$\pi$-Girsanov: A Generalized Method to Construct Markov State Models from Non-Equilibrium and Multiensemble Biased Simulations

We introduce $\pi$-Girsanov, a new method for constructing Markov state models from biased enhanced-sampling molecular dynamics simulations based on Girsanov reweighting. The key idea behind this new method is to separate the reweighting stationary density from the reweighting of the correlation function. We evaluate the effectiveness of this approach on several analytical potentials and on a model biomolecular system, comparing its performance with the original method. Our results show that $\pi$-Girsanov not only improves the estimation in a single-ensemble setting, but also resolves key challenges in estimating transition matrices from multiensemble and non-equilibrium biased trajectories. Overall, $\pi$-Girsanov represents a substantial advance in kinetic reweighting, strengthening the connection between enhanced sampling techniques and Markov state modeling.