scholarly journals Chemical Kinetics Roots and Methods to Obtain the Probability Distribution Function Evolution of Reactants and Products in Chemical Networks Governed by a Master Equation

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 181 ◽  
Author(s):  
José-Luis Muñoz-Cobo ◽  
Cesar Berna
Keyword(s):  
Probability Distribution ◽  
Master Equation ◽  
Factorial Moment ◽  
Probability Generating Function ◽  
Maximum Entropy Principle ◽  
Point Of View ◽  
Chemical System ◽  
Entropy Principle ◽  
Random Part ◽  
Multinomial Coefficients

In this paper first, we review the physical root bases of chemical reaction networks as a Markov process in multidimensional vector space. Then we study the chemical reactions from a microscopic point of view, to obtain the expression for the propensities for the different reactions that can happen in the network. These chemical propensities, at a given time, depend on the system state at that time, and do not depend on the state at an earlier time indicating that we are dealing with Markov processes. Then the Chemical Master Equation (CME) is deduced for an arbitrary chemical network from a probability balance and it is expressed in terms of the reaction propensities. This CME governs the dynamics of the chemical system. Due to the difficulty to solve this equation two methods are studied, the first one is the probability generating function method or z-transform, which permits to obtain the evolution of the factorial moment of the system with time in an easiest way or after some manipulation the evolution of the polynomial moments. The second method studied is the expansion of the CME in terms of an order parameter (system volume). In this case we study first the expansion of the CME using the propensities obtained previously and splitting the molecular concentration into a deterministic part and a random part. An expression in terms of multinomial coefficients is obtained for the evolution of the probability of the random part. Then we study how to reconstruct the probability distribution from the moments using the maximum entropy principle. Finally, the previous methods are applied to simple chemical networks and the consistency of these methods is studied.

scholarly journals A LINK BETWEEN THE MAXIMUM ENTROPY APPROACH AND THE VARIATIONAL ENTROPY FORM

2011 ◽  
Vol 25 (22) ◽  
pp. 1821-1828 ◽  
Author(s):  
E. V. VAKARIN ◽  
J. P. BADIALI
Keyword(s):  
Probability Distribution ◽  
Maximum Entropy ◽  
Variational Formulation ◽  
Variational Approach ◽  
Maximum Entropy Principle ◽  
Random Variable ◽  
Entropy Measure ◽  
Universal Relation ◽  
Amount Of Information ◽  
Entropy Principle

The maximum entropy approach operating with quite general entropy measure and constraint is considered. It is demonstrated that for a conditional or parametrized probability distribution f(x|μ), there is a "universal" relation among the entropy rate and the functions appearing in the constraint. This relation allows one to translate the specificities of the observed behavior θ(μ) into the amount of information on the relevant random variable x at different values of the parameter μ. It is shown that the recently proposed variational formulation of the entropic functional can be obtained as a consequence of this relation, that is from the maximum entropy principle. This resolves certain puzzling points that appeared in the variational approach.

scholarly journals Identifying the Probability Distribution of Fatigue Life Using the Maximum Entropy Principle

Entropy ◽  
2016 ◽  
Vol 18 (4) ◽  
pp. 111 ◽  
Author(s):  
Hongshuang Li ◽  
Debing Wen ◽  
Zizi Lu ◽  
Yu Wang ◽  
Feng Deng
Keyword(s):  
Fatigue Life ◽  
Probability Distribution ◽  
Maximum Entropy ◽  
Maximum Entropy Principle ◽  
Entropy Principle

MAXIMUM ENTROPY PRINCIPLE AND THE LOGISTIC MODEL

1999 ◽  
Vol 07 (01) ◽  
pp. 51-62
Author(s):  
RAYMOND LEBLANC ◽  
STANLEY SHAPIRO
Keyword(s):  
Maximum Entropy ◽  
Odds Ratio ◽  
Logistic Model ◽  
Probability Model ◽  
Maximum Entropy Principle ◽  
Point Of View ◽  
Dichotomous Data ◽  
Multiplicative Effect ◽  
Entropy Principle ◽  
Log Odds

This paper proposes the use of the maximum entropy principle to construct a probability model under constraints for the analysis of dichotomous data using the odds ratio adjusted for covariates. It gives a new understanding of the now famous logistic model. We show that we can do away with the hypothesis of linearity of the log odds and still effectively use the model properly. From a practical point of view, the result implies that we do not have to discuss the plausability of the linearity hypothesis relative to the data or the phenomenon under study. Hence, when using the logistic model, we do not have to discuss the multiplicative effect of the covariates on the odds ratio. This is a major gain in the use of the model if one does not have to establish or justify the multiplicative effect, for instance, of alcohol consumption while considering low birth weight babies.

Use in Probabilistic Design of the Maximum Entrophy Distribution Based on Ranked Data

1980 ◽  
Vol 102 (3) ◽  
pp. 460-468
Author(s):  
J. N. Siddall ◽  
Ali Badawy
Keyword(s):  
Probability Distribution ◽  
Maximum Entropy ◽  
Probability Distributions ◽  
Maximum Entropy Principle ◽  
Random Variable ◽  
Probabilistic Design ◽  
Entropy Principle ◽  
Almost All ◽  
New Distribution

A new algorithm using the maximum entropy principle is introduced to estimate the probability distribution of a random variable, using directly a ranked sample. It is demonstrated that almost all of the analytical probability distributions can be approximated by the new algorithm. A comparison is made between existing methods and the new algorithm; and examples are given of fitting the new distribution to an actual ranked sample.

Probability distribution estimation for Web service QoS based on max entropy principle

2013 ◽  
Vol 32 (10) ◽  
pp. 2728-2731
Author(s):  
Zhi-hua DAI ◽  
Xiao-dong FU ◽  
Yuan HUANG ◽  
Nan JIA
Keyword(s):  
Probability Distribution ◽  
Web Service ◽  
Distribution Estimation ◽  
Entropy Principle
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