Kohtaro Tadaki A Statistical Mechanical Interpretation of Algorithmic Information Theory 9789811507380

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Автор: Kohtaro Tadaki
Название: A Statistical Mechanical Interpretation of Algorithmic Information Theory
ISBN: 9789811507380
Издательство: Springer
Классификация:

Теория информации

Математическая физика

Алгоритмы и структуры данных

ISBN-10: 9811507384
Обложка/Формат: Soft cover
Страницы: 136
Вес: 0.24 кг.
Дата издания: 2019
Серия: SpringerBriefs in Mathematical Physics
Язык: English
Издание: 1st ed. 2019
Иллюстрации: 1 illustrations, black and white; xi, 136 p. 1 illus.
Размер: 234 x 156 x 8
Читательская аудитория: Professional & vocational
Основная тема: Mathematics
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание:

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 Landauers principle is pointed out.

Дополнительное описание: 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 Thermody

A Statistical Mechanical Interpretation of Algorithmic Information Theory, Kohtaro Tadaki