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...

The Uncertainty Principle

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...

The Entropy as a State Function

The Entropy as a State Function

Consider an arbitrary process that moves between two specific states (A and B) in a cyclic manner. This process is reversible and broken down into smaller parts that each follow a Carnot cycle. A Carnot cycle has two isothermal (constant temperature) processes. During these processes, the ratio of the amount of heat transferred to their respective temperature remains constant. The other two processes in the Carnot cycle are also reversible but adiabatic, which means they occur without any heat...

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 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...

You might also read

Related Articles

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

Sort by

Same author

Ontological indistinguishability as a central tenet of quantum theory.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2023

Same author

Resource-theoretic approach to vectorial coherence.

Optics letters·2018

Same author

Detecting dynamical changes in time series by using the Jensen Shannon divergence.

Chaos (Woodbury, N.Y.)·2017

Same author

Distinguishability notion based on Wootters statistical distance: Application to discrete maps.

Chaos (Woodbury, N.Y.)·2017

Same author

Effect of the microtubule-associated protein tau on dynamics of single-headed motor proteins KIF1A.

Physical review. E, Statistical, nonlinear, and soft matter physics·2014

Same author

Shock detection in dynamics of single-headed motor proteins KIF1A via Jensen-Shannon divergence.

Physical review. E, Statistical, nonlinear, and soft matter physics·2011

Search research articles

Related Experiment Video

Updated: Mar 15, 2026

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

Comment on "Quantum Kaniadakis entropy under projective measurement".

G M Bosyk¹, S Zozor², F Holik^1,3

¹IFLP, UNLP, CONICET, Facultad de Ciencias Exactas, Calle 115 y 49, CC 67, 1900 La Plata, Argentina.

Physical Review. E

|September 15, 2016

Summary

We demonstrate that generalized (h,ϕ) entropies, including Kaniadakis entropy, are nondecreasing under projective measurements. This finding simplifies understanding of entropic properties and extends to any bistochastic map.

More Related Videos

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Related Experiment Videos

Last Updated: Mar 15, 2026

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Area of Science:

Quantum Information Theory
Mathematical Physics

Background:

The study addresses the properties of generalized (h,ϕ) entropies.
It comments on specific results concerning Kaniadakis entropy and projective measurements.

Purpose of the Study:

To demonstrate that generalized (h,ϕ) entropies exhibit nondecreasing character under projective measurements.
To show that this property is a special case of a more general framework previously established.
To deepen the understanding of entropic properties and their behavior under measurements.

Main Methods:

Utilizing majorization and Schur-concavity arguments for theoretical proofs.
Analyzing the behavior of entropies under bistochastic maps, with projective measurements as a specific instance.

Main Results:

The nondecreasing character of generalized (h,ϕ) entropies under projective measurements is proven.
Kaniadakis entropy is shown to satisfy this property, along with all majorization-preserving entropies.
The results are shown to hold for any bistochastic map, not just projective measurements.

Conclusions:

The framework presented simplifies proofs and enhances the understanding of entropic properties.
Generalized (h,ϕ) entropies and Kaniadakis entropy possess robust nondecreasing characteristics under specific transformations.
The study highlights the broader applicability of the established theoretical framework.