Statistical Mechanics Foundations of Complexity — Where Do We Stand?

In 2002 SFI hosted a Workshop on Interdisciplinary applications of ideas from nonextensive statistical mechanics and thermodynamics, co-chaired by M. Gell-Mann and C. Tsallis. This workshop summarized the state of art of that area that was quickly developing and resulted in a comprehensive book on the subject by Oxford University Press (Santa Fe Series). During the past decade substantial improvement has been witnessed in what concerns the several important pieces of the foundations of the area, both in the conceptual framework and its applications. After 10 years we feel it is now time to ask where our knowledge on generalized statistical mechanics stands now. We want to summarize and integrate the present status of the field, in particular:  classification of entropies, connections to superstatistics, central limit theorem, scaling laws rooted in generalized statistical mechanics, role of knowledge & constraints, self-organization, large deviation theory, connections to networks, collective motion, and mesoscopic approaches. The central question of the workshop should be to critically assess the achieved theoretical progress, and to discuss the validity of the new technology in real-world applications of non-equilibrium physical, biological and maybe event social processes.