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Updated: Jan 20, 2026
Entropy; State Property and the Second Law of Thermodynamics
Published on: April 30, 2023
Low-temperature atomistic spin relaxation and non-equilibrium intensive properties using steepest-entropy-ascent
Ryo Yamada1, Michael R von Spakovsky2, William T Reynolds1
1Materials Science and Engineering Department, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, United States of America.
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The magnetization of body-centered cubic iron at low temperatures is calculated with the steepest-entropy-ascent quantum thermodynamics (SEAQT) framework. This framework assumes that a thermodynamic property in an isolated system traces the path through state space with the greatest entropy production. Magnetization is calculated from the expected value of a thermodynamic ensemble of quantized spin waves based on the Heisenberg spin model applied to an ensemble of coupled harmonic oscillators. A realistic energy landscape is obtained from a magnon dispersion relation calculated using spin-density-functional-theory. The equilibrium magnetization as well as the evolution of magnetization from a non-equilibrium state to equilibrium are calculated from the path of steepest entropy ascent determined from the SEAQT equation of motion in state space. The framework makes it possible to model the temperature and time-dependence of magnetization without a detailed description of magnetic damping. The approach is also used to define intensive properties (temperature and magnetic field strength) that are fundamentally, i.e. canonically or grand canonically, valid for any non-equilibrium state. Given the assumed magnon dispersion relation, the SEAQT framework is used to calculate the equilibrium magnetization at different temperatures and external magnetic fields and the results are shown to closely agree with experiment for temperatures less than 500 K. The time-dependent evolution of magnetization from different initial states and interactions with a reservoir is also predicted.
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