  Many of the large structures of the cell, such as the cytoskeleton, are
assembled and maintained far from equilibrium. We study the stabilities of
various structures for a simple model of such a far-from-equilibrium organized
assembly in which spherical particles move under the influence of attached
motors. From the variational solutions of the manybody master equation for
Brownian motion with motorized kicking we obtain a closed equation for the
order parameter of localization. Thus we obtain the transition criterion for
localization and stability limits for the crystalline phase and frozen
amorphous structures of motorized particles. The theory also allows an estimate
of nonequilibrium effective temperatures characterizing the response and
fluctuations of motorized crystals and glasses.
