Related papers: A nonextensive statistical model of multiple parti…
We consider statistical methods based on finite samples of locally randomized measurements in order to certify different degrees of multiparticle entanglement in intermediate-scale quantum systems. We first introduce hierarchies of…
The numerical experiments of turbulence conducted by Gotoh et al. are analyzed precisely with the help of the formulae for the scaling exponents of velocity structure function and for the probability density function (PDF) of velocity…
In this paper, we show that 1) additive energy is not appropriate for discussing the validity of Tsallis or R\'enyi statistics for nonextensive systems at meta-equilibrium; 2) $N$-body systems with nonadditive energy or entropy should be…
Using a Fourier spectral method, we provide a detailed numerically investigation of dispersive Schr\"odinger type equations involving a fractional Laplacian. By an appropriate choice of the dispersive exponent, both mass and energy sub- and…
The framework of non-extensive statistical mechanics, proposed by Tsallis, has been used to describe a variety of systems. The non-extensive statistical mechanics is usually introduced in a formal way, using the maximization of entropy. In…
We discuss different aspects of the present status of the Statistical Physics focusing the attention on the non-extensive systems, and in particular, on the so called small systems. Multimicrocanonical Distribution and some of its geometric…
A definition of the nonadditive (nonextensive) conditional entropy indexed by q is presented. Based on the composition law in terms of it, the Shannon-Khinchin axioms are generalized and the uniqueness theorem is established for the Tsallis…
In a recent paper [Phys. Lett. A {\bf335}, 351 (2005)] the authors discussed the equivalence among the various probability distribution functions of a system in equilibrium in the Tsallis entropy framework. In the present letter we extend…
A method is presented that allows exact calculations of fragment multiplicity distributions for a canonical ensemble of non-interacting clusters. Fragmentation properties are shown to depend on only a few parameters. Fragments are shown to…
A method of estimating the joint probability mass function of a pair of discrete random variables is described. This estimator is used to construct the conditional Shannon-R\'eyni-Tsallis entropies estimates. From there almost sure rates of…
Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…
In the framework of the Tsallis nonextensive statistical mechanics we study an assembly of N spins, first in a background magnetic field, and then assuming them to interact via a long-range homogeneous mean field. To take into account the…
Experiments in which thick clay plates and glass rods are fractured have revealed different behavior of fragment mass distribution function in the small and large fragment regions. In this paper we explain this behavior using non-extensive…
There is a conception that Boltzmann-Gibbs statistics cannot yield the long tail distribution. This is the justification for the intensive research of nonextensive entropies (i.e. Tsallis entropy and others). Here the error that caused this…
We construct classes of stochastic differential equations with fluctuating friction forces that generate a dynamics correctly described by Tsallis statistics and nonextensive statistical mechanics. These systems generalize the way in which…
We propose and investigate a simple model which describes the kinetics of aggregation of Brownian particles with stochastic self-replication. An exact solution and the scaling theory are presented alongside numerical simulation which fully…
The information shared among observables representing processes of interest is traditionally evaluated in terms of macroscale measures characterizing aggregate properties of the underlying processes and their interactions. Traditional…
In variational phase-field modeling of brittle fracture, the functional to be minimized is not convex, so that the necessary stationarity conditions of the functional may admit multiple solutions. The solution obtained in an actual…
A mathematical continuum limit of the interaction energy of a random particle chain is shown to yield new insight into the effect of microscopic heterogeneities on macroscopic fracture laws in brittle materials. We derive a formula which…
This work studies time-dependent electromagnetic scattering from obstacles whose interaction with the wave is fully determined by a nonlinear boundary condition. In particular, the boundary condition studied in this work enforces a power…