  The selection of a single molecular handedness, or homochirality across all
living matter, is a mystery in the origin of life. Frank's seminal model showed
in the fifties how chiral symmetry breaking can occur in non-equilibrium
chemical networks. However, an important shortcoming in this classic model is
that it considers a small number of species, while there is no reason for the
prebiotic system, in which homochirality first appeared, to have had such a
simple composition. Furthermore, this model does not provide information on
what could have been the size of the molecules involved in this homochiral
prebiotic system. Here, we show that large molecular systems are likely to
undergo a phase transition towards a homochiral state, as a consequence of the
fact that they contain a large number of chiral species. Using chemoinformatics
tools, we quantify how abundant are chiral species in the chemical universe of
all possible molecules of a given length. Then, we propose that Frank's model
should be extended to include a large number of species, in order to possess
the transition towards homochirality as confirmed by numerical simulations.
Finally, using random matrix theory, we prove that large non-equilibrium
reaction networks possess a generic and robust phase transition towards a
homochiral state.
