A Statistical Mechanical Interpretation of Algorithmic Information Theory
Language: English
Published by Springer Verlag, Singapore, SG, 2019
Series: Book 35 of 40 - SpringerBriefs in Mathematical Physics
- Softcover
- New
Seller: Rarewaves.com UK, London, United KingdomRarewaves.com UK
AbeBooks seller since June 11, 2025
Condition: New
£ 55.32
Quantity: 1 available
Add to basketItem description from seller
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.…
Seller Inventory # LU-9789811507380
- Title
- A Statistical Mechanical Interpretation of Algorithmic Information Theory
- Author
- Kohtaro Tadaki
- Publisher
- Springer Verlag, Singapore, SG
- Publication year
- 2019
- Condition
- New
- Binding
- Paperback
- Language
- English
- ISBN 10
- 9811507384
- ISBN 13
- 9789811507380
- Edition
- 2019 ed.
- Item weight
- 210 grams
- Dimensions
- 15.5 x 0.86 x 23.5 cm
- Series
- Book 35 of 40: SpringerBriefs in Mathematical Physics
"Synopsis" may belong to another edition of this title.
Rarewaves.com UK
London, United Kingdom
AbeBooks seller since June 11, 2025
Shipping rates from United Kingdom to U.S.A.
| Item | 60 to 60 business days | 60 to 60 business days |
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