  We consider the relationship between thermodynamics, fitness, and Darwinian
evolution in autocatalytic molecular replicators. We uncover a thermodynamic
bound that relates fitness, replication rate, and the Gibbs free energy
dissipated per copy. This bound applies to a broad range of systems, including
elementary and non-elementary autocatalytic reactions, polymer-based
replicators, and certain kinds of autocatalytic sets. In addition, we show that
the critical selection coefficient (the minimal fitness difference visible to
selection) is bounded by the Gibbs free energy dissipated per replication. Our
results imply fundamental thermodynamic bounds on the strength of selection in
molecular evolution, complementary to other bounds that arise from finite
population sizes and error thresholds. These bounds may be relevant for
understanding thermodynamic constraints faced by early replicators at the
origin of life. We illustrate our approach on several examples, including a
classic model of replicators in a chemostat.
