  In this paper we study entropy production and transport of heat and matter in
an 1D bipartite fermionic chain. Moreover, we input a phenomenological
dephasing noise in order to show its effect on the dynamics of the system.
Specially, it is shown the importance of such noise in the emergence of the
entropy production. For the fluxes, analytical solutions are obtained using
both Boltzmann and Fermi-Dirac distribuition. Finally, we show that a
particular fluctuation theorem for energy and matter exchange is obeyed even in
the presence of such noise.
