Regensburg 2025 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 22: Poster: Statistical Physics

DY 22.18: Poster

Wednesday, March 19, 2025, 10:00–12:00, P3

Topological and thermodynamic inference in Markov networks with observed and hidden transitions — •Alexander M. Maier¹, Udo Seifert¹, and Jann van der Meer² — ¹II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany — ²Kyoto University, Graduate School of Science, Division of Physics and Astronomy, Oiwakecho 145-10, Kyoto 606-8224, Japan

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. We present what information, locally and globally, of such a Markov network can be inferred from the observed data. In particular, we shed light on operationally accessible information about the topology of shortest paths between visible transitions in the underlying graph and show a rule that allows us to identify potential clusters of states or exclude their existence. Moreover, we show how to estimate entropy production along an observable, coarse-grained path. Combining this with further inferable information, we propose two strategies to reconstruct a graph that is compatible with the observations and part of the original graph underlying the Markov network. This approach highlights how much information waiting-time distributions contain while also paving the way to infer thermodynamically consistent models of observed partially accessible systems.

Keywords: Thermodynamic inference; topological inference; waiting-time distribution; graph; entropy production rate