{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"946ee3fab4cbedcdfb37c500171d24e01e1b777317d4fdd998b84709b7fd467b","created":"2026-10-03T07:18:11Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"538e23fec568ca66157031cb79a5f5b5c590951190ef6955ad58801ea329bed7","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"stat.stochastic-thermodynamics.hidden-dissipation-inference","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"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.","posed_since":"","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.","problem_ref":null,"references":"","settled_by":"A proof that a given estimator attains the minimum of $\\sigma$ over all Markov processes consistent with the observed statistics.","status_note":"Lower bounds from uncertainty relations, waiting-time statistics and Kullback-Leibler irreversibility are known; optimality among all estimators is not established.","title":"Optimal estimate of total dissipation from partial 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