This note presents explicitly a strong connection between the Tsallis thermodynamics and the so-called prospect theory introduced to take into account agent’s decisions under risk. Moreover, using the cumulative prospect theory adapted here for a continuous framework, we show that if the Tsallis parameter q belongs to the interval [0,1], then the prospect theory requirement that extreme events ...

Superstatistics is a ‘statistics of a statistics’ relevant for driven nonequilibrium systems with fluctuating intensive parameters. It contains Tsallis statistics as a special case. We show that probability density functions of velocity differences and accelerations measured in Eulerian and Lagrangian turbulence experiments are well reproduced by simple superstatistics models. We compare fits o...

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 derived. Notions of additivity, extensivity and homogeneity are clarified. The relation between mean code lengths in coding theory and various expressions for ...

We consider the self-similar phase space with reduced fractal dimension d being distributed within domain 0 < d < 1 with spectrum f(d). Related thermostatistics is shown to be governed by the Tsallis’ formalism of the non-extensive statistics, where role of the non-additivity parameter plays inverted value τ̄(q) ≡ 1/τ(q) > 1 of the multifractal function τ(q) = qd(q)− f(d(q)), being the specific ...

We derive analogs of the Jarzynski equality and Crooks relation to characterize the nonequilibrium work associated with changes in the spring constant of an overdamped oscillator in a quadratically varying spatial temperature profile. The stationary state of such an oscillator is described by Tsallis statistics, and the work relations for certain processes may be expressed in terms of q-exponen...

The generalized binomial distribution in Tsallis statistics (power-law system) is explicitly formulated from the precise q-Stirling’s formula. The α-divergence (or q-divergence) is uniquely derived from the generalized binomial distribution in the sense that when α → −1 (i.e., q → 1) it recovers KL divergence obtained from the standard binomial distribution. Based on these combinatorial conside...

The Tsallis measure of mutual information is combined with the simultaneous perturbation stochastic approximation algorithm to register images. It is shown that Tsallis entropy can improve registration accuracy and speed of convergence, compared with Shannon entropy, in the calculation of mutual information. Simulation results show that the new algorithm achieves up to seven times faster conver...