Kolmogorov complexity, cosmic microwave background maps and the curvature of the Universe

Abstract

Addendumi of Europhys. Lett. 35 (9), pp. 114-117 (1999)For technical reasons the above paper has not been published in its final version. The following concluding paragraph has been omitted.Moreover, the CBM properties discussed above can be only one of the manifestations of a much deeper link with the fundamental physical laws, namely, negatively curved space - mixing - complexity - second law of thermodynamics - arrow of time. Thus, we observe the time asymmetry and the second law because we live in a Universe with negative curvature, and those laws may not be the same in flat or positively curved spaces. We plan to discuss curvature/second-law conjecture, including the relations between thermodynamic, cosmological and other arrows of time, in a separate paper.***I am thankful to W. Zurek and my collaborator A. Allahverdyan for valuable discussions and the referee for helpful comments.We apologize to the author for the unpleasant inconvenience.