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
Dynamics, Information and Complexity in Quantum Systems
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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
Quantum phenomena are ubiquitous in complex molecular systems - as revealed by many experimental observations based upon ultrafast spectroscopic techniques - and yet remain a challenge for...
The nature of distributed computation in complex systems has often been described in terms of memory, communication and processing. This thesis presents a complete information-theoretic framework to...
This volume is based on lectures given during the program "Complex Quantum Systems" held at the National University of Singapore's Institute for Mathematical Sciences from 17 February to 27 March...
A unique and accessible book providing a unified framework for studying quantum and classical dynamical systems, both finite and infinite, conservative and dissipative. Many examples and references...
This book leads readers from a basic foundation to an advanced level understanding of dynamical and complex systems. It is the perfect text for graduate or PhD mathematical-science students looking...
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