A Statistical Mechanical Interpretation of Algorithmic Information Theory

Name: A Statistical Mechanical Interpretation of Algorithmic Information Theory
Author: Kohtaro Tadaki
ISBN: 9789811507380

Kohtaro Tadaki

Language: English

Published by Springer Singapore, 2019

9811507384 / 9789811507380

Series: Book 35 of 40 - SpringerBriefs in Mathematical Physics

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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 quantities.

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Title: A Statistical Mechanical Interpretation of Algorithmic Information Theory
Author: Kohtaro Tadaki
Publisher: Springer Singapore
Publication year: 2019
Condition: New
Binding: Kartoniert / Broschiert
Language: English
ISBN 10: 9811507384
ISBN 13: 9789811507380
Series: Book 35 of 40: SpringerBriefs in Mathematical Physics
Seller catalogs: Importe

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.

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