Fermionic Walkers Driven Out of Equilibrium

We consider a discrete-time non-Hamiltonian dynamics of a quantum system consisting of a finite sample locally coupled to several bi-infinite reservoirs of fermions with a translation symmetry. In this setup, we compute the asymptotic state, mean fluxes of fermions into the different reservoirs, as well as the mean entropy production rate of the dynamics. Formulas are explicitly expanded to leading order in the strength of the coupling to the reservoirs.