Spontaneous emergence of self-replication in chemical reaction systems

Explaining the origin of life requires us to explain how self-replication arises. To be specific, how can a self-replicating entity develop spontaneously from a chemical reaction system in which no reaction is self-replicating? Previously proposed mathematical models either supply an explicit framework for a minimal living system or only consider catalyzed reactions, and thus fail to provide a comprehensive theory. We set up a general model for chemical reaction systems that properly accounts for energetics, kinetics and the conservation law. We find that (1) some systems are collectively-catalytic where reactants are transformed into end products with the assistance of intermediates (as in the citric acid cycle), while some others are self-replicating where different parts replicate each other and the system self-replicates as a whole (as in the formose reaction); (2) many alternative chemical universes often contain one or more such systems; (3) it is possible to construct a self-replicating system where the entropy of some parts spontaneously decreases, in a manner similar to that discussed by Schr\"odinger; (4) complex self-replicating molecules can emerge spontaneously and relatively easily from simple chemical reaction systems through a sequence of transitions. Together these results start to explain the origins of prebiotic evolution.