  Motivated by the recently-established connection between Jarzynski's equality
and the theoretical framework of Stochastic Normalizing Flows, we investigate a
protocol relying on out-of-equilibrium lattice Monte Carlo simulations to
mitigate the infamous computational problem of topological freezing. We test
our proposal on $2d$ $\mathrm{CP}^{N-1}$ models and compare our results with
those obtained adopting the Parallel Tempering on Boundary Conditions proposed
by M. Hasenbusch, obtaining comparable performances. Our work thus sets the
stage for future applications combining our Monte Carlo setup with machine
learning techniques.
