A Statistical Mechanical Interpretation of Algorithmic Information Theory. 1st ed. 2019

種類:

電子ブック

責任表示:

by Kohtaro Tadaki

出版情報:

Singapore : Springer Nature Singapore : Imprint: Springer, 2019

著者名:

• Tadaki, Kohtaro.
• SpringerLink (Online service)

シリーズ名:

SpringerBriefs in Mathematical Physics ; 36

ISBN:

9789811507397 [9811507392]    

注記:

Statistical Mechanical Interpretation of Noiseless Source Coding -- Algorithmic Information Theory -- Partial Randomness -- Temperature Equals to Partial Randomness -- Fixed Point Theorems on Partial Randomness -- Statistical Mechanical Meaning of the Thermodynamic Quantities of AIT -- The Partial Randomness of Recursively Enumerable Reals -- Computation-Theoretic Clarification of the Phase Transition at Temperature T=1 -- Other Related Results and Future Development. .
This book is the first one that provides a solid bridge between algorithmic information theory and statistical mechanics. Algorithmic information theory (AIT) is a theory of program size and recently is also known as algorithmic randomness. AIT provides a framework for characterizing the notion of randomness for an individual object and for studying it closely and comprehensively. In this book, a statistical mechanical interpretation of AIT is introduced while explaining the basic notions and results of AIT to the reader who has an acquaintance with an elementary theory of computation. A simplification of the setting of AIT is the noiseless source coding in information theory. First, in the book, a statistical mechanical interpretation of the noiseless source coding scheme is introduced. It can be seen that the notions in statistical mechanics such as entropy, temperature, and thermal equilibrium are translated into the context of noiseless source coding in a natural manner. Then, the framework of AIT is intr

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