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Entropy rate estimates from mutual information.

B D Wissman¹, L C McKay-Jones, P-M Binder

¹Natural Sciences Division, University of Hawaii, Hilo, Hawaii 96720-4091, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|December 21, 2011

Summary

This summary is machine-generated.

Researchers can estimate the Kolmogorov-Sinai entropy rate in chaotic systems using mutual information from experimental data. This method is exact under specific conditions and applicable to both maps and flows.

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Area of Science:

Dynamical Systems and Chaos Theory
Information Theory
Time Series Analysis

Background:

Estimating the Kolmogorov-Sinai entropy rate is crucial for characterizing chaotic systems.
Traditional methods often require detailed system knowledge or extensive data.
Mutual information offers a data-driven approach from experimental time series.

Purpose of the Study:

To present a novel method for estimating Kolmogorov-Sinai entropy rate using mutual information.
To define the conditions for the exactness of this relationship.
To evaluate the method's applicability and robustness for various chaotic systems.

Main Methods:

Utilizing the mutual information function, derived from experimental time series.
Applying the method to both discrete maps and continuous flows.
Investigating convergence properties with respect to time series length.

Main Results:

Demonstrated a direct relationship between mutual information and Kolmogorov-Sinai entropy rate.
Identified specific conditions under which this relationship is exact.
Showcased the method's effectiveness for analyzing chaotic dynamics in different system types.

Conclusions:

Mutual information provides a practical and exact method for estimating Kolmogorov-Sinai entropy rate from experimental data.
The approach is versatile, applicable to diverse chaotic systems (maps and flows).
Further refinements and convergence studies enhance the method's reliability for time series analysis.