The random process of separation of an unknown mixture is characterized by its ultimate uncertainty UU, which is a function of the number of analytes Z and the separation system efficiency N. Therefore, the probabilities of the retention position and a minimal distance between two peaks can be derived on this base. It follows that, within a defined separation space, there will be a certain number of overlapping components, forming clusters containing a predictable number of components.

In multidimensional chromatography, the distribution constant is different in each dimension, and thus the analytes will behave differently in them. The separation will be enhanced in proportion to the number of chromatographic dimensions d and in an ideal case (non correlated dimensions) the increased peak capacity will correspond to the product of the single dimension capacities.

The most general criterion for applicability of a new dimension in multidimensional chromatography approach is evaluation of the information content I . It is based on evaluation of the uncertainty (entropy) prior to an experiment and after it. The uncertainty is thus related to the probability that some input and output events will happen, for example, analyte i will be present when signal k will be observed. These probabilities are conditional and are expressed by the Bayes equation. In a multidimensional system the a priori uncertainty is the same as that in an one dimensional system, but, because of the additivity of the probabilities, the a posteriori probability and thus the information content of the multidimensional system will increase.

The validity of this rule, an increase in the information content in multidimensional systems caused by improved a posteriori probability, constitutes the background for purposeful and substantiated development of analytical instrumentation. It comprises every step of analysis which leads to an improvement in an a posteriori probability, different injection techniques, stationary phases, columns and their combinations, detectors, etc. Generally there are three approaches to the development of a new sophisticated instrumentation:

• the use of a combinatorial approach for improvement of conditional probabilities,
• application of hyphenation to an improvement of the analyte signal probability,
• an application of adaptive expert systems to minimization of the model residual error.

For development of multidimensional chromatography, both hardware (mainly miniaturization) and software (maily deconvolution routines and methods of multidimensional statistics) components are of essential importance. Multidimensional chromatography is the analytical approach to the Bohr principle of complementarity.