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 and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

3.2K
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...
3.2K
Entropy01:18

Entropy

2.9K
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...
2.9K
Gibbs Free Energy02:39

Gibbs Free Energy

34.6K
One of the challenges of using the second law of thermodynamics to determine if a process is spontaneous is that it requires measurements of the entropy change for the system and the entropy change for the surroundings. An alternative approach involving a new thermodynamic property defined in terms of system properties only was introduced in the late nineteenth century by American mathematician Josiah Willard Gibbs. This new property is called the Gibbs free energy (G) (or simply the free...
34.6K
The Second Law of Thermodynamics01:14

The Second Law of Thermodynamics

5.8K
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...
5.8K
An Introduction to Free Energy01:05

An Introduction to Free Energy

9.0K
How can we compare the energy that releases from one reaction to that of another reaction? We use a measurement of free energy to quantitate these energy transfers. Scientists call this free energy Gibbs free energy (abbreviated with the letter G) after Josiah Willard Gibbs, the scientist who developed the measurement. According to the second law of thermodynamics, all energy transfers involve losing some energy in an unusable form such as heat, resulting in entropy. Gibbs free energy...
9.0K
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

2.7K
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.
2.7K

You might also read

Related Articles

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

Sort by
Same author

The Fundamental Theorem of Natural Selection.

Entropy (Basel, Switzerland)·2021
Same journal

Research on a Regional Availability Evaluation Model for Road-Area High-Entropy Energy Based on Synergy Factors.

Entropy (Basel, Switzerland)·2026
Same journal

Atmospheric Turbulence Channel Modeling and Performance Analysis of a CO-ZP-OFDM Coherent Optical Communication System for UAV Air-to-Ground Scenarios.

Entropy (Basel, Switzerland)·2026
Same journal

Information Geometry and Asymptotic Theory for SMML Estimators.

Entropy (Basel, Switzerland)·2026
Same journal

Correlation Entropy and Power-Law Kinetics.

Entropy (Basel, Switzerland)·2026
Same journal

Research on the Contagion of Systemic Financial Risk Under the Impact of Climate Risks-From the Perspective of Complex Networks and Machine Learning.

Entropy (Basel, Switzerland)·2026
Same journal

The Statistical-Mechanical Meaning of the Wave Function of Quantum Mechanics.

Entropy (Basel, Switzerland)·2026
See all related articles

Related Experiment Video

Updated: Sep 21, 2025

Unraveling Entropic Rate Acceleration Induced by Solvent Dynamics in Membrane Enzymes
09:42

Unraveling Entropic Rate Acceleration Induced by Solvent Dynamics in Membrane Enzymes

Published on: January 16, 2016

9.1K

Rényi Entropy and Free Energy.

John C Baez1

  • 1Department of Mathematics, University of California, Riverside, CA 92507, USA.

Entropy (Basel, Switzerland)
|May 28, 2022
PubMed
Summary
This summary is machine-generated.

Rényi entropy, a generalization of entropy dependent on parameter q, is closely linked to free energy. It quantifies maximum work obtainable from thermal systems undergoing temperature changes, applicable to both classical and quantum systems.

Keywords:
Rényi entropyfree energyq-deformation q-derivative

More Related Videos

Differential Scanning Calorimetry — A Method for Assessing the Thermal Stability and Conformation of Protein Antigen
08:13

Differential Scanning Calorimetry — A Method for Assessing the Thermal Stability and Conformation of Protein Antigen

Published on: March 4, 2017

39.4K
Bulk and Thin Film Synthesis of Compositionally Variant Entropy-stabilized Oxides
09:41

Bulk and Thin Film Synthesis of Compositionally Variant Entropy-stabilized Oxides

Published on: May 29, 2018

9.6K

Related Experiment Videos

Last Updated: Sep 21, 2025

Unraveling Entropic Rate Acceleration Induced by Solvent Dynamics in Membrane Enzymes
09:42

Unraveling Entropic Rate Acceleration Induced by Solvent Dynamics in Membrane Enzymes

Published on: January 16, 2016

9.1K
Differential Scanning Calorimetry — A Method for Assessing the Thermal Stability and Conformation of Protein Antigen
08:13

Differential Scanning Calorimetry — A Method for Assessing the Thermal Stability and Conformation of Protein Antigen

Published on: March 4, 2017

39.4K
Bulk and Thin Film Synthesis of Compositionally Variant Entropy-stabilized Oxides
09:41

Bulk and Thin Film Synthesis of Compositionally Variant Entropy-stabilized Oxides

Published on: May 29, 2018

9.6K

Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Quantum Information Theory

Background:

  • Entropy quantifies disorder in classical and quantum systems.
  • Rényi entropy offers a generalized framework for entropy calculations.
  • Understanding the relationship between entropy and free energy is crucial in thermodynamics.

Purpose of the Study:

  • To explore the relationship between Rényi entropy and free energy.
  • To establish a quantitative link between Rényi entropy and the work extractable from thermal systems.
  • To demonstrate the q-deformation aspect of Rényi entropy.

Main Methods:

  • Mathematical derivation connecting Rényi entropy to free energy.
  • Analysis of work extraction from systems undergoing temperature changes.
  • Application of the q-1-derivative formalism.

Main Results:

  • Rényi entropy is shown to be the q-1-derivative of free energy with respect to temperature.
  • The maximum work extractable from a system divided by the temperature change equals its Rényi entropy.
  • The results are valid for both classical and quantum systems.

Conclusions:

  • Rényi entropy provides a generalized measure of information and thermodynamic properties.
  • The study highlights Rényi entropy as a q-deformation of standard entropy.
  • This work bridges concepts in statistical mechanics and information theory.