Recent measurements and simulations of wind farm wakes have highlighted interactions with the atmosphere that are not observed for wakes behind isolated turbines. This raises the question: How do wake recovery and its underlying physical mechanisms vary with wind farm size? In this work, we employ large eddy simulations to study the wake recovery behind 25 different-sized wind farms, ranging from an isolated turbine to an 81-turbine wind farm, in a deep conventionally neutral boundary layer. An analysis of the wake recovery mechanisms indicates a clear distinction between turbine-scale and wind farm-scale wake recovery physics. Turbine wake recovery is driven primarily by spanwise turbulent entrainment of energy, whereas recovery behind wind farms is governed by vertical turbulent entrainment and mechanical energy fluxes. The strong downward energy transport by the mean vertical flow highlights a fundamental difference with the wake development inside large wind farms, where this effect is limited. We further show that large wind farms can influence the atmosphere at high altitudes far downstream, even after the wind speed at hub height has mostly recovered. Finally, we evaluate how well several farm-level engineering models predict hub-height wind farm wake recovery and find that the overall trends are captured. Our findings significantly advance the understanding of wake recovery physics and can help to further improve the tools used for siting wind farms within clusters.