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

We explore the dynamics of information systems. We show that the driving force for 1 information dynamics is determined by both the information landscape and information flux which 2 determines the equilibrium time reversible and the nonequilibrium time-irreversible behaviours 3 of the system respectively. We further demonstrate that the mutual information rate between the 4 two subsystems can be decomposed into the time-reversible and time-irreversible parts respectively, 5 analogous to the information landscape-flux decomposition for dynamics. Finally, we uncover the 6 intimate relation between the nonequilibrium thermodynamics in terms of the entropy production 7 rates and the time-irreversible part of the mutual information rate. We demonstrate the above features 8 by the dynamics of a bivariate Markov chain. 9