  The Ornstein--Uhlenbeck Particle (OUP) model imagines a microscopic swimmer
propelled by an active force which is correlated with itself on a finite
time-scale. Here we investigate the influence of external potentials on an
ideal suspension of OUPs, in both one and two spatial dimensions, with
particular attention paid to the pressure exerted on "confining walls". We
employ a mathematical connection between the local density of OUPs and the
statistics of their propulsion force to demonstrate the existence of an
equation of state in one dimension. In higher dimensions we show that active
particles generate a non-conservative force field in the surrounding medium. A
simplified far-from-equilibrium model is proposed to account for OUP behaviour
in the vicinity of potentials. Building on this, we interpret simulations of
OUPs in more complicated situations involving asymmetrical and spatially curved
potentials, characterising the inhomogeneous local stresses which result in
terms of competing active length-scales.
