Description
After an introduction to large deviations and Markov process [2,5,6], these lectures will try
to show, through simple examples, that non-equilibrium systems have a number of properties
which contrast with those of systems at equilibrium: phase transitions in one dimension [3],
non local free energy functional, long range correlations [1,4,5], etc. . These lectures will also
try to give a review of theoretical methods such as the matrix ansatz, the Bethe ansatz, or the
macroscopic fluctuation theory [1], developed in the theory of non-equilibrium phenomena,
which allow one to calculate the fluctuations and large deviations of the density and of the
current in non-equilibrium steady states [1,4,5] of systems like exclusion processes.