Send to

Choose Destination
Phys Rev Lett. 2009 Aug 28;103(9):094101. Epub 2009 Aug 28.

Time's barbed arrow: irreversibility, crypticity, and stored information.

Author information

Complexity Sciences Center and Physics Department, University of California at Davis, One Shields Avenue, Davis, California 95616, USA.


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.

Supplemental Content

Full text links

Icon for American Physical Society
Loading ...
Support Center