On the fractal characterization of Paretian Poisson processes

Paretian Poisson processes are Poisson processes which are defined on the positive half-line, have maximal points, and are quantified by power-law intensities. Paretian Poisson processes are elemental in statistical physics, and are the bedrock of a host of power-law statistics ranging from Pareto’s law to anomalous diffusion. In this paper we establish evenness-based fractal characterizations of Paretian Poisson processes. Considering an array of socioeconomic evenness-based measures of statistical heterogeneity, we show that: amongst the realm of Poisson processes which are defined on the positive half-line, and have maximal points, Paretian Poisson processes are the unique class of ‘fractal processes’ exhibiting scale-invariance. The results established in this paper are diametric to previous results asserting that the scale-invariance of Poisson processes–with respect to physical randomness-based measures of statistical heterogeneity–is characterized by exponential Poissonian intensities.     

Thermostatistics of the g-on gas

In this study, the particles of the quantum gases, namely bosons and fermions are called g-ons by using the parameter of the fractional exclusion statistics g, where . With this point of departure, the distribution function of the g-on gas is obtained by the variational, steepest descent and statistical methods. The distribution functions which are found by means of these three methods are compared. It is shown that the thermostatistical formulations of quantum gases can be unified. By suitable choices of g, standard relations of statistical mechanics of the Bose and Fermi systems are recovered.Received: 26 March 2003, Published online: 22 September 2003PACS: 05.20.-y Classical statistical mechanics - 03.65.-w Quantum mechanics     

噪声信号特征量分布函数相似特性的研究

应用高速数据采集卡,记录悬浮颗粒计数光电传感器本底噪声信号序列值,研究噪声信号独立特征量, 如信号幅度极值、上升沿幅值、下降沿幅值、极值时序间隔,以及特征量乘积值等统计分布规律. 结果表明,上述独立特征量均能够与以自然数l为自变量的对数正态分布函数高度符合, 噪声信号特征量统计分布呈现出高度相似特征.基于这种统计相似性,还可推出噪声信号不同特征量对应的统计自变量之间的幂函数变换关系.噪声信号特征量统计分布函数相似性可理解为噪声信号集合统计分形特性的一种表现.     

Analyzing statistical errors for measurements of Brillouin scattering by the edge technique

The signal estimate and statistical uncertainty in the measurements of Brillouin shift by the edge technique are analyzed in detail. A signal to noise parameter factor is introduced and is used to discuss the statistical uncertainty in the measurements. The effect of signal averaging and the effect due to background noise are analyzed. Some helpful conclusions are predicted. PACS 42.68.Wt; 42.79.Qx; 78.35.+c     

Statistical mechanics and the ontological interpretation

To complete our ontological interpretation of quantum theory we have to conclude a treatment of quantum statistical mechanics. The basic concepts in the ontological approach are the particle and the wave function. The density matrix cannot play a fundamental role here. Therefore quantum statistical mechanics will require a further statistical distribution over wave functions in addition to the distribution of particles that have a specified wave function. Ultimately the wave function of the universe will he required, but we show that if the universe in not in thermodynamic equilibrium then it can he treated in terms of weakly interacting large scale constituents that are very nearly independent of each other. In this way we obtain the same results as those of the usual approach within the framework of the ontological interpretation.Professor D. Bohm died on 28 October 1992, shortly after this paper was completed.     

Statistical thermodynamics of the liquid surface

The current theoretical situation regarding the structure of the liquid-vapour transition zone and the associated thermodynamic surface properties of simple liquids is reviewed. The thermodynamic and statistical mechanical treatments of the surface structure are assessed, and it is concluded that the former approach has limiting validity only as T→T _crit. Liquid metal systems are discussed, together with the recent experimental evidence supporting the existence of stable density oscillations at the surfaces of certain liquid metals. The liquid inert gas systems, argon in particular, are considered in some detail, and a discussion of the statistical thermodynamics of the liquid ⁴He surface is given.     

