  We study the dynamics of a one-dimensional fluid of orientable hard
rectangles with a non-coarse-grained microscopic mechanism of facilitation. The
length occupied by a rectangle depends on its orientation, which is coupled to
an external field. The equilibrium properties of our model are essentially
those of the Tonks gas, but at high densities, the orientational degrees of
freedom become effectively frozen due to jamming. This is a simple analytically
tractable model of glassy phase. Under a cyclic variation of the pressure,
hysteresis is observed. Following a pressure quench, the orientational
persistence exhibits a two-stage decay characteristic of glassy systems.
