Information dynamics : in classical and quantum systems / / Thomas Dittrich

• Autore: Dittrich Thomas
• Pubblicazione: Cham, Switzerland : , : Springer, , [2022]; ©2022
• Descrizione fisica: 1 online resource (567 pages)
• Disciplina: 003.54
• Soggetto topico: Information theory; Quantum systems
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Intro -- Preface -- Contents -- Part I Natural Systems as Information Processors -- 1 The Concept of Information -- 1.1 Some History -- 1.2 The "Three Dimensions" of Information -- 1.3 From Boltzmann's Entropy to Shannon's Information -- 1.4 Sign: Entropy and Negentropy: Actual Versus Potential Information -- 1.5 Hierarchical Structures -- 1.6 Properties of Shannon's Definition of Information -- 1.6.1 An Extremum Property -- 1.6.2 Equal Probabilities Imply Maximum Entropy -- 1.6.3 Information Content of Tree Structures -- 1.7 Joint, Conditional, Mutual Information, Bayes' Law, Correlations and Redundancy -- 1.8 Information in Continuous Physical Quantities -- 2 Simple Applications -- 2.1 Logics -- 2.1.1 Propositional Logics -- 2.1.2 Boolean Algebra and Electronic Implementations -- 2.1.3 Set Theory -- 2.1.4 Inference Chains -- 2.2 The Genetic Code -- 2.2.1 Syntax -- 2.2.2 Semantics, The Central Dogma -- 2.2.3 Pragmatics and Discussion -- 2.2.4 Genetic Information in Phylogenesis -- 2.3 Fourier Transform -- 2.3.1 Discrete Symmetries in Fourier Transformation -- 2.3.2 Sampling -- 2.3.3 Uncertainty Relations -- 2.3.4 Fast Fourier Transformation -- 3 Epistemological Aspects -- 3.1 Causality -- 3.1.1 Causality from Topology: Markov Chains and Bayesian Networks -- 3.1.2 Causality from Information Flow: Transfer Information -- 3.1.3 Causality in Continuous Time: Kolmogorov-Sinai Entropy -- 3.1.4 Records and Memory -- 3.1.5 Causality and Special Relativity Theory -- 3.1.6 Finality -- 3.2 Prediction -- 3.2.1 Prediction, Anticipation, Simulation -- 3.2.2 Prediction from Within: Self-Fulfilling and Self-Destroying Prophecy -- 3.2.3 Self-Reference and Information-Theoretical Limits of Self-Prediction -- 3.3 Learning and Adaption -- 3.3.1 Detectors of Correlation and Causality -- 3.3.2 Predictors in Society. ; 3.3.3 Darwin's Demons: Anticipatory Systems and Entropy Flow in Ontogeny and Phylogeny -- 4 Information and Randomness -- 4.1 Quantifying Randomness -- 4.2 Randomness According to Structure: Redundancy, Data Compression, and Scientific Induction -- 4.2.1 Induction -- 4.2.2 Pattern Recognition and Algorithmic Complexity -- 4.3 Gödel's Theorem and Incompleteness -- 4.3.1 Formal Systems -- 4.3.2 Gödel's Incompleteness Theorem and Provability of Randomness -- 4.3.3 Interpretations and Consequences of Gödel's Incompleteness Theorem -- 5 Information in Classical Hamiltonian Dynamics -- 5.1 Review of Hamiltonian Dynamics and Symplectic Geometry -- 5.2 Hamiltonian Dynamics of Continuous Density Distributions -- 5.3 Information Density, Information Flow, and Conservation of Information in Hamiltonian Systems -- 5.4 Conservation of Information Without Energy Conservation: Harmonic Oscillator Driven at Resonance -- 5.5 Information Processing in Chaotic Hamiltonian Systems: Bernoulli Shift and Baker Map -- 5.6 Information Exchange Between Degrees of Freedom: Normal Modes in Pairs and Chains of Harmonic Oscillators -- 5.6.1 Two Coupled Harmonic Oscillators in Resonance -- 5.6.2 Chains of N Coupled Harmonic Oscillators -- 6 Information in Classical Dissipative Dynamics -- 6.1 Lyapunov Exponents Measure Vertical Information Flows -- 6.2 Entropy Loss into Microscales: The Dissipative Harmonic Oscillator -- 6.3 The Generic Case: Coexistence of Chaos and Dissipation -- 6.4 Fractals, Dimension, and Information -- 7 Fluctuations, Noise, and Microscopic Degrees of Freedom -- 7.1 Noise, Diffusion, and Information Loss -- 7.2 Fluctuation-Dissipation Theorems: Einstein's Relation and Nyquist's Theorem -- 7.3 The Second Law of Thermodynamics in the Light of Information Flows -- 7.3.1 Mixing and Thermalization -- 7.3.2 Diffusion and Coarse-Graining. ; 7.3.3 Grand Total: The Second Law of Thermodynamics -- 8 Information and Quantum Mechanics -- 8.1 Information Theory Behind the Principles of Quantum Mechanics -- 8.1.1 Postulates of Quantum Mechanics Related to Information -- 8.1.2 Hilbert Space Vectors as Basic Information Carriers -- 8.1.3 Heisenberg's Uncertainty Principle and Information in Phase Space -- 8.1.4 Entanglement and Non-Locality -- 8.2 Quantum Information -- 8.2.1 The Density Operator and Von-Neumann Entropy -- 8.2.2 Entanglement and Quantum Information -- 8.2.3 Decoherence and Quantum Information -- 8.3 Dynamics of Quantum Information -- 8.3.1 Unitary Time Evolution -- 8.3.2 Unitary Transformations Conserve Information -- 8.3.3 Incoherent Processes and Classicality -- 8.4 Quantum Measurement -- 8.4.1 Overview -- 8.4.2 Von-Neumann Theory of Quantum Measurement -- 8.4.3 Entanglement and Non-Locality in Quantum Measurement -- 8.4.4 The Quantum Zeno Effect -- 8.4.5 Quantum Randomness -- 8.4.6 Quantum Causality -- 8.5 Quantum Death and Resurrection of Chaos -- 8.5.1 Quantum Chaos: A Deep Probe into Quantum Information Processing -- 8.5.2 Discretizing Classical Chaos -- 8.5.3 Quantum Death of Classical Chaos -- 8.5.4 Resurrection of Chaos by Decoherence and Dissipation -- 8.6 Mixing, Irreversibility, and Information Production in Quantum Systems -- 8.6.1 The Role of Chaos: Berry's Conjecture -- 8.6.2 Typicality and the Eigenstate Thermalization Hypothesis -- 8.6.3 Many-Body Localization: Threatening Thermalization? -- 8.6.4 Perspectives: Equilibration and Entanglement -- Part II Computers as Natural Systems -- 9 Physical Aspects of Computing -- 9.1 What's so Special About Computing? -- 9.1.1 Computers as Man-Made Tools -- 9.1.2 Computers and Computing in Natural Dynamical Systems -- 9.2 Physical Conditions of Computation. ; 9.2.1 Implementing and Controlling a Single Bit: Macroscopic Discretization -- 9.2.2 Implementing Gates: Reversible and Irreversible Operations -- 9.3 Global Structure of Classical Computing: Moving on Granular Spaces -- 9.3.1 Granular State Spaces -- 9.3.2 Navigation on Granular Spaces -- 9.3.3 Models of Classical Computing: The Turing Machine -- 9.3.4 Cellular Automata: Parallel Computing on Granular Spaces -- 9.3.5 Conway's Game of Life -- 9.4 The Hierarchical Structure of Computation -- 9.4.1 Structured Organization of Computers: An Overview -- 9.4.2 Emergence in the Hierarchy of Computing -- 9.4.3 Emergent Dynamics: Vertical Information Flow and Downward Causation -- 10 Quantum Computation -- 10.1 What's so Special About Quantum Computing? -- 10.2 Tools for Quantum Computation: Qubits and Quantum Gates -- 10.2.1 The Qubit -- 10.2.2 Unitary Operators, Reversible Computation, and Quantum Gates -- 10.3 Strategies for Quantum Computation: Quantum Algorithms -- 10.3.1 Quantum Dense Coding -- 10.3.2 Quantum Parallelism -- 10.3.3 The Deutsch and Deutsch-Jozsa Algorithms -- 10.3.4 Quantum Fourier Transform -- 10.3.5 Quantum Search Algorithms -- 10.4 Decoherence and Error Correction -- 10.4.1 Sources, Types, and Effects of Noise -- 10.4.2 Error Protection and Correction -- 10.4.3 Error Prevention: Computing In Decoherence-Free Subspaces -- 10.5 Physical Implementations -- 10.5.1 Peepholes: Communicating with a Quantum Computer -- 10.5.2 Prototypical Platforms for Quantum Computing -- 11 Epilogue -- Bibliography -- Index.
• Titolo autorizzato: Information Dynamics
• ISBN: 9783030967451; 9783030967444
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910741191703321
• Lo trovi qui: Univ. Federico II
• Serie: Frontiers collection.