Constrained maximization of information entropy yields least biased probability distributions. In statistical physics, this powerful inference method yields classical thermodynamics under the constraints implied by conservation laws. Here we apply this method to ecology, starting with logically necessary constraints formed from ratios of ecological state variables, and derive realistic abundance distributions, species-area relationships, spatial aggregation patterns, body-size distributions, and metrics of network structure over a wide range of taxonomic groups, habitats and spatial scales. Progress at the frontier, extension of the theory to systems undergoing rapid change, will be discussed.