  A central task in finite-time thermodynamics is to minimize the excess or
dissipated work $W_{\rm diss}$ when manipulating the state of a system immersed
in a thermal bath. We consider this task for an $N$-body system whose
constituents are identical and uncorrelated at the beginning and end of the
process. In the regime of slow but finite-time processes, we show that $W_{\rm
diss}$ can be dramatically reduced by considering collective protocols in which
interactions are suitably created along the protocol. This can even lead to a
sub-linear growth of $W_{\rm diss}$ with $N$: $W_{\rm diss}\propto N^x$ with
$x<1$; to be contrasted to the expected $W_{\rm diss}\propto N$ satisfied in
any non-interacting protocol. We derive the fundamental limits to such
collective advantages and show that $x=0$ is in principle possible, however it
requires long-range interactions. We explore collective processes with spin
models featuring two-body interactions and achieve noticeable gains under
realistic levels of control in simple interaction architectures. As an
application of these results, we focus on the erasure of information in finite
time and prove a faster convergence to Landauer's bound.
