  Recent studies of nonequilibrium phase transitions have shown that in many
systems which have transitions involving an arrested phase, the arrested states
show suppressed density fluctuations and a cusp in the configurational entropy
at the transition point. We study quasistatic driving in the 1D fixed-energy
abelian sandpile model, and in conserved lattice gases with range $n$ in 1D,
and exactly determine the measure over the absorbing states for both cases,
along with the behaviour of density fluctuations and the configurational
entropy of absorbing states. We show that both models exhibit hyperuniformity
near the transition, and also that the configurational entropy shows a cusp at
the transition point in the conserved lattice gases.
