Application of eigen microstate theory to polymer diffusion

In complex media, polymer diffusion is additionally constrained by geometry and polymer-environment interactions, making the dynamics substantially more complex than those of a freely diffusing Rouse chain and preventing a straightforward mode decomposition. This difficulty motivates us to use eigen microstate theory, which directly extracts dominant modes and their evolution from high-dimensional time-series data, providing a data-driven framework for the dynamical analysis of complex systems. We argue that this framework can be extended to polymer dynamics in porous media or complex polymer architectures. In this work, we take the diffusion of a polymer chain in an idealized two-dimensional model porous medium as a representative example and apply eigen microstate decomposition to the modal analysis of polymer-chain trajectories obtained from molecular dynamics simulations. The decomposition separates the confined chain dynamics into center-of-mass motion and internal conformational motion, and shows that the increasing contribution of the internal component correlates with a renormalization of the chain-length scaling of the long-time diffusion coefficient.