The number of observable degrees of freedom is typically limited in
experiments. Here, we consider discrete Markov networks in which an observer
has access to a few visible transitions and the waiting times between these
transitions. Focusing on the underlying structure of a discrete network, we
present methods to infer local and global properties of the network from
observed data. First, we derive bounds on the microscopic entropy production
along the hidden paths between two visible transitions, which complement extant
bounds on mean entropy production and affinities of hidden cycles. Second, we
demonstrate how the operationally accessible data encodes information about the
topology of shortest hidden paths, which can be used to identify potential
clusters of states or exclude their existence. Finally, we outline a systematic
way to combine the inferred data, resulting in an algorithm that finds the
candidates for a minimal graph of the underlying network, i.e., a graph that is
part of the original one and compatible with the observations. Our results
highlight the interplay between thermodynamic methods, waiting-time
distributions and topological aspects like network structure, which can be
expected to provide novel insights in other set-ups of coarse graining as well.

Questo articolo esplora i giri e le loro implicazioni.

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