Unravelling nonequilibrium features of a mesoscopic process through the estimation of information flow

Nonequilibrium systems evolve through a sequence of states shaped by the interplay among internal degrees of freedom, the environment, and external controls or feedback. At each stage, energy can be dissipated. While the total entropy production rate provides a global measure of dissipation in such systems, tracing the precise origin of nonequilibrium behaviour in complex, interacting setups remains challenging. In this work, we use information-theoretic tools - such as mutual information and its polymorphs - to gain insight into these dynamics. Here, we study an experimental system consisting of two hydrodynamically coupled colloidal particles -- of which one is driven by an exponentially correlated noise and estimate mutual information across different bivariate subspaces to understand how interactions shape steady-state dependencies. This approach also helps us resolve a previously counterintuitive observation regarding the relationship between irreversibility and interaction strength in various coarse-grained subspaces of the system. Further, by computing time-delayed mutual information and transfer entropy, we identify the direction of information flow and the specific degrees of freedom that drive nonequilibrium behaviour in each phase space. The behaviour of these time-delayed measures reveals clear signs of unidirectional energy and information flow under strong nonequilibrium conditions, along with a suppression of information backflow, emphasizing the essential role of nonequilibrium activity in enabling effective signalling pathways.