Beyond Boltzmann-Gibbs statistical mechanics in optical lattices

Cold atoms in dissipative optical lattices exhibit an unusual transport behaviour that cannot be described within Boltzmann-Gibbs statistical mechanics. New theoretical tools and concepts need thus be developed to account for their observable macroscopic properties. Here we review recent progress achieved in the study of these processes. We emphasize the generality of the findings for a broad class of physical, chemical and biological systems, and discuss open questions and perspectives for future work.