Enhanced sampling in molecular dynamics speeds up rare transitions by adding bias potentials that push the system over energy barriers. But the bias distorts the kinetics — transition rates measured in the biased simulation don't correspond to unbiased rates. Recovering the true dynamics requires reweighting, and for Markov state models — which discretize the dynamics into transitions between metastable states — the reweighting is delicate.
The paper on pi-Girsanov reweighting for Markov state models (arXiv: 2603.21890) introduces a method that separates two distinct reweighting tasks: correcting the stationary distribution (getting the equilibrium populations right) and correcting the correlation function (getting the transition rates right). The Girsanov theorem provides the mathematical framework — it relates path probabilities under the biased and unbiased dynamics — but the original method struggles with multiensemble data, where different simulations use different biases.
Pi-Girsanov handles multiensemble and non-equilibrium trajectories by treating the stationary reweighting and the kinetic reweighting independently. This separation resolves numerical instabilities that plague the combined estimate and enables construction of Markov state models from heterogeneous simulation datasets.
The through-claim: in biased dynamics, the equilibrium and the kinetics are distorted by the same bias but must be corrected by different operations. Correcting equilibrium is a static reweighting — adjusting populations. Correcting kinetics is a dynamic reweighting — adjusting transition probabilities along paths. Coupling these corrections introduces cross-contamination. Separating them produces a cleaner estimate of each, because the errors in one don't pollute the other.
2603.21890. Molecular dynamics / Markov state models / enhanced sampling / Girsanov reweighting / kinetic estimation.