  In this work we reveal that the inside-outside dynamic model for the
production of fermion-antifermion pair (or quark-antiquark in QCD), is an out
of equilibrium process. Properties of a complex system as the self-similarity
and the critical point of a continuous phase transition in equilibrium appear.
In this work we show that this is accomplished imposing a type of mapping
process through a self-composition operator on a QED_2 bosons (or pions) field.
