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Entropy

Entropy

Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...

Entropy

Entropy

The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...

Third Law of Thermodynamics

Third Law of Thermodynamics

A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single microstate, as its purity, perfect crystallinity,and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.

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...

Second Law of Thermodynamics

Second Law of Thermodynamics

In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the...

Second Law of Thermodynamics

Second Law of Thermodynamics

The Second Law of Thermodynamics states that entropy, or the amount of disorder in a system, increases each time energy is transferred or transformed. Each energy transfer results in a certain amount of energy that is lost—usually in the form of heat—that increases the disorder of the surroundings. This can also be demonstrated in a classic food web. Herbivores harvest chemical energy from plants and release heat and carbon dioxide into the environment. Carnivores harvest the...

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Related Experiment Video

Updated: Dec 30, 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

Thermal state entanglement entropy on a quantum graph.

Alberto D Verga¹, Ricardo Gabriel Elías²

¹Aix-Marseille Université, CPT, Campus de Luminy, case 907, 13288 Marseille, France.

Physical Review. E

|January 23, 2020

Summary

This summary is machine-generated.

A particle

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Area of Science:

Quantum physics
Graph theory
Condensed matter physics

Background:

Particles interacting with local spins on graphs are a key area of study.
Understanding entanglement entropy is crucial in quantum systems.

Purpose of the Study:

To investigate the relationship between entanglement entropy and graph structure.
To explore the nature of thermal states in such systems.

Main Methods:

Simulating particle behavior on a graph with interacting spins.
Calculating entanglement entropy.
Analyzing graph properties, specifically the minimum cycle basis.

Main Results:

Entanglement entropy of the particle with the spin network correlates with the minimum cycle basis length.
The thermal state exhibits a structure similar to string nets found in spin liquids.

Conclusions:

Graph topology, specifically the minimum cycle basis, plays a significant role in determining entanglement entropy.
The findings offer insights into the complex behavior of quantum systems and their connection to topological phases.