Dynamics, Information and Complexity in Quantum Systems

1 Introduction Part I Classical Dynamical Systems 2 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 Systems 5 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 Entropy 7 Quantum Mechanics of Infinite Degrees of Freedom 7.1 Observables, States and Dynamics 7.2 Entropy Density 7.3 Quantum Spin Chains as Quantum Sources Part III Quantum Dynamical Entropies and Complexities 8 Quantum Dynamical Entropies 8.1 CNT Entropy: Decompositions of States 8.2 AFL Entropy: OPUs 9 Quantum Algorithmic Complexity 9.1 Quantum Algorithmic Complexities References