  Antiferromagnets are promising candidates as active components in spintronic
applications. They share features with ferrimagnets in that opposing spin
orientations exist in two or more sublattices. Spin transfer torque and spin
pumping are essential ingredients in antiferromagnetic and ferrimagnet
spintronics. This paper develops an out-of-equilibrium quantum theory of the
spin dynamics of collinear magnets containing many spins coupled to normal
metal reservoirs. At equilibrium, the spins are parallel or antiparallel to the
easy axis. The theory, therefore, covers collinear antiferromagnets and
ferrimagnets. We focus on the resulting semi-classical spin dynamics. The
dissipation in the spin dynamics is enhanced due to spin-pumping. Spin
accumulations in the normal metals induce deterministic spin-transfer torques
on the magnet. Additionally, each electron's discrete spin angular momentum
causes stochastic fluctuating torques on the antiferromagnet or ferrimagnet. We
derive these fluctuating torques. The fluctuation-dissipation theorem holds at
high temperatures, including the effects of spin-pumping. At low temperatures,
we derive shot noise contributions to the fluctuations.
