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.
@article{1590,
title = {Algorithmic complexity and statistical mechanics},
journal = {CUBO, A Mathematical Journal},
volume = {9},
year = {2007},
language = {en},
url = {http://dml.mathdoc.fr/item/1590}
}
V'yugin, Vladimir; Maslov, Victor. Algorithmic complexity and statistical mechanics. CUBO, A Mathematical Journal, Tome 9 (2007) 22 p. http://gdmltest.u-ga.fr/item/1590/