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Title: Optimal estimate of total dissipation from partial observation
Plain: 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: 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.
Settled by: A proof that a given estimator attains the minimum of $\sigma$ over all Markov processes consistent with the observed statistics.
Kind: well-posed
Answer type: value
References: (empty)
Literature status: partially-resolved
Status note: Lower bounds from uncertainty relations, waiting-time statistics and Kullback-Leibler irreversibility are known; optimality among all estimators is not established.
Posed since: (empty)