Thermodynamics of prebiotic synthesis

TL;DR

This paper explores the thermodynamics of prebiotic chemical systems by linking vector partitions with dynamical systems, analyzing conditions favoring RNA polymer formation at equilibrium through the concept of limiting shapes.

Contribution

It introduces a novel approach connecting vector partitions with dynamical systems to study prebiotic chemistry and RNA polymerization.

Findings

Identifies conditions favoring long RNA polymers at equilibrium

Establishes a link between vector partitions and system equilibrium properties

Provides a framework for analyzing prebiotic chemical reaction networks

Abstract

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.