Although basic equilibrium concepts like state variables, thermodynamic potentials, etc do not straightforwardly extend for non-equilibrium states, an analogue of Landau free energy characterising macroscopic fluctuations could be defined based on a theory of large deviations. I shall discuss a few old and new results for such a quantity in a class of non-equilibrium transport models. These are interacting classical many-body systems with relations to quantum spin chains. Our new results show that similar to a thermodynamic potential, these free-energy-analogues (large deviation functions) are robust against variations of coupling with external baths. I shall explain how these results are derived from an exact solution for the symmetric exclusion process. For a larger class of systems our results are derived using a hydrodynamic theory. Particularly, for the large deviations of density, I shall present a solution of the associated variational problem for generic diffusivity and mobility.