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 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...

The Second Law of Thermodynamics

The Second Law of Thermodynamics

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...

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.

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.

Standard Entropy Change for a Reaction

Standard Entropy Change for a Reaction

Entropy is a state function, so the standard entropy change for a chemical reaction (ΔS°rxn) can be calculated from the difference in standard entropy between the products and the reactants.

You might also read

Related Articles

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

Sort by

Same author

Varying-Coefficient Additive Models with Density Responses and Functional Auto-Regressive Error Process.

Entropy (Basel, Switzerland)·2025

Same author

Defective regression models for cure rate data with competing risks.

Journal of biopharmaceutical statistics·2024

Same author

Family of bivariate distributions on the unit square: theoretical properties and applications.

Journal of applied statistics·2024

Same author

Goodness of fit test for uniform distribution with censored observation.

Journal of the Korean Statistical Society·2023

Same author

Jackknife empirical likelihood test for testing one-sided Lévy distribution.

Journal of applied statistics·2022

Same author

Nonparametric inference for panel count data with competing risks.

Journal of applied statistics·2022

Search research articles

Related Experiment Video

Updated: Sep 26, 2025

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy

Published on: June 27, 2013

A Generalized Measure of Cumulative Residual Entropy.

Sudheesh Kumar Kattumannil¹, E P Sreedevi², Narayanaswamy Balakrishnan³

¹Applied Statistics Unit, Indian Statistical Institute, Chennai 600029, India.

Entropy (Basel, Switzerland)

|April 23, 2022

Summary

This study introduces a generalized cumulative residual entropy measure, unifying various existing entropy types. New generalized cumulative entropy and relationships between entropy and extropy are also established.

Keywords:

Tsallis entropy cumulative entropy cumulative residual entropy extropy weighted cumulative residual entropy

More Related Videos

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

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

Published on: August 16, 2017

Microstate and Omega Complexity Analyses of the Resting-state Electroencephalography

Microstate and Omega Complexity Analyses of the Resting-state Electroencephalography

Published on: June 15, 2018

Related Experiment Videos

Last Updated: Sep 26, 2025

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy

Published on: June 27, 2013

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

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

Published on: August 16, 2017

Microstate and Omega Complexity Analyses of the Resting-state Electroencephalography

Microstate and Omega Complexity Analyses of the Resting-state Electroencephalography

Published on: June 15, 2018

Area of Science:

Information Theory
Probability Theory
Statistical Mechanics

Background:

Existing entropy measures lack a unified framework.
Need for generalized entropy definitions in data analysis.

Purpose of the Study:

Introduce a generalized cumulative residual entropy.
Develop a generalized cumulative entropy measure.
Explore relationships between entropy and extropy.

Main Methods:

Formulation of generalized entropy measures.
Utilizing a generating function approach for entropy derivation.
Deriving specific entropy forms like Sharma-Taneja-Mittal entropy.

Main Results:

Demonstrated that cumulative residual entropy, weighted cumulative residual entropy, and cumulative residual Tsallis entropy are special cases of the generalized measure.
Introduced a generalized cumulative entropy measure encompassing cumulative entropy, weighted cumulative entropy, and cumulative Tsallis entropy.
Established novel connections between entropy and extropy using the new measures.

Conclusions:

The proposed generalized entropy framework offers a unified approach to various entropy measures.
The generating function method provides a versatile tool for deriving entropy measures.
The study advances understanding of entropy and extropy relationships in information theory.