Quantum dynamics, measurement and entropy

The aim of this paper is to present a line of ideas, centred around entropy production andquantum dynamics, emerging from von Neumannʹs work on foundations of quantum mechanics and leading to current research. The concepts of measurement, dynamical evolution and entropy were central in J. von Neumannʹs work. Further developments led to the introduction of generalized measurements in terms of positive operator-valued measures, closely connected to the theory of open systems. Fundamental properties of quantum entropy were derived and Kolmogorov and Sinai related the chaotic properties of classical dynamical systems with asymptotic entropy production. Finally, entropy production in quantum dynamical systems was linked with repeated measurement processes and a whole research area on nonequilibrium phenomena in quantum dynamical systems seems to emerge.