scholarly journals Relativistic equilibrium distribution by relative entropy maximization

2009 ◽  
Vol 88 (4) ◽  
pp. 40009 ◽  
Author(s):  
T. K. Nakamura
Keyword(s):  
Relative Entropy ◽  
Equilibrium Distribution ◽  
Entropy Maximization

scholarly journals A Second Law for Open Markov Processes

2016 ◽  
Vol 23 (01) ◽  
pp. 1650006 ◽  
Author(s):  
Blake S. Pollard
Keyword(s):  
Free Energy ◽  
Markov Process ◽  
Markov Processes ◽  
Relative Entropy ◽  
Upper Bound ◽  
Equilibrium Distribution ◽  
Detailed Balance ◽  
Rate Of Change ◽  
Second Law ◽  
Boundary States

In this paper we define the notion of an open Markov process. An open Markov process is a generalization of an ordinary Markov process in which populations are allowed to flow in and out of the system at certain boundary states. We show that the rate of change of relative entropy in an open Markov process is less than or equal to the flow of relative entropy through its boundary states. This can be viewed as a generalization of the Second Law for open Markov processes. In the case of a Markov process whose equilibrium obeys detailed balance, this inequality puts an upper bound on the rate of change of the free energy for any non-equilibrium distribution.

Entropy Maximizations on Electron Density

1993 ◽  
Vol 48 (1-2) ◽  
pp. 68-74 ◽  
Author(s):  
Douglas M. Collins
Keyword(s):  
Density Distribution ◽  
Charge Density ◽  
Image Enhancement ◽  
Electron Density ◽  
Relative Entropy ◽  
Particle Density ◽  
Informational Entropy ◽  
Charge Density Distribution ◽  
Entropy Maximization ◽  
Imperfect Data

Abstract Incomplete and imperfect data characterize the problem of constructing electron density representations from experimental information. One fundamental concern is identification of the proper protocol for including new information at any stage of a density reconstruction. An axiomatic approach developed in other fields specifies entropy maximization as the desired protocol. In particular, if new data are used to modify a prior charge density distribution without adding extraneous prejudice, the new distribution must both agree with all the data, new and old, and be a function of maximum relative entropy. The functional form of relative entropy is s = - r In (r/t), where r and t respectively refer to new and prior distributions normalized to a common scale.Entropy maximization has been used to deal with certain aspects of the phase problem of X-ray diffraction. Varying degrees of success have marked the work which may be roughly assigned to categories as direct methods, data reduction and analysis, and image enhancement. Much of the work has been expressed in probabilistic language, although image enhancement has been somewhat more physical or geometric in description. Whatever the language, entropy maximization is a specific and deterministic functional manipulation. A recent advance has been the description of an algorithm which, quite deterministically, adjusts a prior positive charge density distribution to agree exactly with a specified subset of structure-factor moduli by a constrained entropy maximization.Entropy on an N-representable one-particle density matrix is well defined. The entropy is the expected form, and it is a simple function of the one-matrix eigenvalues which all must be non-negative. Relationships between the entropy functional and certain properties of a one-matrix are discussed, as well as a conjecture concerning the physical interpretation of entropy. Throughout this work reference is made to informational entropy, not the entropy of thermodynamics.

Efficient Steganography Algorithm Based On DCT And Entropy Thresholding Technique

2018 ◽  
Vol 8 (1) ◽  
pp. 45
Author(s):  
Satvir Singh
Keyword(s):  
Relative Entropy ◽  
Experimental Work ◽  
Random Function ◽  
Signal To Noise Ratio ◽  
Binary Sequence ◽  
Threshold Value ◽  
Absolute Difference ◽  
Secret Message ◽  
Signal To Noise ◽  
Confidential Information

Steganography is the special art of hidding important and confidential information in appropriate multimedia carrier. It also restrict the detection of  hidden messages. In this paper we proposes steganographic method based on dct and entropy thresholding technique. The steganographic algorithm uses random function in order to select block of the image where the elements of the binary sequence of a secret message will be inserted. Insertion takes place at the lower frequency  AC coefficients of the  block. Before we insert the secret  message. Image under goes dc transformations after insertion of the secret message we apply inverse dc transformations. Secret message will only be inserted into a particular block if  entropy value of that particular block is greater then threshold value of the entropy and if block is selected by the random function. In  Experimental work we calculated the peak signal to noise ratio(PSNR), Absolute difference , Relative entropy. Proposed algorithm give high value of PSNR  and low value of Absolute difference which clearly indicate level of distortion in image due to insertion of secret message is reduced. Also value of  relative entropy is close to zero which clearly indicate proposed algorithm is sufficiently secure. 

