In 1982, Tsallis derived a formula which proposed an exact value of 0.522372078 . . . for the bond percolation threshold of the kagome lattice. We use the substitution method, which is based on stochastic ordering, to compare the probability distribution of connections in the homogeneous bond percolation model on the kagome lattice to those of an exactly-solved inhomogeneous bond percolation mo...

We have discussed dynamical properties of the Tsallis entropy and the generalized Fisher information in nonextensive systems described by the Langevin model subjected to additive and multiplicative noise. Analytical expressions for the timedependent Tsallis entropy and generalized Fisher information have been obtained with the use of the q-moment approach to the Fokker-Planck equation developed...

In this work, we develop a multilevel edge detection method based on the Kapur and Tsallis entropies. The multilevel thresholding approach gives rise to an NP-hard optimization problem. We have used the Classical Genetic Algorithm (CGA) and the Quantum Genetic Algorithm (QGA) to solve this problem. The performance of the QGA has been tested on ten sample images and it is shown that the QGA outp...

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 which the system is characterized by a series of discrete eigenstates of the Hamiltonian. Using these discrete PD’s as “weights” leads to density operators ...

In this paper we consider the Monte Carlo simulated annealings based on the Tsallis and threshold acceptance probabilities. This is done by applying them to the 2D system of many particles both interacting among themselves by a dipole–dipole potential and affected by the gravitational force. Our results confirm that for large and negative values of the Tsallis parameter q, the generalized metho...

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 ...