Stability of Tsallis antropy and instabilities of Renyi and normalized Tsallis entropies: A basis for q-exponential distributions

The q-exponential distributions, which are generalizations of the Zipf-Mandelbrot power-law distribution, are frequently encountered in complex systems at their stationary states. From the viewpoint of the principle of maximum entropy, they can apparently be derived from three different generalized entropies: the Renyi entropy, the Tsallis entropy, and the normalized Tsallis entropy. Accordingly, mere fittings of observed data by the q-exponential distributions do not lead to identification of the correct physical entropy. Here, stabilities of these entropies, i.e., their behaviors under arbitrary small deformation of a distribution, are examined. It is shown that, among the three, the Tsallis entropy is stable and can provide an entropic basis for the q-exponential distributions, whereas the others are unstable and cannot represent any experimentally observable quantities.Comment: 20 pages, no figures, the disappeared "primes" on the distributions are added. Also, Eq. (65) is correcte

Exponents of 2-multiarrangements and multiplicity lattices

We introduce a concept of multiplicity lattices of 2-multiarrangements, determine the combinatorics and geometry of that lattice, and give a criterion and method to construct a basis for derivation modules effectively.Comment: 14 page

C2C_2-cofiniteness of 2-cyclic permutation orbifold models

In this article, we consider permutation orbifold models of $C_2$-cofinite vertex operator algebras of CFT type. We show the $C_2$-cofiniteness of the 2-cyclic permutation orbifold model $(V\otimes V)^{S_2}$ for an arbitrary $C_2$-cofinite simple vertex operator algebra $V$ of CFT type. We also give a proof of the $C_2$-cofiniteness of a $\Z_2$-orbifold model $V_L^+$ of the lattice vertex operator algebra $V_L$ associated with a rank one positive definite even lattice $L$ by using our result and the $C_2$-cofiniteness of $V_L$.Comment: 25 pages, no figure, some typo are correcte

On Observing Top Quark Production at the Tevatron

A technique for separating top quark production from Standard Model background events is introduced. It is applicable to the channel in which one top quark decays semi-leptonically and its anti-quark decays hadronically into three jets, or vice versa. The method is shown to discriminate dramatically between Monte Carlo generated events with and without simulated top quarks of mass around 120 GeV and above. The simulations were performed with CDF detector characteristics incorporated, showing that the method is applicable to existing data.Comment: 8 pages, TUFTS-TH-92-G01 (Two minor TeX mistakes corrected

Negative s and Light New Physics

Motivated by the difference between SLD's recent measurement of ALR and the corresponding LEP results, we explore which kinds of new particles can (1) contribute dominantly to new physics through oblique corrections, (2) produce negative values for S and T, and (3) not be in conflict with any other experiments, on or off the Z resonance. We are typically led to models which involve new particles which are not much heavier than MZ/2, and so which may also have implications for other experiments in the near future. For such light particles, we show how the oblique-parameter analysis of purely Z-pole data requires the interpretation of the data in terms of modified parameters, S' and T', whose difference from S and T improves the available parameter space of the models.Comment: plain TeX, 16 pages, 6 figures attached as a uuencoded file, McGill-94/27, NEIP-94-00

IKT approach for quantum hydrodynamic equations

A striking feature of standard quantum mechanics is its analogy with classical fluid dynamics. In particular it is well known the Schr\"{o}dinger equation can be viewed as describing a classical compressible and non-viscous fluid, described by two (quantum) fluid fields {\rho ,% \mathbf{V}} , to be identified with the quantum probability density and velocity field. This feature has suggested the construction of a phase-space hidden-variable description based on a suitable inverse kinetic theory (IKT; Tessarotto et al., 2007). The discovery of this approach has potentially important consequences since it permits to identify the classical dynamical system which advances in time the quantum fluid fields. This type of approach, however requires the identification of additional fluid fields. These can be generally identified with suitable directional fluid temperatures $T_{QM,i}$ (for $i=1,2,3$), to be related to the expectation values of momentum fluctuations appearing in the Heisenberg inequalities. Nevertheless the definition given previously for them (Tessarotto et al., 2007) is non-unique. In this paper we intend to propose a criterion, based on the validity of a constant H-theorem, which provides an unique definition for the quantum temperatures.Comment: Contributed paper at RGD26 (Kyoto, Japan, July 2008

Three-Jet Event Orientation in e+e- Annihilation: New Tests of the Standard Model

We discuss the orientation of e+e- -> q qbar g events in terms of the polar and azimuthal angles of the event plane w.r.t. the electron beam direction. We define an asymmetry of the azimuthal-angle distribution, which, along with the left-right forward-backward polar-angle asymmetry, is sensitive to parity-violating effects in three-jet events; these have yet to be explored experimentally. We have evaluated these observables at O(alpha_s) in perturbative QCD and present their dependence on longitudinal beam polarisation and c.m. energy. We also define a moments analysis in terms of the orientation angles that allows a new and more detailed test of QCD by isolating the six independent helicity cross-sections.Comment: 15 pages, 5 figures in eps format. This version replaces the garbled Figure 2 in the original submission. Submitted to Physics Letters B