scholarly journals Rényi entropies, the analytic bootstrap, and 3D quantum gravity at higher genus

2015 ◽  
Vol 2015 (7) ◽  
Author(s):  
Matthew Headrick ◽  
Alexander Maloney ◽  
Eric Perlmutter ◽  
Ida G. Zadeh
Keyword(s):  
Quantum Gravity ◽  
Rényi Entropies ◽  
Higher Genus ◽  
Renyi Entropies

scholarly journals Time-independence of gravitational Rényi entropies and unitarity in quantum gravity

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Donald Marolf ◽  
Zhencheng Wang
Keyword(s):  
Quantum Gravity ◽  
Saddle Points ◽  
Cauchy Surface ◽  
Convergence Condition ◽  
Point Of View ◽  
Back Reaction ◽  
Unitary Evolution ◽  
Invariant Surfaces ◽  
Rényi Entropies ◽  
Renyi Entropies

Abstract The Hubeny-Rangamani-Takayanagi surface γHRT computing the entropy S(D) of a domain of dependence D on an asymptotically AdS boundary is known to be causally inaccessible from D. We generalize this gravitational result to higher replica numbers n > 1 by considering the replica-invariant surfaces (aka ‘splitting surfaces’) γ of real-time replica-wormhole saddle-points computing Rényi entropies Sn(D) and showing that there is a sense in which D must again be causally inaccessible from γ when the saddle preserves both replica and conjugation symmetry. This property turns out to imply the Sn(D) to be independent of any choice of any Cauchy surface ΣD for D, and also that the Sn(D) are independent of the choice of boundary sources within D. This is a key hallmark of unitary evolution in any dual field theory. Furthermore, from the bulk point of view it adds to the evidence that time evolution of asymptotic observables in quantum gravity is implemented by a unitary operator in each baby universe superselection sector. Though we focus here on pure Einstein-Hilbert gravity and its Kaluza-Klein reductions, we expect the argument to extend to any two-derivative theory who satisfies the null convergence condition. We consider both classical saddles and the effect of back-reaction from quantum corrections.

scholarly journals Analytic critical points of charged Rényi entropies from hyperbolic black holes

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Jie Ren
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Study Phase ◽  
Zero Temperature ◽  
Charged Scalar ◽  
Yang Mills ◽  
Gravitational Systems ◽  
Rényi Entropies ◽  
Zero Entropy ◽  
Renyi Entropies

Abstract We analytically study phase transitions of holographic charged Rényi entropies in two gravitational systems dual to the $$ \mathcal{N} $$ N = 4 super-Yang-Mills theory at finite density and zero temperature. The first system is the Reissner-Nordström-AdS5 black hole, which has finite entropy at zero temperature. The second system is a charged dilatonic black hole in AdS5, which has zero entropy at zero temperature. Hyperbolic black holes are employed to calculate the Rényi entropies with the entangling surface being a sphere. We perturb each system by a charged scalar field, and look for a zero mode signaling the instability of the extremal hyperbolic black hole. Zero modes as well as the leading order of the full retarded Green’s function are analytically solved for both systems, in contrast to previous studies in which only the IR (near horizon) instability was analytically treated.

scholarly journals Effect of dissociation energy on Shannon and Rényi entropies

2018 ◽  
Vol 4 (1) ◽  
pp. 134-142 ◽  
Author(s):  
C.A. Onate ◽  
A.N. Ikot ◽  
M.C. Onyeaju ◽  
O. Ebomwonyi ◽  
J.O.A. Idiodi
Keyword(s):  
Dissociation Energy ◽  
Rényi Entropies ◽  
Renyi Entropies

Upper bounds on Shannon and Rényi entropies for central potentials

2011 ◽  
Vol 52 (2) ◽  
pp. 022105 ◽  
Author(s):  
P. Sánchez-Moreno ◽  
S. Zozor ◽  
J. S. Dehesa
Keyword(s):  
Upper Bounds ◽  
Rényi Entropies ◽  
Renyi Entropies

scholarly journals Quench action and Rényi entropies in integrable systems

2017 ◽  
Vol 96 (11) ◽  
Author(s):  
Vincenzo Alba ◽  
Pasquale Calabrese
Keyword(s):  
Integrable Systems ◽  
Rényi Entropies ◽  
Renyi Entropies
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