Parabola stationary point

The stationary point of the parabola (2.37) is obtained by solving the root-finding problem with its first derivative ... 

Under the hypothesis of a symmetric and positive definite matrix G, each onedimensional search can be approximated using a parabola with a minimum for the stationary point. 

Equation (3.340) yields a paraboloid-like change of dissipation with respect to forces A, andX2, as seen in Figure 3.4. The system tends to minimize the entropy and eventually reaches zero entropy production if there are no restrictions on the forces. On the other hand, if we externally fix the value of one of the forces, for example, A 2 = X20, then the system will tend toward the stationary state characterized by the minimum entropy production at X2 = X20. The system will move along the parabola of Figure 3.4 and stop at point [Pg.147]

It was Ford and Wheeler(1959) who realized that this observation is nothing but the mathematical expression of our classical intuition. They skilfully applied this idea to elastic scattering on a simple potential curve, but Matsuzawa (1968) remarked that it applies as well to scattering on two crossing curves. In the lowest order stationary phase approximation the phase shifts tf b are developed around the points of stationary phase at /, and approximated by a parabola. The inelastic scattering amplitude can be written as a sum over separate contributions ... 

---