It is increasingly recognized that producing a consistent explanation for the origination of life will require us to explain how Darwinian evolution may have gradually emerged from a non-biological world. Gradually rather than suddenly, that is, without assuming that natural selection only came into play once chance alone had produced the first obvious "replicators", displaying the same heritable variance as extent organisms. Under this perspective of a smooth transition from physics to biology, natural selection is hypothesized to be acting already in the "prebiotic" soup as a driver to complexity, but in a rudimentary and currently unrecognizable fashion. 

In this talk, we will introduce a modelling scheme aimed at exploring this path: a dynamic mixture of physical objects, maintained out of thermodynamic equilibrium through a constant influx of primary entities that may combine, alike atoms or small molecules, into larger composite objects. Like others, we focus on autocatalytic cycles – that is on sets of entities whose presence facilitates the production of the very same entities –  as putatively important players in the emergence of evolution. Not because they can evolve themselves (devoid as they are of the potential to generate heritable variance) but because self-amplification may facilitate the emergence of “multistability” at a higher scale : the existence of multiple locally stable stationary states, that can be seen as distinct configurations of a “physico-chemical ecosystem”.

After developing the appropriate tools to compute the list of all autocatalytic loops in this system, we explore its potential for multistability. This is a crucial step to assess the underlying hypothesis that transitions among locally stable states could constitute elementary “mutations” among multiple heritable states, which might be key for the emergence of Darwinian dynamics.