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