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Phase Transition and Strong Predictability | | Kohtaro Tadaki
; | | Date: |
25 Apr 2013 | | Abstract: | The statistical mechanical interpretation of algorithmic information theory
(AIT, for short) was introduced and developed in our former work [K. Tadaki,
Local Proceedings of CiE 2008, pp.425-434, 2008], where we introduced the
notion of thermodynamic quantities into AIT. These quantities are real
functions of temperature T>0. The values of all the thermodynamic quantities
diverge when T exceeds 1. This phenomenon corresponds to phase transition in
statistical mechanics. In this paper we introduce the notion of strong
predictability for an infinite binary sequence and then apply it to the
partition function Z(T), which is one of the thermodynamic quantities in AIT.
We then reveal a new computational aspect of the phase transition in AIT by
showing the critical difference of the behavior of Z(T) between T=1 and T<1 in
terms of the strong predictability for the base-two expansion of Z(T). | | Source: | arXiv, 1304.6858 | | Services: | Forum | Review | PDF | Favorites | |
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