Dynamics, Information and Complexity in Quantum Systems
Samenvatting
The aim of this book is to o?er a self-consistent overview of a series of - sues relating entropy, information and dynamics in classical and quantum physics. My personal point of view regarding these matters is the result of what I had the good fortune to learn in the course of the years from various scientists: Heide Narnhofer in the ?rst place, who introduced me to qu- tum dynamical entropies and was a precious guide ever since, then Robert Alicki, Mark Fannes, Giancarlo Ghirardi, Andreas Knauf, John Lewis, - o?rey Sewell, Franco Strocchi, Walter Thirring, Armin Uhlmann. To me, all of them have been a constant example of rigorous mathematics and physical intuition jointly at work. Last but not least, my deep gratitude goes to my family and to the many friends on whom I could always count for support and encouragement with a special thought for Traude and Wolfgang Georgiades.
Specificaties
Inhoudsopgave
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