  The one dimensional symmetric simple exclusion process (SSEP) is one of the
very few exactly soluble models of non-equilibrium statistical physics. It
describes a system of particles which diffuse with hard core repulsion on a one
dimensional lattice in contact with two reservoirs of particles at unequal
densities. The goal of this note is to review the two main approaches which
lead to the exact expression of the large deviation functional of the density
of the SSEP in its steady state: a microscopic approach (based on the matrix
product ansatz and an additivity property) and a macroscopic approach (based on
the macroscopic fluctuation theory of Bertini, De Sole, Gabrielli, Jona-Lasinio
and Landim).
