We revisit the first law of thermodynamics for nonextensive statistics by recourse to the optimal Lagrange multipliers (OLM) formalism. We show firstly that information theory allows one to obtain thermodynamics' first law in a general ensemble by dealing just with variations in the density...

Tsallis’ non-extensive thermostatistics (Tsallis et al., Physica A 261 (1998) 534; Tsallis, in: Abe, Okamoto (Eds.), Nonextensive Statistical Mechanics and its Applications, Lecture Notes in Physics, Springer, Berlin, 2000; Tsallis, Braz. J. Phys. 29 (1991) 1; Plastino and Plastino, in: Ludeña (Ed.),...

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.