It is shown that the Fisher droplet model, percolation, and nuclear multifragmentation share the common features of reducibility (stochasticity in multiplicity distributions) and thermal scaling (one-fragment production probabilities are Boltzmann factors). Barriers obtained, for cluster production on percolation lattices, from the Boltzmann factors show a power-law dependence on cluster size with an exponent of 0.42+/-0.02. The EOS Collaboration Au multifragmentation data yield barriers with a power-law exponent of 0.68+/-0.03. Values of the surface energy coefficient of a low density nuclear system are also extracted.