Journal
CHAOS
Volume 21, Issue 3, Pages -Publisher
AMER INST PHYSICS
DOI: 10.1063/1.3637502
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Funding
- NSF [PHY-0748828]
- Defense Advanced Research Projects Agency (DARPA) [9060-000709]
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We investigate a stationary process's crypticity-a measure of the difference between its hidden state information and its observed information-using the causal states of computational mechanics. Here, we motivate crypticity and cryptic order as physically meaningful quantities that monitor how hidden a hidden process is. This is done by recasting previous results on the convergence of block entropy and block-state entropy in a geometric setting, one that is more intuitive and that leads to a number of new results. For example, we connect crypticity to how an observer synchronizes to a process. We show that the block-causal-state entropy is a convex function of block length. We give a complete analysis of spin chains. We present a classification scheme that surveys stationary processes in terms of their possible cryptic and Markov orders. We illustrate related entropy convergence behaviors using a new form of foliated information diagram. Finally, along the way, we provide a variety of interpretations of crypticity and cryptic order to establish their naturalness and pervasiveness. This is also a first step in developing applications in spatially extended and network dynamical systems. (C) 2011 American Institute of Physics. [doi:10.1063/1.3637502]
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