Non-equilibrium and stationary fluctuations of a slowed boundary symmetric exclusion

Abstract We consider a one-dimensional symmetric simple exclusion process in contact with slowed reservoirs: at the left (resp. right) boundary, particles are either created or removed at rates given by α ∕ n or ( 1 − α ) ∕ n (resp. β ∕ n or ( 1 − β ) ∕ n ) where α , β > 0 and n is a scaling parameter. We obtain the non-equilibrium fluctuations and from the latter we obtain also the non-equilibrium stationary fluctuations.