Information-theoretic tools for parametrized coarse-graining of non-equilibrium extended systems

In this paper we focus on the development of new methods suitable for efficient and reliable coarse-graining of {\it non-equilibrium} molecular systems. In this context, we propose error estimation and controlled-fidelity model reduction methods based on Path-Space Information Theory, and combine it with statistical parametric estimation of rates for non-equilibrium stationary processes. The approach we propose extends the applicability of existing information-based methods for deriving parametrized coarse-grained models to Non-Equilibrium systems with Stationary States (NESS). In the context of coarse-graining it allows for constructing optimal parametrized Markovian coarse-grained dynamics, by minimizing information loss (due to coarse-graining) on the path space. Furthermore, the associated path-space Fisher Information Matrix can provide confidence intervals for the corresponding parameter estimators. We demonstrate the proposed coarse-graining method in a non-equilibrium system with diffusing interacting particles, driven by out-of-equilibrium boundary conditions.