  We derive the equations of motion of relativistic magnetohydrodynamics, as
well as microscopic expressions for all of its transport coefficients, from the
Boltzmann equation using the method of moments. In contrast to reference Phys.
Rev. D 98(7) 2018, where a single component gas was considered, we perform our
derivation for a locally neutral fluid composed of two massless particle
species with opposite charges. We demonstrate that the magnetohydrodynamical
equations of motion become dramatically different for this more realistic
system. The shear-stress tensor no longer obeys a single differential equation;
it breaks into three non-degenerate components with respect to the magnetic
field, each evolving according to different dynamical equations. For large
magnetic fields, we further show that the solution of this theory displays
oscillatory behaviour that can no longer be described by an Israel-Stewart-like
theory. Finally, we investigate the derived equations in a Bjorken flow
scenario.
