scholarly journals Concentration functions and entropy bounds for discrete log-concave distributions

2021 ◽  
pp. 1-19
Author(s):  
Sergey G. Bobkov ◽  
Arnaud Marsiglietti ◽  
James Melbourne
Keyword(s):  
Probability Distributions ◽  
Concentration Functions ◽  
Rényi Entropies ◽  
Entropy Bounds ◽  
Renyi Entropies

Abstract Two-sided bounds are explored for concentration functions and Rényi entropies in the class of discrete log-concave probability distributions. They are used to derive certain variants of the entropy power inequalities.

scholarly journals The structure of Rényi entropic inequalities

2013 ◽  
Vol 469 (2158) ◽  
pp. 20120737 ◽  
Author(s):  
Noah Linden ◽  
Milán Mosonyi ◽  
Andreas Winter
Keyword(s):  
Quantum State ◽  
Probability Distributions ◽  
Negative Numbers ◽  
Entropic Inequalities ◽  
Von Neumann ◽  
Strong Subadditivity ◽  
Universal Inequalities ◽  
Homogeneous Relation ◽  
Rényi Entropies ◽  
Renyi Entropies

We investigate the universal inequalities relating the α -Rényi entropies of the marginals of a multi-partite quantum state. This is in analogy to the same question for the Shannon and von Neumann entropies ( α =1), which are known to satisfy several non-trivial inequalities such as strong subadditivity. Somewhat surprisingly, we find for 0< α <1 that the only inequality is non-negativity: in other words, any collection of non-negative numbers assigned to the non-empty subsets of n parties can be arbitrarily well approximated by the α -entropies of the 2 n −1 marginals of a quantum state. For α >1, we show analogously that there are no non-trivial homogeneous (in particular, no linear) inequalities. On the other hand, it is known that there are further, nonlinear and indeed non-homogeneous, inequalities delimiting the α -entropies of a general quantum state. Finally, we also treat the case of Rényi entropies restricted to classical states (i.e. probability distributions), which, in addition to non-negativity, are also subject to monotonicity. For α ≠0,1, we show that this is the only other homogeneous relation.

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
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