Over the past half century of serious research on the origin of life, several schools of thought have emerged that focus on “worlds” and what came first in the pathway to the origin of life. One example is the RNA World, a term coined by Walter Gilbert after the discovery of ribozymes. Other examples include the Iron-Sulfur World of Günther Wächtershäuser and the Lipid World proposed by Doron Lancet and coworkers. Then we have a competition between “metabolism first” and “replication first” schools. The worlds and schools have the positive effect of sharpening arguments and forcing us to think carefully, but they also can lock researchers into defending their individual approaches rather than looking for patterns in a larger perspective. One of the main themes of this book is the notion that the first living cells were systems of functional polymers working together within membranous compartments. Therefore, it is best not to think of “worlds” and “firsts” as fundamentals but instead as components evolving together toward the assembly of an encapsulated system of functional polymers. At first the polymers will be composed of random sequences of their monomers, and the compartments will contain random assortments of polymers. Here, we refer to these structures as protocells which are being produced in vast numbers as they form and decompose in continuous cycles driven by a variety of impinging, free-energy sources. This chapter describes how thermodynamic principles can be used to test the feasibility of a proposed mechanism by which random polymers can be synthesized. There is a current consensus that early life may have passed through a phase in which RNA served as a ribozyme catalyst, as a replicating system, and as a means for storing and expressing genetic information. For this reason, we will use RNA as a model polymer, but condensation reactions also produce peptide bonds and oligopeptides. At some point in the evolutionary steps leading to life, peptides and RNA formed complexes with novel functional properties beyond those of the individual molecular species.