The Past and the Future in the Present
Chaotic Dynamics
2010-12-03 v1 Information Theory
Dynamical Systems
math.IT
Statistics Theory
Statistics Theory
Abstract
We show how the shared information between the past and future---the excess entropy---derives from the components of directional information stored in the present---the predictive and retrodictive causal states. A detailed proof allows us to highlight a number of the subtle problems in estimation and analysis that impede accurate calculation of the excess entropy.
Keywords
Cite
@article{arxiv.1012.0356,
title = {The Past and the Future in the Present},
author = {James P. Crutchfield and Christopher J. Ellison},
journal= {arXiv preprint arXiv:1012.0356},
year = {2010}
}
Comments
7 pages, 1 figure; http://cse.ucdavis.edu/~cmg/compmech/pubs/pafip.htm