  We examine the entropy of non-equilibrium stationary states of boundary
driven totally asymmetric simple exclusion processes. As a consequence, we
obtain that the Gibbs-Shannon entropy of the non equilibrium stationary state
converges to the Gibbs-Shannon entropy of the local equilibrium state.
Moreover, we prove that its fluctuations are Gaussian, except when the mean
displacement of particles produced by the bulk dynamics agrees with the
particle flux induced by the density reservoirs in the maximal phase regime.
