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dittrich t information dynamics classical quantum systems 2022

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Textbook in PDF format This wide-ranging book introduces information as a key concept not only in physics, from quantum mechanics to thermodynamics, but also in the neighboring sciences and in the humanities. The central part analyzes dynamical processes as manifestations of information flows between microscopic and macroscopic scales and between systems and their environment. Quantum mechanics is interpreted as a reconstruction of mechanics based on fundamental limitations of information processing on the smallest scales. These become particularly manifest in quantum chaos and in quantum computing. Covering subjects such as causality, prediction, undecidability, chaos, and quantum randomness, the book also provides an information-theoretical view of predictability. More than 180 illustrations visualize the concepts and arguments. The book takes inspiration from the author's graduate-level topical lecture but is also well suited for undergraduate studies and is a valuable resource for researchers and professionals. Natural Systems as Information Processors The Concept of Information Some History The “Three Dimensions” of Information From Boltzmann's Entropy to Shannon's Information Sign: Entropy and Negentropy: Actual Versus Potential Information Hierarchical Structures Properties of Shannon’s Definition of Information An Extremum Property Equal Probabilities Imply Maximum Entropy Information Content of Tree Structures Joint, Conditional, Mutual Information, Bayes’ Law, Correlations and Redundancy Information in Continuous Physical Quantities Simple Applications Logics Propositional Logics Boolean Algebra and Electronic Implementations Set Theory Inference Chains The Genetic Code Syntax Semantics, The Central Dogma Pragmatics and Discussion Genetic Information in Phylogenesis Fourier Transform Discrete Symmetries in Fourier Transformation Sampling Uncertainty Relations Fast Fourier Transformation Epistemological Aspects Causality Causality from Topology: Markov Chains and Bayesian Networks Causality from Information Flow: Transfer Information Causality in Continuous Time: Kolmogorov-Sinai Entropy Records and Memory Causality and Special Relativity Theory Finality Prediction Prediction, Anticipation, Simulation Prediction from Within: Self-Fulfilling and Self-Destroying Prophecy Self-Reference and Information-Theoretical Limits of Self-Prediction Learning and Adaption Detectors of Correlation and Causality Predictors in Society Darwin's Demons: Anticipatory Systems and Entropy Flow in Ontogeny and Phylogeny Information and Randomness Quantifying Randomness Randomness According to Structure: Redundancy, Data Compression, and Scientific Induction Induction Pattern Recognition and Algorithmic Complexity Gödel’s Theorem and Incompleteness Formal Systems Gödel’s Incompleteness Theorem and Provability of Randomness Interpretations and Consequences of Gödel’s Incompleteness Theorem Information in Classical Hamiltonian Dynamics Review of Hamiltonian Dynamics and Symplectic Geometry Hamiltonian Dynamics of Continuous Density Distributions Information Density, Information Flow, and Conservation of Information in Hamiltonian Systems Conservation of Information Without Energy Conservation: Harmonic Oscillator Driven at Resonance Information Processing in Chaotic Hamiltonian Systems: Bernoulli Shift and Baker Map Information Exchange Between Degrees of Freedom: Normal Modes in Pairs and Chains of Harmonic Oscillators Two Coupled Harmonic Oscillators in Resonance Chains of N Coupled Harmonic Oscillators Information in Classical Dissipative Dynamics Lyapunov Exponents Measure Vertical Information Flows Entropy Loss into Microscales: The Dissipative Harmonic Oscillator The Generic Case: Coexistence of Chaos and Dissipation Fractals, Dimension, and Information Fluctuations, Noise, and Microscopic Degrees of Freedom Noise, Diffusion, and Information Loss Fluctuation–Dissipation Theorems: Einstein’s Relation and Nyquist’s Theorem The Second Law of Thermodynamics in the Light of Information Flows Mixing and Thermalization Diffusion and Coarse-Graining Grand Total: The Second Law of Thermodynamics Information and Quantum Mechanics Information Theory Behind the Principles of Quantum Mechanics Postulates of Quantum Mechanics Related to Information Hilbert Space Vectors as Basic Information Carriers Heisenberg’s Uncertainty Principle and Information in Phase Space Entanglement and Non-Locality Quantum Information The Density Operator and Von-Neumann Entropy Entanglement and Quantum Information Decoherence and Quantum Information Dynamics of Quantum Information Unitary Time Evolution Unitary Transformations Conserve Information Incoherent Processes and Classicality Quantum Measurement Overview Von-Neumann Theory of Quantum Measurement Entanglement and Non-Locality in Quantum Measurement The Quantum Zeno Effect Quantum Randomness Quantum Causality Quantum Death and Resurrection of Chaos Quantum Chaos: A Deep Probe into Quantum Information Processing Discretizing Classical Chaos Quantum Death of Classical Chaos Resurrection of Chaos by Decoherence and Dissipation Mixing, Irreversibility, and Information Production in Quantum Systems The Role of Chaos: Berry’s Conjecture Typicality and the Eigenstate Thermalization Hypothesis Many-Body Localization: Threatening Thermalization? Perspectives: Equilibration and Entanglement Computers as Natural Systems Physical Aspects of Computing What’s so Special About Computing? Computers as Man-Made Tools Computers and Computing in Natural Dynamical Systems Physical Conditions of Computation Implementing and Controlling a Single Bit: Macroscopic Discretization Implementing Gates: Reversible and Irreversible Operations Global Structure of Classical Computing: Moving on Granular Spaces Granular State Spaces Navigation on Granular Spaces Models of Classical Computing: The Turing Machine Cellular Automata: Parallel Computing on Granular Spaces Conway’s Game of Life The Hierarchical Structure of Computation Structured Organization of Computers: An Overview Emergence in the Hierarchy of Computing Emergent Dynamics: Vertical Information Flow and Downward Causation Quantum Computation What’s so Special About Quantum Computing? Tools for Quantum Computation: Qubits and Quantum Gates The Qubit Unitary Operators, Reversible Computation, and Quantum Gates Strategies for Quantum Computation: Quantum Algorithms Quantum Dense Coding Quantum Parallelism The Deutsch and Deutsch-Jozsa Algorithms Quantum Fourier Transform Quantum Search Algorithms Decoherence and Error Correction Sources, Types, and Effects of Noise Error Protection and Correction Error Prevention: Computing In Decoherence-Free Subspaces Physical Implementations Peepholes: Communicating with a Quantum Computer Prototypical Platforms for Quantum Computing Epilogue

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dittrich t information dynamics classical quantum systems 2022