Dynamical and stationary non-equilibrium fluctuations for a boundary-driven exclusion process with energy

Abstract: We consider the exclusion process with energy, a model with mass and energy conservation, and we put it in a boundary-driven setting. We are interested in its hydrodynamic and hydrostatic limits, together with the associated dynamical and stationary fluctuations. We provide a new proof for the derivation of dynamical fluctuations that does not require explicit estimates on the two-point correlation functions. While the hydrodynamic limit is given by two uncoupled heat equations, the dynamical fluctuations are described by a system of coupled generalized Ornstein-Uhlenbeck processes.