Related papers: Generalized diffusion and asymptotics induced by T…
We give the tight bounds of Tsallis relative operator entropy by using Hermite-Hadamard's inequality. Some reverse inequalities related to Young inequalities are also given. In addition, operator inequalities for normalized positive linear…
We present our view in a standing debate about the definition and meaning of power-law entropies for continuous systems. Our suggestion is that such arguments should take into account the generalized operations of addition and…
We show that if one uses the invariant form of the Boltzmann-Shannon continuous entropy, it is possible to obtain the generalized Pareto-Tsallis density function, using an appropriate "prior" measure m_{q}(x) and a "Boltzman constraint"…
An axiomatic foundation regarding the entropy for complex systems is established. Missing from decades of research was the requirement that entropy must measure the uncertainty at the informational scale of the maximizing distribution,…
An analysis of the thermodynamic behavior of quantum systems can be performed from a geometrical perspective investigating the structure of the state space. We have developed such an analysis for nonextensive thermostatistical frameworks,…
We investigate the thermodynamic properties of stellar self-gravitating system arising from the Tsallis generalized entropy. In particular, physical interpretation of the thermodynamic instability, as has been revealed by previous…
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…
A formalism is presented to obtain closed evolution equations for asymptotic probability distribution functions of turbulence magnitudes. The formalism is derived for a generic evolution equation, so that the final result can be easily…
The thermodynamic stability condition (TSC) of Tsallis' entropy is revisited. As Ramshaw [Phys. Lett. A {\bf 198} (1995) 119] has already pointed out, the concavity of Tsallis' entropy with respect to the internal energy is not sufficient…
We find the value of constants related to constraints in characterization of some known statistical distributions and then we proceed to use the idea behind maximum entropy principle to derive generalized version of this distributions using…
We review the consequences of intrinsic, nonstatistical temperature fluctuations as seen in observables measured in high energy collisions. We do this from the point of view of nonextensive statistics and Tsallis distributions. Particular…
We expand the Tsallis distribution in a Taylor series of powers of (q-1), where q is the Tsallis parameter, assuming q is very close to 1. This helps in studying the degree of deviation of transverse momentum spectra and other thermodynamic…
The short-time asymptotic behavior of the transition density function of the diffusion process generated by the general Grushin operator will be investigated, by using its explicit expression in terms of expectation. Further the dependence…
We determine a general link between two different solutions of the MaxEnt variational problem, namely, the ones that correspond to using either Shannon's or Tsallis' entropies in the concomitant variational problem. It is shown that the two…
Tsallis q-extension of statistics and fractal generalization of dynamics are two faces of the same physical reality, as well as the Kernel modern complexity theory. The fractal generalization dynamics is based at the multiscale -…
We obtain the asymptotics, as $t + |x| \rightarrow \infty$, of the fundamental solution to the heat equation with a compactly supported potential. It is assumed that the corresponding stationary operator has at least one positive…
Entropy is useful in statistical problems as a measure of irreversibility, randomness, mixing, dispersion, and number of microstates. However, there remains ambiguity over the precise mathematical formulation of entropy, generalized beyond…
The microscopic foundation of the generalized equilibrium statistical mechanics based on the Tsallis entropy is given by using the Gibbs idea of statistical ensembles of the classical and quantum mechanics. The equilibrium distribution…
Consider the one-dimensional elliptic operator given by \begin{equation*} (L_\epsilon f)(x) \;=\; b (x) \, f'(x) \,+\, \epsilon\, a (x)\, f''(x) \;, \end{equation*} where the drift $b\colon R \to R$ and the diffusion coefficient $a\colon R…
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…