Algorithmic complexity and statistical mechanics
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Vladimir V'yugin
vyugin@iitp.ru
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Victor Maslov
v.p.maslov@mail.ru
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Abstract
We apply the algorithmic complexity theory to statistical mechanics; in particular, we consider the maximum entropy principle and the entropy concentration theorem for non-ordered data in a non-probabilistic setting. The main goal of this paper is to deduce asymptotic relations for the frequencies of energy levels in a non-ordered collection ωN = [ω1, ..., ωN] from the assumption of maximality of the Kolmogorov complexity K(ωN) given a constraint 
, where E is a number and f is a numerical function; f(ωi) is an energy level. We also consider a combinatorial model of the securities market and give some applications of the entropy concentration theorem to finance.
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