Constrains for non-standard statistical models of particle creations by identified hadron multiplicity results at LHC energies

We analysed the identified hadron multiplicity predictions of the modified thermodynamical model of the multiparticle production processes with non-extensive statistic. The replacement of the standard Boltzmann exponential factor by the eventually much slower falling Tsallis one is suggested by the analysis of the transverse momentum distributions measured at high energies. The increase of high transverse momenta should accord with the abundance of heavy secondary particles, in particular multistrange barions. The introduction to the thermodynamical model of suppression factors similar to the ones in a quark jet fragmentation models is discussed.