We study convexity properties of the Rényi entropy as function $\alpha >0$ on finite alphabets. also describe robustness alphabets, and it turns out that rate respective convergence depends initial alphabet. establish disturbed when distribution is uniform but number events increases to ? prove limit binomial equal Poisson distribution.

The R\'enyi entropies of quasiparticle excitations in the many-body gapped systems show a remarkable universal picture which can be understood partially by combination semiclassical argument with quantum effect (in)distinguishability. are independent model, momenta, and connectedness subsystem. In this letter we calculate exactly single-interval double-interval fermions, bosons, XY chains. We f...