In this paper, we show that 1) additive energy is not appropriate for discussing the validity of Tsallis or Rényi statistics for nonextensive systems at equilibrium; 2) equilibrium N-body systems with nonad-ditive energy or entropy should be described by generalized statistics whose nature is prescribed by the existence of thermodynamic equilibrium. The nonextensive statistics may be Tsallis or...

We generalize the topological entanglement entropy to a family of topological Rényi entropies parametrized by a parameter alpha, in an attempt to find new invariants for distinguishing topologically ordered phases. We show that, surprisingly, all topological Rényi entropies are the same, independent of alpha for all nonchiral topological phases. This independence shows that topologically ordere...

EHS/NA22 Collaboration The entropy properties are analyzed by Ma's coincidence method in π + p and K + p collisions of the NA22 experiment at 250 GeV/c incident momentum. By using the Rényi entropies, we test the scaling law and additivity properties in rapidity space. The behavior of the Rényi entropies as a function of the average number of particles is investigated. The results are compared ...

We formulate two types of extensions of the large deviation theory initiated by Bahadur in a non-regular setting. One can be regarded as a bound of the point estimation, the other can be regarded as the limit of a bound of the interval estimation. Both coincide in the regular case, but do not necessarily coincide in a non-regular case. Using the limits of relative Rényi entropies, we derive the...

Recent improvements in the method of estimating Renyi entropies from measurements of coincidences between the events observed in high energy collisions are reviewed. A new, more precise, formulation of the method is presented and its accuracy analyzed.

Compressed Counting (CC) was recently proposed for approximating the αth frequency moments of data streams, for 0 < α ≤ 2. Under the relaxed strict-Turnstile model, CC dramatically improves the standard algorithm based on symmetric stable random projections, especially as α → 1. A direct application of CC is to estimate the entropy, which is an important summary statistic in Web/network measure...