Algorithmic information theory for physicists and natural scientists /

Algorithmic information theory (AIT), or Kolmogorov complexity as it is known to mathematicians, can provide a useful tool for scientists to look at natural systems, however some critical conceptual issues need to be understood and the advances already made collated and put in a form accessible to s...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Devine, Sean (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2020]
Colección:IOP ebooks. 2020 collection.
Temas:
Kolmogorov complexity.
Information theory.
COMPUTERS / Information Theory.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 2. Computation and algorithmic information theory
  • 2.1. The computational requirements for workable algorithms
  • 2.2. The Turing machine
  • 2.3. Measure theory
  • 3. AIT and algorithmic complexity
  • 3.1. Shorter algorithms imply order
  • 3.2. Machine dependence and the invariance theorem
  • 3.3. Self-delimiting coding and the Kraft inequality
  • 3.4. Optimum coding and Shannon's noiseless coding theorem
  • 3.5. Entropy relative to the common framework
  • 3.6. Entropy and probability
  • 3.7. The fountain of all knowledge : Chaitin's Omega
  • 3.8. Gödel's theorem and formal axiomatic systems
  • 3.9. The algorithmic entropy, the universal semi-measure and inference
  • 4. The algorithmic entropy of strings with structure and variation
  • 4.1. Identical algorithmic approaches to strings with variation
  • 4.2. The provisional entropy
  • 4.3. The specification by a probability distribution
  • 4.4. How to specify noisy data
  • 4.5. The non-typical state and the thermodynamic entropy
  • 5. Modelling and the minimum description length
  • 5.1. Introduction
  • 5.2. The algorithmic entropy approach to modelling
  • 5.3. The minimum description length approach
  • 6. The non-typical string and randomness
  • 6.1. Outline on perspectives on randomness
  • 6.2. Martin-Löf test of randomness
  • 7. Order and entropy
  • 7.1. The meaning of order
  • 7.2. Algorithmic entropy and the traditional entropy
  • 8. Reversibility, and Landauer's principle
  • 8.1. Introduction
  • 8.2. Landauer's principle
  • 8.3. Outline of Landauer's argument
  • 8.4. The simulation of a reversible real-world computation
  • 8.5. The algorithmic entropy as a function of state
  • 8.6. External interventions to restore a degraded system
  • 9. The algorithmic equivalent of the second law of thermodynamics
  • 9.1. The meaning of 'equilibrium'
  • 9.2. The increase in thermodynamic entropy as a system trends to the most probable set of states
  • 9.3. The relationship between algorithmic entropy and the thermodynamic entropy of a macrostate
  • 10. How replication processes maintain a system far from the most probable set of states
  • 10.1. Maintaining a system distant from the equilibrium
  • 10.2. Examples of the computational issues around the degradation of simple systems
  • 10.3. Entropy balances in a reversible system
  • 10.4. Homeostasis and second law evolution
  • 10.5. Replication processes generate order to counter the second law of thermodynamics
  • 10.6. Simple illustrative examples of replication
  • 10.7. The algorithmic entropy cost of replica variations
  • 10.8. A replicating living system
  • 10.9. Selection processes to sustain a natural system
  • 10.10. Summary of system regulation and AIT
  • 11. Sustainability requirements of a viable economy distant from equilibrium
  • 11.1. Introduction
  • 11.2. A reminder of the principles of AIT
  • 11.3. An economy seen as a replicating system
  • 11.4. Order creation through the know-how of economic agents
  • 11.5. A narrative to capture economic development
  • 11.6. Are there resource limits to economic growth?
  • 11.7. Order and GDP
  • 11.8. Complementary approaches to human systems
  • 11.9. Implications of the algorithmic approach
  • 11.10. Conclusions for economic systems
  • 12. AIT and philosophical issues
  • 12.1. Algorithmic descriptions, learning and artificial intelligence
  • 12.2. The mathematical implications of algorithmic information theory
  • 12.3. How can we understand the Universe?
  • 12.4. Closing thoughts.
  • 1. Introduction
  • 1.1. Brief outline of the book
  • 1.2. What are complex systems?
  • 1.3. Some approaches to complex or organised systems
  • 1.4. Algorithmic information theory (AIT)
  • 1.5. Algorithmic information theory and mathematics
  • 1.6. Real-world systems

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