98,296 research outputs found

### 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

### 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

### Measurements of time dependent CP asymmetry in $B \to VV$ 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

### 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

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