Bekenstein Inequalities and Nonlinear Electrodynamics

Bekenstein and Mayo proposed a generalised bound for the entropy, which implies some inequalities between the charge, energy, angular momentum, and the size of the macroscopic system. Dain has shown that Maxwell's electrodynamics satisfies all three inequalities. We investigate the validity of these relations in the context of nonlinear electrodynamics and show that Born-Infeld electrodynamics satisfies all of them. However, contrary to the linear theory, there is no rigidity statement in Born-Infeld. We study the physical meaning and the relationship between these inequalities and, in particular, we analyse the connection between the energy-angular momentum inequality and causality.Comment: Accepted for publication Phys. Rev.

A new symmetry of the relativistic wave equation

In this paper we show that there exists a new symmetry in the relativistic wave equation for a scalar field in arbitrary dimensions. This symmetry is related to redefinitions of the metric tensor which implement a map between non-equivalent manifolds. It is possible to interpret these transformations as a generalization of the conformal transformations. In addition, one can show that this set of manifolds together with the transformation connecting its metrics forms a group. As long as the scalar field dynamics is invariant under these transformations, there immediately appears an ambiguity concerning the definition of the underlying background geometry.Comment: 4 page

A Holistic Approach to Log Data Analysis in High-Performance Computing Systems: The Case of IBM Blue Gene/Q

The complexity and cost of managing high-performance computing infrastructures are on the rise. Automating management and repair through predictive models to minimize human interventions is an attempt to increase system availability and contain these costs. Building predictive models that are accurate enough to be useful in automatic management cannot be based on restricted log data from subsystems but requires a holistic approach to data analysis from disparate sources. Here we provide a detailed multi-scale characterization study based on four datasets reporting power consumption, temperature, workload, and hardware/software events for an IBM Blue Gene/Q installation. We show that the system runs a rich parallel workload, with low correlation among its components in terms of temperature and power, but higher correlation in terms of events. As expected, power and temperature correlate strongly, while events display negative correlations with load and power. Power and workload show moderate correlations, and only at the scale of components. The aim of the study is a systematic, integrated characterization of the computing infrastructure and discovery of correlation sources and levels to serve as basis for future predictive modeling efforts.Comment: 12 pages, 7 Figure

Hidden geometries in nonlinear theories: a novel aspect of analogue gravity

We show that non-linear dynamics of a scalar field {\phi} may be described as a mod- ification of the spacetime geometry. Thus, the self-interaction is interpreted as a coupling of the scalar field with an effective gravitational metric that is constructed with {\phi} itself. We prove that this process is universal, that is, it is valid for arbi- trary Lagrangian. Our results are compared to usual analogue models of gravitation, where the emergence of a metric appears as a consequence of linear perturbation

The Wheeler-DeWitt Quantization Can Solve the Singularity Problem

We study the Wheeler-DeWitt quantum cosmology of a spatially flat Friedmann cosmological model with a massless free scalar field. We compare the consistent histories approach with the de Broglie-Bohm theory when applied to this simple model under two different quantization schemes: the Schr\"odinger-like quantization, which essentially takes the square-root of the resulting Klein-Gordon equation through the restriction to positive frequencies and their associated Newton-Wigner states, or the induced Klein-Gordon quantization, that allows both positive and negative frequencies together. We show that the consistent histories approach can give a precise answer to the question concerning the existence of a quantum bounce if and only if one takes the single frequency approach and within a single family of histories, namely, a family containing histories concerning properties of the quantum system at only two specific moments of time: the infinity past and the infinity future. In that case, as shown by Craig and Singh \cite{CS}, there is no quantum bounce. In any other situation, the question concerning the existence of a quantum bounce has no meaning in the consistent histories approach. On the contrary, we show that if one considers the de Broglie-Bohm theory, there are always states where quantum bounces occur in both quantization schemes. Hence the assertion that the Wheeler-DeWitt quantization does not solve the singularity problem in cosmology is not precise. To address this question, one must specify not only the quantum interpretation adopted but also the quantization scheme chosen.Comment: 13 pages, 1 figur