Inferring entropy production rate from partially observed Langevin dynamics systems under coarse-graining

The entropy production rate (EPR) is a measure of irreversibility in systems operating far from equilibrium. The challenge in quantifying the EPR for a system obeying Langevin dynamics lies in the finite spatiotemporal resolution and the limited accessibility to all of the non-equilibrium degrees of freedom. In this talk, I will present an estimation of a lower bound on the EPR in an observed system variable following Langevin dynamics, coarse-grained into a few discrete states. In the observed variable space, the underlying driven process follows semi-Markov statistics, and thus the probability density functions of the waiting times associated with the transitions are distance-time dependent. By invoking the underlying broken time-reversal symmetry, we calculate the EPR from the Kullback-Leibler divergence of the density functions. We show that with finer spatial resolution, the mean dwell-time asymmetry factor increases, and that the lower bound on the EPR is highly correlated with the mean dwell-time asymmetry factor.