Multivariate Extension of Matrix-based Renyi's α-order Entropy Functional

2019 ◽  
pp. 1-1 ◽  
Author(s):  
Shujian Yu ◽  
Luis Gonzalo Sanchez Giraldo ◽  
Robert Jenssen ◽  
Jose C. Principe
Keyword(s):  
Multivariate Extension ◽  
Entropy Functional

scholarly journals Entanglement entropy in cubic gravitational theories

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Elena Cáceres ◽  
Rodrigo Castillo Vásquez ◽  
Alejandro Vilar López
Keyword(s):  
Entanglement Entropy ◽  
Gravitational Theory ◽  
Riemann Tensor ◽  
Holographic Entanglement Entropy ◽  
Gravitational Theories ◽  
Entropy Functional ◽  
Wide Range ◽  
Splitting Problem ◽  
Range Of Values

Abstract We derive the holographic entanglement entropy functional for a generic gravitational theory whose action contains terms up to cubic order in the Riemann tensor, and in any dimension. This is the simplest case for which the so-called splitting problem manifests itself, and we explicitly show that the two common splittings present in the literature — minimal and non-minimal — produce different functionals. We apply our results to the particular examples of a boundary disk and a boundary strip in a state dual to 4- dimensional Poincaré AdS in Einsteinian Cubic Gravity, obtaining the bulk entanglement surface for both functionals and finding that causal wedge inclusion is respected for both splittings and a wide range of values of the cubic coupling.

A multivariate extension of an inequality of Brenner–Alzer

2012 ◽  
Vol 98 (3) ◽  
pp. 277-287 ◽  
Author(s):  
Allal Guessab ◽  
Otheman Nouisser ◽  
Josip Pečarić
Keyword(s):  
Multivariate Extension

scholarly journals A logarithmic correction in the entropy functional formalism

2016 ◽  
Vol 25 (07) ◽  
pp. 1650080 ◽  
Author(s):  
Fayçal Hammad ◽  
Mir Faizal
Keyword(s):  
Quantum Gravity ◽  
Modified Gravity ◽  
Correction Term ◽  
Modified Theories Of Gravity ◽  
Logarithmic Correction ◽  
Functional Formalism ◽  
Entropy Formula ◽  
Entropy Functional ◽  
Modified Gravity Theories ◽  
Theories Of Gravity

The entropy functional formalism allows one to recover general relativity, modified gravity theories, as well as the Bekenstein–Hawking entropy formula. In most approaches to quantum gravity, the Bekenstein–Hawking’s entropy formula acquires a logarithmic correction term. As such terms occur almost universally in most approaches to quantum gravity, we analyze the effect of such terms on the entropy functional formalism. We demonstrate that the leading correction to the micro-canonical entropy in the entropy functional formalism can be used to recover modified theories of gravity already obtained with an uncorrected micro-canonical entropy. Furthermore, since the entropy functional formalism reproduces modified gravity, the rise of gravity-dependent logarithmic corrections turns out to be one way to impose constraints on these theories of modified gravity. The constraints found here for the simple case of an [Formula: see text]-gravity are the same as those obtained in the literature from cosmological considerations.

scholarly journals A New Interpretation of Vortex-Split Sudden Stratospheric Warmings in Terms of Equilibrium Statistical Mechanics

2017 ◽  
Vol 74 (12) ◽  
pp. 3915-3936 ◽  
Author(s):  
Yuki Yasuda ◽  
Freddy Bouchet ◽  
Antoine Venaille
Keyword(s):  
Statistical Mechanics ◽  
Equilibrium State ◽  
Stationary State ◽  
Large Scale ◽  
Saddle Points ◽  
Polar Vortex ◽  
Equilibrium Statistical Mechanics ◽  
Entropy Functional ◽  
Quasi Stationary State ◽  
Vortex Split

Abstract Vortex-split sudden stratospheric warmings (S-SSWs) are investigated by using the Japanese 55-year Reanalysis, a spherical barotropic quasigeostrophic (QG) model, and equilibrium statistical mechanics. The statistical mechanics theory predicts a large-scale steady state as the most probable outcome of turbulent stirring, and such a state can be computed without describing all the details of the dynamics. The theory is applied to a disk domain that is modeled on the polar cap north of 45°N in the stratosphere. The equilibrium state is obtained by computing the maximum of an entropy functional. In the range of parameters relevant to the winter stratosphere, this state is anticyclonic. By contrast, cyclonic states are quasi-stationary states corresponding to saddle points of the entropy functional. These results indicate that the mean state of the stratosphere associated with the polar vortex is not close to an equilibrium state but to a quasi-stationary state. The theoretical calculations are compared with the results of a quasi-static experiment in which a wavenumber-2 topographic amplitude is increased linearly and slowly with time. The results suggest that the S-SSW can be qualitatively interpreted as the transition from the cyclonic quasi-stationary state toward the anticyclonic equilibrium state. The polar vortex splits during the transition toward the equilibrium state.

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