Pathway Model, Superstatistics, Tsallis Statistics, and a Generalized Measure of Entropy

The pathway model of Mathai (2005) is shown to be inferable from the maximization of a certain generalized entropy measure. This entropy is a variant of the generalized entropy of order 'alpha', considered in Mathai and Rathie (1975), and it is also associated with Shannon, Boltzmann-Gibbs, Renyi, Tsallis, and Havrda-Charvat entropies. The generalized entropy measure introduced here is also shown to haveinteresting statistical properties and it can be given probabilistic interpretations in terms of inaccuracy measure, expected value, and information content in a scheme. Particular cases of the pathway model are shown to be Tsallis statistics (Tsallis, 1988) and superstatistics introduced by Beck and Cohen (2003). The pathway model's connection to fractional calculus is illustrated by considering a fractional reaction equation.Comment: LaTeX, 22 page

Generalized Measure of Entropy, Mathai's Distributional Pathway Model, and Tsallis Statistics

The pathway model of Mathai (2005) mainly deals with the rectangular matrix-variate case. In this paper the scalar version is shown to be associated with a large number of probability models used in physics. Different families of densities are listed here, which are all connected through the pathway parameter 'alpha', generating a distributional pathway. The idea is to switch from one functional form to another through this parameter and it is shown that basically one can proceed from the generalized type-1 beta family to generalized type-2 beta family to generalized gamma family when the real variable is positive and a wider set of families when the variable can take negative values also. For simplicity, only the real scalar case is discussed here but corresponding families are available when the variable is in the complex domain. A large number of densities used in physics are shown to be special cases of or associated with the pathway model. It is also shown that the pathway model is available by maximizing a generalized measure of entropy, leading to an entropic pathway. Particular cases of the pathway model are shown to cover Tsallis statistics (Tsallis, 1988) and the superstatistics introduced by Beck and Cohen (2003).Comment: LaTeX, 13 pages, title changed, introduction, conclusions, and references update

On the Cut-Off Prescriptions Associated with Power-Law Generalized Thermostatistics

We revisit the cut-off prescriptions which are needed in order to specify completely the form of Tsallis' maximum entropy distributions. For values of the Tsallis entropic parameter $q>1$ we advance an alternative cut-off prescription and discuss some of its basic mathematical properties. As an illustration of the new cut-off prescription we consider in some detail the $q$-generalized quantum distributions which have recently been shown to reproduce various experimental results related to high $T_c$ superconductors

Deviation of the Nucleon Shape From Spherical Symmetry: Experimental Status

In this brief pedagogical overview the physical basis of the deviation of the nucleon shape from spherical symmetry will be presented along with the experimental methods used to determine it by the gamma* p -> Delta reaction.The fact that significant non-spherical electric(E2) and Coulomb quadrupole(C2) amplitudes have been observed will be demonstrated. These multipoles for the N,Delta system as a function of Q^2 from the photon point through 4 GeV^2 have been measured with modest precision. Their precise magnitude remains model dependent due to the contributions of the background amplitudes, although rapid progress is being made to reduce these uncertainties. A discussion of what is required to perform a model independent analysis is presented. All of the data to date are consistent with a prolate shape for the proton (larger at the poles) and an oblate shape(flatter at the poles) for the Delta. It is suggested here that the fundamental reason for this lies in the spontaneous breaking of chiral symmetry in QCD and the resulting, long range(low Q^2), effects of the pion cloud. This verification of this suggestion, as well as a more accurate measurement of the deviation from spherical symmetry, requires further experimental and theoretical effort.Comment: 8 pages, 8 figures, enhanced conference proceeding

Experimental Lagrangian Acceleration Probability Density Function Measurement

We report experimental results on the acceleration component probability distribution function at $R_\lambda = 690$ to probabilities of less than $10^{-7}$. This is an improvement of more than an order of magnitude over past measurements and allows us to conclude that the fourth moment converges and the flatness is approximately 55. We compare our probability distribution to those predicted by several models inspired by non-extensive statistical mechanics. We also look at acceleration component probability distributions conditioned on a velocity component for conditioning velocities as high as 3 times the standard deviation and find them to be highly non-Gaussian.Comment: submitted for the special issue of Physica D: "Anomalous Distributions" 11 pages, 6 figures revised version: light modifications of the figures and the tex

