Nonlinear flux-force relations and equipartition theorems for the state of minimum entropy production
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.
scientific article; zbMATH DE number 5015638