Main Results:

  • The information entropy's non-maximal behavior at the threshold is attributed to distinct scaling forms of cluster-size distributions above and below the threshold.
  • The first derivative of information entropy exhibits a negative minimum at the threshold.
  • The second derivative of information entropy shows negative divergence on the left and positive divergence on the right of the threshold.

Conclusions:

  • The study clarifies the behavior of information entropy in explosive percolation by identifying different scaling laws for cluster-size distributions.
  • Established scaling behaviors of entropy derivatives provide a theoretical basis for simulation predictions regarding the transition dynamics.