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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.

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...

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.

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 vector...

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.

Work-Energy Theorem for Motion Along a Curve

Work-Energy Theorem for Motion Along a Curve

The work-energy theorem can be generalized to the motion of a particle along any curved path. The simple argument here is that the curved path can be considered a sum of many infinitesimal paths, each of which is a straight path. The force on the particle can be considered constant along any such infinitesimal path so that the work-energy theorem can be applied along it. So, it is also valid for the sum of these paths. The net work done is the integral of the work done along the infinitesimal...

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Related Experiment Video

Updated: Nov 27, 2025

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

Leggett-Garg Inequalities for Quantum Fluctuating Work.

Harry J D Miller¹, Janet Anders¹

¹Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter EX4 4QL, UK.

Entropy (Basel, Switzerland)

|December 3, 2020

Summary

Quantum mechanics defies classical explanations for work. Leggett-Garg inequalities, when applied to quantum thermodynamics, show violations, proving classical macrorealism cannot describe quantum work.

Keywords:

Leggett-Garg inequalities macrorealism quantum work

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Last Updated: Nov 27, 2025

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Area of Science:

Quantum mechanics
Thermodynamics
Quantum information science

Background:

Leggett-Garg inequalities test quantum correlations against classical macrorealism.
Quantum thermodynamics explores work extraction in quantum systems.

Purpose of the Study:

To apply Leggett-Garg inequalities to fluctuating quantum work.
To determine if quantum work can be described by classical macrorealism.

Main Methods:

Derivation of Leggett-Garg inequalities for time-driven quantum systems.
Analysis of work statistics in a driven two-level system.
Investigation using standard and weak measurement schemes.

Main Results:

Leggett-Garg inequalities are violated in a driven two-level quantum system.
Demonstration that quantum work lacks a general macrorealistic description.
Violations observed across different measurement schemes.

Conclusions:

Quantum correlations in work extraction differ fundamentally from classical thermodynamics.
Temporal correlations play a crucial role in quantum work extraction.
Classical macrorealism is insufficient to describe quantum thermodynamic phenomena.