Nonlinear flux-force relations and equipartition theorems for the state of minimum entropy production
type: Item
instance of: scholarly article
title: Nonlinear flux-force relations and equipartition theorems for the state of minimum entropy production
zbMATH Open document ID: 1087.80005
DOI: 10.1515/JNETDY.2005.009
author: Eivind Johannessen
author: Signe Kjelstrup
published in: Journal of Non-Equilibrium Thermodynamics
publication date: 2006-03-28T00:00:00Z
review text: The authors consider ordinary differential equations of the kind \(d{y} /dz={A}( {y}) {\Gamma J}( {y}, {x}) \), where \(z\) is a space or time variable, \({A}\) and \({\Gamma }\) are matrices, \({J}\) is a vector which depends on both the state variables \({y}\) and the control variables \({x}\). The entropy is defined through \(( dS/dt) _{\text{irr} }=\int_{0}^{L}{x}^{\text{T}}{\Gamma J}( {y}, {x})\,dz\). The authors compute the Hamiltonian of this optimal control problem and then specialize to the case of a chemical reactor with a single reaction, introducing the conservation of energy and a mole balance. They indeed consider the situation with one state variable (the temperature). Changing this state variable to the force of the reaction in the rate expression, they prove that they can use the above context, as an approximation, under some further hypotheses. They refer to two other papers they wrote for further detailed explanations.
Mathematics Subject Classification ID: 80A25
Mathematics Subject Classification ID: 49J15
zbMATH DE Number: 5015638
zbMATH Keywords: entropy production
zbMATH Keywords: nonlinear flux-force relation
zbMATH Keywords: chemical reaction
zbMATH Keywords: optimal control theory
Wikidata QID: Q62058313
reviewed by: Alain Brillard
MaRDI profile type: Publication
cites work: Optimization of processes by equipartition
full work available at URL: jnetdy.2005.009
OpenAlex ID: W2061651494
description: scientific article; zbMATH DE number 5015638