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

30.4K
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...
30.4K
The Second Law of Thermodynamics01:14

The Second Law of Thermodynamics

5.4K
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...
5.4K
Second Law of Thermodynamics02:49

Second Law of Thermodynamics

24.0K
In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic...
24.0K
Entropy and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

2.9K
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...
2.9K
Third Law of Thermodynamics02:38

Third Law of Thermodynamics

19.1K
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.
19.1K
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

2.6K
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.
2.6K

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

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

Chaos (Woodbury, N.Y.)·2025
Same author

Reminiscences of Half a Century of Life in the World of Theoretical Physics.

Entropy (Basel, Switzerland)·2024
Same author

de Broglie-Bohm analysis of a nonlinear membrane: From quantum to classical chaos.

Chaos (Woodbury, N.Y.)·2024
Same author

First-Principle Validation of Fourier's Law: One-Dimensional Classical Inertial Heisenberg Model.

Entropy (Basel, Switzerland)·2024
Same author

Medical Applications of Nonadditive Entropies.

Entropy (Basel, Switzerland)·2023

Related Experiment Video

Updated: Jul 29, 2025

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

33.8K

Senses along Which the Entropy S Is Unique.

Constantino Tsallis1,2,3

  • 1Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology of Complex Systems, Rua Xavier Sigaud 150, Rio de Janeiro 22290-180, RJ, Brazil.

Entropy (Basel, Switzerland)
|May 27, 2023
PubMed
Summary

Nonextensive statistical mechanics, using the nonadditive entropy Sq, addresses complex systems where traditional Boltzmann-Gibbs entropy fails. This study explores the unique mathematical properties of Sq within this framework.

Keywords:
Boltzmann–Gibbs statistical mechanicsentropic uniqueness theoremsnonadditive entropiesnonextensive statistical mechanics

More Related Videos

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

14.8K
A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

2.6K

Related Experiment Videos

Last Updated: Jul 29, 2025

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

33.8K
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

14.8K
A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

2.6K

Area of Science:

  • Statistical Mechanics
  • Complex Systems
  • Information Theory

Background:

  • The Boltzmann-Gibbs-von Neumann-Shannon entropy (SBG) is foundational to statistical mechanics but struggles with complex systems.
  • Complex systems in nature, artificial intelligence, and society increasingly defy the applicability of traditional statistical mechanics.
  • Nonextensive statistical mechanics, developed in 1988, offers a generalized framework using nonadditive entropy (Sq).

Purpose of the Study:

  • To investigate the unique mathematical properties of the nonadditive entropy Sq.
  • To understand why Sq plays a special role in nonextensive statistical mechanics and complexity studies.
  • To provide a mathematical answer to the question of Sq's uniqueness.

Main Methods:

  • Mathematical analysis of entropic functionals.
  • Exploration of the properties of the nonadditive entropy Sq.
  • Comparison of Sq with other existing entropic functionals.

Main Results:

  • Sq is a key component in numerous theoretical, experimental, and computational validations within complexity science (plectics).
  • Over fifty mathematically defined entropic functionals exist, highlighting the need to understand Sq's distinctiveness.
  • The study provides a non-exhaustive mathematical explanation for the unique role of Sq.

Conclusions:

  • The nonadditive entropy Sq is crucial for understanding complex systems where traditional methods fall short.
  • Sq's unique mathematical characteristics underpin its wide applicability in diverse scientific validations.
  • Further mathematical exploration is needed to fully elucidate the uniqueness and implications of Sq.