Mapping free-energy landscapes has proved to be a powerful tool for studying reaction mechanisms. Many complex biomolecular assembly processes, however, have remained challenging to access using this approach, including the aggregation of peptides and proteins into amyloid fibrils implicated in a range of disorders. Here, we generalize the strategy used to probe free-energy landscapes in protein folding to determine the activation energies and entropies that characterize each of the molecular steps in the aggregation of the amyloid-β peptide (Aβ42), which is associated with Alzheimer's disease. Our results reveal that interactions between monomeric Aβ42 and amyloid fibrils during fibril-dependent secondary nucleation fundamentally reverse the thermodynamic signature of this process relative to primary nucleation, even though both processes generate aggregates from soluble peptides. By mapping the energetic and entropic contributions along the reaction trajectories, we show that the catalytic efficiency of Aβ42 fibril surfaces results from the enthalpic stabilization of adsorbing peptides in conformations amenable to nucleation, resulting in a dramatic lowering of the activation energy for nucleation.