  Inspired by the recent work of Bertini and Posta, who introduced the boundary
driven Brownian gas on $[0,1]$, we study boundary driven systems of independent
particles in a general setting, including particles jumping on finite graphs
and diffusion processes on bounded domains in $\mathbb{R}^d$. We prove duality
with a dual process that is absorbed at the boundaries, thereby creating a
general framework that unifies dualities for boundary driven systems in the
discrete and continuum setting. We use duality first to show that from any
initial condition the systems evolve to the unique invariant measure, which is
a Poisson point process with intensity the solution of a Dirichlet problem.
Second, we show how the boundary driven Brownian gas arises as the diffusive
scaling limit of a system of independent random walks coupled to reservoirs
with properly rescaled intensity.