Complete monotonicity of entropy production in chemical reaction

1981 ◽  
Vol 46 (2) ◽  
pp. 452-456
Author(s):  
Milan Šolc
Keyword(s):  
Entropy Production ◽  
Equilibrium Constant ◽  
Chemical Reaction ◽  
Relative Entropy ◽  
Order Reaction ◽  
Complete Monotonicity ◽  
First Order Reaction ◽  
First Order ◽  
Completely Monotonic ◽  
Derivatives Of

The successive time derivatives of relative entropy and entropy production for a system with a reversible first-order reaction alternate in sign. It is proved that the relative entropy for reactions with an equilibrium constant smaller than or equal to one is completely monotonic in the whole definition interval, and for reactions with an equilibrium constant larger than one this function is completely monotonic at the beginning of the reaction and near to equilibrium.

The effect of systematic errors of the equilibrium distribution concentrations on the number of stages of countercurrent extraction with various consumption of extractant

1989 ◽  
Vol 54 (4) ◽  
pp. 981-989
Author(s):  
Ján Dojčanský ◽  
Soňa Bafrncová ◽  
Július Surový
Keyword(s):  
Equilibrium Distribution ◽  
Systematic Errors ◽  
Mutual Solubility ◽  
Operating Conditions ◽  
Liquid Equilibrium ◽  
Countercurrent Extraction ◽  
Absolute Deviation ◽  
Line Slope ◽  
Tie Line ◽  
Calculated Number

On using five hypothetical systems differing in the extent of mutual solubility of components, tie-line slope, and type of binodal curve, the effect is evaluated of systematic errors in the form of absolute deviation in the liquid-liquid equilibrium distribution concentrations on the accuracy of calculated number of theoretical stages of isothermal countercurrent extraction under various operating conditions.

A novel q-rung orthopair fuzzy TODIM approach for multi-criteria group decision making based on Shapley value and relative entropy

2021 ◽  
Vol 40 (1) ◽  
pp. 235-250
Author(s):  
Liuxin Chen ◽  
Nanfang Luo ◽  
Xiaoling Gou
Keyword(s):  
Decision Making ◽  
Relative Entropy ◽  
Group Decision Making ◽  
Shapley Value ◽  
Group Decision ◽  
Similarity Measures ◽  
Entropy Measure ◽  
Shapley Values ◽  
Interactive Relationship ◽  
The Difference

In the real multi-criteria group decision making (MCGDM) problems, there will be an interactive relationship among different decision makers (DMs). To identify the overall influence, we define the Shapley value as the DM’s weight. Entropy is a measure which makes it better than similarity measures to recognize a group decision making problem. Since we propose a relative entropy to measure the difference between two systems, which improves the accuracy of the distance measure.In this paper, a MCGDM approach named as TODIM is presented under q-rung orthopair fuzzy information.The proposed TODIM approach is developed for correlative MCGDM problems, in which the weights of the DMs are calculated in terms of Shapley values and the dominance matrices are evaluated based on relative entropy measure with q-rung orthopair fuzzy information.Furthermore, the efficacy of the proposed Gq-ROFWA operator and the novel TODIM is demonstrated through a selection problem of modern enterprises risk investment. A comparative analysis with existing methods is presented to validate the efficiency of the approach.

scholarly journals Analysis of Genetic Structure and Dispersal Patterns in a Population of Sea Beet

Genetics ◽  
1998 ◽  
Vol 149 (4) ◽  
pp. 1975-1985
Author(s):  
Jarle Tufto ◽  
Alan F Raybould ◽  
Kjetil Hindar ◽  
Steinar Engen
Keyword(s):  
Equilibrium Distribution ◽  
Pollen Dispersal ◽  
Migration Pattern ◽  
Likelihood Ratio Tests ◽  
Frequency Data ◽  
Gene Frequencies ◽  
Dispersal Patterns ◽  
Parametric Bootstrapping ◽  
Estimated Parameters ◽  
Multivariate Stochastic Process

Abstract A model of the migration pattern in a metapopulation of sea beet (Beta vulgaris L. ssp. maritima), based on the continuous distributions of seed and pollen movements, is fitted to gene frequency data at 12 isozyme and RFLP loci by maximum likelihood by using an approximation of the simultaneous equilibrium distribution of the gene frequencies generated by the underlying multivariate stochastic process of genetic drift in the population. Several alternative restrictions of the general model are fitted to the data, including the island model, a model of complete isolation, and a model in which the seed and pollen dispersal variances are equal. Several likelihood ratio tests between these alternatives are performed, and median bias in the estimated parameters is corrected by using parametric bootstrapping. To assess the fit of the selected model, the predicted covariances are compared with covariances computed from the data directly. The dependency of estimated parameters on the ratio between effective and absolute subpopulation sizes, which is treated as a known parameter in the analysis, is also examined. Finally, we note that the data also appear to contain some information about this ratio.

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