  We analyse a one-dimensional model of hard particles, within ensembles of
trajectories that are conditioned (or biased) to atypical values of the
time-averaged dynamical activity. We analyse two phenomena that are associated
with these large deviations of the activity: phase separation (at low activity)
and the formation of hyperuniform states (at high activity). We consider a
version of the model which operates at constant volume, and a version at
constant pressure. In these non-equilibrium systems, differences arise between
the two ensembles, because of the extra freedom available to the
constant-pressure system, which can change its total density. We discuss the
relationships between different ensembles, mechanical equilibrium, and the
probability cost of rare density fluctuations.
