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Updated: Jun 19, 2026
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Gradient Echo Quantum Memory in Warm Atomic Vapor
Published on: November 11, 2013
Time's barbed arrow: irreversibility, crypticity, and stored information
James P Crutchfield1, Christopher J Ellison, John R Mahoney
1Complexity Sciences Center and Physics Department, University of California at Davis, One Shields Avenue, Davis, California 95616, USA. chaos@cse.ucdavis.edu
Physical Review Letters
|October 2, 2009
Summary
We resolve a long-standing puzzle in information theory: why excess entropy (past-future information) differs from statistical complexity (present information). Our findings introduce new system invariants, causal irreversibility and crypticity.
Area of Science:
- Information theory
- Statistical mechanics
- Complex systems
Background:
- Excess entropy quantifies information flow between past and future.
- Statistical complexity measures information stored in the present.
- A discrepancy exists between these two measures, posing a prediction challenge.
Purpose of the Study:
- To explain the difference between excess entropy and statistical complexity.
- To derive a unified framework for understanding information dynamics in systems.
- To introduce novel system invariants related to information processing.
Main Methods:
- Developed a closed-form expression for excess entropy.
- Utilized optimal causal predictors and retrodictors from computational mechanics.
- Analyzed system dynamics through the lens of information theory.
Main Results:
- Established that excess entropy and statistical complexity are not generally equal.
- Derived a formula connecting excess entropy to predictors and retrodictors.
- Identified two new system invariants: causal irreversibility and crypticity.
Conclusions:
- The study clarifies the relationship between predictive and stored information.
- Causal irreversibility and crypticity offer new metrics for characterizing system behavior.
- The findings advance the understanding of information processing in complex systems.
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