Variational and extremum properties of homogeneous chemical kinetics. II. Minimum dissipation approaches

We continue our work on variational and extremum approaches to homogeneous chemical kinetics of complex reaction systems far from equilibrium and consider minimum dissipation approaches in both the energy and entropy representations. We generalize the linear results of Onsager and Onsager-Machlup to nonlinear (transient and nonisothermal) situations and show that the generalization obey their general thermodynamic schemes.With the help of an error criterion it is shown that the Onsager-Machlup linear variational scheme can be generalized to arbitrary nonlinear systems described by a set of coordinates not all of which need be independent and with dissipation quadratic with respect to rates; an outcome of this generalization is an integral principle of least entropy growth along the natural path governed by the dissipative Lagrange equations of motion and the balance constraints (in the entropy representation). The Lagrangian multipliers associated with the constraints are interpreted as the uniquenonequilibrium temperature and (negative) Planck potentials. They replace their well known equilibrium counterparts in extended expressions describing entropy flow far from equilibrium. The absolute nature of the minimum of the related power expressions is shown; this again corresponds to the dissipative Lagrange equations of motion.

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