Abstract
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.
Highlights
IntroductionThere is growing interest in studying two interacting information systems in the fields of control theory, information theory, communication theory, nonequilibrium physics and biophysics [1,2,3,4,5,6,7,8,9]
There is growing interest in studying two interacting information systems in the fields of control theory, information theory, communication theory, nonequilibrium physics and biophysics [1,2,3,4,5,6,7,8,9].Significant progresses has been made recently towards the understanding of the information system in terms of information thermodynamics [10,11,12,13]
We show that for marginal Markovian information systems, the information dynamics is determined by both the information landscape and information flux
Summary
There is growing interest in studying two interacting information systems in the fields of control theory, information theory, communication theory, nonequilibrium physics and biophysics [1,2,3,4,5,6,7,8,9]. The information landscape can be used to construct the driving force responsible for the equilibrium time-reversible part of the information dynamics. The information flux explicitly breaks the detailed balance and provides a quantitative measure of the degree of nonequilibrium or time-irreversibility. It is responsible for the time-irreversible part of the information dynamics. When the two subsystems act as Markov chains, this decomposition can be expressed in terms of information landscape-flux decomposition for Markovian dynamics. We show that the decomposition of the MIR and the relationship between the EPRs and the time-irreversible part of the MIR still hold for more general stationary and ergodic cases
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