Introduction: From Efficient Quantum Computation to Nonextensive Statistical Mechanics

Abstract

A short overview of several contributions to this volume which concern rather diverse topics is briefly discussed. The relation of nonextensive statistics to the stability of quantum motion "on the edge of quantum chaos", information theoretic foundations of generalized (nonextensive) statistics, the possible generalization of Boltzmann kinetics, again, formulated in terms of nonextensive statistics, state-of-the-art open problems in spin glasses and on the notion of complexity there, quantum-like uncertainty relations and decoherence appearing in the description of perpetual tasks of the brain, and the contribution on the measurement and information extraction in the simulation of complex dynamics by a quantum computer are reviewed.