Quasi-static large deviations

We consider the symmetric simple exclusion with open boundaries that are in contact with particle reservoirs at different densities. The reservoir densities changes at a slower time scale with respect to the natural time scale the system reaches the stationary state. This gives rise to the quasi static hydrodynamic limit proven in (Journal of Statistical Physics 161 (5) (2015) 1037-1058). We study here the large deviations with respect to this limit for the particle density field and the total current. We identify explicitely the large deviation functional and prove that it satisfies a fluctuation relation.