, where ϕ i and ψ i are, respectively, the eigenfunctions of the propagator and transfer operator . Therefore, in the language of these operators, we want to show that the contributions corresponding to non-stationary distributions (i ̸ = 1) get smaller after reweighting. Under the assumptions of infinite sampling and domain coverage (meaning that the surrogate model assigns a non-zero probability to all possible states in state pace), the reweighted distribution (p r ) is exactly the Boltzmann distribution. We confirm this by computing