Narrow Results

We study the behavior of the numbers in 412 light curves of cataclysmic variables, x-ray binary systems, galaxies, pulsars, supernovae remnants and other x-ray sources present in the public data collected by the instrument All Sky Monitor on board of the satellite Rossi x-ray timing explorer. The temporal light curves were analyzed applying Newcomb-Benford Law. The first digit of the x-ray light curves coming from astrophysical systems obeys the Newcomb-Benford Law as an intrinsic behavior. The nonextensive statistical mechanics behavior of astrophysical sources seem to be the cause for these sources to obey the Newcomb-Benford law. Some x-ray binary systems, however, do not follow this behavior. These systems obey either a gaussian or a bimodal distribution.

The main studies on pitting consist in proposing Markovian stochastic models, based on the statistics of extreme values and focused on growing the depth of wells, especially the deepest one. We show that a non-Markovian model, described by a nonlinear Fokker–Planck (nFP) equation, properly depicts the time evolution of a distribution of depth values of pits that were experimentally obtained. The solution of this equation in a steady-state regime is a q-Gaussian distribution, i.e. a long-tail probability distribution that is the main characteristic of a nonextensive statistical mechanics. The proposed model, that is applied to data from four inspections conducted on a section of a line of regular water service in power water reactor (PWR) nuclear power plants, is in agreement with experimental results.

To the best of our knowledge, for the first time, the quantum Hall effect (QHE) is considered in thermal non-equilibrium conditions (TNEC) via $q$-algebra. The $q$-algebra is a topological tool that provides a controlling $q$-parameter to approximate theoretical results to the laboratory ones. We obtain the QHE spectrum and $q$-deformed Hall potential (or Hall potential in TNEC) via the density probability current. Because of the Pauli Exclusion Principle, we model the QHE using relativistic Fermi electron gas and the $q$-deformed Fermi–Dirac distribution. We find the dependence of deformed Hall potential to temperature and magnetic field for different geometric $q$-regions. Further, we geometrically prove that the magnitude of the Hall potentials depends on the $q$-regions (i.e. $\left|V_H^{(q>1)}\right|>\left|V_H^{(q=1)}\right|>\left|V_H^{(q<1)}\right|$). We find that for some $q$-amounts, the Landau energy gap on graphene-based materials can be explained in the room-temperature quantum Hall effect (RTQHE). Our method may be applied to analyze new electronic devices based on graphene in TNEQ.

Net proton rapidity distributions are calculated, reproduce very well data obtained at AGS, SPS, RHIC and predict results for the LHC experiment.¹ Presence of non-ideal plasma effects due to strongly coupled plasma in the early stage of relativistic heavy-ion collisions is investigated in the framework of non-conventional statistical mechanics.

We study the applications of nonextensive Tsallis statistics to high energy and hadron physics. These applications include studies of $pp$ collisions, equation of state of QCD, as well as Bose–Einstein condensation. We also analyze the connections of Tsallis statistics with thermofractals, and address some of the conceptual aspects of the fractal approach, which are expressed in terms of the renormalization group equation and the self-energy corrections to the parton mass. We associate these well-known concepts with the origins of the fractal structure in the quantum field theory.

In this letter, we evaluate the effective velocities probability distribution associated to a classical ideal gas in thermodynamical equilibrium, but in the presence of fluctuations of the (inertial) mass parameter of the molecules. We obtain in the context of linear response theory of the mass fluctuations and the usual Boltzman framework the combined statistics of Boltzman and Tsallis as an outcome of the study for our effective Fractal gas distribution probability. This result explains from first principles the Tsallis-inverse power law distribution previously only speculated on in the literature. Finally, we give a new mathematical proof of the Boltzman ergodic theorem in classical statistics mechanics.

In this paper, we investigate the fluctuation of the energy in the canonical ensemble in the setting of unnormalized q-expectation value theory in Tsallis statistics. After obtaining the general expression, we compare it with the energy fluctuation deduced from the generalized fluctuation-dissipation theorem. The results show that they are the same. Then, we take the classical ideal gas model as an example to explore the energy fluctuations of it. It shows that if the value of q is not in the vicinity of unity, the relative fluctuation of the energy is large. Thus, the energy in the canonical ensemble greatly deviates from the mean value.

In this work, we present the coexistence of self-organized criticality (SOC) and low-dimensional chaos at solar activity with results obtained by using the intermittent turbulence theory, the nonextensive q-statistics of Tsallis as well as the singular value decomposition analysis. Particularly, we show the independent dynamics of sunspot system related to the convection zone of sun and the solar flare system related to the lower solar atmosphere. However, both systems reveal nonequilibrium phase transition process from a high-dimensional intermittent turbulence state with SOC profile to a low-dimensional and chaotic intermittent turbulence state. The high-dimensional SOC state in both dynamical systems underlying the sunspot and solar flare signal is related with low q-values and low Flatness values (F) while the low-dimensional chaotic state is related with higher q-values and Flatness F-values. The higher q- and F-values reveal strong character of long-range correlations corresponding to system-wide global process while the lower q- and F-values reveal scale invariant local avalanche process. Also, the high-dimensional SOC state corresponds to second order nonequilibrium critical phase transition process while the low-dimensional chaotic state corresponds to first order nonequilibrium phase transition process. Finally, for both dynamics underlying sunspot index and solar flare, at both states of phase transition process, the multiscale and multifractal character was found to exist but with different profile or strength.

