An entropy formula over the dynamical balls and its applications

2021 ◽  
Author(s):  
Tao Wang
Keyword(s):  
Entropy Formula

scholarly journals Bra-ket wormholes in gravitationally prepared states

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Yiming Chen ◽  
Victor Gorbenko ◽  
Juan Maldacena
Keyword(s):  
Hyperbolic Space ◽  
Path Integral ◽  
Flat Space ◽  
Low Energy ◽  
Two Dimensional ◽  
De Sitter ◽  
Euclidean Case ◽  
Fine Grained ◽  
Entropy Formula ◽  
First Case

Abstract We consider two dimensional CFT states that are produced by a gravitational path integral.As a first case, we consider a state produced by Euclidean AdS2 evolution followed by flat space evolution. We use the fine grained entropy formula to explore the nature of the state. We find that the naive hyperbolic space geometry leads to a paradox. This is solved if we include a geometry that connects the bra with the ket, a bra-ket wormhole. The semiclassical Lorentzian interpretation leads to CFT state entangled with an expanding and collapsing Friedmann cosmology.As a second case, we consider a state produced by Lorentzian dS2 evolution, again followed by flat space evolution. The most naive geometry also leads to a similar paradox. We explore several possible bra-ket wormholes. The most obvious one leads to a badly divergent temperature. The most promising one also leads to a divergent temperature but by making a projection onto low energy states we find that it has features that look similar to the previous Euclidean case. In particular, the maximum entropy of an interval in the future is set by the de Sitter entropy.

ON LOCAL ENTROPY OF RANDOM TRANSFORMATIONS

2008 ◽  
Vol 08 (02) ◽  
pp. 197-207 ◽  
Author(s):  
YUJUN ZHU
Keyword(s):  
Local Entropy ◽  
Entropy Formula

In this paper, Brin–Katok's local entropy formula is established for random transformations.

Smoothness of stable holonomies inside center-stable manifolds

2021 ◽  
pp. 1-26
Author(s):  
AARON BROWN
Keyword(s):  
Compact Manifolds ◽  
Stable Manifolds ◽  
Entropy Formula ◽  
Partially Hyperbolic

Abstract Under a suitable bunching condition, we establish that stable holonomies inside center-stable manifolds for $C^{1+\beta }$ diffeomorphisms are uniformly bi-Lipschitz and, in fact, $C^{1+\mathrm {H\ddot{o}lder}}$ . This verifies the ergodicity of suitably center-bunched, essentially accessible, partially hyperbolic $C^{1+\beta }$ diffeomorphisms and verifies that the Ledrappier–Young entropy formula holds for $C^{1+\beta }$ diffeomorphisms of compact manifolds.

Copper macrocyclic complex with trans-di[benzo]-porphyrazine and two oxo ligands: DFT quantum-chemical design

2021 ◽  
pp. A-F
Author(s):  
Oleg V. Mikhailov ◽  
Denis V. Chachkov
Keyword(s):  
Quantum Chemical ◽  
Structural Parameters ◽  
Dft Method ◽  
Nbo Analysis ◽  
Macrocyclic Complex ◽  
Chemical Calculation ◽  
Entropy Formula ◽  
Energy Formula ◽  
Thermodynamic Parameters Of Formation ◽  
Benzo Derivative

Based on the results of a quantum chemical calculation using the DFT method in the OPBE/TZVP and B3PW91/TZVP, the possibility of the existence of a copper heteroligand complex with trans-di[benzo]derivative of 3,7,11,15-tetraazaporphine (trans-di[benzo]porphyrazine) and two oxygen (O[Formula: see text] ions that is still unknown for this element was shown. In addition, the data on the structural parameters, the multiplicity of the ground state, NBO analysis and standard thermodynamic parameters of formation (standard enthalpy [Formula: see text], entropy [Formula: see text] and Gibbs’s energy [Formula: see text] for this complex are presented.

scholarly journals The Katok's entropy formula for amenable group actions

2018 ◽  
Vol 38 (9) ◽  
pp. 4467-4482
Author(s):  
Xiaojun Huang ◽  
◽  
Jinsong Liu ◽  
Changrong Zhu ◽  
◽  
...  
Keyword(s):  
Amenable Group ◽  
Group Actions ◽  
Entropy Formula

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 HOLLOWGRAPHY DRIVEN HOLOGRAPHY: BLACK HOLE WITH VANISHING VOLUME INTERIOR

2010 ◽  
Vol 19 (14) ◽  
pp. 2345-2351 ◽  
Author(s):  
AHARON DAVIDSON ◽  
ILYA GURWICH
Keyword(s):  
Phase Transition ◽  
General Relativity ◽  
Black Hole ◽  
Degrees Of Freedom ◽  
Schwarzschild Solution ◽  
Entropy Formula ◽  
Gravitational Theories ◽  
Hollow Interior ◽  
Spatial Volume ◽  
Self Similar

Hawking–Bekenstein entropy formula seems to tell us that no quantum degrees of freedom can reside in the interior of a black hole. We suggest that this is a consequence of the fact that the volume of any interior sphere of finite surface area simply vanishes. Obviously, this is not the case in general relativity. However, we show that such a phenomenon does occur in various gravitational theories which admit a spontaneously induced general relativity. In such theories, due to a phase transition (one-parameter family degenerates) which takes place precisely at the would-have-been horizon, the recovered exterior Schwarzschild solution connects, by means of a self-similar transition profile, with a novel "hollow" interior exhibiting a vanishing spatial volume and a locally varying Newton constant. This constitutes the so-called "hollowgraphy" driven holography.

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