scholarly journals The Case for Shifting the Renyi Entropy

Entropy ◽  
2019 ◽  
Vol 21 (1) ◽  
pp. 46 ◽  
Author(s):  
Francisco Valverde-Albacete ◽  
Carmen Peláez-Moreno
Keyword(s):  
Partition Function ◽  
Statistical Mechanics ◽  
Cross Entropy ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Rényi Entropies ◽  
Hölder Mean ◽  
New Formulation ◽  
Relationship Of ◽  
The Relationship

We introduce a variant of the Rényi entropy definition that aligns it with the well-known Hölder mean: in the new formulation, the r-th order Rényi Entropy is the logarithm of the inverse of the r-th order Hölder mean. This brings about new insights into the relationship of the Rényi entropy to quantities close to it, like the information potential and the partition function of statistical mechanics. We also provide expressions that allow us to calculate the Rényi entropies from the Shannon cross-entropy and the escort probabilities. Finally, we discuss why shifting the Rényi entropy is fruitful in some applications.

Statistical mechanics based on Renyi entropy

2000 ◽  
Vol 280 (3-4) ◽  
pp. 337-345 ◽  
Author(s):  
E.K. Lenzi ◽  
R.S. Mendes ◽  
L.R. da Silva
Keyword(s):  
Statistical Mechanics ◽  
Renyi Entropy ◽  
Rényi Entropy

scholarly journals Semiclassical limit of topological Rényi entropy in 3d Chern-Simons theory

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Siddharth Dwivedi ◽  
Vivek Kumar Singh ◽  
Abhishek Roy
Keyword(s):  
Semiclassical Limit ◽  
Entanglement Entropy ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Simons Theory ◽  
Yang Mills ◽  
Rényi Entropies ◽  
Chern Simons ◽  
Chern Simons Theory ◽  
Torus Links

Abstract We study the multi-boundary entanglement structure of the state associated with the torus link complement S3\Tp,q in the set-up of three-dimensional SU(2)k Chern-Simons theory. The focal point of this work is the asymptotic behavior of the Rényi entropies, including the entanglement entropy, in the semiclassical limit of k → ∞. We present a detailed analysis of several torus links and observe that the entropies converge to a finite value in the semiclassical limit. We further propose that the large k limiting value of the Rényi entropy of torus links of type Tp,pn is the sum of two parts: (i) the universal part which is independent of n, and (ii) the non-universal or the linking part which explicitly depends on the linking number n. Using the analytic techniques, we show that the universal part comprises of Riemann zeta functions and can be written in terms of the partition functions of two-dimensional topological Yang-Mills theory. More precisely, it is equal to the Rényi entropy of certain states prepared in topological 2d Yang-Mills theory with SU(2) gauge group. Further, the universal parts appearing in the large k limits of the entanglement entropy and the minimum Rényi entropy for torus links Tp,pn can be interpreted in terms of the volume of the moduli space of flat connections on certain Riemann surfaces. We also analyze the Rényi entropies of Tp,pn link in the double scaling limit of k → ∞ and n → ∞ and propose that the entropies converge in the double limit as well.

scholarly journals Indicators of wavefunction (de)localisation for avoided crossing in a quadrupole quantum billiard

2021 ◽  
Author(s):  
Kyu-Won Park ◽  
Juman Kim ◽  
Jisung Seo ◽  
Songky Moon ◽  
Kabgyun Jeong
Keyword(s):  
Root Mean Square ◽  
Image Contrast ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Mean Square ◽  
Inverse Participation Ratio ◽  
Participation Ratio ◽  
Avoided Crossing ◽  
Quantum Billiard ◽  
The Relationship

Abstract The relationship between wavefunction (de)localisation and avoided crossing in a quadrupole billiard is analysed. The following three-types of measures are employed for wavefunction (de)localisation: inverse participation ratio, inverse of Rényi entropy, and root-mean-square (RMS) image contrast. All these measures exhibit minimal values at the centre of the avoided crossing, where the wavefunction is maximally delocalised. Our results indicate that these quantities can be sufficient for the indication of wavefunction (de)localisation.

scholarly journals Study of Quantile-Based Cumulative Renyi Information Measure

2020 ◽  
Vol 9 (4) ◽  
pp. 886-909
Author(s):  
Rekha ◽  
Vikas Kumar
Keyword(s):  
Order Statistic ◽  
Random Variable ◽  
Information Measure ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Reliability Measure ◽  
Extreme Order Statistic ◽  
The Relationship

In this paper, we proposed a quantile version of cumulative Renyi entropy for residual and past lifetimes and study their properties. We also study quantile-based cumulative Renyi entropy for extreme order statistic when random variable untruncated or truncated in nature. Some characterization results are studied using the relationship between proposed information measure and reliability measure. We also examine it in relation to some applied problems such as weighted and equillibrium models.

