Work

From observed transitions to hidden paths in Markov networks

Year: 2025

Type: article

Abstract: 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 setups of coarse graining as well.

Source: Physical Review Research

DOI: 10.1103/p4k1-1dvb

Authors: Alexander M. Maier, Udo Seifert, Jann van der Meer

Institutions: University of Stuttgart, Kyoto University

Language: English

Topic: Advanced Thermodynamics and Statistical Mechanics

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,625

Funder: Japan Society for the Promotion of Science