A Study of Phase Transition in Black Hole Thermodynamics

This paper deals with five-dimensional black hole solutions in (a) Einstein-Maxwell-Gauss-Bonnet theory with a cosmological constant and (b)Einstein-Yang-Mills-Gauss-Bonnet theory for spherically symmetric space time. In both the cases the possibility of phase transition is examined and it is analyzed whether the phase transition is a Hawking-Page type phase transition or not.Comment: 16 figure

The geometry of the higher dimensional black hole thermodynamics in Einstein-Gauss-Bonnet theory

This paper deals with five-dimensional black hole solutions in (a) Einstein-Yang-Mills-Gauss-Bonnet theory and (b)Einstein-Maxwell-Gauss-Bonnet theory with a cosmological constant for spherically symmetric space time. The geometry of the black hole thermodynamics has been studied for both the black holes.Comment: 8 page

Fredholm Modules on P.C.F. Self-Similar Fractals and their Conformal Geometry

The aim of the present work is to show how, using the differential calculus associated to Dirichlet forms, it is possible to construct Fredholm modules on post critically finite fractals by regular harmonic structures. The modules are d-summable, the summability exponent d coinciding with the spectral dimension of the generalized laplacian operator associated with the regular harmonic structures. The characteristic tools of the noncommutative infinitesimal calculus allow to define a d-energy functional which is shown to be a self-similar conformal invariant.Comment: 16 page

A motif-based approach to network epidemics

Networks have become an indispensable tool in modelling infectious diseases, with the structure of epidemiologically relevant contacts known to affect both the dynamics of the infection process and the efficacy of intervention strategies. One of the key reasons for this is the presence of clustering in contact networks, which is typically analysed in terms of prevalence of triangles in the network. We present a more general approach, based on the prevalence of different four-motifs, in the context of ODE approximations to network dynamics. This is shown to outperform existing models for a range of small world networks

Evolution of the Schr\"odinger--Newton system for a self--gravitating scalar field

Using numerical techniques, we study the collapse of a scalar field configuration in the Newtonian limit of the spherically symmetric Einstein--Klein--Gordon (EKG) system, which results in the so called Schr\"odinger--Newton (SN) set of equations. We present the numerical code developed to evolve the SN system and topics related, like equilibrium configurations and boundary conditions. Also, we analyze the evolution of different initial configurations and the physical quantities associated to them. In particular, we readdress the issue of the gravitational cooling mechanism for Newtonian systems and find that all systems settle down onto a 0--node equilibrium configuration.Comment: RevTex file, 19 pages, 26 eps figures. Minor changes, matches version to appear in PR

Generalised second law of thermodynamics for interacting dark energy in the DGP brane world

In this paper, we investigate the validity of the generalized second law of thermodynamics (GSLT) in the DGP brane world when universe is filled with interacting two fluid system: one in the form of cold dark matter and other is holographic dark energy. The boundary of the universe is assumed to be enclosed by the dynamical apparent horizon or the event horizon. The universe is chosen to be homogeneous and isotropic FRW model and the validity of the first law has been assumed here

Geometrothermodynamics of five dimensional black holes in Einstein-Gauss-Bonnet-theory

We investigate the thermodynamic properties of 5D static and spherically symmetric black holes in (i) Einstein-Maxwell-Gauss-Bonnet theory, (ii) Einstein-Maxwell-Gauss-Bonnet theory with negative cosmological constant, and in (iii) Einstein-Yang-Mills-Gauss-Bonnet theory. To formulate the thermodynamics of these black holes we use the Bekenstein-Hawking entropy relation and, alternatively, a modified entropy formula which follows from the first law of thermodynamics of black holes. The results of both approaches are not equivalent. Using the formalism of geometrothermodynamics, we introduce in the manifold of equilibrium states a Legendre invariant metric for each black hole and for each thermodynamic approach, and show that the thermodynamic curvature diverges at those points where the temperature vanishes and the heat capacity diverges.Comment: New sections added, references adde

High Pressure Thermoelasticity of Body-centered Cubic Tantalum

We have investigated the thermoelasticity of body-centered cubic (bcc) tantalum from first principles by using the linearized augmented plane wave (LAPW) and mixed--basis pseudopotential methods for pressures up to 400 GPa and temperatures up to 10000 K. Electronic excitation contributions to the free energy were included from the band structures, and phonon contributions were included using the particle-in-a-cell (PIC) model. The computed elastic constants agree well with available ultrasonic and diamond anvil cell data at low pressures, and shock data at high pressures. The shear modulus $c_{44}$ and the anisotropy change behavior with increasing pressure around 150 GPa because of an electronic topological transition. We find that the main contribution of temperature to the elastic constants is from the thermal expansivity. The PIC model in conjunction with fast self-consistent techniques is shown to be a tractable approach to studying thermoelasticity.Comment: To be appear in Physical Review

Continuity of the Maximum-Entropy Inference

We study the inverse problem of inferring the state of a finite-level quantum system from expected values of a fixed set of observables, by maximizing a continuous ranking function. We have proved earlier that the maximum-entropy inference can be a discontinuous map from the convex set of expected values to the convex set of states because the image contains states of reduced support, while this map restricts to a smooth parametrization of a Gibbsian family of fully supported states. Here we prove for arbitrary ranking functions that the inference is continuous up to boundary points. This follows from a continuity condition in terms of the openness of the restricted linear map from states to their expected values. The openness condition shows also that ranking functions with a discontinuous inference are typical. Moreover it shows that the inference is continuous in the restriction to any polytope which implies that a discontinuity belongs to the quantum domain of non-commutative observables and that a geodesic closure of a Gibbsian family equals the set of maximum-entropy states. We discuss eight descriptions of the set of maximum-entropy states with proofs of accuracy and an analysis of deviations.Comment: 34 pages, 1 figur