Asymptotic stability,Onsager fluxes and reaction kinetics

This paper constitutes a first step in the derivation of thermodynamics directly from the dynamics of physical systems. The existence of an asymptotically stable equilibrium point is used to construct a family of admissible entropy functions. These functions have nonnegative entropy production and assume an absolute maximum at the equilibrium point. A nonlinear generalization of the Onsager theory is then used to obtain a one-to-one correspondence between entropy production functions and the governing system of autonomous rate equations. The theory is applied to well stirred chemically reacting systems with constant temperature and pressure. This allows the derivation of chemical potentials, Gibbs' potentials and enthalpy for such systems. The rate equations for reaction kinetics and for classical thermodynamic reaction theory are obtained. Classic thermodynamic reaction theory is shown to give maximum entropy for constant enthalpy at the equilibrium point, while reaction kinetics gives this result only to within quadratic terms in the departure from equilibrium.