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CORR
2008
Springer

A statistical mechanical interpretation of algorithmic information theory

13 years 11 months ago
A statistical mechanical interpretation of algorithmic information theory
Abstract. We develop a statistical mechanical interpretation of algorithmic information theory by introducing the notion of thermodynamic quantities, such as free energy, energy, statistical mechanical entropy, and specific heat, into algorithmic information theory. We investigate the properties of these quantities by means of program-size complexity from the point of view of algorithmic randomness. It is then discovered that, in the interpretation, the temperature plays a role as the compression rate of the values of all these thermodynamic quantities, which include the temperature itself. Reflecting this self-referential nature of the compression rate of the temperature, we obtain fixed point theorems on compression rate. Key words: algorithmic information theory, algorithmic randomness, Chaitin's , compression rate, fixed point theorem, statistical mechanics, temperature
Kohtaro Tadaki
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2008
Where CORR
Authors Kohtaro Tadaki
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