  Recent experiments have detected 4He supersolidity, but the observed
transition is rather unusual. In this paper, we describe a supersolid as a
normal lattice suffused by a Bose gas. With this approach, we can explain the
central aspects of the recent observations as well as previous experimental
results. We conclude that detailed balance is violated in part of the 4He phase
diagram, so that even in steady state contact with a thermal reservoir, the
material is not in equilibrium.
