Figure 1.

Ensemble of conditioned paths and dynamic information exchange: (a) $\Gamma$ and ${\Gamma }_{x_{\tau },y_{\tau }}$ denote respectively the set of all trajectories during process ${\lambda }_t$ for $0\le t\le \tau$ and that of paths that reach $(x_{\tau },y_{\tau })$ at time $\tau$. Red curves schematically represent some members of ${\Gamma }_{x_{\tau },y_{\tau }}$. (b) We magnified a single trajectory in the left panel to represent a detailed view of dynamic coupling of $(x_{\tau },y_{\tau })$ during process ${\lambda }_t$. The point-wise mutual information $I_t(x_t,y_t)$ may vary not necessarily monotonically.