Particle production in the toy world: multiplicity distribution and entropy

In this paper we found the multiplicity distribution of the produced dipoles in the final state for dipole-dipole scattering in the zero dimension toy models. This distribution shows the great differences from the distributions of partons in the wave function of the projectile. However, in spite of this difference the entropy of the produced dipoles turns out to be the same as the entropy of the dipoles in the wave function. This fact is not surprising since in the parton approach only dipoles in the hadron wave function which can be produced at $t = +\infty$ and measured by the detectors. We can also confirm the result of Kharzeev and Levin that this entropy is equal to $S_E = \ln\bigl(xG(x)\bigr)$, where we denote by $xG$ the mean multiplicity of the dipoles in the deep inelastic scattering. The evolution equations for $\sigma_n$ are derived.