Why Kolmogorov Complexity in Physical Equations?

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Abstract

Several researchers, including M. Gell-Mann, argue that the notion of Kolmogorov complexity developed in algorithmic information theory is useful in physics (i.e., in the description of the physical world). Their arguments are rather convincing, but there seems to be a gap between traditional physical equations and Kolmogorov complexity: namely, it is not clear how the standard equations of physics can lead to algorithmic notions underlying Kolmogorov complexity. In this paper, this “gap” is bridged: we explain how Kolmogorov complexity naturally appears in physical equations.

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