The scaling and additivity properties of Rényi entropy in rapidity space of the instanton final state （IFS） and current jet identified by the r-sorting method from the QCDINS Monte Carlo event sample are studied. Asymptotic scaling of the Rényi entropy H2 is observed for the IFS while H2 for the current jet jtends to saturation with decreasing phase space scale. Furthermore, it is found that the additivity of H2 holds well for the IFS in narrow rapidity windows at different positions. These results indicate that the IFS produced in the instanton-induced process of deep inelastic scattering has reached local equilibrium.
A study of the dynamical fluctuation properties at various c.m. energies in e^＋e^- collisions is performed using the Monte Carlo method. The results suggest that, after the normalized factorial moments of 3-dimensional phase space are analyzed using an isotropical phase space partition, the NFM describing non- linear dynamical properties show a power-law scaling, i.e., the dynamical fluctuations in higher dimensional phase space are isotropic. For c.m. energies √s≤ 80 GeV, the scaling exponents φq increase rapidly with the c.m. energy and for c.m. energies √s 〉 80 GeV, the φq gradually saturate.
