scholarly journals Maximum Renyi Entropy Principle for Systems with Power-Law Hamiltonians

2004 ◽  
Vol 93 (13) ◽  
Author(s):  
A. G. Bashkirov
Keyword(s):  
Power Law ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Entropy Principle

scholarly journals Dynamics of non-stationary processes that follow the maximum of the Rényi entropy principle

2016 ◽  
Vol 472 (2185) ◽  
pp. 20150324 ◽  
Author(s):  
Dmitry S. Shalymov ◽  
Alexander L. Fradkov
Keyword(s):  
Limit Distribution ◽  
Mass Conservation ◽  
Random Variable ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Stationary Processes ◽  
Entropy Principle ◽  
Gradient Principle ◽  
Probability Density Function Pdf ◽  
Speed Gradient

We propose dynamics equations which describe the behaviour of non-stationary processes that follow the maximum Rényi entropy principle. The equations are derived on the basis of the speed-gradient principle originated in the control theory. The maximum of the Rényi entropy principle is analysed for discrete and continuous cases, and both a discrete random variable and probability density function (PDF) are used. We consider mass conservation and energy conservation constraints and demonstrate the uniqueness of the limit distribution and asymptotic convergence of the PDF for both cases. The coincidence of the limit distribution of the proposed equations with the Rényi distribution is examined.

Infrared Electric Image Enhancement Based On Fuzzy Renyi Entropy and Quantum Genetic Algorithm

2011 ◽  
Vol 66-68 ◽  
pp. 1774-1780
Author(s):  
Song Hai Fan ◽  
Shu Hong Yang ◽  
Pu He ◽  
Hong Yu Nie
Keyword(s):  
Genetic Algorithm ◽  
Infrared Image ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Maximal Entropy ◽  
Infrared Images ◽  
Low Contrast ◽  
Quantum Genetic Algorithm ◽  
Entropy Principle ◽  
Electric Equipment

Infrared thermograph has been applied in electric equipment inspection widely, but the visual effects of infrared images are always undesirable. Considering the limitation of low luminance，low contrast in infrared images，an enhancement method based on fuzzy Renyi entropy and quantum genetic algorithm is presented in this paper．Firstly，the contrast-sketching function presented in [1] is improved based on the idea of segmentation. Then, in order to segment the infrared image, Renyi entropy is extend to fuzzy domain considering the fuzzy nature of infrared image, and is employed to threshold the infrared image following maximal entropy principle. In order to meet the real-time demand of online monitoring, quantum genetic algorithm is employed to search the optimal parameters of the transform function. The experimental results indicate that the method can well improve the visual effect of infrared electric images．

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.

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.

A new Rényi entropy-based local image descriptor for object recognition

2010 ◽  
Author(s):  
S. Gabarda ◽  
G. Cristóbal ◽  
P. Rodríguez ◽  
C. Miravet ◽  
J. M. del Cura
Keyword(s):  
Object Recognition ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Image Descriptor ◽  
Local Image Descriptor ◽  
Local Image

scholarly journals Holographic calculations of Rényi entropy

2011 ◽  
Vol 2011 (12) ◽  
Author(s):  
Ling-Yan Hung ◽  
Robert C. Myers ◽  
Michael Smolkin ◽  
Alexandre Yale
Keyword(s):  
Renyi Entropy ◽  
Rényi Entropy
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