Dynamics, information and complexity in quantum systems

Content: 1 Introduction Part I Classical Dynamical Systems2 Classical Dynamics and Ergodic Theory 2.1 Classical Dynamical Systems 2.2 Symbolic Dynamics 2.3 Ergodicity and Mixing 2.4 Information and Entropy 3 Dynamical Entropy and Information 3.1 Dynamical Entropy 3.2 Codes and Shannon Theorems 4 Algorithmic Complexity 4.1 Kolmogorov Complexity 4.2 Algorithmic Complexity and Entropy Rate 4.3 Pre_x Algorithmic Complexity Part II Quantum Dynamical Systems5 Quantum Mechanics of Finite Degrees of Freedom 5.1 Hilbert Space and Operator Algebras 5.2 Algebras of Bounded Operators on H 5.3 Quantum Systems with Finite Degrees of Freedom 5.4 Quantum States 5.5 Dynamics and State-Transformations 6 Quantum Information Theory 6.1 Quantum Information Theory 6.2 Bipartite Entanglement 6.3 Relative Entropy7 Quantum Mechanics of Infinite Degrees of Freedom7.1 Observables, States and Dynamics7.2 Entropy Density 7.3 Quantum Spin Chains as Quantum SourcesPart III Quantum Dynamical Entropies and Complexities8 Quantum Dynamical Entropies 8.1 CNT Entropy: Decompositions of States 8.2 AFL Entropy: OPUs 9 Quantum Algorithmic Complexity9.1 Quantum Algorithmic Complexities References