  We present a framework for modeling the transport of any number of globally
conserved quantities in any spatial configuration and apply it to obtain a
model of magnetization transport for spin-systems that is valid in new regimes
(including high-polarization). The framework allows an entropy function to
define a model that explicitly respects the laws of thermodynamics. Three
facets of the model are explored. First, it is expressed as nonlinear partial
differential equations that are valid for the new regime of high dipole-energy
and polarization. Second, the nonlinear model is explored in the limit of low
dipole-energy (semi-linear), from which is derived a physical parameter
characterizing separative magnetization transport (SMT). It is shown that the
necessary and sufficient condition for SMT to occur is that the parameter is
spatially inhomogeneous. Third, the high spin-temperature (linear) limit is
shown to be equivalent to the model of nuclear spin transport of Genack and
Redfield. Differences among the three forms of the model are illustrated by
numerical solution with parameters corresponding to a magnetic resonance force
microscopy (MRFM) experiment. A family of analytic, steady-state solutions to
the nonlinear equation is derived and shown to be the spin-temperature analog
of the Langevin paramagnetic equation and Curie's law. Finally, we analyze the
separative quality of magnetization transport, and a steady-state solution for
the magnetization is shown to be compatible with Fenske's separative mass
transport equation.
