Correlated Gaussian systems exhibiting additive power-law entropies

We show, on purely statistical grounds and without appeal to any physical model, that a power-law $q-$entropy $S_q$, with $0<q<1$, can be {\it extensive}. More specifically, if the components $X_i$ of a vector $X \in \mathbb{R}^N$ are distributed according to a Gaussian probability distribution $f$, the associated entropy $S_q(X)$ exhibits the extensivity property for special types of correlations among the $X_i$. We also characterize this kind of correlation.Comment: 2 figure

Enigma of ultraluminous X-ray sources may be resolved by 3D-spectroscopy (MPFS data)

The ultraluminous X-ray sources (ULXs) were isolated in external galaxies for the last 5 years. Their X-ray luminosities exceed 100-10000 times those of brightest Milky Way black hole binaries and they are extremely variable. There are two models for the ULXs, the best black hole candidates. 1. They are supercritical accretion disks around a stellar mass black hole like that in SS433, observed close to the disk axes. 2. They are Intermediate Mass Black Holes (of 100-10000 solar masses). Critical observations which may throw light upon the ULXs nature come from observations of nebulae around the ULXs. We present results of 3D-spectroscopy of nebulae around several ULXs located in galaxies at 3-6 Mpc distances. We found that the nebulae to be powered by their central black holes. The nebulae are shocked and dynamically perturbed probably by jets. The nebulae are compared with SS433 nebula (W50).Comment: Proceedings of the ESO and Euro3D Workshop "Science Perspectives for 3D Spectroscopy", Garching (Germany), October 10-14, 2005. M. Kissler-Patig, M.M. Roth and J.R. Walsh (eds.

Thermodynamics with long-range interactions: from Ising models to black-holes

New methods are presented which enables one to analyze the thermodynamics of systems with long-range interactions. Generically, such systems have entropies which are non-extensive, (do not scale with the size of the system). We show how to calculate the degree of non-extensivity for such a system. We find that a system interacting with a heat reservoir is in a probability distribution of canonical ensembles. The system still possesses a parameter akin to a global temperature, which is constant throughout the substance. There is also a useful quantity which acts like a {\it local temperatures} and it varies throughout the substance. These quantities are closely related to counterparts found in general relativity. A lattice model with long-range spin-spin coupling is studied. This is compared with systems such as those encountered in general relativity, and gravitating systems with Newtonian-type interactions. A long-range lattice model is presented which can be seen as a black-hole analog. One finds that the analog's temperature and entropy have many properties which are found in black-holes. Finally, the entropy scaling behavior of a gravitating perfect fluid of constant density is calculated. For weak interactions, the entropy scales like the volume of the system. As the interactions become stronger, the entropy becomes higher near the surface of the system, and becomes more area-scaling.Comment: Corrects some typos found in published version. Title changed 22 pages, 2 figure

How fundamental is the character of thermal uncertainty relations?

We show that thermodynamic uncertainties do not preserve their form if the underlying probability distribution is transformed into an escort one. Heisenberg's relations, on the other hand, are not affected by such transformation. We conclude therefore that the former uncertainty cannot be as fundamental as the quantum one.Comment: 4 pages, no figure

Generalized thermodynamics and Fokker-Planck equations. Applications to stellar dynamics, two-dimensional turbulence and Jupiter's great red spot

We introduce a new set of generalized Fokker-Planck equations that conserve energy and mass and increase a generalized entropy until a maximum entropy state is reached. The concept of generalized entropies is rigorously justified for continuous Hamiltonian systems undergoing violent relaxation. Tsallis entropies are just a special case of this generalized thermodynamics. Application of these results to stellar dynamics, vortex dynamics and Jupiter's great red spot are proposed. Our prime result is a novel relaxation equation that should offer an easily implementable parametrization of geophysical turbulence. This relaxation equation depends on a single key parameter related to the skewness of the fine-grained vorticity distribution. Usual parametrizations (including a single turbulent viscosity) correspond to the infinite temperature limit of our model. They forget a fundamental systematic drift that acts against diffusion as in Brownian theory. Our generalized Fokker-Planck equations may have applications in other fields of physics such as chemotaxis for bacterial populations. We propose the idea of a classification of generalized entropies in classes of equivalence and provide an aesthetic connexion between topics (vortices, stars, bacteries,...) which were previously disconnected.Comment: Submitted to Phys. Rev.

