Algorithmic complexity and statistical mechanics

Vladimir V'yugin vyugin@iitp.ru
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 Ï‰^N= [Ï‰₁, ..., Ï‰_N] from the assumption of maximality of the Kolmogorov complexity K(Ï‰^N) given a constraint , where E is a number and f is a numerical function; f(Ï‰_i) 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.

Keywords

Algorithmic complexity , algorithmic information theory , statistical mechanics , maximum entropy principle , Jaynes‘ entropy concentration theorem , distribution of investments

Vladimir V'yugin Institute for information transmission problems, Russian academy of sciences, Bol'shoi Karetnyi per. 19, Moscow GSP-4, 127994, Russia.
Victor Maslov Moscow State University, Physical Faculty, Vorobyevy Gory, Moscow 119899, Russia.

Pages: 15-36
Date Published: 2007-08-01
Vol. 9 No. 2 (2007): CUBO, A Mathematical Journal

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Published

2007-08-01

How to Cite

[1]

V. V’yugin and V. Maslov, “Algorithmic complexity and statistical mechanics”, CUBO, vol. 9, no. 2, pp. 15–36, Aug. 2007.

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Vol. 9 No. 2 (2007): CUBO, A Mathematical Journal

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