English

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

R2 v1 2026-06-21T16:52:15.246Z