  The extent to which active matter might be described by effective equilibrium
concepts like temperature and pressure is currently being discussed intensely.
Here we study the simplest model, an ideal gas of non-interacting active
Brownian particles. While the mechanical pressure exerted onto confining walls
has been linked to correlations between particles' positions and their
orientations, we show that these correlations are entirely controlled by
boundary effects. We also consider a definition of local pressure, which
describes interparticle forces in terms of momentum exchange between different
regions of the system. We present three pieces of analytical evidence which
indicate that such a local pressure exists, and we show that its bulk value
differs from the mechanical pressure exerted on the walls of the system. We
attribute this difference to the fact that the local pressure in the bulk does
not depend on boundary effects, contrary to the mechanical pressure. We
carefully examine these boundary effects using a channel geometry, and we show
a virial formula for the pressure correctly predicts the mechanical pressure
even in finite channels. However, this result no longer holds in more complex
geometries, as exemplified for a channel that includes circular obstacles.
