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Atomic Nuclei: Nuclear Spin State Population Distribution

Atomic Nuclei: Nuclear Spin State Population Distribution

Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.

Atomic Nuclei: Nuclear Spin State Overview

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NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of one, the...

Atomic Nuclei: Nuclear Relaxation Processes

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Spin–Spin Coupling Constant: Overview

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Updated: Jun 3, 2026

Neutron Spin Echo Spectroscopy as a Unique Probe for Lipid Membrane Dynamics and Membrane-Protein Interactions

Neutron Spin Echo Spectroscopy as a Unique Probe for Lipid Membrane Dynamics and Membrane-Protein Interactions

Published on: May 27, 2021

Consistent thermodynamics for spin echoes.

Charis Anastopoulos¹, Ntina Savvidou

¹Department of Physics, University of Patras, GR-26500 Patras, Greece. anastop@physics.upatras.gr

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|March 17, 2011

Summary

This summary is machine-generated.

Spin-echo experiments do not violate the second law of thermodynamics. Accounting for molecular spin and translational motion reveals that entropy remains constant during dephasing and increases during dissipation.

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Last Updated: Jun 3, 2026

Neutron Spin Echo Spectroscopy as a Unique Probe for Lipid Membrane Dynamics and Membrane-Protein Interactions

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Study of Protein Dynamics via Neutron Spin Echo Spectroscopy

Study of Protein Dynamics via Neutron Spin Echo Spectroscopy

Published on: April 13, 2022

Area of Science:

Thermodynamics
Quantum Mechanics
Statistical Mechanics

Background:

Spin-echo experiments are often misinterpreted as violating the second law of thermodynamics.
Previous analyses failed to account for coupled spin and translational molecular dynamics.

Purpose of the Study:

To provide a thermodynamically consistent explanation for spin-echo experiments.
To re-evaluate the thermodynamic behavior of spin-echo phenomena by incorporating molecular correlations.

Main Methods:

Developed an entropy functional based on Boltzmann macrostates.
Incorporated both spin and translational degrees of freedom into the thermodynamic treatment.
Analyzed the relationship between quantum mechanical descriptions and thermodynamic macrostates.

Main Results:

Dephasing in spin echoes is shown to be Hamiltonian evolution, preserving entropy.
Dissipation processes are identified as the source of entropy increase.
No phase of entropy decrease was observed during the echo formation.

Conclusions:

Spin-echo experiments do not exhibit antithermodynamic behavior or violate the second law.
The decay of net magnetization serves as a reliable indicator of entropy change.
A comprehensive thermodynamic framework requires consideration of coupled degrees of freedom.