Statistical mechanical foundations of power-law distributions

The foundations of the Boltzmann-Gibbs (BG) distributions for describing equilibrium statistical mechanics of systems are examined. Broadly, they fall into: (i) probabilistic paaroaches based on the principle of equal a priori probability (counting technique and method of steepest descents), law of large numbers, or the state density considerations and (ii) a variational scheme -- maximum entropy principle (due to Gibbs and Jaynes) subject to certain constraints. A minimum set of requirements on each of these methods are briefly pointed out: in the first approach, the function space and the counting algorithm while in the second, "additivity" property of the entropy with respect to the composition of statistically independent systems. In the past few decades, a large number of systems, which are not necessarily in thermodynamic equilibrium (such as glasses, for example), have been found to display power-law distributions, which are not describable by the above-mentioned methods. In this paper, parallel to all the inquiries underlying the BG program described above are given in a brief form. In particular, in the probabilistic derivations, one employs a different function space and one gives up "additivity" in the variational scheme with a different form for the entropy. The requirement of stability makes the entropy choice to be that proposed by Tsallis. From this a generalized thermodynamic description of the system in a quasi-equilibrium state is derived. A brief account of a unified consistent formalism associated with systems obeying power-law distributions precursor to the exponential form associated with thermodynamic equilibrium of systems is presented here.Comment: 19 pages, no figures. Invited talk at Anomalous Distributions, Nonlinear Dynamics and Nonextensivity, Santa Fe, USA, November 6-9, 200

Measurements of time dependent CP asymmetry in B→VVB \to VV decays with BELLE

A study of CP violation in $B\to J/\psi K^*(K_S^0\pi^0)$ decays by time dependent angular analysis is discussed. Status of time independent analyses for other $B\to VV$ decays is also reported. The data used for the analyses are taken with the Belle detector at KEK.Comment: 4 pages, 3 figures, Proceeding of the talk in parallel session (CP-3-5) at ICHEP2002, Amsterdam, Netherland, 24-31 July (2002

Dynamical evolution of clustering in complex network of earthquakes

The network approach plays a distinguished role in contemporary science of complex systems/phenomena. Such an approach has been introduced into seismology in a recent work [S. Abe and N. Suzuki, Europhys. Lett. 65, 581 (2004)]. Here, we discuss the dynamical property of the earthquake network constructed in California and report the discovery that the values of the clustering coefficient remain stationary before main shocks, suddenly jump up at the main shocks, and then slowly decay following a power law to become stationary again. Thus, the network approach is found to characterize main shocks in a peculiar manner.Comment: 10 pages, 3 figures, 1 tabl

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

B Physics at SLD

We review recent $B$ physics results obtained in polarized $e^+ e^-$ interactions at the SLC by the SLD experiment. The excellent 3-D vertexing capabilities of SLD are exploited to extract precise \bu and \bd lifetimes, as well as measurements of the time evolution of $B^0_d - \bar{B^0_d}$ mixing.Comment: 7 pages, 4 figure

Monotonic decrease of the quantum nonadditive divergence by projective measurements

Nonadditive (nonextensive) generalization of the quantum Kullback-Leibler divergence, termed the quantum q-divergence, is shown not to increase by projective measurements in an elementary manner.Comment: 10 pages, no figures. Errors in the published version are correcte

Nonextensive thermodynamic relations

The generalized zeroth law of thermodynamics indicates that the physical temperature in nonextensive statistical mechanics is different from the inverse of the Lagrange multiplier, beta. This leads to modifications of some of thermodynamic relations for nonextensive systems. Here, taking the first law of thermodynamics and the Legendre transform structure as the basic premises, it is found that Clausius definition of the thermodynamic entropy has to be appropriately modified, and accordingly the thermodynamic relations proposed by Tsallis, Mendes and Plastino [Physica A 261 (1998) 534] are also to be rectified. It is shown that the definition of specific heat and the equation of state remain form invariant. As an application, the classical gas model is reexamined and, in marked contrast with the previous result obtained by Abe [Phys. Lett. A 263 (1999) 424: Erratum A 267 (2000) 456] using the unphysical temperature and the unphysical pressure, the specific heat and the equation of state are found to be similar to those in ordinary extensive thermodynamics.Comment: 17 pages. The discussion about the Legendre transform structure is modified and some additional comments are mad

Quasicanonical Gibbs distribution and Tsallis nonextensive statistics

We derive and study quasicanonical Gibbs distribution function which is characterized by the thermostat with finite number of particles (quasithermostat). We show that this naturally leads to Tsallis nonextensive statistics and thermodynamics, with Tsallis parameter q is found to be related to the number of particles in the quasithermostat. We show that the chi-square distribution of fluctuating temperature used recently by Beck can be partially understood in terms of normal random momenta of particles in the quasithermostat. Also, we discuss on the importance of the time scale hierarchy and fluctuating probability distribution functions in understanding of Tsallis distribution, within the framework of kinetics of dilute gas and weakly inhomogeneous systems.Comment: 22 pages, 1 eps-figur

A Scintillator Tile-Fiber Preshower Detector for the CDF Central Calorimeter

The front face of the CDF central calorimeter is being equipped with a new Preshower detector, based on scintillator tiles read out by WLS fibers, in order to cope with the luminosity increase provided by the Main Injector during the Tevatron's Run II data taking. A light yield of about 40 pe/MIP at the tile exit was obtained, exceeding the design requirements.Comment: 4 pages, 8 figures. Proceedings of `9th Topical Seminar on Innovative Particle and Radiation Detectors', 23-26 May 2004, Siena, Ital

Comparison of Three-jet Events in Proton-Antiproton Collisions at sqrt{s}=1.8 TeV to Predictions from a Next-to-leading Order QCD Calculation

The properties of three-jet events with total transverse energy greater than 320 GeV and individual jet energy greater than 20 GeV have been analyzed and compared to absolute predictions from a next-to-leading order (NLO) perturbative QCD calculation. These data, of integrated luminosity 86 pb^-1, were recorded by the CDF Experiment for proton-antiproton collisions at sqrt{s}=1.8 TeV. This study tests a model of higher order QCD processes that result in gluon emission and can be used to estimate the magnitude of the contribution of processes higher than NLO. The total cross section is measured to be 466 \pm 3(stat.)^{+207}_{-70}(syst.) pb. The differential cross section is furthermore measured for all kinematically accessible regions of the Dalitz plane, including those for which the theoretical prediction is unreliable. While the measured cross section is consistent with the theoretical prediction in magnitude, the two differ somewhat in shape in the Dalitz plane.Comment: For the CDF Collaboration. Contributed to the proceedings of the Eleventh High-Energy Physics International Conference on QCD, Montpellier, France, July 200