  Nonequilibrium sampling is potentially much more versatile than its
equilibrium counterpart, but it comes with challenges because the invariant
distribution is not typically known when the dynamics breaks detailed balance.
Here, we derive a generic importance sampling technique that leverages the
statistical power of configurations transported by nonequilibrium trajectories,
and can be used to compute averages with respect to arbitrary target
distributions. As a dissipative reweighting scheme, the method can be viewed in
relation to the annealed importance sampling (AIS) method and the related
Jarzynski equality. Unlike AIS, our approach gives an unbiased estimator, with
provably lower variance than directly estimating the average of an observable.
We also establish a direct relation between a dynamical quantity, the
dissipation, and the volume of phase space, from which we can compute
quantities such as the density of states and Bayes factors. We illustrate the
properties of estimators relying on this sampling technique in the context of
density of state calculations, showing that it scales favorable with
dimensionality -- in particular, we show that it can be used to compute the
phase diagram of the mean-field Ising model from a single nonequilibrium
trajectory. We also demonstrate the robustness and efficiency of the approach
with an application to a Bayesian model comparison problem of the type
encountered in astrophysics and machine learning.
