Introduction to Nonextensive Statistical Mechanics: Approaching a Complex World

Metaphors, generalizations and unifications are natural and desirable ingredients of the evolution of scientific theories and concepts. Physics, in particular, obviously walks along these paths since its very beginning. This book focuses on nonextensive statistical mechanics, a current generalization of Boltzmann-Gibbs (BG) statistical mechanics, one of the greatest monuments of contemporary physics. Conceived more than 130 years ago by Maxwell, Boltzmann and Gibbs, the BG theory exhibits uncountable - some of them impressive - successes in physics, chemistry, mathematics, and computational sciences, to name a few. Presently, more than two thousand publications, by over 1800 scientists around the world, have been dedicated to the nonextensive generalization. Remarkable applications have emerged, and its mathematical grounding is by now relatively well established. A pedagogical introduction to its concepts - nonlinear dynamics, extensivity of the nonadditive entropy, global correlations, generalization of the standard CLT's, among others - is presented in this book as well as a selection of paradigmatic applications in various sciences together with diversified experimental verifications of some of its predictions.

• This is the first pedagogical book on the subject, written by the proponent of the theory
• Presents many applications to interdisciplinary complex phenomena in virtually all sciences, ranging from physics to medicine, from economics to biology, through signal and image processing and others
• Offers a detailed derivation of results, illustrations and for the first time detailed presentation of Nonextensive Statistical Mechanics

Constantino Tsallis is a physicist in the area of statistical mechanics, Emeritus Professor at the Department of Theoretical Physics of the Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil, and founding member of the National Institute of Science and Technology for Complex Systems, Brazil. He is also External Faculty Fellow of the Santa Fe Institute, New Mexico, USA, External Faculty of the Complexity Science Hub Vienna, Austria, and Professor at the Dottorato in Sistemi Complessi per le Scienze Fisiche, Socio-economiche e della Vita of the University of Catania. He is Docteur d´État ès Sciences Physiques of the University of Paris-France (1974). He worked in a variety of theoretical subjects in the areas of critical phenomena, chaos and nonlinear dynamics, economics, cognitive psychology, immunology, population evolution, among others. For the last three decades, he has focused on the entropy and the foundations of statistical mechanics, as well as on some of their scientific and technological applications. Indeed, he proposed in 1988 a generalization of Boltzmann-Gibbs entropy and statistical mechanics. This generalization is presently being actively studied around the world; a regularly updated bibliography containing more than 8,500 directly related articles by over 15,000 scientists from all over the world is available online.

Prof. Tsallis' contributions have received over 22,000 citations at the ISI Web of Science, 6,000 of them for his 1988 paper, which currently makes him one among the most cited scientists of all times in Latin America. He has received many distinctions (Guggenheim Foundation Award, Mexico Prize for Science and Technology, Rio de Janeiro Prize of Science and Technology, among many others), and has been given the title of Doctor Honoris Causa by Universities from Argentina (Cordoba), Brazil (Maringa and Natal) and Greece (the Thessaloniki Aristotelian University). He was awarded the highest distinction of the Academy of Athens (originally founded by Plato). He is member of the Academy of Sciences of Brazil, of the Academy of Economical, Political and Social Sciences of Brazil, and of the Academy of Sciences of Latin America. He is Honorary Editor of Physica A, and has supervised close to 40 Doctor and Master Thesis. He has given regular undergraduate and graduate courses in Physics in Brazil, Argentina, USA, France, Italy and Germany, and has delivered over 1,000 invited lectures around the world. In 2005 and 2006, he did basic research at the Santa Fe Institute, New Mexico, where he coauthored several papers with Murray Gell-Mann.