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.

Equilibrium Conditions for a Particle

Equilibrium Conditions for a Particle

When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...

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...

First Law: Particles in One-dimensional Equilibrium

First Law: Particles in One-dimensional Equilibrium

Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If...

Reaction Quotient

Reaction Quotient

The status of a reversible reaction is conveniently assessed by evaluating its reaction quotient (Q). For a reversible reaction described by m A + n B ⇌ x C + y D, the reaction quotient is derived directly from the stoichiometry of the balanced equation as

You might also read

Related Articles

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

Sort by

Same author

Modeling interfacial electron transfer using path integral molecular dynamics.

The Journal of chemical physics·2026

Same author

Molecular Insight into How Alcohol Catalyzes the Interfacial Chlorination of Squalene.

The journal of physical chemistry. B·2026

Same author

Transport of Delocalized Excitons through DNA-Based Molecular Photonic Wires.

ACS nano·2025

Same author

Accelerated Chlorination at the Air-Organic Interface Revealed by Molecular Simulations and Kinetic Modeling.

The journal of physical chemistry letters·2025

Same author

Competitive Carbonate Binding Hinders Electrochemical CO<sub>2</sub> Reduction to CO on Cu Surfaces at Low Overpotentials.

Journal of the American Chemical Society·2025

Same author

Deriving the Landauer Principle From the Quantum Shannon Entropy.

The journal of physical chemistry letters·2025

Search research articles

Related Experiment Video

Updated: Oct 13, 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

Nonequilibrium Work Relations and Response Theories in Ensemble Quantum Systems.

Amro Dodin¹, Adam P Willard¹

¹Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States.

The Journal of Physical Chemistry Letters

|November 10, 2021

Summary

We developed a new quantum response theory to distinguish ensemble heterogeneity from quantum uncertainty in macroscopic quantum systems. This P-ensemble theory guides single-molecule experiments.

More Related Videos

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

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

Related Experiment Videos

Last Updated: Oct 13, 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

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

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

Area of Science:

Quantum mechanics
Statistical mechanics
Physical chemistry

Background:

Macroscopic quantum systems are often described using ensemble averages.
Distinguishing ensemble heterogeneity from intrinsic quantum uncertainty is crucial for accurate theoretical descriptions.
Current methods may not fully capture the complexities of heterogeneous quantum ensembles.

Purpose of the Study:

To develop a novel nonequilibrium response theory for macroscopic quantum systems.
To explicitly separate ensemble heterogeneity from quantum uncertainty.
To provide a framework for analyzing single-molecule experiments.

Main Methods:

Introduction of the quantum P-ensemble formalism, extending the density matrix description.
Development of quantum generalizations of linear response theory and the Jarzynski nonequilibrium work relation.
Derivation from a Bochkov-Kuzovlev generating functional for quantum P-ensembles.

Main Results:

A theoretical framework that disentangles classical heterogeneity from quantum uncertainty in ensembles.
Quantum analogs of linear response and Jarzynski relations derived using the P-ensemble.
Demonstration of the P-ensemble formalism's ability to generate higher-order response theories.

Conclusions:

The quantum P-ensemble theory offers a more nuanced description of macroscopic quantum systems.
This formalism provides a valuable tool for interpreting and designing single-molecule experiments.
The theory advances our understanding of nonequilibrium quantum phenomena in heterogeneous systems.