Foundations of Complexity

The present project has several goals. Epistemologically speaking, its main one is to show that living and living-like systems (e.g., languages, financial markets, urban growth, earthquakes, high-energy collisions of elementary particles, quantum-entanglement, cognitive psychology, among others) exhibit a very selected, hierarchical-like, occupancy of phase-space, which is caused by weak chaos, typically violating the ergodic hypothesis, and mandating nonadditive entropies in order to satisfy thermodynamics. This approach ultimately leads to powerful generalizations of the Boltzmann-Gibbs entropy and its associated statistical mechanics.
This leads to Big Questions including
-What are the specific properties of those weakly chaotic systems that cannot be handled within the Boltzmann-Gibbs theory?
-Can nonadditive entropies reveal deeper principles that govern complex systems in physical sciences?
-Will such principles be applicable to other, e.g., social and biological systems?
Such project will give consistency, unification and neat development to activities in Latin America along similar lines. (i) We will organize in 2014 a School in Rio de Janeiro in order that close to 100 highly selected and fully supported students from Latin America, who, during one month, will receive lectures from world-level scientists in the area of complexity. In the middle of the School a short international workshop will be held. (ii) We will implement three post-doc positions, carefully selected from all over the world, to address very specific and relevant questions along the above lines. (iii) We will also stimulate visitors to participate in the various activities. As outputs we intend to publish papers in high-quality journals, propitiate lectures at both technical and large-audience levels. In my understanding, all this should be very beneficial and enduring consequences for Latin America and its interaction with the rest of the world on relevant longstanding questions.