A statistical mechanical interpretation of algorithmic information theory

Algorithmic entropy, thermodynamics, and game interpretation

Basic relations for the mean length and algorithmic entropy are obtained by solving a new extremal problem. Using this extremal problem, they are obtained in a most simple and general way. The length and entropy are considered as two players of a new type of a game, in which we follow the scheme of our previous work on thermodynamic characteristics in quantum and classical approaches.

A statistical mechanical interpretation of algorithmic information theory III: Composite systems and fixed points

The statistical mechanical interpretation of algorithmic information theory (AIT, for short) was introduced and developed by our former works [K. Tadaki, Local Proceedings of CiE 2008, pp.425-434, 2008] and [K. Tadaki, Proceedings of LFCS'09, Springer's LNCS, vol.5407, pp.422-440, 2009], where we introduced the notion of thermodynamic quantities, such as partition function Z(T), free energy F(T), energy E(T), and statistical mechanical entropy S(T), into AIT. We then discovered that, in the interpretation, the temperature T equals to the partial randomness of the values of all these thermodyna…

An algorithmic complexity interpretation of Lin's third law of information theory

Instead of static entropy we assert that the Kolmogorov complexity of a static structure such as a solid is the proper measure of disorder (or chaoticity). A static structure in a surrounding perfectly-random universe acts as an interfering entity which introduces local disruption in randomness. This is modeled by a selection rule $R$ which selects a subsequence of the random input sequence that hits the structure. Through the inequality that relates stochasticity and chaoticity of random binary sequences we maintain that Lin's notion of stability corresponds to the stability of the frequency …

A statistical mechanical interpretation of instantaneous codes

In this paper we develop a statistical mechanical interpretation of the noiseless source coding scheme based on an absolutely optimal instantaneous code. The notions in statistical mechanics such as statistical mechanical entropy, temperature, and thermal equilibrium are translated into the context of noiseless source coding. Especially, it is discovered that the temperature 1 corresponds to the average codeword length of an instantaneous code in this statistical mechanical interpretation of noiseless source coding scheme. This correspondence is also verified by the investigation using box-cou…

An Algorithmic Approach to Information and Meaning

I will survey some matters of relevance to a philosophical discussion of information, taking into account developments in algorithmic information theory (AIT). I will propose that meaning is deep in the sense of Bennett's logical depth, and that algorithmic probability may provide the stability needed for a robust algorithmic definition of meaning, one that takes into consideration the interpretation and the recipient's own knowledge encoded in the story attached to a message.

由采用的规则通用图灵机引起的算法温度

Algorithmic Temperature Induced by Adopted Regular Universal Turing Machine

该研究证明规则通用图灵机的算法结构可自然涌现有效温度，通过冗余增长产生玻尔兹曼加权，建立算法信息论与统计力学桥梁，并揭示温度作为观察者分辨率的认识论意义。