Review article: large fluctuations in non-equilibrium physics

Abstract. Non-equilibrium is dominant in geophysical and climate phenomena. However the study of non-equilibrium is much more difficult than equilibrium and the relevance of probabilistic simplified models has been emphasized. Large deviation rates have been used recently in climate science. In this paper after recalling progress during the last decades in understanding the role of large deviations in a class of non-equilibrium systems we point out differences between equilibrium and non-equilibrium. For example in non-equilibrium: a) large deviation rates may be extensive but not simply additive. b) In non-equilibrium there are generically long range space correlations so large deviation rates are non-local. c) Singularities in large deviation rates denote the existence of phase transitions often not possible in equilibrium. To exemplify we shall refer to lattice gas models like the symmetric simple exclusion process and other models which are playing an important role in the understanding of non-equilibrium physics. Reasons why all this may be of interest in climate physics will be briefly indicated.