A.R. Plastino

A Maxwellian path to the q-nonextensive velocity distribution function

Abstract Maxwells first derivation of the equilibrium distribution function for a dilute gas is generalized in the spirit of the nonextensive q-statistics proposed by Tsallis. As an application, the q-Doppler broadening of spectral lines due to the random thermal motion of the radiating atoms is derived.

Information gain within nonextensive thermostatistics

We discuss the information theoretical foundations of the Kullback information gain, recently generalized within a nonextensive thermostatistical formalism. General properties are studied and, in particular, a consistent test for measuring the degree of correlation between random variables is proposed. In addition, minimum entropy distributions are discussed and the H-theorem is proved within the generalized context.

Brain electrical activity analysis using wavelet-based informational tools

The traditional way of analyzing brain electrical activity, on the basis of Electroencephalography (EEG) records, relies mainly on visual inspection and years of training. Although it is quite useful, of course, one has to acknowledge its subjective nature that hardly allows for a systematic protocol. In order to overcome this undesirable feature, a quantitative EEG analysis has been developed over the years that introduces objective measures, reflecting not only the characteristics of the brain activity itself but also giving clues concerning the underlying associated neural dynamics. The processing of information by the brain is reflected in dynamical changes of the electrical activity in (i) time, (ii) frequency, and (iii) space. Therefore, the concomitant studies require methods capable of describing the qualitative variation of the signal in both time and frequency. In the present work we introduce new information tools based on the wavelet transform for the assessment of EEG data as adapted to a non-extensive scenario.

Multiqubit systems : highly entangled states and entanglement distribution

A comparison is made of various searching procedures, based upon different entanglement measures or entanglement indicators, for highly entangled multiqubits states. In particular, our present results are compared with those recently reported by Brown et al (J. Phys. A: Math. Gen. 2005 38 1119). The statistical distribution of entanglement values for the aforementioned multiqubit systems is also explored.

Rènyi entropies and Fisher informations as measures of nonextensivity in a Tsallis setting

We study nonextensive statistical scenarios a la Tsallis with reference to Fisher’s information and Renyi’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 customary procedure. A connection between the information measures of Fisher’s and Renyi’s is found. We show that Fisher’s measure for translation families remains additive even in a non-extensive Tsallis setting.

Schrödinger link between nonequilibrium thermodynamics and Fisher information

It is known that equilibrium thermodynamics can be deduced from a constrained Fisher information extemizing process. We show here that, more generally, both nonequilibrium and equilibrium thermodynamics can be obtained from such a Fisher treatment. Equilibrium thermodynamics corresponds to the ground-state solution, and nonequilibrium thermodynamics corresponds to excited-state solutions, of a Schrödinger wave equation (SWE). That equation appears as an output of the constrained variational process that extremizes Fisher information. Both equilibrium and nonequilibrium situations can thereby be tackled by one formalism that clearly exhibits the fact that thermodynamics and quantum mechanics can both be expressed in terms of a formal SWE, out of a common informational basis. As an application, we discuss viscosity in dilute gases.

On the use and abuse of Newton's second law for variable mass problems

We clarify some misunderstandings currently found in the literature that arise from improper application of Newtons second law to variable mass problems. In the particular case of isotropic mass loss, for example, several authors introduce a force that actually does not exist.

Tsallis entropy and quantal distribution functions

In connection with Tsallis generalized statistical mechanics, we discuss the associated quantal distribution functions recently advanced by Buyukkilic et al. [Phys. Lett. A 197 (1995) 209] and show, by recourse to elementary considerations, that they can be regarded only as rather rough approximations. Numerical calculations in a simple model show that, for some values of the temperature and the chemical potential, results obtained with the approximate distributions appreciably deviate from the exact ones.

Nonextensive Statistical Mechanics: Some Links with Astronomical Phenomena

A variety of astronomical phenomena appear to not satisfy the ergodic hypothesis in the relevant stationary state, if any. As such, there is no reason for expecting the applicability of Boltzmann–Gibbs (BG) statistical mechanics. Some of these phenomena appear to follow, instead, nonextensive statistical mechanics. In the same manner that the BG formalism is based on the entropy SBG=−k∑ipi ln pi, the nonextensive one is based on the form Sq=k(1 −∑ipiq)/(q− 1) (with S1=SBG). The stationary states of the former are characterized by an exponential dependence on the energy, whereas those of the latter are characterized by an (asymptotic) power law. A brief review of this theory is given here, as well as of some of its applications, such as the solar neutrino problem, polytropic self-gravitating systems, galactic peculiar velocities, cosmic rays and some cosmological aspects. In addition to these, an analogy with the Keplerian elliptic orbits versus the Ptolemaic epicycles is developed, where we show that optimizing Sq with a few constraints is equivalent to optimizing SBG with an infinite number of constraints.

Robe's restricted three-body problem revisited

Robes restricted three-body problem is reanalyzed with a view to incorporate a new assumption, namely that the configuration of the fluid body is that described by an hydrostatic equilibrium figure (Roches ellipsoid). In the concomitant gravitational field a full treatment of the buoyancy force is given. The pertinent equations of motion are derived, the linear stability of the equilibrium solution is studied and the connection between the effect of the buoyancy forces and a perturbation of the Coriolis force is pointed out.