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Entropy 2018, 20(9), 678; https://doi.org/10.3390/e20090678

On Differences between Deterministic and Stochastic Models of Chemical Reactions: Schlögl Solved with ZI-Closure

Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA
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Received: 3 July 2018 / Revised: 29 August 2018 / Accepted: 4 September 2018 / Published: 6 September 2018
(This article belongs to the Special Issue Information Theory and Stochastics for Multiscale Nonlinear Systems)
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Abstract

Deterministic and stochastic models of chemical reaction kinetics can give starkly different results when the deterministic model exhibits more than one stable solution. For example, in the stochastic Schlögl model, the bimodal stationary probability distribution collapses to a unimodal distribution when the system size increases, even for kinetic constant values that result in two distinct stable solutions in the deterministic Schlögl model. Using zero-information (ZI) closure scheme, an algorithm for solving chemical master equations, we compute stationary probability distributions for varying system sizes of the Schlögl model. With ZI-closure, system sizes can be studied that have been previously unattainable by stochastic simulation algorithms. We observe and quantify paradoxical discrepancies between stochastic and deterministic models and explain this behavior by postulating that the entropy of non-equilibrium steady states (NESS) is maximum. View Full-Text
Keywords: closure scheme; maximum entropy; non-equilibrium steady state; Schlögl closure scheme; maximum entropy; non-equilibrium steady state; Schlögl
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Vlysidis, M.; Kaznessis, Y.N. On Differences between Deterministic and Stochastic Models of Chemical Reactions: Schlögl Solved with ZI-Closure. Entropy 2018, 20, 678.

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