scholarly journals Rényi entropy, mutual information, and fluctuation properties of Fermi liquids

2012 ◽  
Vol 86 (4) ◽  
Author(s):  
Brian Swingle
Keyword(s):  
Mutual Information ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Fermi Liquids

scholarly journals Conditional Rényi Entropy and the Relationships between Rényi Capacities

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 526
Author(s):  
Gautam Aishwarya ◽  
Mokshay Madiman
Keyword(s):  
Mutual Information ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Basic Properties ◽  
Reference Measure ◽  
Definition Of ◽  
Discrete Setting

The analogues of Arimoto’s definition of conditional Rényi entropy and Rényi mutual information are explored for abstract alphabets. These quantities, although dependent on the reference measure, have some useful properties similar to those known in the discrete setting. In addition to laying out some such basic properties and the relations to Rényi divergences, the relationships between the families of mutual informations defined by Sibson, Augustin-Csiszár, and Lapidoth-Pfister, as well as the corresponding capacities, are explored.

scholarly journals A Two-Moment Inequality with Applications to Rényi Entropy and Mutual Information

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1244
Author(s):  
Galen Reeves
Keyword(s):  
Mutual Information ◽  
Upper Bound ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Conditional Density ◽  
Moment Inequality ◽  
Single Moment ◽  
Variance Decompositions ◽  
Moment Constraint ◽  
Maximum Entropy Distributions

This paper explores some applications of a two-moment inequality for the integral of the rth power of a function, where 0<r<1. The first contribution is an upper bound on the Rényi entropy of a random vector in terms of the two different moments. When one of the moments is the zeroth moment, these bounds recover previous results based on maximum entropy distributions under a single moment constraint. More generally, evaluation of the bound with two carefully chosen nonzero moments can lead to significant improvements with a modest increase in complexity. The second contribution is a method for upper bounding mutual information in terms of certain integrals with respect to the variance of the conditional density. The bounds have a number of useful properties arising from the connection with variance decompositions.

ANALYSIS OF THE α-RENYI ENTROPY AND ITS APPLICATION FOR MEDICAL IMAGE REGISTRATION

2017 ◽  
Vol 29 (03) ◽  
pp. 1750020
Author(s):  
Meisen Pan ◽  
Fen Zhang
Keyword(s):  
Image Registration ◽  
Mutual Information ◽  
Parameter Optimization ◽  
Medical Image ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Registration Accuracy ◽  
Computational Load ◽  
Image Registrations ◽  
Parameter Ranges

In this paper, the [Formula: see text]-Renyi entropy and [Formula: see text]-Renyi-based mutual information (RMI) are first introduced. Then the influence of the parameter [Formula: see text] on the curve of the RMI and the computational load of image registration are discussed and analyzed to explore the appropriate parameter ranges. Finally, the RMI with the appropriate parameter [Formula: see text] is viewed as the similarity measure between the reference and floating images. In the experiments, the Simplex method is chosen as the multi-parameter optimization one. The experimental results reveal that the proposed method has low computational load, fast registration and good registration accuracy. It is adapted to both mono-modality and multi-modality image registrations.

scholarly journals Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory. Part I. Single-particle states

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Jiaju Zhang ◽  
M.A. Rajabpour
Keyword(s):  
Excited States ◽  
Single Particle ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Large Momentum ◽  
Particle State ◽  
Two Dimensional ◽  
Universal Form ◽  
Conformal Field ◽  
Harmonic Chain

Abstract We investigate the Rényi entropy of the excited states produced by the current and its derivatives in the two-dimensional free massless non-compact bosonic theory, which is a two-dimensional conformal field theory. We also study the subsystem Schatten distance between these states. The two-dimensional free massless non-compact bosonic theory is the continuum limit of the finite periodic gapless harmonic chains with the local interactions. We identify the excited states produced by current and its derivatives in the massless bosonic theory as the single-particle excited states in the gapless harmonic chain. We calculate analytically the second Rényi entropy and the second Schatten distance in the massless bosonic theory. We then use the wave functions of the excited states and calculate the second Rényi entropy and the second Schatten distance in the gapless limit of the harmonic chain, which match perfectly with the analytical results in the massless bosonic theory. We verify that in the large momentum limit the single-particle state Rényi entropy takes a universal form. We also show that in the limit of large momenta and large momentum difference the subsystem Schatten distance takes a universal form but it is replaced by a new corrected form when the momentum difference is small. Finally we also comment on the mutual Rényi entropy of two disjoint intervals in the excited states of the two-dimensional free non-compact bosonic theory.

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