On the features of statistical behaviour of the O(<Superscript>3</Superscript>P)+HCl(v = 2, j = 1,6,9) → OH + Cl reaction

The O(³P)+HCl(v = 2, j = 1,2,6) → OH+Cl reaction has been theoretically studied by means of a statistical quantum model and an exact time independent method. Although the statistical method is based on the assumption of a complex-forming mechanism, which seems not be the case for this process, the OH(v' = 1) product channel, specially when the HCl reagent is rotationally excited to j = 1, exhibits features of statistical behaviour. In fact, experimental rotational distributions and previous exact quantum mechanical integral cross sections are well described by present statistical results. A possible explanation for this feature is given in terms of the existence of a dynamical well which strongly correlates the initial (v = 2, j = 1) state with the v'=1 final manifold. The method is not capable though to account for the vibrational inversion seen for this process and results obtained for the vibrationless OH formation are in clear disagreement with previous findings.     

A practical prediction method for the stochastic insulation effect of a sound barrier with arbitrary random noise excitation

A sound barrier is often used as a typical noise control device to modify sound propagation characteristics. Also, statistical parameters such as the median value of sound level, $\text{L}{}_{\mathrm{x}}$, as well as the lower order statistical values of sound energy or level, are important for noise evaluation and regulation problems. In this paper, a new trial of statistical prediction for the stochastic insulation effect of a sound barrier is proposed in a special case where the insulation system parameters have to be improved, especially from a methodological viewpoint. Moreover, the improved probability density function (pdf) of output response corresponding to the above parameter change is expressed in the general form of a statistical series expansion taking the original pdf before the system improvement as the first expansion term. The experimental results of applying it in trial to the actual noise data are in good agreement with theory.     

Thermodynamics is more powerful than the role to it reserved by Boltzmann-Gibbs statistical mechanics

We briefly review the connection between statistical mechanics and thermodynamics. We show that, in order to satisfy thermo-dynamics and its Legendre transformation mathematical frame, the celebrated Boltzmann-Gibbs (BG) statistical mechanics is sufficient but not necessary. Indeed, the N →∞ limit of statistical mechanics is expected to be consistent with thermodynamics. For systems whose elements are generically independent or quasi-independent in the sense of the theory of probabilities, it is well known that the BG theory (based on the additive BG entropy) does satisfy this expectation. However, in complete analogy, other thermostatistical theories (e.g., q-statistics), based on nonadditive entropic functionals, also satisfy the very same expectation. We illustrate this standpoint with systems whose elements are strongly correlated in a specific manner, such that they escape the BG realm.     

Evolution of the q-entropy and energy dissipation during irreversible processes in nonextensive systems

Evolution of the Havrda-Charvat-Daroczy entropy and energy dissipation during irreversible processes in open nonextensive systems is considered. The kinetic equation and statistical criterion of nonextensive system evolution are presented. Nonequilibrium statistical and variational methods of derivation of the kinetic equation with a source being a fluctuation of a physical quantity are described. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 35–41, February, 2006.     

Does the simple statistical model describe delayed neutron emission?: The cases of 85As, 87Br, 135Sb and 137I

Delayed neutron spectra and branching ratios to excited states in final nuclei calculated with the statistical model are compared to experimental data for the decay of ⁸⁷Br, ¹³⁷I, ⁸⁵As and ¹³⁵Sb. For the first two precursors, the calculations support the experimental β-strength functions reported previously. For the latter two, it is shown that the statistical model cannot simultaneously reproduce both spectra and branching ratios for any choice of β-strength function when all levels populated by neutron emission are included in the calculations. The comparisons demonstrate that partial widths for neutron emission are not compatible with optical-model transmission coefficients. We conclude, as pointed out previously, that structure effects in the energy range probed by delayed neutron emission are not averaged out to the extent required by the statistical assumptions.     

A fresh look at the statistical bootstrap model

A new interpretation of the statistical bootstrap model is proposed, on the basis of which the statistical bootstrap equation is modified. A deep relationship between the statistical bootstrap model and the Pomeranchuk model for multiple hadron production is established and as a result the significance of the volume V in the statistical bootstrap model is elucidated.     

Statistical isotropy of the cosmic microwave background

The breakdown of statistical homogeneity and isotropy of cosmic perturbations is a generic feature of ultra-large scale structure of the cosmos, in particular, of non-trivial cosmic topology. The statistical isotropy (SI) of the cosmic microwave background temperature fluctuations (CMB anisotropy) is sensitive to this breakdown on the largest scales comparable to, and even beyond the cosmic horizon. We propose a set of measures,K _l (l = 1, 2,3,...) which for non-zero values indicate and quantify statistical isotropy violations in a CMB map. We numerically compute the predictedK _l spectra for CMB anisotropy in flat torus universe models. Characteristic signatures of different models in theK _l spectrum are noted.     

