Effective estimation of entropy production with lacking data

Observing stochastic trajectories with rare transitions between states, practically undetectable on time scales accessible to experiments, makes it impossible to directly quantify the entropy production and thus infer whether and how far systems are from equilibrium. To solve this issue for Markovian jump dynamics, we show a lower bound that outperforms any other estimation of entropy production (including Bayesian approaches) in regimes lacking data due to the strong irreversibility of state transitions. Moreover, in the limit of complete irreversibility, our effective version of the thermodynamic uncertainty relation sets a lower bound to entropy production that depends only on nondissipative aspects of the dynamics. Such an approach is also valuable when dealing with jump dynamics with a deterministic limit, such as irreversible chemical reactions.