Information amount

MSn are of particular interest. MSn stands for the n-fold coupling of mass spectrometers, alternatively serving as separation and detection instrument. By hyphenated techniques the dimensionality of analytical information (see Sect. 3.4) and, therefore, also the information amount (see Sect. 9.3) is significantly increased (Eckschlager and Danzer [1994]). 

Multispecies analyses require two-dimensional analytical information y = f(x)y see Sect. 3.4, mostly in the form of spectra and chromatograms. By evaluation of various signals or the entire signal function, simultaneous information on several sample components can be obtained (in the extreme case on all the constituents contained in the sample). The relevant quantity that characterizes multicomponent analyses is the information amount,... 

For the case that all the n constituents have similar expectation ranges, equally probable signal levels and are estimated with comparable precision, the maximum information amount becomes (Danzer et al. [1987])... 

In the concrete case of qualitative tests on n components, the maximum information amount is M(n)quai = n bit. 

The information amount increases further, if the n identified components additionally have to be determined quantitatively. In the simplest case, the maximum information amount according to Eq. (9.24) increases by the amount n lbm, given in Eq. (9.22) into... 

This information amount is independent of the way in which it is obtained, viz if different techniques are used to recognize the number of constituents (/ ), identify them and quantitatively determine them, or all of this is done by one and the same procedure like GC-MS. Examples are given in Eckschlager and Danzer [1994], p 56, and Danzer et al. [2001], p 65. From the analytical problem, it has be to distinguish between indentifica-tion of n unknown constituents and the analysis of n known components as characterized by Eq. (9.22). 

The potential information amount Mpot of an analytical method is directly characterized by their signal resolution power (analytical resolution power) Rz = N... 

On the other hand, not only the enormous number of signals in multicomponent methods but also the large number of species that can be detected in highly resolved spectra and chromatograms, respectively, influence the information amount. Therefore, Matherny and Eckschlager [1996] proposed the introduction of so-called relevancy coefficients, k, into the system of information-theoretical assessment. In analytical practice, the coefficients k can be considered as being weight factors of the information contents of the respective species with which Eq. (9.21) becomes... 

The information amount of process analyses (under which term all time-dependent studies from chemical process control up to dynamic and kinetic studies are summarized) increases by the factor of time resolving power... 

Similar is the situation in the case of geometrically resolved information (image information in the most general sense). The information amount increases in the following cases (see also Table 3.1) ... 

Compared with that of common analyses which determine an average composition of the sample, the information amount of spatially resolved analyses increases by the factor of geometrical resolving power RA that may be in the concrete case... 

For distribution analysis and analytical images the potential information amount increases by the factor A in case that all the distinguishable points (all the pixels or voxels, respectively) are analyzed. In the ideal case, it results in... 

The relationships at Eqs. (9.37) and (9.38) do not take into account a possible loss of precision with increasing geometrical resolving power as well as errors in adjusting the measuring points. Furthermore, the independence of all the Ra measuring points must be presupposed for the estimation of the ideal information amount. 

Another limiting case is given by the real information amount of a given distribution-analytical result or problem, respectively,... 

Both time- and position-dependent concentration functions can be dealt with by the theory of stochastic processes (Bohacek [1977]). Time functions playing a role in process analysis can be assessed not only by means of information amount M(n)t but also - sometimes in a more effective way -by means of the information flow, J, which is generally given by... 

Then, for the whole information amount AA /kTw of our combined cycle it is valid that... 

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