A Statistical Mechanical Interpretation of Algorithmic Information Theory

• Main Author: Tadaki, Kohtaro (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Singapore : Springer Singapore : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Series: SpringerBriefs in Mathematical Physics, 36
• Subjects: Mathematical physics.; Algorithms.; Data structures (Computer science).; Statistical physics.; Mathematical Physics.; Data Structures and Information Theory.; Statistical Physics and Dynamical Systems.

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 r...

Table of Contents:

• 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. .