Non equilibrium stationary state for the SEP with births and deaths
  We consider the symmetric simple exclusion process in the interval $\La_N:=[-N,N]\cap\mathbb Z$ with births and deaths taking place respectively on suitable boundary intervals $I_+$ and $I_-$, as introduced in De Masi et al. (J. Stat. Phys. 2011). We study the stationary measure density profile in the limit $N\to\infty$ 
Anna De Masi, Errico Presutti, Dimitrios Tsagkarogiannis and Maria   Eulalia Vares
math-ph math.MP