Concurrence and Foliations Induced by Some 1-Qubit Channels

We start with a short introduction to the roof concept. An elementary discussion of phase-damping channels shows the role of antilinear operators in representing their concurrences. A general expression for some concurrences is derived. We apply it to 1-qubit channels of length 2, getting the induced foliations of the state space, the optimal decompositions, and the entropy of a state with respect to these channels. For amplitude-damping channels one obtains an expression for the Holevo capacity allowing for easy numerical calculations.     

Tight approximations to total scattering intensities from electron-pair density quantities

Three different mathematical techniques (maximum-entropy, Stieltjes-type and Padé-like approximants) are used to obtain tight approximations to scattering intensities in terms of a few local and/or global quantities related to the electron-pair density. The accuracy of the approximations is analyzed and compared by means of Hylleraas-type atomic wavefunctions.     

New and old bounds for standard quadratic optimization: dominance,equivalence and incomparability

A standard quadratic optimization problem (StQP) consists in minimizing a quadratic form over a simplex. Among the problems which can be transformed into a StQP are the general quadratic problem over a polytope, and the maximum clique problem in a graph. In this paper we present several new polynomial-time bounds for StQP ranging from very simple and cheap ones to more complex and tight constructions. The main tools employed in the conception and analysis of most bounds are Semidefinite Programming and decomposition of the objective function into a sum of two quadratic functions, each of which is easy to minimize. We provide a complete diagram of the dominance, incomparability, or equivalence relations among the bounds proposed in this and in previous works. In particular, we show that one of our new bounds dominates all the others. Furthermore, a specialization of such bound dominates Schrijver’s improvement of Lovász’s θ function bound for the maximum size of a clique in a graph.      

Surface segregation of highly branched polymer additives in linear hosts

Entropy‐driven segregation of various branched and hyperbranched polymeric additives in chemically similar linear polymer hosts is studied using self‐consistent (SCF) mean‐field lattice simulations. The simulations account for the effect of molecular architecture on local configurational entropy in the blends, but ignores the effect of architecture on local density and blend compressibility. Star, dendrimer, and comb‐like additives are all found to be enriched at the surface of chemically identical linear host polymers. The magnitude of their surface excess increases with increased number of chain ends and decreases with increased segmental crowding near the branch point. Provided the number of arms and molecular weight of the branched additives are maintained constant, we find that the simplest branched architecture, the symmetric star, exhibits the strongest preference for the surface of binary polymer blends. We show that a single variable, here termed the “entropic driving force density,” controls the relative surface affinities of branched additives possessing a wide range of architectures. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1788–1801, 2008     

Volume entropy,weighted girths and stable balls on graphs

We prove new isoperimetric inequalities on graphs involving quantities linked with concepts from differential geometry. First, we bound from above the product of the volume entropy (defined as the log of the exponential growth rate of the universal cover) and the girth of weighted graphs in terms of their cyclomatic number. In a second part, we study a natural polyhedron associated to a weighted graph: the stable ball. In particular, we relate the volume of this polyhedron, the weight of the graph and its cyclomatic number. © 2007 Wiley Periodicals, Inc. J Graph Theory 55: 291–305, 2007     

Entropy Maximization for Markov and Semi-Markov Processes

The literature about maximum of entropy for Markov processes deals mainly with discrete-time Markov chains. Very few papers dealing with continuous-time jump Markov processes exist and none dealing with semi-Markov processes. It is the aim of this paper to contribute to fill this lack. We recall the basics concerning entropy for Markov and semi-Markov processes and we study several problems to give an overview of the possible directions of use of maximum entropy in connection with these processes. Numeric illustrations are presented, in particular in application to reliability.     

Standard model on D-branes

I briefly outline previous work on getting the (supersymmetric) standard model from string theory, and then describe two ecent attempts using D-branes. The first uses D3-and D7-branes and gives a supersymmetric standard model with extra vector-like matter and an intermediate unification scale. The second uses intersecting D4-branes and yields a non-supersymmetric spectrum with TeV-scale unification.     

On Thermodynamic Limits of Entropy Densities

We give some sufficient conditions which guarantee that the entropy density in the thermodynamic limit is equal to the thermodynamic limit of the entropy densities of finite-volume (local) Gibbs states.     

熵指数对多重数分布的宽度和形状的依赖性

通过运用蒙特卡罗方法,研究了熵指数对多重数分布的宽度和形状的依赖性,并和NA2?2实验结果作比较.发现,熵指数对多重数分布的形状变化不敏感,但是却随着分布宽度的增加而减小.这一发现和通常基于熵指数的物理意义的期待是矛盾的     

Temperature, entropy, and kinetic theory

The relation between the concepts of temperature and entropy and the kinetic theory of gases is discussed, with particular attention to the aspects which are frequently treated as obvious or not even mentioned. In order to show that the usual thermodynamic relations are by no means obvious and may be contradictory, the model of a discrete velocity gas is used. It is also shown that the usual relation between the entropy rate and the heat supplied to a gas is not valid (even close to equilibrium) unless the theory is Galilei invariant (which is obviously not the case for a discrete velocity gas) and must be replaced by another one that eliminates all the paradoxical aspects of the matter.