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Special Issue "Probability Distributions and Maximum Entropy in Stochastic Chemical Reaction Networks"

A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: 30 September 2018

Special Issue Editor

Guest Editor
Dr. Yiannis N. Kaznessis

Department of Chemical Engineering and Materials Science, University of Minnesota
E-Mail
Phone: 612/624-4197
Interests: stochastic kinetics; statistical thermodynamics; molecular simulations; antimicrobials

Special Issue Information

Dear Colleagues,

According to the second law of thermodynamics, when isolated systems are at an equilibrium state, their entropy is maximum. Numerous attempts have been made to establish a similar criterion for non-equilibrium steady states (NESS). For decades, the question has been posed whether NESS are stable when the entropy or the rate of entropy production is maximum or minimum. A satisfactory answer has yet to be provided, and there is no established criterion for NESS.

Chemical reaction networks away from the thermodynamic limit have drawn considerable attention in the past two decades with the advent of numerous stochastic simulation algorithms. Instead of the canonical continuous-deterministic models of reaction kinetics, reactions with small numbers of reactants are modeled with discrete-stochastic (e.g., Gillespie algorithms) or continuous-stochastic (e.g., Langevin equations) models. The outcome of these models is a probability distribution of the number of molecules for each of the reactants or products in the system. Because of the probabilistic nature of these networks, which can be studied in non-equilibrium steady states, the entropy may be computed and parallels may be drawn with molecular thermodynamics of systems at equilibrium, as well as with information theory arguments.

In this Special Issue, we welcome papers reporting on the progress of stochastic kinetic models for reaction networks. We welcome review and original papers in subjects that include, but are not limited to, the following areas:

  • NESS of stochastic reaction networks
  • Stochastic simulation algorithms
  • Hybrid and multiscale modeling formalisms
  • Chemical master equations
  • Steady state probabilities of reaction networks
  • Entropy and entropy production in reaction networks
Dr. Yiannis N. Kaznessis
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1500 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Stochastic chemical reactions
  • Non-equilibrium steady states (NESS)
  • Probability distributions
  • Entropy and entropy production in NESS

Published Papers (2 papers)

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Research

Open AccessArticle Solving Stochastic Reaction Networks with Maximum Entropy Lagrange Multipliers
Entropy 2018, 20(9), 700; https://doi.org/10.3390/e20090700
Received: 3 August 2018 / Revised: 5 September 2018 / Accepted: 6 September 2018 / Published: 12 September 2018
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Abstract
The time evolution of stochastic reaction networks can be modeled with the chemical master equation of the probability distribution. Alternatively, the numerical problem can be reformulated in terms of probability moment equations. Herein we present a new alternative method for numerically solving the
[...] Read more.
The time evolution of stochastic reaction networks can be modeled with the chemical master equation of the probability distribution. Alternatively, the numerical problem can be reformulated in terms of probability moment equations. Herein we present a new alternative method for numerically solving the time evolution of stochastic reaction networks. Based on the assumption that the entropy of the reaction network is maximum, Lagrange multipliers are introduced. The proposed method derives equations that model the time derivatives of these Lagrange multipliers. We present detailed steps to transform moment equations to Lagrange multiplier equations. In order to demonstrate the method, we present examples of non-linear stochastic reaction networks of varying degrees of complexity, including multistable and oscillatory systems. We find that the new approach is as accurate and significantly more efficient than Gillespie’s original exact algorithm for systems with small number of interacting species. This work is a step towards solving stochastic reaction networks accurately and efficiently. Full article
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Open AccessArticle Gradient and GENERIC Systems in the Space of Fluxes, Applied to Reacting Particle Systems
Entropy 2018, 20(8), 596; https://doi.org/10.3390/e20080596
Received: 2 July 2018 / Revised: 2 August 2018 / Accepted: 8 August 2018 / Published: 9 August 2018
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Abstract
In a previous work we devised a framework to derive generalised gradient systems for an evolution equation from the large deviations of an underlying microscopic system, in the spirit of the Onsager–Machlup relations. Of particular interest is the case where the microscopic system
[...] Read more.
In a previous work we devised a framework to derive generalised gradient systems for an evolution equation from the large deviations of an underlying microscopic system, in the spirit of the Onsager–Machlup relations. Of particular interest is the case where the microscopic system consists of random particles, and the macroscopic quantity is the empirical measure or concentration. In this work we take the particle flux as the macroscopic quantity, which is related to the concentration via a continuity equation. By a similar argument the large deviations can induce a generalised gradient or GENERIC system in the space of fluxes. In a general setting we study how flux gradient or GENERIC systems are related to gradient systems of concentrations. This shows that many gradient or GENERIC systems arise from an underlying gradient or GENERIC system where fluxes rather than densities are being driven by (free) energies. The arguments are explained by the example of reacting particle systems, which is later expanded to include spatial diffusion as well. Full article
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