Based on the definition of information, integral optimizing functional (IOF) in the discrete spacetime format, H~s(t~k), was obtained to indicate separation efficiency. The physical essential of H~s(t~k) is the information amount that the solute system gains from its separation surroundings in time-varying external force fields, which can accurately indicate integral and 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 seapration science (e. g. theoretical plate high, resolution, resolution product, peak capacity, the chromatographic resolution statistic and the variety of them, etc.) are based on a common measure yardstick-zone width, which fails in measuring non- uniform distributions of solute zones in the topological space that the solute occupies. The linear portion is only a special case of H~s (t~k) if the number of volume elements is assumed to be one in the whole topological space. The non-linear portion is an indispensable correction of the linear portion for accurately measure of actual zone distributions, and it depends upon the type of homeomorphism configurations of zone distributions. The results of computer simulation of Gaussian and various exponentially modified Gaussian peaks support the theoretical predictions. The discovery of H~s(t~k) lays a solid foundation of real-time control and dynamic optimization of actual separation processes with non-equilibrium thermodynamic separation theory.

Key words: SEPARATION EFFICIENCY, THERMODYNAMICS