We investigate the main features of a pilot wave representation of the nonlinear Schrödinger equation recently advanced by Nobre, Rego-Monteiro, and Tsallis (NRT) on the basis of Tsallis q-thermo-statistical formalism. The present approach sheds new light upon the NRT equation. In particular,...

We give an exact information-theory treatment of the n-dimensional black-body radiation process in a non-extensive scenario. We develop a q-generalization of the laws of (i) Stefan–Boltzmann, (ii) Planck, and (iii) Wien, and show that conventional, canonical results are obtained at...

We study mixed quantum states described by a statistical operator ρ̂=B̂n,n real, with B̂ quadratic in the position and momentum operators. These states are parameterized as density matrices exhibiting the maximum q-entropy (q-MaxEnt) form. They can be regarded as the mixed-state counterpart...

An exact analysis of the N-dimensional blackbody radiation process in a nonextensive à la Tsallis scenario is performed for values of the nonextensive's index in the range (0q1). The recently advanced “Optimal Lagrange Multipliers” technique has been employed. The results are consistent...

We study nonextensive statistical scenarios à la Tsallis with reference to Fisher’s information and Rènyi’s entropy. A new way of evaluating Tsallis’ generalized expectation values is examined within such a context, and is shown to lead to a much better Cramer–Rao bound than the...

Given a closed system described via an amplitude function ψ(x), what is its level of order? We consider here a quantity R defined by the property that it decreases (or stays constant) after the system is coarse grained. It was recently found that (i) this quantity exhibits a series of...

We revisit the nonextensive treatment advanced by Tsallis, et al. (Physica A 261 (1998) 534) in order to perform a rather exhaustive study of its properties and compare them with the earlier formalism devised by Curado and Tsallis (J. Phys. A 24 (1991) L69). Some interesting features are in this...

We highlight the potentiality of a special Information Theory (IT) approach in order to unravel the intricacies of nonlinear dynamics, the methodology being illustrated with reference to the logistic map. A rather surprising dynamic feature→plane-topography map becomes available.

We prove that the gravitational binding energy Ω of a self gravitating system described by a mass density distribution ρ(x) admits an upper bound B[ρ(x)] given by a simple function of an appropriate, non-additive Tsallis’ power-law entropic functional Sq evaluated on the density ρ. The...

We show that effective masses in nonrelativistic quantum mechanics arise in a natural fashion from the Frieden and Soffer's Principle of Extremal Information (EPI) when the mean values of operators involving the momentum p̂ and exhibiting the form p̂f(x̂)p̂ are included as constraints. A...