  Theoretical models and rate equations relevant to the Soai reaction are
reviewed. It is found that in a production of chiral molecules from an achiral
substrate autocatalytic processes can induce either enantiomeric excess (ee)
amplification or chiral symmetry breaking. Former terminology means that the
final ee value is larger than the initial value but depends on this, whereas
the latter means the selection of a unique value of the final ee, independent
of the initial value. The ee amplification takes place in an irreversible
reaction such that all the substrate molecules are converted to chiral products
and the reaction comes to a halt. The chiral symmetry breaking is possible when
recycling processes are incorporated. Reactions become reversible and the
system relaxes slowly to a unique final state. The difference between the two
behaviors is apparent in the flow diagram in the phase space of chiral molecule
concentrations. The ee amplification takes place when the flow terminates on a
line of fixed points (or a fixed line), whereas symmetry breaking corresponds
to the dissolution of the fixed line accompanied by the appearance of fixed
points. Relevance of the Soai reaction to the homochirality in life is also
discussed.
