Bulletin of the American Physical Society
Four Corners Section 2023 Meeting
Friday–Saturday, October 20–21, 2023; River Woods Conference Center, Logan, Utah
Session K01: Poster Session
4:06 PM,
Friday, October 20, 2023
Riverwoods Conference Center
Room: Grand Reception Hall
Abstract: K01.00019 : Information Anatomy on Partition Space
Presenter:
Nathan W Jackson
(University of Utah)
Authors:
Nathan W Jackson
(University of Utah)
Ryan G James
(University of California, Davis)
James P Crutchfield
(University of California, Davis)
Mikhael Semaan
(University of Utah)
However, the entropy rate is not sensitive to what kind of generating partition: colloquially, an instrument must be at least accurate enough, but can be more fine-grained as desired. In contrast, its breakdown into a piece which affects future measurements (“bound”) and a piece which does not (“ephemeral”) depends quite dramatically on the choice of generating partition. We ask, then: is there a canonical partitioning scheme for which the full suite of information measures relate to dynamical invariants?
To tackle this, we simulate the well-known tent and logistic maps, sweeping over all two-boundary partitions, calculating the full information anatomies for each. We find that ephemeral and bound information are extremized by the single-boundary coarsest generating partition, suggesting a canonical role for the simplest “good enough” instrument. The remaining multivariate measures, meanwhile, reveal hitherto-unseen structure in the process of imperfect measurement.
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