Strong evidence is provided for significant far from equilibrium complex processes in the seismogenic layer of the North Aegean region (Greece), after applying modern nonlinear methods to various seismicity time series. The data used are subsets of the regional catalogue compiled in the central Seismological Station of Geophysics Department, Aristotle University of Thessaloniki and concern 4367 earthquakes of magnitude greater than 3.8, which took place during the period of 1968–2008. We present results, derived from the application of nonlinear algorithms, concerning the estimation of correlation dimension, mutual information, largest Lyapunov exponent, flatness coefficient and q-value which correspond to Tsallis nonextensive statistics. These quantities are estimated for two seismic time series corresponding to the basic focal parameters of earthquakes, namely origin time and magnitude. The obtained results can be associated with novel far from equilibrium complex dynamics such as low dimensional chaos, Self Organized Criticality (SOC) and intermittent turbulence. Furthermore, in this study, new information is provided about the nonlinear turbulent character of the Hellenic lithospheric dynamics related to the Tsallis nonextensive statistical theory. Our analysis indicates the coexistence of two different lithospheric processes, one low dimensional (chaotic) and the other high dimensional (SOC), revealing the strongly turbulent character of the Greek lithospheric system. In particular, the low dimensional chaotic process corresponds to the temporal manifestation of earthquakes, whereas the high dimensional nonlinear (SOC) process corresponds to the burst energy releases, a result that has significant implications concerning the ability of earthquake prediction.

The effect of the non-extensive form of statistical mechanics proposed by Tsallis on the formation of a quark-gluon plasma (QGP) has been recently investigated in Ref. 1. The results show that for small deviations (≈ 10%) from Boltzmann–Gibbs (BG) statistics in the QGP phase, the critical temperature for the formation of a QGP does not change substantially for a large variation of the chemical potential. In the present paper we use the extensive κ-deformed statistical mechanics constructed by Kaniadakis to represent the constituents of the QGP and compare the results with Ref. 1.

The nonextensive behavior of entropy is exploited to explain the regularity in multiplicity distributions in $e^{+}{e}^{-}$ collisions at high energies. The experimental data are analyzed by using Tsallis $q$-statistics. We propose a new approach of applying Tsallis $q$-statistics, wherein the multiplicity distribution is divided into two components; two-jet and multijet components. A convoluted Tsallis distribution is fitted to the data. It is shown that this method gives the best fits which are several orders better than the conventional fit of Tsallis distribution.

We give a survey on sequential structures of escort distributions and sequential structures of statistical manifolds. For a deformed exponential family, the notion of escort distribution has been introduced in nonextensive statistical physics, and an expectation with respect to its escort distribution has been discussed. The author introduced a sequential structure of escort distributions, and discussed statistical manifold structures derived from sequential escort distributions. In this paper, after reviewing basic facts on information geometry, we study sequential structures of statistical manifolds. A divergence function which is a distance-like function on a statistical manifold plays an important role in this framework.

Geometry for q-exponential families is studied in this paper. A q-exponential family is a set of probability distributions, which is a natural generalization of the standard exponential family. A q-exponential family has information geometric structure and a dually flat structure. To describe these relations, generalized conformal structures for statistical manifolds are studied in this paper. As an application of geometry for q-exponential families, a geometric generalization of statistical inference is also studied.

A q-normal distribution is a natural generalization of the standard normal distribution, which is introduced in Tsallis nonextensive statistical mechanics. In the case 1 < q < 3, the set of q-normal distributions can be regarded as a two dimensional manifold, and the manifold naturally has two kinds of Riemannian metrics, the Fisher metric and the q-Fisher metric. In this paper, geometry of these Riemannian metrics is discussed, and it is shown that these two metrics are conformally equivalent. In addition, it is shown that the set of q-normal distributions with the Fisher metric is a space of constant negative sectional curvature k = -q/(3 - q).

We give a survey on geometry of statistical manifolds in terms of estimating functions. A statistical model naturally has a statistical manifold structure. In particular, a q-exponential family which is a generalization of an exponential family admits several statistical manifold structures. An estimating function can be regarded as a tangent vector of a statistical model, and it gives rise to dualistic structures on a statistical manifold. In this paper, we construct statistical manifold structures on statistical models and divergence functions from the viewpoint of estimating functions. We also study geometry of nonintegrable estimating functions.