The celebrated Boltzmann-Gibbs (BG) statistical mechanics is grounded on the well-known additive entropy which satisfies S_BG(A+B)= S_BG(A) + S_BG(B). A simple generalization is to consider the nonadditive entropy S_q which satisfies S_q(A+B)/k= S_q(A)/k + S_q(B)/k + (1-q) [S_q(A)/k] [S_q(B)/k]. This is the most general (symmetric) form which is linear in both S_q(A) and S_q(B) and satisfies S_q(A+B)=S_q(A) if S_q(B) vanishes. We will show that this apparently innocuous generalization opens a wide door to the world of natural, technological and social complex systems, where emergence phenomena, power-laws, and generalized Central Limit Theorems appear plethorically. After a brief introduction to the main concepts, we will present selected illustrations in the real world. The BG theory is recovered by this generalized statistical mechanics in the 1/k=0 limit (or, equivalently, q=1 limit), analogously to Newtonian mechanics which is recovered by the theory of relativity in the 1/c = 0 limit, and also by quantum mechanics in the limit h=0. Bibliography is available here. 

If you wish to attend this seminar online, please send an email to f.a.nobregasantos@uva.nl to receive the zoom-link.

About the speaker:

Constantino Tsallis is a theoretical physicist at the Centro Brasileiro de Pesquisas Físicas in Rio de Janeiro and a member of the external faculty at the Santa Fe Institute and Complexity Hub in Vienna. His research spans statistical mechanics, entropy, nonlinear dynamics, and complex systems. In 1988, he proposed a generalization of Boltzmann–Gibbs entropy that became the basis of nonextensive statistical mechanics. His work explores both the foundations of the theory and its applications across the natural and social sciences.