The integral optimizing functional (IOF) indicating separation efficiency in discrete space-time format

Based on the definition of information, integral optimizing functional (IOF ) in the discrete space-time format, H-s(t(k)), was obtained to indicate se paration efficiency. The physical essential of H-s(t(k)) is the information amount that the solute system gains from its separation surroundings in ti me-varying external force fields, which can accurately indicate integral an d time-varying separation efficiency in any actual separation process. H-s( t(k)) can be naturally partitioned into both linear and non-linear portions . The linear portion and almost all the parameters of separation efficiency in contemporary separation science (e.g. theoretical plate high, resolutio n, resolution product, peak capacity, the chromatographic resolution statis tic and the variety of them, etc.) are based on a common measure yardstick- zone width, which fails in measuring non-uniform distributions of solute zo nes in the topological space that the solute occupies. The linear portion i s only a special case of H-s(t(k)) if the number of volume elements is assu med to be one in the whole topological space. The non-linear portion is an indispensable correction of the linear portion for accurately measure of ac tual zone distributions, and it depends upon the type of homeomorphism conf igurations of zone distributions. The results of computer simulation of Gau ssian and various exponentially modified Gaussian peaks support the theoret ical predictions. The discovery of H-s(t(k)) lays a solid foundation of rea l-time control and dynamic optimization of actual separation processes with non-equilibrium thermodynamic separation theory.