We propose a generalized entropy maximization procedure, which takes into account the generalized averaging procedures and information gain definitions underlying the generalized entropies. This novel generalized procedure is then applied to Rényi and Tsallis entropies. The generalized entropy maximization procedure for Rényi entropies results in the exponential stationary distribution asymptot...

Abstract. The Maxwell-Boltzmannian approach to nuclear reaction rate theory is extended to cover Tsallis statistics (Tsallis, 1988) and more general cases of distribution functions. An analytical study of respective thermonuclear functions is being conducted with the help of statistical techniques. The pathway model, recently introduced by Mathai (2005), is utilized for thermonuclear functions ...

In the present paper are analysing the conditions for the validity of the Tsallis Statistics. The same have been doing following the analogy with the traditional case: starting from the microcanonical description of the systems and analysing the scaling properties of the fundamental macroscopic observables in the Thermodynamic Limit. It is shown that the Generalized Legendre Formalism in the Ts...

In the present paper are analyzed the conditions for the validity of the Tsallis Statistics. The same have been done following the analogy with the traditional case: starting from the microcanonical description of the systems and analysing the scaling properties of the fundamental macroscopic observables in the Thermodynamic Limit. It is shown that the Generalized Legendre Formalism in the Tsal...

Within the generalized thermostatistics of Tsallis, we propose for the spin-1⁄2 Ising ferromagnet a transmissivity variable which extends that defined by Tsallis and Levy for thermal magnetic systems. By using this generalized transmissivity as well as duality arguments, we calculate the q-dependence of the critical temperature corresponding to the square lattice, where q is the entropic index ...

There are numerous characterizations of Shannon entropy and Tsallis entropy as measures of information obeying certain properties. Using work by Faddeev and Furuichi, we derive a very simple characterization. Instead of focusing on the entropy of a probability measure on a finite set, this characterization focuses on the “information loss”, or change in entropy, associated with a measure-preser...

We link, by means of a semiclassical approach, the fractional statistics of particles obeying the Haldane exclusion principle to the Tsallis statistics and derive a generalized quantum entropy and its associated statistics. PACS number(s): 05.20.-y, 05.30.-d, 05.40.+j, 05.60.+w The generalized non-extensive statistics and the fractional exclusion statistics have excited great interest because o...