Thermodynamics of prebiotic synthesis

In this paper, I outline the correspondence of vector partitions with the combinatorics of dynamical systems whose states are partitions of multisets. I use the notion of a limiting shape of vector partitions to determine properties of the equilibrium distribution for these systems. I investigate prebiotic systems as ergodic series of chemical reactions as an example. I determine under what conditions long polymers of RNA are favorable at equilibrium using the limit shape of the vector partitions.