Connections between Tsallis' formalisms employing the standard linear average energy and ones employing the normalized qq-average energy

Tsallis' thermostatistics with the standard linear average energy is revisited by employing $S_{2-q}$, which is the Tsallis entropy with $q$ replaced by $2-q$. We explore the connections among the $S_{2-q}$ approach and the other different versions of Tsallis formalisms. It is shown that the normalized $q$-average energy and the standard linear average energy are related to each other. The relations among the Lagrange multipliers of the different versions are revealed. The relevant Legendre transform structures concerning the Lagrange multipliers associated with the normalization of probability are studied. It is shown that the generalized Massieu potential associated with $S_{2-q}$ and the linear average energy is related to one associated with the normalized Tsallis entropy and the normalized $q$-average energy.Comment: 16 pages, no figure, submitted to Physics Letter

Toward a High-Frequency Pulsed-Detonation Actuator

This paper describes the continued development of an actuator, energized by pulsed detonations, that provides a pulsed jet suitable for flow control in high-speed applications. A high-speed valve, capable of delivering a pulsed stream of reactants a mixture of H2 and air at rates of up to 1500 pulses per second, has been constructed. The reactants burn in a resonant tube and the products exit the tube as a pulsed jet. High frequency pressure transducers have been used to monitor the pressure fluctuations in the device at various reactant injection frequencies, including both resonant and off-resonant conditions. Pulsed detonations have been demonstrated in the lambda/4 mode of an 8 inch long tube at approx. 600 Hz. The pulsed jet at the exit of the device has been observed using shadowgraph and an infrared camera

R-matrix theory of driven electromagnetic cavities

Resonances of cylindrical symmetric microwave cavities are analyzed in R-matrix theory which transforms the input channel conditions to the output channels. Single and interfering double resonances are studied and compared with experimental results, obtained with superconducting microwave cavities. Because of the equivalence of the two-dimensional Helmholtz and the stationary Schroedinger equations, the results present insight into the resonance structure of regular and chaotic quantum billiards.Comment: Revtex 4.

Classical motion in force fields with short range correlations

We study the long time motion of fast particles moving through time-dependent random force fields with correlations that decay rapidly in space, but not necessarily in time. The time dependence of the averaged kinetic energy and mean-squared displacement is shown to exhibit a large degree of universality; it depends only on whether the force is, or is not, a gradient vector field. When it is, p^{2}(t) ~ t^{2/5} independently of the details of the potential and of the space dimension. Motion is then superballistic in one dimension, with q^{2}(t) ~ t^{12/5}, and ballistic in higher dimensions, with q^{2}(t) ~ t^{2}. These predictions are supported by numerical results in one and two dimensions. For force fields not obtained from a potential field, the power laws are different: p^{2}(t) ~ t^{2/3} and q^{2}(t) ~ t^{8/3} in all dimensions d\geq 1

The history of chemical enrichment in the intracluster medium from cosmological simulations

The distribution of metals in the intracluster medium (ICM) of galaxy clusters provides valuable information on their formation and evolution, on the connection with the cosmic star formation and on the effects of different gas processes. By analysing a sample of simulated galaxy clusters, we study the chemical enrichment of the ICM, its evolution, and its relation with the physical processes included in the simulation and with the thermal properties of the core. These simulations, consisting of re-simulations of 29 Lagrangian regions performed with an upgraded version of the smoothed particle hydrodynamics (SPH) gadget-3 code, have been run including two different sets of baryonic physics: one accounts for radiative cooling, star formation, metal enrichment and supernova (SN) feedback, and the other one further includes the effects of feedback from active galactic nuclei (AGN). In agreement with observations, we find an anti-correlation between entropy and metallicity in cluster cores, and similar radial distributions of heavy-element abundances and abundance ratios out to large cluster-centric distances ( 3cR180). In the outskirts, namely outside of 3c0.2 R180, we find a remarkably homogeneous metallicity distribution, with almost flat profiles of the elements produced by either SNIa or SNII. We investigated the origin of this phenomenon and discovered that it is due to the widespread displacement of metal-rich gas by early (z > 2-3) AGN powerful bursts, acting on small high-redshift haloes. Our results also indicate that the intrinsic metallicity of the hot gas for this sample is on average consistent with no evolution between z = 2 and z = 0, across the entire radial range