Quasi-homogeneous black hole thermodynamics

Although the fundamental equations of ordinary thermodynamic systems are known to correspond to first-degree homogeneous functions, in the case of non-ordinary systems like black holes the corresponding fundamental equations are not homogeneous. We present several arguments, indicating that black holes should be described by means of quasi-homogeneous functions of degree different from one. In particular, we show that imposing the first-degree condition leads to contradictory results in thermodynamics and geometrothermodynamics of black holes. As a consequence, we show that in generalized gravity theories the coupling constants like the cosmological constant, the Born-Infeld parameter or the Gauss-Bonnet constant must be considered as thermodynamic variables

Gowdy T3T^3 Cosmological Models in N=1 Supergravity

We investigate the canonical quantization of supergravity N=1 in the case of a midisuperspace described by Gowdy $T^3$ cosmological models. The quantum constraints are analyzed and the wave function of the universe is derived explicitly. Unlike the minisuperspace case, we show the existence of physical states in midisuperspace models. The analysis of the wave function of the universe leads to the conclusion that the classical curvature singularity present in the evolution of Gowdy models is removed at the quantum level due to the presence of the Rarita-Schwinger field.Comment: 25 pages and 2 figure

Curvature as a Measure of the Thermodynamic Interaction

We present a systematic and consistent construction of geometrothermodynamics by using Riemannian contact geometry for the phase manifold and harmonic maps for the equilibrium manifold. We present several metrics for the phase manifold that are invariant with respect to Legendre transformations and induce thermodynamic metrics on the equilibrium manifold. We review all the known examples in which the curvature of the thermodynamic metrics can be used as a measure of the thermodynamic interaction

Geometrothermodynamic description of magnetic materials

We perform a statistical and geometrothermodynamic analysis of three different models of magnetic materials, namely, the translational free model, the spin model, and the mean-field model. First, we derive the fundamental equation for each model, which is then used as input to compute the metrics of the corresponding equilibrium spaces. Analyzing the corresponding geometrothermodynamic curvatures, we conclude that they can be used to describe thermodynamic interaction, stability conditions, and the phase transition structure of the modeled substances. In all the cases, we reproduce their well-known behavior close to the Curie temperature. Moreover, in the case of the model with spin, we found a curvature singularity which corresponds to a novel transition, where a particular response function diverges, indicating the presence of second order phase transition, according to Ehrenfest classification

Geometrothermodynamics of asymptotically anti - de Sitter black holes

We apply the formalism of geometrothermodynamics to the case of black holes with cosmological constant in four and higher dimensions. We use a thermodynamic metric which is invariant with respect to Legendre transformations and determines the geometry of the space of equilibrium states. For all known black holes in higher dimensions, we show that the curvature scalar of the thermodynamic metric in all the cases is proportional to the heat capacity. As a consequence, phase transitions, which correspond to divergencies of the heat capacity, are represented geometrically as true curvature singularities. We interpret this as a further indication that the curvature of the thermodynamic metric is a measure of thermodynamic interaction.Comment: Section on statistical ensembles and new references adde

Simulación y evaluación de la confiabilidad de un proceso de sistema de producción

En el presente trabajo se estudia la confiabilidad y la supervivencia de datos en una empresa que comercializa equipos de tecnología para desarrollar labores administrativas cotidianas. Primero se realiza un preámbulo de la historia e importancia de la confiabilidad de aparatos o sistemas ya sea en el campo de la medicina o en el campo industrial; dando a conocer también algunos conceptos básicos de la teoría de la confiabilidad o supervivencia. Luego se manifiestan los diversos modelos de supervivencia, y demás técnicas estadísticas y actuariales ligadas con este tipo de análisis. Como paso siguiente se realiza un estudio de las técnicas para la estimación no paramétrica, apropiado para este análisis de los tiempos de falla o también denominados tiempos de supervivencia. En la siguiente parte se realizarán los respectivos cálculos para estimar de forma paramétrica y no paramétrica la función de supervivencia de los datos obtenidos dentro de la empresa comercializadora de equipos con tecnología. Por último, se realizarán las conclusiones obtenidas del desarrollo del estudio, junto con las respectivas recomendaciones para la obtención de mejoras para próximos análisis