Parameter Inference and Nonequilibrium Identification for Markov Networks Based on Coarse-Grained Observations

Area of Science:

• Statistical Mechanics
• Computational Chemistry
• Physical Chemistry

Background:

• Molecular experiments often yield coarse-grained data, obscuring internal microstates.
• Extracting complete statistical information from limited observations is a significant challenge.

Purpose of the Study:

• To develop a theoretical framework for parameter inference and nonequilibrium identification in Markov networks.
• To utilize sufficient statistics from infinitely long coarse-grained trajectories.
• To generalize existing nonequilibrium criteria for broader applicability.

Main Methods:

• Derivation of sufficient statistics from coarse-grained trajectories.
• Development of a theoretical framework for parameter inference.
• Establishment of a quantitative criterion for nonequilibrium identification.

Main Results:

• Obtained sufficient statistics that capture all information from coarse-grained observations.
• Developed a framework applicable to arbitrary Markov networks with varying microstates and partitioning.
• Proposed a generalized nonequilibrium criterion capable of detecting wider nonequilibrium regions.

Conclusions:

• The framework allows for empirical estimation of unknown parameters in molecular systems.
• The novel nonequilibrium criterion offers improved detection capabilities over classical methods.
• This work advances the analysis of complex molecular dynamics from limited experimental data.