Statistical mechanical interpretation of algorithmic information theory

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540142
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Chuo University
• Principal Investigator: TADAKI Kohtaro 中央大学, 研究開発機構, 機構准教授 (70407881)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: アルゴリズム的情報理論 / アルゴリズム的ランダムネス / 統計力学 / partial randomness / 相転移 / ChaitinのΩ / 不動点 / ランダムネス

Outline of Final Research Achievements

Algorithmic information theory is a theory of program-size complexity, where program-size complexity gives the theoretical limit of the compression of a finite binary string. In our former works, we introduced the statistical mechanical interpretation of algorithmic information theory by identifying a program and its size with an energy eigenstate and its energy, respectively, in a quantum system, and we investigated the properties of the interpretation. In the interpretation, the compression rate of each of all thermodynamic quantities equals to the temperature when we measure the compression rate by program-size complexity, and moreover, the phase transition happens when the temperature exceeds 1. In this KAKENHI research, we have revealed the detail of the mechanism of the phase transition.

Free Research Field

アルゴリズム的ランダムネス