Rate of Mutual Information Between Coarse-Grained Non-Markovian Variables

The problem of calculating the rate of mutual information between two coarse-grained variables that together specify a continuous time Markov process is addressed. As a main obstacle, the coarse-grained variables are in general non-Markovian, therefore, an expression for their Shannon entropy rates...

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Bibliographic Details
Published inJournal of statistical physics Vol. 153; no. 3; pp. 460 - 478
Main Authors Barato, Andre C., Hartich, David, Seifert, Udo
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.11.2013
Springer
Subjects
Markov processes
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
Entropy production
Non-Markov processes
Mutual information
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Summary:The problem of calculating the rate of mutual information between two coarse-grained variables that together specify a continuous time Markov process is addressed. As a main obstacle, the coarse-grained variables are in general non-Markovian, therefore, an expression for their Shannon entropy rates in terms of the stationary probability distribution is not known. A numerical method to estimate the Shannon entropy rate of continuous time hidden-Markov processes from a single time series is developed. With this method the rate of mutual information can be determined numerically. Moreover, an analytical upper bound on the rate of mutual information is calculated for a class of Markov processes for which the transition rates have a bipartite character. Our general results are illustrated with explicit calculations for four-state networks.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-013-0834-5