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Statistical Mechanics of Extreme Events

The study of extreme events in systems with many degrees of freedom belongs to the foundations of equilibrium statistical mechanics, but is important also outside equilibrium in optimization problems or when damage may arise as consequence of an extreme event. The causes of extreme events in non-equilibrium systems are generally very difficult to investigate theoretically since their properties are encoded in the tails of the unknown probability distribution of some complicated many-body dynamics. In the last decade, however, there has been substantial progress in understanding several key features of probability tails in systems far from thermal equilibrium. In particular, the Gallavotti-Cohen symmetry provides a quantitative prediction for the entropy production. We discuss the significance of this symmetry relation and show in the context of a generic class of mass transfer models that the occurrence of an extreme event, viz., a condensation phenomenon, causes a breakdown of the Gallavotti Cohen symmetry. From a broader perspective this result is an encouraging instance where a statistical mechanics model provides detailed insight into the dynamical origin and consequences of extreme events. It leads us beyond the purely descriptive treatment of traditional extreme value statistics.

coloquio-schutz-2009