An optimization principle for deriving nonequilibrium statistical models of Hamiltonian dynamics

A general method for deriving closed reduced models of Hamiltonian dynamical systems is developed using techniques from optimization and statistical estimation. As in standard projection operator methods, a set of resolved variables is selected to capture the slow, macroscopic behavior of the system, and the family of quasi-equilibrium probability densities on phase space corresponding to these resolved variables is employed as a statistical model. The macroscopic dynamics of the mean resolved variables is determined by optimizing over paths of these probability densities. Specifically, a cost function is introduced that quantifies the lack-of-fit of such paths to the underlying microscopic dynamics; it is an ensemble-averaged, squared-norm of the residual that results from submitting a path of trial densities to the Liouville equation. The evolution of the macrostate is estimated by minimizing the time integral of the cost function. The value function for this optimization satisfies the associated Hamilton-Jacobi equation, and it determines the optimal relation between the statistical parameters and the irreversible fluxes of the resolved variables, thereby closing the reduced dynamics. The resulting equations for the macroscopic variables have the generic form of governing equations for nonequilibrium thermodynamics, and they furnish a rational extension of the classical equations of linear irreversible thermodynamics beyond the near-equilibrium regime. In particular, the value function is a thermodynamic potential that extends the classical dissipation function and supplies the nonlinear relation between thermodynamics forces and fluxes

Topological String Amplitudes, Complete Intersection Calabi-Yau Spaces and Threshold Corrections

We present the most complete list of mirror pairs of Calabi-Yau complete intersections in toric ambient varieties and develop the methods to solve the topological string and to calculate higher genus amplitudes on these compact Calabi-Yau spaces. These symplectic invariants are used to remove redundancies in examples. The construction of the B-model propagators leads to compatibility conditions, which constrain multi-parameter mirror maps. For K3 fibered Calabi-Yau spaces without reducible fibers we find closed formulas for all genus contributions in the fiber direction from the geometry of the fibration. If the heterotic dual to this geometry is known, the higher genus invariants can be identified with the degeneracies of BPS states contributing to gravitational threshold corrections and all genus checks on string duality in the perturbative regime are accomplished. We find, however, that the BPS degeneracies do not uniquely fix the non-perturbative completion of the heterotic string. For these geometries we can write the topological partition function in terms of the Donaldson-Thomas invariants and we perform a non-trivial check of S-duality in topological strings. We further investigate transitions via collapsing D5 del Pezzo surfaces and the occurrence of free Z2 quotients that lead to a new class of heterotic duals.Comment: 117 pages, 1 Postscript figur

Gamma-Ray Bursts: The Underlying Model

A pedagogical derivation is presented of the ``fireball'' model of gamma-ray bursts, according to which the observable effects are due to the dissipation of the kinetic energy of a relativistically expanding wind, a ``fireball.'' The main open questions are emphasized, and key afterglow observations, that provide support for this model, are briefly discussed. The relativistic outflow is, most likely, driven by the accretion of a fraction of a solar mass onto a newly born (few) solar mass black hole. The observed radiation is produced once the plasma has expanded to a scale much larger than that of the underlying ``engine,'' and is therefore largely independent of the details of the progenitor, whose gravitational collapse leads to fireball formation. Several progenitor scenarios, and the prospects for discrimination among them using future observations, are discussed. The production in gamma- ray burst fireballs of high energy protons and neutrinos, and the implications of burst neutrino detection by kilometer-scale telescopes under construction, are briefly discussed.Comment: In "Supernovae and Gamma Ray Bursters", ed. K. W. Weiler, Lecture Notes in Physics, Springer-Verlag (in press); 26 pages, 2 figure

Staffing and Training Aspects of Hospital Management: Some Issues for Research

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68624/2/10.1177_107755878904600205.pd