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

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

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dc.contributor.author Muñoz-Cobo, José-Luis es_ES
dc.contributor.author Berna, Cesar es_ES
dc.date.accessioned 2021-01-26T04:31:43Z
dc.date.available 2021-01-26T04:31:43Z
dc.date.issued 2019-02 es_ES
dc.identifier.issn 1099-4300 es_ES
dc.identifier.uri http://hdl.handle.net/10251/159834
dc.description.abstract [EN] 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. es_ES
dc.description.sponsorship This research received no external funding This paper is devoted to Raphael B. Perez, Emeritus Professor of the University of Tennessee at Knoxville, to celebrate his 90 years birth day. es_ES
dc.language Inglés es_ES
dc.publisher MDPI AG es_ES
dc.relation.ispartof Entropy es_ES
dc.rights Reconocimiento (by) es_ES
dc.subject Maximum entropy principle es_ES
dc.subject Chemical master equation es_ES
dc.subject Chemical propensity es_ES
dc.subject Updating probability distribution functions es_ES
dc.subject Chemical reaction networks es_ES
dc.subject.classification INGENIERIA NUCLEAR es_ES
dc.subject.classification ESTADISTICA E INVESTIGACION OPERATIVA es_ES
dc.title Chemical Kinetics Roots and Methods to Obtain the Probability Distribution Function Evolution of Reactants and Products in Chemical Networks Governed by a Master Equation es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.3390/e21020181 es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Estadística e Investigación Operativa Aplicadas y Calidad - Departament d'Estadística i Investigació Operativa Aplicades i Qualitat es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Ingeniería Química y Nuclear - Departament d'Enginyeria Química i Nuclear es_ES
dc.description.bibliographicCitation Muñoz-Cobo, J.; Berna, C. (2019). 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. 21(2):1-37. https://doi.org/10.3390/e21020181 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.3390/e21020181 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 37 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 21 es_ES
dc.description.issue 2 es_ES
dc.relation.pasarela S\407943 es_ES
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