  Entropy production is one of the most important characteristics of
non-equilibrium steady states. We study here the steady-state entropy
production, both at short times as well as in the long-time limit, of two
important classes of non-equilibrium systems: transport systems and
reaction-diffusion systems. The usefulness of the mean entropy production rate
and of the large deviation function of the entropy production for
characterizing non-equilibrium steady states of interacting many-body systems
is discussed. We show that the large deviation function displays a kink-like
feature at zero entropy production that is similar to that observed for a
single particle driven along a periodic potential. This kink is a direct
consequence of the detailed fluctuation theorem fulfilled by the probability
distribution of the entropy production and is therefore a generic feature of
the corresponding large deviation function.
