Publication
Entropy in Spin Relaxation, Spintronics, and Magnetic Resonance
Abstract
The entropy change during spin relaxation for a realistic model system is studied, whose spin dynamics can be handled with the Boltzmann equation. The time evolution of the von Neumann entropy is monitored during the process and is compared with the recently introduced concept of the Loschmidt echo envelope. The time evolution of the two quantities is remarkably similar which helps to distinguish reversible and irreversible changes to the ensemble spin state. The method is also demonstrated for a toy model of nuclear magnetic resonance, where the usual pi spin echo is performed numerically, and the echo envelope also follows the time evolution of the von Neumann entropy. The numerical approach highlights the utility of the entropy concept in analyzing various processes which occur during spin relaxation.
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Related concepts (32)
Entropy
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of information theory.
Entropy (information theory)
In information theory, the entropy of a random variable is the average level of "information", "surprise", or "uncertainty" inherent to the variable's possible outcomes. Given a discrete random variable , which takes values in the alphabet and is distributed according to : where denotes the sum over the variable's possible values. The choice of base for , the logarithm, varies for different applications. Base 2 gives the unit of bits (or "shannons"), while base e gives "natural units" nat, and base 10 gives units of "dits", "bans", or "hartleys".
Entropy (statistical thermodynamics)
The concept entropy was first developed by German physicist Rudolf Clausius in the mid-nineteenth century as a thermodynamic property that predicts that certain spontaneous processes are irreversible or impossible. In statistical mechanics, entropy is formulated as a statistical property using probability theory. The statistical entropy perspective was introduced in 1870 by Austrian physicist Ludwig Boltzmann, who established a new field of physics that provided the descriptive linkage between the macroscopic observation of nature and the microscopic view based on the rigorous treatment of large ensembles of microstates that constitute thermodynamic systems.
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