Thermodynamic uncertainty relations and first-passage times for information flows in co-evolving systems

Many systems are composed of multiple co-evolving subsystems. Information flowing between those subsystems can be quantified, with an information-theoretic measure of how much each subsystem affects the dynamics of the others, on average. This "information flow" has been shown to affect how much each subsystem's interactions with the others contributes to the global entropy production rate. Here, we introduce trajectory-level information flows, as well as conditional information flows. As we show, in a non-equilibrium steady state (NESS), these flows are currents, and therefore subject to the thermodynamic uncertainty relations. Therefore the statistical precision of the information flows across a system in an NESS are bounded by local and global entropy productions. We also investigate the thermodynamic properties of first-passage times for these inter-subsystem information flows. Finally, we derive relations between information flows and other measures of correlation among subsystems, such as the inclusion-exclusion information and multi-divergence.