This book analyses the physics of complex systems to elaborate the problems encountered in teaching and research. Inspired by the of Kurt Gödel (including his incompleteness theorems) it considers the concept of time, the idea of models and the concept of complexity before trying to assess the state of physics in general. Using both general and practical examples, the idea of information is discussed, emphasizing its physical interpretation, debates ideas in depth using examples and evidence to provide detailed considerations on the topics. Based on the authors’ own research on these topics, this book puts forward the idea that the application of information measures can provide new results in the study of complex systems. Helpful for those already familiar with the concepts who wish to deepen their critical understanding, Physics of Complex Systems will be extremely valuable both for people that are already involved in complex systems and also readers beginning their journey into the subject. This work will encourage readers to follow and continue these ideas, enabling them to investigate the various topics further.
Author(s): Dragutin Mihailović, Darko Kapor, Siniša Crvenković, Anja Mihailović
Publisher: CRC Press
Year: 2023
Language: English
Pages: 201
City: Boca Raton
Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Preface
About the Authors
Chapter 1: Prolegomenon
1.1 The Generality of Physics
1.2 Physics: A Crisis that Has Been Lasting for a Century! Is that Really So?
1.3 Complex Systems in Physics
1.4 Physics and Mathematics Walk Together Along a Narrow Path
References
Chapter 2: Gödel’s Incompleteness Theorems and Physics
2.1 Gödel’s Biography and the Historical Background of Incompleteness Theorems
2.2 An Informal Proof of Gödel’s Incompleteness Theorems of Formal Arithmetic
2.3 Gödel’s Incompleteness Theorems as a Metaphor. Real Possibilities and Misrepresentation in their Applications
2.4 Gödel’s Work in Physical Problems and Computer Science
References
Chapter 3: Time in Physics
3.1 Time in Philosophy and Physics: Beyond Gödel’s Time
3.2 Does the Quantum of Time Exist?
3.3 Continuous and Discrete Time
3.4 Time in Complex Systems
References
Chapter 4: Are Model and Theory Synonymous in Physics?: Between Epistemology and Practice
4.1 Some Background Concepts and Epistemology
4.2 Choice in Model Building
4.3 The Discrete Versus Continuous Dichotomy: Time and Space in Model Building
4.4 The Predictability of Complex Systems. Lyapunov and Kolmogorov Time
4.5 Chaos in Environmental Interfaces in Climate Models
References
Chapter 5: How Can We Assimilate Hitherto Inaccessible Information?
5.1 The Physicality, Abstractness, and Concept of Information
5.2 The Metaphysics of Chance (Probability)
5.3 Shannon Information. The Triangle of the Relationships Between Energy, Matter, and Information
5.4 Rare Events in Complex Systems: What Information Can Be Derived From Them?
5.5 Information in Complex Systems
References
Chapter 6: Kolmogorov and Change Complexity and Their Applications to Physical Complex Systems
6.1 Kolmogorov Complexity: An Incomputable Measure and Lempel-Ziv Algorithm
6.2 Change Complexity: A Measure that Detects Change
6.3 Kolmogorov Complexity in the Analysis of the LIGO Signals and Bell’s Experiments
6.4 Change Complexity in the Search for Patterns in River Flows
References
Chapter 7: The Separation of Scales in Complex Systems: “Breaking” Point at the Time Scale
7.1 The Generalization of Scaling in Gödel’s World. Scaling in Phase Transitions and Critical Phenomena
7.2 The Separation of Scales and Capabilities of the Renormalization Group
7.3 A Phase Transition Model Example: The Longevity of the Heisenberg Model
7.4 Complexity and Time Scale: The “Breaking” Point with an Experimental Example
References
Chapter 8: The Representation of the Randomness and Complexity of Turbulent Flows
8.1 The Randomness of Turbulence in Fluids
8.2 The Representation of the Randomness and Complexity of Turbulent Flows with Kolmogorov Complexity
8.3 The Complexity of Coherent Structures in the Turbulent Mixing Layer
8.4 Information Measures Describing the River Flow as a Complex Natural Fluid System
References
Chapter 9: The Physics of Complex Systems and Art
9.1 An Attempt to Grasp the Complexity of the Human Brain
9.2 The Dualism Between Science and Art
9.3 Perception: Change Complexity in Psychology
9.4 Entropy, Change Complexity, and Kolmogorov Complexity in Observing Differences in Painting
References
Chapter 10: The Modeling of Complex Biophysical Systems
10.1 The Role of Physics in the Modeling of the Human Body’s Complex Systems
10.2 The Stability of the Synchronization of Intercellular Communication in the Tissue with the Closed Contour Arrangement of Cells
10.3 The Instability of the Synchronization of Intercellular Communication in the Tissue with a Closed Contour Arrangement of Cells: A Potential Trigger for Autoimmune Disorders
10.4 The Search for Information in Brain Disorders
References
Appendix A
Appendix B
Index
