---

＜電子ブック＞
A Statistical Mechanical Interpretation of Algorithmic Information Theory / by Kohtaro Tadaki
(SpringerBriefs in Mathematical Physics. ISSN:21971765 ; 36)

版	1st ed. 2019.
出版者	(Singapore : Springer Nature Singapore : Imprint: Springer)
出版年	2019
本文言語	英語
大きさ	XI, 136 p. 1 illus : online resource
著者標目	*Tadaki, Kohtaro author SpringerLink (Online service)
件　名	LCSH:Mathematical physics LCSH:Algorithms LCSH:Data structures (Computer science) LCSH:Information theory FREE:Mathematical Physics FREE:Algorithms FREE:Data Structures and Information Theory FREE:Theoretical, Mathematical and Computational Physics
一般注記	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 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 mathematicaland 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 HTTP:URL=https://doi.org/10.1007/978-981-15-0739-7

 類似資料