Single-particle distribution in the hydrodynamic and statistical thermodynamic models of multiparticle production

We find that the single-particle distribution $\frac{\mathrm{EdN}}{d^{3}p}$ for an expanding relativistic gas described by a distribution function obeying the Boltzmann transport equation is not of the form of an integral over collective motions of a velocity weight function times a "Lorentz-transformed" rest-frame distribution function. This casts doubt on the algorithms of Milekhin and Hagedorn for determining the single-particle distribution function in their models of particle production. For the hydrodynamic model, the correct algorithm is presented.