  Following the quark-hadron duality concept, we show that the number of
hadrons generated in the deconfinement matter is entirely determined by the
exact non-equilibrium Green's functions of partons in the medium and the vertex
function governing the probability of the confinement-deconfinement phase
transition. In such an approach, compactifying the standard (3+1)
chromodynamics into $ QCD_{xy} + QCD_{zt}$, the rate of the hadrons produced in
particle collisions is derived in the explicit form provided that the
hadronization is the first order phase transition. The pion production is found
to be in good agreement to the experimental results on the pion yield in pp
collisions.
