Optimal estimate of total dissipation from partial observation
In plain words
Experiments usually track only a few variables of a molecular machine, yet one wants its total energy dissipation. The question is the best lower bound on that dissipation that can be extracted from such partial data.
Precise statement
Given a stationary Markov process of which only a coarse-grained observable is recorded (a subset of transitions, or lumped states), determine the largest lower bound on the total entropy production rate $\sigma$ computable from the observed statistics (waiting-time distributions, current fluctuations, time-irreversibility of observed trajectories), and the conditions under which it equals $\sigma$. An answer is an estimator with a proof that no other estimator using the same data does better.
What would settle it
A proof that a given estimator attains the minimum of $\sigma$ over all Markov processes consistent with the observed statistics.
Status in the literature
Lower bounds from uncertainty relations, waiting-time statistics and Kullback-Leibler irreversibility are known; optimality among all estimators is not established.