In practice, the previous assumptions do not necessarily hold. Sampling time is limited by our computing budget and we cannot guarantee domain coverage. However, we do observe empirically that our model does not under-sample, but, if anything, tends to over-sample states not observed in long simulations. After reweighting, the distribution will not be exactly Boltzmann distributed, in contrast to our derivation, but states with lower energy will be favored as more efficient starting points for our simulation while balancing state populations. Furthermore, after the short simulation, we expect that fast-decaying contributions of the distribution vanish pushing our samples further closer to the stationary distribution. Figure : Scenario in which reweighting can cause longer convergence times. In the left (a), we show a double-well potential with its corresponding stationary distribution and possible surrogate density. In the right (b), we show the second (slowest) eigenfunction of the system. When the surrogate distribution is reweighted, the states on the negative part are assigned very small statistical weight. However, running a short simulation would transport those steps to a high-density area in a few steps, following the steep potential.