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

Quantifying Work

Quantifying Work

As a system undergoes a change, its internal energy can change, and energy can be transferred from the system to the surroundings, or from the surroundings to the system.

The Quantum-Mechanical Model of an Atom

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.

Work-energy Theorem

Work-energy Theorem

According to Newton’s second law of motion, the sum of all the forces acting on a particle (net force) determines the rate of change in the momentum of the particle (motion). Therefore, we should consider the work done by all forces acting on a particle, or the net work, to see its effect on the particle’s motion.
The work-energy theorem equates work done by all the forces on an object to the change in its kinetic energy. The theorem can be used to calculate work done by a force...

The de Broglie Wavelength

The de Broglie Wavelength

In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...

Atomic Nuclei: Nuclear Spin State Population Distribution

Atomic Nuclei: Nuclear Spin State Population Distribution

Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.

Quantum Numbers

Quantum Numbers

It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.

You might also read

Related Articles

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

Sort by

Same author

Quantum reservoir computing for photonic entanglement witnessing.

Science advances·2025

Same author

Nonequilibrium Thermodynamics of Precision through a Quantum-Centric Computation.

Physical review letters·2025

Same author

Typical thermalization of low-entanglement states.

Communications physics·2025

Same author

Critical Assessment of Information Back-Flow in Measurement-Free Teleportation.

Entropy (Basel, Switzerland)·2024

Same author

Generalized Linear Response Theory for the Full Quantum Work Statistics.

Physical review letters·2024

Same author

Experimental Property Reconstruction in a Photonic Quantum Extreme Learning Machine.

Physical review letters·2024

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

Search research articles

Related Experiment Video

Updated: Nov 27, 2025

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

Quantum Work Statistics with Initial Coherence.

María García Díaz¹, Giacomo Guarnieri², Mauro Paternostro³

¹Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, ES-08193 Bellaterra (Barcelona), Spain.

Entropy (Basel, Switzerland)

|December 8, 2020

Summary

This summary is machine-generated.

The Margenau-Hill scheme allows for non-equilibrium initial states in thermodynamic work calculations, unlike the standard two-point measurement scheme. Differences in work moments and entropy production are linked to initial state coherence.

Keywords:

quantum coherence quantum thermodynamics work distribution

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

Author Spotlight: Unlocking New Insights in fNIRS Studies - A Novel Framework for Inter-Brain Synchrony Analysis

Author Spotlight: Unlocking New Insights in fNIRS Studies - A Novel Framework for Inter-Brain Synchrony Analysis

Published on: October 6, 2023

Related Experiment Videos

Last Updated: Nov 27, 2025

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

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Author Spotlight: Unlocking New Insights in fNIRS Studies - A Novel Framework for Inter-Brain Synchrony Analysis

Author Spotlight: Unlocking New Insights in fNIRS Studies - A Novel Framework for Inter-Brain Synchrony Analysis

Published on: October 6, 2023

Area of Science:

Quantum Thermodynamics
Statistical Mechanics

Background:

The two-point measurement scheme for thermodynamic work requires initial equilibrium.
The Margenau-Hill scheme extends this to non-equilibrium initial states.

Purpose of the Study:

To quantitatively compare the two-point measurement and Margenau-Hill schemes.
To analyze the role of initial state coherence in thermodynamic work calculations.

Main Methods:

Utilizing the l1-coherence measure to quantify initial state coherence.
Comparing work moments (first moments, variances) and average entropy production between schemes.

Main Results:

Differences in work moments and average entropy production are functions of initial coherence.
Average entropy production can yield negative values within the Margenau-Hill framework.

Conclusions:

Initial state coherence is a key factor differentiating thermodynamic work calculations in equilibrium and non-equilibrium scenarios.
The Margenau-Hill scheme offers a broader framework for studying thermodynamic processes, including potential for negative entropy production.