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The Drake equation was formulated to organize a famously underdetermined problem -- the probability to encounter extraterrestrial civilization -- into a hierarchy of conditional probabilities that reflected necessary dependencies, even if some of the factors themselves remain underdetermined. We can try to identify a similar hierarchy of stages through which matter must pass in the long and complex transition from abiotic early-planetary chemistry to a biosphere. In this sequence the dependencies are conditional entropies, or equivalently, increments of information. In the physics of matter, such hierarchies are the result of phase transitions, each of which is both a threshold and a platform. Each transition requires conditions capable of restricting a system's exploration of its states, but if those are met, the restricted phase serves as a pre-ordered and stable input to further transitions. The same combinatorics applies to life, first in its employment of distinctive ordered states of matter, and then in the costs of exploration and population of new forms by unguided processes that we call evolution. We will argue that metabolites, folded matter, and coded matter are information gateways in a Drake-like sequence of entropy reductions, and that the complex requirements of each that create a threshold for its formation play essential roles in making subsequent transitions possible.