SpringerBriefs in Mathematical Physics

A Statistical Mechanical Interpretation of Algorithmic Information Theory

Authors: Tadaki, Kohtaro

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  • Is the first book to provide a solid bridge between algorithmic information theory and statistical mechanicsClarifies a new aspect of the notion of temperature as the compression rate of the values of all thermodynamic quantitiesServes as an introduction both to algorithmic information theory and to the fundamental framework of equilibrium statistical mechanics

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  • ISBN 978-981-15-0739-7
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Softcover $59.99
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  • ISBN 978-981-15-0738-0
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About this book

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.

Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook $44.99
price for USA in USD (gross)
  • ISBN 978-981-15-0739-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
  • ISBN 978-981-15-0738-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
A Statistical Mechanical Interpretation of Algorithmic Information Theory
Authors
Series Title
SpringerBriefs in Mathematical Physics
Series Volume
36
Copyright
2019
Publisher
Springer Singapore
Copyright Holder
The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
eBook ISBN
978-981-15-0739-7
DOI
10.1007/978-981-15-0739-7
Softcover ISBN
978-981-15-0738-0
Series ISSN
2197-1757
Edition Number
1
Number of Pages
XI, 136
Number of Illustrations
1 b/w illustrations
Topics