Ensembles in Classical Statistical Mechanics

2019 ◽  
pp. 231-257
Author(s):  
Robert H. Swendsen
Keyword(s):  
Molecular Dynamics ◽  
Monte Carlo ◽  
Free Energy ◽  
Partition Function ◽  
Statistical Mechanics ◽  
Harmonic Oscillators ◽  
Canonical Partition Function ◽  
Classical Statistical Mechanics ◽  
Classical Models ◽  
The Relationship

This chapter explores more powerful methods of calculation than were seen previously. Among them are Molecular Dynamics (MD) and Monte Carlo (MC) computer simulations. Another is the canonical partition function, which is related to the Helmholtz free energy. The derivation of thermodynamic identities within statistical mechanics is illustrated by the relationship between the specific heat and the fluctuations of the energy. It is shown how the canonical ensemble allows us to integrate out the momentum variables for many classical models. The factorization of the partition function is presented as the best trick in statistical mechanics, because of its central role in solving problems. Finally, the problem of many simple harmonic oscillators is solved, both for its importance and as an illustration of the best trick.

scholarly journals Rényi Entropy and Rényi Divergence in Product MV-Algebras

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 587 ◽  
Author(s):  
Dagmar Markechová ◽  
Beloslav Riečan
Keyword(s):  
Shannon Entropy ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Rényi Divergence ◽  
New Concepts ◽  
Leibler Divergence ◽  
Mv Algebra ◽  
The Relationship ◽  
Mv Algebras

This article deals with new concepts in a product MV-algebra, namely, with the concepts of Rényi entropy and Rényi divergence. We define the Rényi entropy of order q of a partition in a product MV-algebra and its conditional version and we study their properties. It is shown that the proposed concepts are consistent, in the case of the limit of q going to 1, with the Shannon entropy of partitions in a product MV-algebra defined and studied by Petrovičová (Soft Comput.2000, 4, 41–44). Moreover, we introduce and study the notion of Rényi divergence in a product MV-algebra. It is proven that the Kullback–Leibler divergence of states on a given product MV-algebra introduced by Markechová and Riečan in (Entropy2017, 19, 267) can be obtained as the limit of their Rényi divergence. In addition, the relationship between the Rényi entropy and the Rényi divergence as well as the relationship between the Rényi divergence and Kullback–Leibler divergence in a product MV-algebra are examined.

The relationship of the scleractinian corals to the rugose corals

Paleobiology ◽  
1980 ◽  
Vol 6 (02) ◽  
pp. 146-160 ◽  
Author(s):  
William A. Oliver
Keyword(s):  
Critical Points ◽  
Scleractinian Corals ◽  
Convincing Evidence ◽  
Early Triassic ◽  
Rugose Corals ◽  
History Of ◽  
The Subject ◽  
Relationship Of ◽  
The Relationship ◽  
Biologic Factors

The Mesozoic-Cenozoic coral Order Scleractinia has been suggested to have originated or evolved (1) by direct descent from the Paleozoic Order Rugosa or (2) by the development of a skeleton in members of one of the anemone groups that probably have existed throughout Phanerozoic time. In spite of much work on the subject, advocates of the direct descent hypothesis have failed to find convincing evidence of this relationship. Critical points are:(1) Rugosan septal insertion is serial; Scleractinian insertion is cyclic; no intermediate stages have been demonstrated. Apparent intermediates are Scleractinia having bilateral cyclic insertion or teratological Rugosa.(2) There is convincing evidence that the skeletons of many Rugosa were calcitic and none are known to be or to have been aragonitic. In contrast, the skeletons of all living Scleractinia are aragonitic and there is evidence that fossil Scleractinia were aragonitic also. The mineralogic difference is almost certainly due to intrinsic biologic factors.(3) No early Triassic corals of either group are known. This fact is not compelling (by itself) but is important in connection with points 1 and 2, because, given direct descent, both changes took place during this only stage in the history of the two groups in which there are no known corals.

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