The Past and the Future in the Present
James P. Crutchfield, Christopher J. Ellison

TL;DR
This paper explores how the excess entropy, representing shared information between past and future, originates from present causal states, and discusses challenges in its estimation.
Contribution
It provides a detailed proof linking excess entropy to causal states and highlights estimation challenges in information analysis.
Findings
Excess entropy derives from present causal states.
Estimation of excess entropy involves subtle problems.
The paper clarifies the relationship between past, present, and future information.
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.
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Taxonomy
TopicsChaos control and synchronization · Fractal and DNA sequence analysis · Cellular Automata and Applications
