Numerical optimization in allocation, storage and recovery of thermal energy and resources 257 7.6. MEAN AND LOCAL INTENSITIES IN DISCRETE PROCESSES Further transformations are easier if the following intensity criterion is intro- duced: n n 1 - T 0 T n 1/n (7.51) To identify the physical meaning of let us calculate its limiting value for n approaching infinity (continuous process). Since n lim n 1 - T 0 T n 1/n 0 n = lim 1 - (T /T ) = ln x0 x x T n T 0 we obtain from Equation (7.51) n lim lim n n 1 - n T 0 T n 1/n n 0 = ln T - ln T n (7.52) Therefore defined by Equation (7.51) is a discrete counterpart of the mean relaxation rate of the temperature logarithm for the n-stage process. For an arbitrary stage n we can also introduce a local intensity of a discrete process n T n - T n-1 T n  n (7.53) This quantity can be obtained after careful use of Equation (7.51) for n = 1 and appropriate change of symbols. Its limit for n is instantaneous logarithmic rate of state change in a continuous process: lim T n - T n-1 d ln T = = T n  n d (7.54) n Applying the geometric sequence property for optimal path in the considered example T 0 T 0 T 1 T n-1 = 1 2 ··· = T n T n T T T n-1 T n n (7.55)