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Stochastic thermodynamics provides the framework to analyze thermodynamiclaws and quantities along individual trajectories of small but fully observablesystems. If the observable level fails to capture all relevant degrees offreedom, some form of effective, coarse-grained dynamics naturally emerges forwhich the principles of stochastic thermodynamics generally cease to beapplicable straightforwardly. Our work unifies the notion of entropy productionalong an individual trajectory with that of a coarse-grained dynamics byestablishing a framework based on snippets and Markovian events as fundamentalbuilding blocks. A key asset of a trajectory-based fluctuating entropyproduction is the ability to localize individual contributions to the totalentropy production in time and space. As an illustration and potentialapplication for inference we introduce a method for the detection of hiddendriving. The framework applies equally to even and odd variables and,therefore, includes the peculiar case of entropy production in underdampedLangevin dynamics.

Fluctuating Entropy Production on the Coarse-Grained Level: Inference and Localization of Irreversibility