Temperature dependent effects and statistical gamma-ray multiplicities in the147Sm(3He, α)146Sm reaction

Gamma-ray multiplicities associated with the statistical decay from highly excited states in¹⁴⁶Sm are calculated. The formalism, which accounts for the temperature dependence of the level density parameter, is applied to the analysis of the statistical gamma decay from states populated by the (³He, α) reaction. The results are found to be in a reasonable agreement with the experimental data.     

A mathematical structure for the generalization of conventional algebra

An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic or statistical systems. It is shown that, from a mathematical point of view, any bijective function can in principle be used to formulate an algebra in which the conventional algebraic rules are generalized.      

Four mathematical expressions of the uncertainty relation

The uncertainty relation in quantum mechanics has been explicated sometimes as a statistical relation and at other times as a relation concerning precision of simultaneous measurements. In the present paper, taking the indefiniteness of individual experiments as represented by diameters of Borel sets in projection-valued measure, we mathematically distinguish four expressions, two statistical and two concerning simultaneous measurements, of the uncertainty relation, study their interrelations, and prove that they are nonequivalent to each other and to the eigenvector condition (EV) in infinite-dimensional Hilbert space.     

A Statistical Study of the Correlation between Geomagnetic Storms and M ≥ 7.0 Global Earthquakes during 1957–2020

In order to find out whether the geomagnetic storms and large-mega earthquakes are correlated or not, statistical studies based on Superposed Epoch Analysis (SEA), significance analysis, and Z test have been applied to the Dst index data and M ≥ 7.0 global earthquakes during 1957–2020. The results indicate that before M ≥ 7.0 global earthquakes, there are clearly higher probabilities of geomagnetic storms than after them. Geomagnetic storms are more likely to be related with shallow earthquakes rather than deep ones. Further statistical investigations of the results based on cumulative storm hours show consistency with those based on storm days, suggesting that the high probability of geomagnetic storms prior to large-mega earthquakes is significant and robust. Some possible mechanisms such as a reverse piezoelectric effect and/or electroosmotic flow are discussed to explain the statistical correlation. The result might open new perspectives in the complex process of earthquakes and the Lithosphere-Atmosphere-Ionosphere (LAI) coupling.     

Finite-Temperature Field Theory on the Light Front

The formulation of statistical physics using light-front quantization, instead of conventional equal-time boundary conditions, has important advantages for describing relativistic statistical systems, such as heavy ion collisions. We develop light-front field theory at finite temperature and density with special attention to quantum chromodynamics. First, we construct the most general form of the statistical operator allowed by the Poincaré algebra. In light-front quantization, the Green’s functions of a quark in a medium can be defined in terms of just two-component spinors and do not lead to doublers in the transverse directions. Since the theory is non-local along the light cone, we use causality arguments to construct a solution to the related zero-mode problem. A seminal property of light-front Green’s functions is that they are related to parton densities in coordinate space. Namely, the diagonal and off-diagonal parton distributions measured in hard scattering experiments can be interpreted as light-front density matrices.     

Results from the CMS collaboration on the search of heavy dilepton and diphoton resonances

A survey of the results on the search of new heavy resonances decaying into muon, electron, or photon pairs in the CMS experiment at proton beams of the LHC in the run of 2015 for the total center of mass energy √s = 13 TeV is presented. The limits for heavy resonance production cross sections are set. Excess of diphoton events in the region of mass spectra near 750 GeV with a local statistical significance of 3.4 σ and a global statistical significance of 1.6 σ is observed.     

Is Nonlocality Responsible for the Violation of Bell’s Inequalities?

Bell’s theorem has been widely argued to show that some of the predictions of quantum mechanics which are obtained by applying the Born’s rule to a class of entangled states, are not compatible with any local-causal statistical model, via the violation of Bell’s inequalities. On the other hand, in the previous works, we have shown that quantum dynamics and kinematics are emergent from a statistical model that is singled out uniquely by the principle of Locality. Here we shall show that the local-causal model supports entangled states and give the statistical origin of their generation. We then study the Stern-Gerlach experiment to show that the Born’s rule can also be derived as a mathematical theorem in the local-causal model. These results lead us to argue that nonlocality is not responsible for the quantum mechanical and most importantly experimental violation of Bell’s inequalities. The source(s) of violation has to be sought somewhere else.