The lambda calculus chemistry model of Fontana and Buss is a classic in the literature on open-ended evolution. However, it lacks any notion of thermodynamic constraints, which in turn means that there is nothing that must be “used up” in order for replication to occur. By adding reverse reactions to a similar model, we are able to implement thermodynamically reasonable kinetics, although the system still lacks mass conservation. Here we outline our implementation and present some very preliminary results from initial investigations. In particular, we find that (i) the reverse reactions mean that nothing can be permanently lost from the system, enhancing its ability to continue generating novelty, and (ii) reverse reactions seem to create an implicit selection pressure against simple copy operations, removing the need to explicitly remove them from the system as in the original model. We believe that this approach will lead to a better understanding of the role that thermodynamic considerations must play in understanding the origin of life.