From observed transitions to hidden paths in Markov networks
arXiv:2504.16015 · doi:10.1103/p4k1-1dvb
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 set-ups of coarse graining as well.
References in corpus (29)
- Stochastic thermodynamics, fluctuation theorems, and molecular machines
- Thermodynamic uncertainty relation for biomolecular processes
- Dissipation bounds all steady-state current fluctuations
- Stochastic thermodynamics under coarse-graining
- Estimating dissipation from single stationary trajectories
- Speed Limit for Classical Stochastic Processes
- Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits
- Fluctuation Theorem for Partially-masked Nonequilibrium Dynamics
- Lower bounds on dissipation upon coarse graining
- Inferring broken detailed balance in the absence of observable currents
- Stochastic time-evolution, information geometry and the Cramer-Rao Bound
- Multiple-scale stochastic processes: decimation, averaging and beyond
- Minimum entropy production, detailed balance and Wasserstein distance for continuous-time Markov processes
- Emergent memory and kinetic hysteresis in strongly driven networks
- Thermodynamic Bound on the Asymmetry of Cross-Correlations
- Universal thermodynamic bounds on nonequilibrium response with biochemical applications
- Time-resolved statistics of snippets as general framework for model-free entropy estimators
- Effective fluctuation and response theory
- Milestoning estimators of dissipation in systems observed at a coarse resolution: When ignorance is truly bliss
- Thermodynamic cost for precision of general counting observables
- Non-invasive estimation of dissipation from non-equilibrium fluctuations in chemical reactions
- Fluctuating Entropy Production on the Coarse-Grained Level: Inference and Localization of Irreversibility
- Entropy production limits all fluctuation oscillations
- General theory for localizing the where and when of entropy production meets single-molecule experiments
- Extreme value statistics of edge currents in Markov jump processes and their use for entropy production estimation
- Model-free inference of memory in conformational dynamics of a multi-domain protein
- Beat of a current
- Inferring kinetics and entropy production from observable transitions in partially accessible, periodically driven Markov networks
- Infinite variety of thermodynamic speed limits with general activities