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Variational and extremum properties of homogeneous chemical kinetics. I: Lagrangian- and Hamiltonian-like formulations. (English) Zbl 0895.92038

Open Syst. Inf. Dyn. 1, No. 2, 149-182 (1992); errata ibid. 1, No. 3, 459 (1992).
Summary: Variational and extremum approaches to homogeneous chemical kinetics of complex reaction systems far from equilibrium are synthesized with particular attention paid to nonlinearities and transients. The purpose of the synthesis is a unification of chemical dynamics with the dynamics of other sorts of processes (e.g. mechanical ones). Although such a unification is an a posteriori formalism, it simplifies the treatment of coupling between chemical and nonchemical processes. The relations between earlier methods and those proposed in this paper are shown in the contexts of stationary actions, dissipative Lagrange equations and extrema of thermodynamic potentials.
A new method based on the concept of an action functional is developed, where irreversibility is taken into account by the explicit presence of the action itself in the Lagrangian. It is shown that the method removes some drawbacks to earlier approaches of this sort and it allows one to include inertial-inductive effects in the formalism. The chemaction is introduced as the action of a chemical reaction, and its rôle in describing highly nonstationary nonlinear chemical is shown. Dissipative Lagrangian and Hamiltonian sets are developed for nonstationary kinetics and external transport. The formulation leads directly to the Guldberg-Waage law in the stationary case. For highly nonstationary kinetics a nonlocal generalization of that law is obtained, which obeys the general thermodynamic schemes of Casimir and Onsager-Machlup.

MSC:

92E20 Classical flows, reactions, etc. in chemistry
49S05 Variational principles of physics
82C35 Irreversible thermodynamics, including Onsager-Machlup theory
80A30 Chemical kinetics in thermodynamics and heat transfer

Citations:

Zbl 0895.92040
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