  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.
