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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.

First Law: Particles in Two-dimensional Equilibrium

First Law: Particles in Two-dimensional Equilibrium

Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about...

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...

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...

Free Energy Changes for Nonstandard States

Free Energy Changes for Nonstandard States

The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; concentrations other than 1 M) is related to the standard free energy change according to this equation:

where R is the gas constant (8.314 J/K·mol), T is the absolute temperature in kelvin, and Q is the reaction quotient. This equation may be used to predict the spontaneity of a process under any given set of conditions.
Reaction Quotient...

Alternative Sets of Equilibrium Equations

Alternative Sets of Equilibrium Equations

When analyzing the behavior of structures, engineers often rely on the concept of equilibrium. This refers to the state where all forces and moments acting on a system balance each other, resulting in no net movement or rotation. In many cases, equilibrium can be described by a set of standard equations. However, in some situations, alternative sets of equilibrium equations must be used to describe the system's behavior accurately.
One example of such a situation can be observed in a...

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Related Experiment Video

Updated: Oct 1, 2025

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

Reformulation of the No-Free-Lunch Theorem for Entangled Datasets.

Kunal Sharma^1,2, M Cerezo^1,3, Zoë Holmes⁴

¹Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.

Physical Review Letters

|March 4, 2022

Summary

This summary is machine-generated.

Quantum machine learning

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Spatial Separation of Molecular Conformers and Clusters

Spatial Separation of Molecular Conformers and Clusters

Published on: January 9, 2014

Area of Science:

Quantum Computing
Machine Learning Theory

Background:

The no-free-lunch (NFL) theorem restricts classical function learning.
Quantum machine learning (QML) explores quantum computation for learning tasks.

Purpose of the Study:

Investigate a quantum analog of the NFL theorem for learning unitary processes.
Determine the impact of quantum entanglement on QML learnability.

Main Methods:

Formulated a quantum NFL theorem accounting for entanglement.
Utilized Rigetti's quantum computer for experimental validation.

Main Results:

Entangled datasets appear to violate the classical NFL theorem.
Proved a quantum NFL theorem where entanglement reduces learning limits.
Demonstrated entanglement as a valuable resource in QML.

Conclusions:

Entanglement fundamentally alters learnability in quantum machine learning.
The developed quantum NFL theorem provides a new framework for QML.
Experimental results confirm the theoretical predictions on entanglement's role.