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A complete account of the energetics of small-scale systems necessitates that all relevant degrees of freedom are resolved. However, in experimental situations this is not always feasible. With the help of example systems, e.g., a simple microswimmer model [1], we show the importance of observing all degrees of freedom for correctly assessing energy dissipation. In dealing with the presence of hidden degrees of freedom, a first attempt is to map a Markov process to the observed data. However, this results in the breaking of fluctuation theorems, which quickly exposes this flawed description. The reason for this is the non-Markovianity of the visible variables, as we show using a simple model [2]. A more promising approach is to consider the full non-Markovian statistics of the observed data and try to find an underlying hidden Markov model responsible for generating them. We discuss preliminary results and challenges in this undertaking.
[1] J. Ehrich and M. Kahlen, Phys. Rev. E 99, 012118 (2019) [2] M. Kahlen and J. Ehrich, J. Stat. Mech. (2018) 063204