Date: Wednesday 15th of December 2021, 13:30 (GMT).
Location: Online MS Teams meeting

‘Statistical mechanics at the edge of chaos’

by Prof Constantino Tsallis, Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology of Complex Systems, Rio de Janeiro, Brazil.

Abstract:

Together with Newtonian mechanics, Maxwell electromagnetism, Einstein theory of relativity and quantum mechanics, Boltzmann-Gibbs (BG) statistical mechanics constitutes one of the pillars of contemporary theoretical physics, with uncountable applications in science and technology. This theory is based on strongly chaotic nonlinear dynamical systems, i.e., with positive Lyapunov exponents in their classical versions. It applies impressively well to a plethora of physical systems. Still, it fails in the field of complex systems, which are characterised by generically nonlocal space-time entanglement of their elements, e.g., in the presence of long-range interactions, which lead to weak chaos, i.e., vanishing maximal Lyapunov exponent. On the basis of nonadditive entropies (defined by an index q, which recovers the celebrated Boltzmann-Gibbs-von Neumann-Shannon entropy for q=1), it is possible to generalise the BG theory. We will briefly review the foundations of this generalisation, its relevant connections with nonlinear dynamical systems at the edge of chaos, Pesin identity, Central Limit Theorem, Large Deviations Theory, as well as its applications in mathematics and natural, artificial and social systems.

A regularly updated Bibliography is available at http://tsallis.cat.cbpf.br/biblio.htm. See also https://en.wikipedia.org/wiki/Constantino_Tsallis.