One-dimensional boundary-driven lattice gases can provide good examples of simple nonequilibrium models.
However, except in some specific cases, the tools developed at equilibrium (e.g. the classical entropy
methods) are usually not adapted to study their macroscopic behavior. I will explain how we can avoid
the shortcomings of the entropy methods, which was developped for equilibrium models, and use duality
to obtain some macroscopic results on classes of boundary-driven models whose left boundary dynamics
is not reversible w.r.t. reference product measures. As an overture, I will also briefly present a
simple one-dimensional model exhibiting metastable shifts at the left boundary, illustrating the
rich array of behavior displayed by simple boundary-driven models. Based on joint work with
C. Landim and T. Xu.