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Open AccessArticle

Information Landscape and Flux, Mutual Information Rate Decomposition and Connections to Entropy Production

by Qian Zeng 1 and Jin Wang 1,2,*
1
State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Changchun, Jilin 130022, China
2
Department of Chemistry and Physics, State University of New York, Stony Brook, NY 11794, USA
*
Author to whom correspondence should be addressed.
Entropy 2017, 19(12), 678; https://doi.org/10.3390/e19120678
Received: 29 September 2017 / Revised: 27 November 2017 / Accepted: 6 December 2017 / Published: 11 December 2017
(This article belongs to the Special Issue Thermodynamics and Statistical Mechanics of Small Systems)
We explored the dynamics of two interacting information systems. We show that for the Markovian marginal systems, the driving force for information dynamics is determined by both the information landscape and information flux. While the information landscape can be used to construct the driving force to describe the equilibrium time-reversible information system dynamics, the information flux can be used to describe the nonequilibrium time-irreversible behaviors of the information system dynamics. The information flux explicitly breaks the detailed balance and is a direct measure of the degree of the nonequilibrium or time-irreversibility. We further demonstrate that the mutual information rate between the two subsystems can be decomposed into the equilibrium time-reversible and nonequilibrium time-irreversible parts, respectively. This decomposition of the Mutual Information Rate (MIR) corresponds to the information landscape-flux decomposition explicitly when the two subsystems behave as Markov chains. Finally, we uncover the intimate relationship between the nonequilibrium thermodynamics in terms of the entropy production rates and the time-irreversible part of the mutual information rate. We found that this relationship and MIR decomposition still hold for the more general stationary and ergodic cases. We demonstrate the above features with two examples of the bivariate Markov chains. View Full-Text
Keywords: nonequilibrium thermodynamics; landscape-flux decomposition; mutual information rate; entropy production rate nonequilibrium thermodynamics; landscape-flux decomposition; mutual information rate; entropy production rate
MDPI and ACS Style

Zeng, Q.; Wang, J. Information Landscape and Flux, Mutual Information Rate Decomposition and Connections to Entropy Production. Entropy 2017, 19, 678.

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