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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...

Maxwell's Thermodynamic Relations

Maxwell's Thermodynamic Relations

Maxwell's thermodynamic relations are very useful in solving problems in thermodynamics. Each of Maxwell's relations relates a partial differential between quantities that can be hard to measure experimentally to a partial differential between quantities that can be easily measured. These relations are a set of equations derivable from the symmetry of the second derivatives and the thermodynamic potentials.
All thermodynamic potentials are exact differentials. Therefore, their second-order...

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...

The Second Law of Thermodynamics

The 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. Scientists refer to the measure of randomness or disorder within a system as entropy. High entropy means high disorder and low energy. To better understand entropy, think of a student’s bedroom. If no energy or work were put into it, the room would quickly become messy. It would exist in a very disordered state, one of high entropy. Energy must be...

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.

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Analysis of SEC-SAXS data via EFA deconvolution and Scatter

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Maxwell Relation between Entropy and Atom-Atom Pair Correlation.

Raymon S Watson¹, Caleb Coleman¹, Karen V Kheruntsyan¹

¹School of Mathematics and Physics, <a href="https://ror.org/00rqy9422">University of Queensland</a>, Brisbane, Queensland 4072, Australia.

Physical Review Letters

|September 20, 2024

Summary

This summary is machine-generated.

Researchers derived a Maxwell relation connecting particle-pair correlations to entropy in 1D Bose gases. This allows calculating entropy from easily measured correlations, simplifying quantum gas analysis.

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Area of Science:

Quantum physics
Thermodynamics
Statistical mechanics

Background:

Local particle-pair correlation functions are thermodynamic quantities in many-particle systems.
The Hellmann-Feynman theorem enables calculation of these correlations.
Entropy calculation in quantum gases is computationally challenging.

Purpose of the Study:

Derive a thermodynamic Maxwell relation between local pair correlation and entropy.
Apply this relation to determine the entropy of a 1D Bose gas.
Demonstrate a novel method for entropy measurement in quantum gases.

Main Methods:

Utilized the Hellmann-Feynman theorem to establish the thermodynamic property of local pair correlation.
Derived a Maxwell relation linking local pair correlation to entropy.
Applied the derived relation within the stochastic projected Gross-Pitaevskii equation (SPGPE) formalism.

Main Results:

Successfully derived a Maxwell relation for 1D Bose gases.
Demonstrated that entropy can be determined from the atom-atom pair correlation function.
Showcased the feasibility of calculating entropy computationally via correlation functions.

Conclusions:

The derived Maxwell relation provides a practical link between measurable correlations and entropy.
This method simplifies entropy determination for finite-temperature 1D Bose gases.
Presents a proof-of-principle for an experimental technique to measure quantum gas entropy from correlations.