  We propose the characterization of fragmentation functions by the energy
fraction x, a hadron takes away from the energy of the jet measured in the
frame co-moving with the jet. Besides, we propose the usage of the jet mass as
the fragmentation scale Q. We show that these two Lorentz-invariant variables
emerge naturally in a microcanonical ensemble with conserved fourmomentum.
Then, we construct a statistical hadronisation model, in which, two features of
the hadronic final states in various high-energy reactions (power law spectra
and negative-binomial multiplicity distributions) can be connected simply.
Finally, we analyse the scale dependence of the parameters of the model (power
of the spectrum and mean energy per hadron) in the phi^3 theory. Fitting
fragmentation functions in diffractive positron-proton collisions, we obtain a
prediction for the jet mass dependence of the hadron multiplicity distribution
inside jets.
