The fluctuation theorem for entropy production is a remarkable symmetry ofthe distribution of produced entropy that holds universally in non-equilibriumsteady states with Markovian dynamics. However, in systems with slow degrees offreedom that are hidden from the observer, it is not possible to infer theamount of produced entropy exactly. Previous work suggested that a relationsimilar to the fluctuation theorem may hold at least approximately for suchsystems if one considers an apparent entropy production. By extending thenotion of apparent entropy production to discrete bipartite systems weinvestigate which criteria have to be met for such a modified fluctuationtheorem to hold in the large deviation limit. We use asymptotic approximationsof the large deviation function to show that the probabilities of extremeevents of apparent entropy production always obey a modified fluctuationtheorem and, moreover, that it is possible to infer otherwise hiddenproperties. For the paradigmatic case of two coupled colloidal particles onrings the rate function of the apparent entropy production is calculated toillustrate this asymptotic behavior and to show that the modified fluctuationtheorem observed experimentally for short observation times does not persist inthe long time limit.
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