Temperature of nonextensive system: Tsallis entropy as Clausius entropy

The problem of temperature in nonextensive statistical mechanics is studied. Considering the first law of thermodynamics and a "quasi-reversible process", it is shown that the Tsallis entropy becomes the Clausius entropy if the inverse of the Lagrange multiplier, $beta$, associated with the constraint on the internal energy is regarded as the temperature. This temperature is different from the previously proposed "physical temperature" defined through the assumption of divisibility of the total system into independent subsystems. A general discussion is also made about the role of Boltzmann's constant in generalized statistical mechanics based on an entropy, which, under the assumption of independence, is nonadditive.Comment: 14 pages, no figure

A Semi-relativistic Equation of State for Stellar Interiors

Using the technique of Pade Approximants for the correlation contributions of charged particles we are able to reproduce complex mathematical expressions by simple algebraic formulas. The Pade formulas are analytical expressions, which interpolate between certain density-temperature regions and are characterized by exact asymptotics. We present a semi-relativistic description of the thermodynamics applicable for stellar interiors. Comparisons with equation-of-state data obtained by other calculational schemes are presented.Comment: 4 pages including 2 PostScript figures, also available from http://www.speckle.mpifr-bonn.mpg.de/publications.html, accepted for publication in Contributions to Plasma Physic

Nonextensivity in Geological Faults?

Geological fault systems, as the San Andreas fault (SAF) in USA, constitute typical examples of self-organizing systems in nature. In this paper, we have considered some geophysical properties of the SAF system to test the viability of the nonextensive models for earthquakes developed in [Phys. Rev. E {\bf 73}, 026102, 2006]. To this end, we have used 6188 earthquakes events ranging in the magnitude interval $2 < m < 8$ that were taken from the Network Earthquake International Center catalogs (NEIC, 2004-2006) and the Bulletin of the International Seismological Centre (ISC, 1964-2003). For values of the Tsallis nonextensive parameter $q \simeq 1.68$, it is shown that the energy distribution function deduced in above reference provides an excellent fit to the NEIC and ISC SAF data.Comment: 9 pages, 1 figure, standard LaTeX fil

Accessing directly the strange quark content of the proton at HERA

We investigate a double-spin asymmetry for the semi-inclusive $\Lambda$ hyperon production in the longitudinally deep inelastic lepton-proton scattering, the sign of which can provide us with important information about the strange quark helicity distribution in the proton.On the basis of the interpretation of the longitudinal deep inelastic lepton-nucleon scattering data as a negative strange quark polarization in the proton and the preliminary results on the measurement of the longitudinal $\Lambda$ polarization at the $Z$ resonance in electron-positron annihilation,we predict a minus sign for the suggested observable. The experimental condition required for our suggestion is met by the HERA facilities, so the asymmetry considered can be measured by the HERMES experiments at HERA in the near future.Comment: 10 pages, Revtex, completely rephrased, references adde

Mean Field Fluid Behavior of the Gaussian Core Model

We show that the Gaussian core model of particles interacting via a penetrable repulsive Gaussian potential, first considered by Stillinger (J. Chem. Phys. 65, 3968 (1976)), behaves like a weakly correlated ``mean field fluid'' over a surprisingly wide density and temperature range. In the bulk the structure of the fluid phase is accurately described by the random phase approximation for the direct correlation function, and by the more sophisticated HNC integral equation. The resulting pressure deviates very little from a simple, mean-field like, quadratic form in the density, while the low density virial expansion turns out to have an extremely small radius of convergence. Density profiles near a hard wall are also very accurately described by the corresponding mean-field free-energy functional. The binary version of the model exhibits a spinodal instability against de-mixing at high densities. Possible implications for semi-dilute polymer solutions are discussed.Comment: 13 pages, 2 columns, ReVTeX epsfig,multicol,amssym, 15 figures; submitted to Phys. Rev. E (change: important reference added

Equation of state of fully ionized electron-ion plasmas

Thermodynamic quantities of Coulomb plasmas consisting of point-like ions immersed in a compressible, polarizable electron background are calculated for ion charges Z=1 to 26 and for a wide domain of plasma parameters ranging from the Debye-Hueckel limit to the crystallization point and from the region of nondegenerate to fully degenerate nonrelativistic or relativistic electrons. The calculations are based on the linear-response theory for the electron-ion interaction, including the local-field corrections in the electronic dielectric function. The thermodynamic quantities are calculated in the framework of the N-body hypernetted-chain equations and fitted by analytic expressions. We present also accurate analytic approximations for the free energy of the ideal electron gas at arbitrary degeneracy and relativity and for the excess free energy of the one-component plasma of ions (OCP) derived from Monte Carlo simulations. The extension to multi-ionic mixtures is discussed within the framework of the linear mixing rule. These formulae provide a completely analytic, accurate description of the thermodynamic quantities of fully ionized electron-ion Coulomb plasmas, a useful tool for various applications from liquid state theory to dense stellar matter.Comment: 13 pages, 2 tables, 7 figures, REVTeX using epsf.sty. To be published in Phys. Rev. E, vol. 58 (1998

Naturalness and Focus Points with Non-Universal Gaugino Masses

Relations between the gaugino masses have been shown to alleviate the degree of fine-tuning in the MSSM. In this paper we consider specific models of supersymmetry breaking with gravity mediation and demonstrate that within both GUT and string constructions it is possible to generate these relations in a natural way. We have numerically studied the degree of fine-tuning in these models, including one-loop corrections, and have found regions of parameter space that can satisfy all known collider constraints with fine-tunings less than 20%. We discuss some of the phenomenological features of these models within the regions of reduced fine-tuning.Comment: 31 pages, 21 figures. Version accepted for publication in Nuclear Physics

Structure Functions of Unstable Lithium Isotopes

We study both the spin-average and spin-dependent structure functions of the lithium isotopes, $^{6-11}$Li, which could be measured at RIKEN and other nuclear facilities in the future. It is found that the light-cone momentum distribution of the valence neutron in the halo of $^{11}$Li is very sharp and symmetric around y = 1, because of the weak binding. The EMC ratios for Li isotopes are then calculated. We study the possibility of extracting the neutron structure function from data for the nuclear structure functions of the Li isotopes. Next we calculate the spin-dependent structure functions of $^{7,9,11}$Li isotopes, which have spin of 3/2. The effect of the nuclear binding and Fermi motion on the multipole spin structure function, $^{3/2}_{~1}g_1$, is about 10% in the region x < 0.7, but it becomes quite important at large x. The spin structure function of $^{3/2}_{~3}g_1$ is also investigated. Finally, we discuss the modification of the Gottfried and Bjorken integrals in a nuclear medium and point out several candidates for a pair of mirror nuclei to study the flavor-nonsinglet quark distributions in nuclei.Comment: 23 pages + 7 tables + 15 figure

Screening of Spherical Colloids beyond Mean Field -- A Local Density Functional Approach

We study the counterion distribution around a spherical macroion and its osmotic pressure in the framework of the recently developed Debye-H"uckel-Hole-Cavity (DHHC) theory. This is a local density functional approach which incorporates correlations into Poisson-Boltzmann theory by adding a free energy correction based on the One Component Plasma. We compare the predictions for ion distribution and osmotic pressure obtained by the full theory and by its zero temperature limit with Monte Carlo simulations. They agree excellently for weakly developed correlations and give the correct trend for stronger ones. In all investigated cases the DHHC theory and its computationally simpler zero temperature limit yield better results than the Poisson-Boltzmann theory.Comment: 10 pages, 4 figures, 2 tables, RevTeX4-styl