Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Entropy

Entropy

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...

Entropy

Entropy

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...

Entropy and the Second Law of Thermodynamics

Entropy and the Second Law of Thermodynamics

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...

Entropy Change in Reversible Processes

Entropy Change in Reversible Processes

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.

Entropy and Solvation

Entropy and Solvation

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...

Third Law of Thermodynamics

Third Law of Thermodynamics

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.

You might also read

Related Articles

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

Sort by

Same author

Synergy mediates long-range correlations in the visual cortex near criticality.

Frontiers in computational neuroscience·2026

Same author

Synergy mediates Long-Range Correlations in the Visual Cortex Near Criticality.

bioRxiv : the preprint server for biology·2025

Same author

Group Structure as a Foundation for Entropies.

Entropy (Basel, Switzerland)·2024

Same author

Information theory-based direct causality measure to assess cardiac fibrillation dynamics.

Journal of the Royal Society, Interface·2023

Same author

Economic Trading Susceptibility: Constructing Networks of Mutual Influence through the Fitness of Countries.

Entropy (Basel, Switzerland)·2023

Same author

Information Geometry, Complexity Measures and Data Analysis.

Entropy (Basel, Switzerland)·2022

Search research articles

Related Experiment Video

Updated: Nov 27, 2025

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

Group Entropies: From Phase Space Geometry to Entropy Functionals via Group Theory.

Henrik Jeldtoft Jensen^1,2, Piergiulio Tempesta^3,4

¹Centre for Complexity Science and Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK.

Entropy (Basel, Switzerland)

|December 3, 2020

Summary

Group theoretic entropies generalize Boltzmann-Gibbs entropy by replacing additivity with composability. These generalized entropies depend on degrees of freedom (N) and offer new information-theoretical perspectives.

Keywords:

formal groups generalised entropies phase space growth rate

More Related Videos

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Related Experiment Videos

Last Updated: Nov 27, 2025

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Area of Science:

Information Theory
Statistical Mechanics
Group Theory

Background:

The standard Boltzmann-Gibbs entropy relies on four axioms, including additivity.
Generalized entropies are crucial for understanding systems with varying degrees of freedom.

Purpose of the Study:

To explore group theoretic entropies as a generalization of Boltzmann-Gibbs entropy.
To investigate the role of the composability axiom and degrees of freedom (N).

Main Methods:

Reviewing group theoretic entropies and their mathematical framework.
Analyzing the composability axiom as a replacement for additivity.
Examining the dependence of entropy on the number of degrees of freedom (N).

Main Results:

Group theoretic entropies generalize standard entropy by incorporating a composability axiom.
These entropies are shown to depend significantly on the number of degrees of freedom (N).
The functional form of group entropies relates to the dependence of phase space volume (W) on N.

Conclusions:

Group entropies offer a more general framework than Boltzmann-Gibbs entropy.
The composability axiom and dependence on N are key features of group entropies.
Group entropies hold particular relevance for information-theoretical applications.