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Gauss's Law

Gauss's Law

If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.

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 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.

Gauss's Law: Problem-Solving

Gauss's Law: Problem-Solving

Gauss's law helps determine electric fields even though the law is not directly about electric fields but electric flux. In situations with certain symmetries (spherical, cylindrical, or planar) in the charge distribution, the electric field can be deduced based on the knowledge of the electric flux. In these systems, we can find a Gaussian surface S over which the electric field has a constant magnitude. Furthermore, suppose the electric field is parallel (or antiparallel) to the area...

The Pauli Exclusion Principle

The Pauli Exclusion Principle

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:

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.

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Related Experiment Video

Updated: Sep 16, 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 entanglement and extractable work for Gaussian states.

Jaewon Lee¹, Changsuk Noh², Kabgyun Jeong^3,4

¹Kyungpook National University, Daegu, 41566, Korea.

Scientific Reports

|July 7, 2025

Summary

Quantum correlations in two-mode Gaussian states significantly impact extractable work. This quantum thermodynamics study quantifies differences in work based on state properties like entanglement.

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Area of Science:

Quantum Thermodynamics
Quantum Information Theory

Background:

Quantum principles influence thermodynamic processes.
Quantum correlations distinguish quantum from classical thermodynamics.
Understanding extractable work in quantum systems is crucial.

Purpose of the Study:

To investigate the relationship between extractable work and quantum correlations.
To analyze how quantum correlations in two-mode Gaussian states affect thermodynamic properties.
To differentiate thermodynamic features enabled by quantum correlations.

Main Methods:

Analysis of extractable work for two-mode Gaussian states.
Examination of local energy changes due to Gaussian measurements on one party.
Classification of states based on quantum correlations: separable, entangled, and steerable.

Main Results:

A clear quantitative difference in extractable work was observed.
The amount of extractable work depends on the quantum correlation class of the two-mode state.
Quantum correlations demonstrably alter thermodynamic potential.

Conclusions:

Quantum correlations are a key resource in quantum thermodynamics.
The nature of quantum correlations (e.g., entanglement, steerability) directly impacts the extractable work.
Findings highlight the distinct thermodynamic capabilities arising from quantum phenomena.