  Collisional Brownian engines have been proposed as alternatives for
nonequilibrium nanoscale engines. However, most studies have focused on the
simpler overdamped case, leaving the role of inertia much less explored. In
this work, we introduce the idea of collisional engines to underdamped Brownian
particles, where each stage is sequentially subjected to a distinct driving
force. A careful comparison between the performance of underdamped and
overdamped Brownian work-to-work engines has been undertaken. The results show
that underdamped Brownian engines generally outperform their overdamped
counterparts. A key difference is the presence of a resonant regime in
underdamped engines, in which both efficiency and power output are enhanced
across a broad set of parameters. Our study highlights the importance of
carefully selecting dynamics and driving protocols to achieve optimal engine
performance.
