Time's barbed arrow: irreversibility, crypticity, and stored information.
We show why the amount of information communicated between the past and future-the excess entropy-is not in general the amount of information stored in the present-the statistical complexity. This is a puzzle, and a long-standing one, since the former describes observed behavior, while optimal prediction requires the latter. We present a closed-form expression for the excess entropy in terms of optimal causal predictors and retrodictors-both machines of computational mechanics. This leads us to two new system invariants: causal irreversibility-the asymmetry between the causal representations-and crypticity-the degree to which a process hides its state information.
Complexity Sciences Center and Physics Department, University of California at Davis, One Shields Avenue, Davis, California 95616, USA. chaos@cse.ucdavis.edu
James P
JP
Crutchfield
Christopher J
CJ
Ellison
John R
JR
Mahoney