## ＜電子ブック＞A Statistical Mechanical Interpretation of Algorithmic Information Theory

責任表示 by Kohtaro Tadaki Tadaki, Kohtaro SpringerLink (Online service) 1st ed. 2019. English (英語) Springer Singapore Imprint: Springer 2019- Singapore, Singapore シリーズ SpringerBriefs in Mathematical Physics ; 36 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 introduced. On this basis, the introduction of a statistical mechanical interpretation of AIT is begun. Namely, the notion of thermodynamic quantities, such as free energy, energy, and entropy, is introduced into AIT. In the interpretation, the temperature is shown to be equal to the partial randomness of the values of all these thermodynamic quantities, where the notion of partial randomness is a stronger representation of the compression rate measured by means of program-size complexity. Additionally, it is demonstrated that this situation holds for the temperature itself as a thermodynamic quantity. That is, for each of all the thermodynamic quantities above, the computability of its value at temperature T gives a sufficient condition for T to be a fixed point on partial randomness. In this groundbreaking book, the current status of the interpretation from both mathematical and physical points of view is reported. For example, a total statistical mechanical interpretation of AIT that actualizes a perfect correspondence to normal statistical mechanics can be developed by identifying a microcanonical ensemble in the framework of AIT. As a result, the statistical mechanical meaning of the thermodynamic quantities of AIT is clarified. In the book, the close relationship of the interpretation to Landauer's principle is pointed out.続きを見る Statistical Mechanical Interpretation of Noiseless Source CodingAlgorithmic Information TheoryPartial RandomnessTemperature Equals to Partial RandomnessFixed Point Theorems on Partial RandomnessStatistical Mechanical Meaning of the Thermodynamic Quantities of AITThe Partial Randomness of Recursively Enumerable RealsComputation-Theoretic Clarification of the Phase Transition at Temperature T=1Other Related Results and Future Development. . http://hdl.handle.net/2324/1001687076 Full text available from Springer Mathematics and Statistics eBooks 2019 English/International

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レコードID 3644092 QA401-425 QC19.2-20.85 530.15 Mathematical physics. Algorithms. Data structures (Computer science). Statistical physics. Mathematical Physics. Algorithms. Data Structures and Information Theory. Statistical Physics and Dynamical Systems. ssj0002240553 9789811507380[9811507384](print) 9789811507403[9811507406](print) 9789811507397[9811507392] 2020.06.27 2020.06.28