Related papers: A composition of different $q$ nonextensive system…
It is pointed out that the constraint to be imposed to the maximization of the entropy for processes outside the class of thermodynamical systems, is generally not well defined. In fact, any probability distribution can be derived from…
Examples of joint probability distributions are studied in terms of Tsallis' nonextensive statistics both for correlated and uncorrelated variables, in particular it is explicitely shown how correlations in the system can make Tsallis…
We present an argument justifying the origin of the escort distributions used in calculations involving the Tsallis entropy. We rely on an induced hyperbolic Riemannian metric reflecting the generalized composition property of the Tsallis…
We have discussed the Tsallis entropy in finite $N$-unit nonextensive systems, by using the multivariate $q$-Gaussian probability distribution functions (PDFs) derived by the maximum entropy methods with the normal average and the…
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)…
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…
We show that the function beta(E) derived from the density of states of a constant heat capacity reservoir coupled to some system of interest is not identical to the physically measurable (transitive) temperature. There are, however,…
The Tsallis entropy, which possesses non-extensive property, is derived from the first principle employing the non-extensive Hamiltonian or the $q$-deformed Hamiltonian with the canonical ensemble assumption in statistical mechanics. Here,…
We show that the non-additivity relation of the Tsallis entropies in nonextensive statistical mechanics has a simple physical interpretation for systems with fluctuating temperature or fluctuating energy dissipation rate. We also show that…
We comment on some open questions and theoretical peculiarities in Tsallis nonextensive statistical mechanics. It is shown that the theoretical basis of the successful Tsallis' generalized exponential distribution shows some worrying…
The Tsallis entropy, which is a generalization of the Boltzmann-Gibbs entropy, plays a central role in nonextensive statistical mechanics of complex systems. A lot of efforts have recently been made on establishing a dynamical foundation…
The Tsallis entropy is shown to be an additive entropy of degree-q that information scientists have been using for almost forty years. Neither is it a unique solution to the nonadditive functional equation from which random entropies are…
We show that Abe's general pseudoadditivity for entropy prescribed by thermal equilibrium in nonextensive systems holds not only for entropy, but also for energy. The application of this general pseudoadditivity to Tsallis entropy tells us…
The original canonical ensemble formalism for the nonextensive entropy thermostatistics is reconsidered. It is shown that the unambiguous connection of the statistical mechanics with the equilibrium thermodynamics is provided if the…
We show that Tsallis ensemble of power-law distributions provides a mechanical model of nonextensive equilibrium thermodynamics for small interacting Hamiltonian systems, i.e., using Boltzmann's original nomenclature, we prove that it is an…
We studied the thermodynamic quantities and the probability distribution, expressing the probability distribution as a function of the energy, in the canonical ensemble within the framework of the Tsallis statistics, which is characterized…
Tsallis' non-extensive entropy $S_q$ enables us to treat both a power and exponential evolutions of underlying microscopic dynamics on equal footing by adjusting the variable entropic index $q$ to proper one $q^*$. We propose an alternative…
Quite general, analytical (both exact and approximate) forms for discrete probability distributions (PD's) that maximize Tsallis entropy for a fixed variance are here investigated. They apply, for instance, in a wide variety of scenarios in…
The properties of the nonextensive parameter q and the Tsallis distribution for self-gravitating systems are studied. A mathematical expression of q is deduced based on the generalized Boltzmann equation, the q-H theorem and the generalized…
Experimental particle spectra can be successfully described by power-law tailed energy distributions characteristic to canonical equilibrium distributions associated to R\'enyi's or Tsallis' entropy formula - over a wide range of energies,…