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.

main text: 5 pages, 1 figure; total: 17 pages, 8 figures