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Fluctuation relations are powerful equalities that hold far from equilibrium.However, the standard approach to include measurement and feedback schemes maybecome inapplicable in certain situations, including continuous measurements,precise measurements of continuous variables, and feedback inducedirreversibility. Here we overcome these shortcomings by providing a recipe forproducing detailed fluctuation relations. Based on this recipe, we derive afluctuation relation which holds for arbitrary measurement and feedbackcontrol. The key insight is that fluctuations inferable from the measurementoutcomes may be suppressed by post-selection. Our detailed fluctuation relationresults in a stringent and experimentally accessible inequality on theextractable work, which is saturated when the full entropy production isinferable from the data.

Detailed Fluctuation Relation for Arbitrary Measurement and Feedback Schemes