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

Format:

Book

Author/Creator:

Dittrich, Thomas, author.

Series:

Frontiers collection

Language:

English

Subjects (All):

Information theory.

Quantum systems.

Physical Description:

1 online resource (xv, 557 pages) : illustrations (some color).

Place of Publication:

Cham : Springer, [2022]

Summary:

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.

Contents:

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

Notes:

Includes bibliographical references and index.

Online resource; title from PDF title page (SpringerLink, viewed December 9, 2022).

ISBN:

9783030967451

303096745X

OCLC:

1351657505

Access Restriction:

Restricted for use by site license.