Entropy production rates for different notions of partial information

Experimentally monitoring the dynamics of a physical system, one cannot possibly resolve all the microstates or all the transitions between them. Theoretically, these partially observed systems are modeled by considering only the observed states and transitions while the rest are hidden, by merging microstates into a single mesostate, or by decimating unobserved states. The deviation of a system from thermal equilibrium can be characterized by a non-zero value of the entropy production rate (EPR). Based on the partially observed information of the states or transitions, one can only infer a lower bound on the total EPR. Previous studies focused on several approaches to optimize the lower bounds on the EPR, fluctuation theorems associated with the apparent EPR, information regarding the network topology inferred from partial information, etc. Here, we calculate partial EPR values of Markov chains driven by external forces from different notions of partial information. We calculate partial EPR from state-based coarse-graining, namely decimation and two lumping protocols with different constraints, either preserving transition flux, or the occupancy number correlation function. Finally, we compare these partial EPR values with the EPR inferred from the observed cycle affinity. Our results can further be extended to other networks and various external driving forces.